A writing recognition system of an intelligent blackboard

Abstract

The application provides a writing recognition system of an intelligent blackboard, and relates to the technical field of artificial intelligence, comprising: a collection module, which is used for collecting the writing operation of a teacher on the intelligent blackboard, generating original writing track data, performing handwriting smoothing and graphic standardization correction, and obtaining writing handwriting features; an identification module, which is used for performing content identification based on the writing handwriting features, obtaining mathematical symbols, graphics and question texts, and forming mathematical content; and an analysis module, which is used for constructing a writing space relationship model and performing structure feature analysis based on the mathematical content and in combination with a plurality of preset calibration anchor points on the intelligent blackboard, and generating dynamic optimization parameters. The application recognizes writing content, improves teaching interaction efficiency and information recording accuracy.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence technology, and in particular to a writing recognition system for an intelligent blackboard. Background Technology

[0002] With the popularization of intelligent educational equipment, intelligent blackboards integrating handwriting recognition and formula libraries have been applied to the teaching of subjects such as mathematics and physics. Most of these systems provide teachers with formula prompts by capturing handwriting, recognizing symbols and matching them with pre-stored formula libraries, aiming to improve teaching efficiency. However, when faced with teaching content involving complex mathematical modeling and spatial relationships, especially in basic engineering courses such as the key stress state analysis in mechanics of materials and elasticity, the auxiliary capabilities of existing systems have some limitations.

[0003] Specifically, when teaching the classic topic of plane stress state analysis, teachers typically need to write the stress components on the blackboard and then guide students to derive the principal stresses and directions. This process involves constructing the stress matrix, solving the characteristic equations and eigenvectors, and performing necessary geometric representations. Existing smart blackboard systems, when dealing with such tasks, mostly only understand the formulas at the symbol matching level. For example, when a teacher writes the expression for the plane stress state, the system may only be able to match the general formula form from the database based on keywords, but it cannot further analyze the core mathematical structure of matrix operations and eigenvalue problems implied by the formula. It lacks a deep understanding of the application scenarios and calculation logic of the formula, and therefore cannot automatically trigger the subsequent characteristic equation construction and solution process. Teachers still need to perform manual calculations and derivations step by step, which disrupts the continuity of the teaching process and results in a weak intelligent interactive experience. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a writing recognition system for an intelligent blackboard that can recognize the writing content and improve the efficiency of teaching interaction and the accuracy of information recording.

[0005] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: Firstly, a writing recognition system for an intelligent blackboard includes: The data acquisition module is used to collect teachers' writing operations on the smart blackboard, generate raw writing trajectory data, and perform handwriting smoothing and graphic standardization correction to obtain handwriting features. The recognition module is used to perform content recognition based on handwriting features to obtain mathematical symbols, graphics, and problem text, thus forming mathematical content. The parsing module is used to construct a writing space relationship model based on mathematical content and multiple preset calibration anchor points on the smart blackboard, and to perform structural feature parsing to generate dynamic optimization parameters. The matching module is used to match the corresponding formula in the preset common formula database according to the dynamic optimization parameters. If the match is successful, the corresponding common formula is retrieved and obtained. When the matching result is a stress state expression, the characteristic equation of the stress state matrix is ​​constructed and solved based on the plane stress components, and the values ​​of the two principal stresses and the principal direction angle are calculated. If the match fails, the new formula capture and learning process is entered. The fusion module is used in the new formula capture and learning process to obtain the teacher's complete handwriting for the current mathematical content as a new problem-solving formula, record it, perform logical verification and knowledge fusion processing on the new problem-solving formula, and update it to the formula database. The adjustment module is used to dynamically adjust the display brightness, handwriting contrast, and response sensitivity based on real-time collected ambient light data, screen temperature data, and teacher operation time distribution characteristics, so as to achieve adaptive handwriting recognition.

[0006] In a second aspect, a computer-readable storage medium storing a program that, when executed by a processor, implements the system.

[0007] The above-described solution of the present invention has at least the following beneficial effects: By smoothing the writing trajectory and standardizing and correcting the graphics, the quality of the original writing data is optimized, improving the regularity and recognizability of basic handwriting features. Simultaneously, mathematical symbols, geometric figures, and problem text are recognized, specifically adapting to the writing content recognition needs of math teaching scenarios. Combined with writing space relationship models and structural feature analysis, the matching and analysis of complex mathematical formulas and professional stress state expressions are improved, accurately calculating principal stress values ​​and principal direction angles. Coupled with a new formula capture learning and knowledge fusion update mechanism, it can autonomously collect personalized problem-solving formulas and iteratively optimize the database, breaking through the limitations of preset formulas and adapting to diverse math problem types and teachers' personalized writing logic. Furthermore, relying on dynamic adaptive adjustment of ambient light, screen temperature, and operational features, it can balance display effects, handwriting clarity, and writing response sensitivity under different usage environments, while also considering recognition stability and writing interaction experience. Overall, it achieves recognition, structured analysis, autonomous learning optimization, and full-scene adaptive adaptation of mathematical writing content, supporting digital writing interaction and content transformation in smart blackboard math teaching scenarios. Attached Figure Description

[0008] Figure 1 This is a schematic diagram of a writing recognition system for an intelligent blackboard provided by an embodiment of the present invention.

[0009] Figure 2 This is a flowchart illustrating the process of obtaining mathematical symbols, graphics, and question text by performing content recognition based on handwriting features, as provided in an embodiment of the present invention, to form mathematical content. Detailed Implementation

[0010] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0011] like Figure 1 As shown, an embodiment of the present invention proposes a writing recognition system for an intelligent blackboard, comprising: The data acquisition module is used to collect teachers' writing operations on the smart blackboard, generate raw writing trajectory data, and perform handwriting smoothing and graphic standardization correction to obtain handwriting features. The recognition module is used to perform content recognition based on handwriting features to obtain mathematical symbols, graphics, and problem text, thus forming mathematical content. The parsing module is used to construct a writing space relationship model based on mathematical content and multiple preset calibration anchor points on the smart blackboard, and to perform structural feature parsing to generate dynamic optimization parameters. The matching module is used to match the corresponding formula in the preset common formula database according to the dynamic optimization parameters. If the match is successful, the corresponding common formula is retrieved and obtained. When the matching result is a stress state expression, the characteristic equation of the stress state matrix is ​​constructed and solved based on the plane stress components, and the values ​​of the two principal stresses and the principal direction angle are calculated. If the match fails, the new formula capture and learning process is entered. The fusion module is used in the new formula capture and learning process to obtain the teacher's complete handwriting for the current mathematical content as a new problem-solving formula, record it, perform logical verification and knowledge fusion processing on the new problem-solving formula, and update it to the formula database. The adjustment module is used to dynamically adjust the display brightness, handwriting contrast, and response sensitivity based on real-time collected ambient light data, screen temperature data, and teacher operation time distribution characteristics, so as to achieve adaptive handwriting recognition.

[0012] In this embodiment of the invention, the quality of the original writing data is optimized by smoothing the writing trajectory and standardizing and correcting the graphics, thereby improving the regularity and recognizability of basic handwriting features. Simultaneously, mathematical symbols, geometric figures, and problem text are recognized, specifically adapting to the writing content recognition needs of mathematical teaching scenarios. Combined with a writing space relationship model and structural feature analysis, the matching and analysis of complex mathematical formulas and professional stress state expressions are improved, accurately completing the calculation and solution of principal stress values ​​and principal direction angles. Coupled with a new formula capture learning and knowledge fusion update mechanism, it can autonomously collect personalized problem-solving formulas and iteratively optimize the database, breaking through the limitations of preset formulas and adapting to diverse mathematical problem types and teachers' personalized writing logic. Simultaneously, relying on the dynamic adaptive adjustment of ambient light, screen temperature, and operation characteristics, it can balance the display effect, handwriting clarity, and writing response sensitivity under different usage environments, while also considering recognition stability and writing interaction experience. Overall, it achieves the recognition, structured analysis, autonomous learning optimization, and full-scene adaptive adaptation of mathematical writing content, supporting digital writing interaction and content transformation in intelligent blackboard mathematical teaching scenarios.

[0013] In a preferred embodiment of the present invention, the teacher's writing operations on the smart blackboard are collected to generate original writing trajectory data, and handwriting smoothing and graphic standardization correction are performed to obtain writing handwriting features, which may include: In this embodiment of the invention, the pressure sensor array and touch layer built into the smart blackboard are used to collect the contact point coordinates, pressure values, and timestamp information generated by writing operations in real time, generating raw writing trajectory data including multiple trajectory points. Specifically, the writing area of ​​the smart blackboard is uniformly arranged with a fixed spacing, and the spacing between each sensor is consistent to ensure that contact actions at any position in the writing area can be captured. At the same time, a touch layer is integrated below the writing area. The pressure sensor array and the touch layer are connected through internal circuitry to respond to writing operations in a coordinated manner. When the teacher holds a stylus and touches the writing surface of the blackboard and performs actions such as moving, pausing, or lifting, the pressure sensor corresponding to the contact position of the stylus tip will immediately feel the pressure applied by the pen tip. When the pressure reaches the sensor's preset trigger threshold, the sensor will start data recording, read its own horizontal and vertical coordinate numbers in the blackboard's preset global coordinate system, and convert the coordinate numbers into corresponding actual coordinate values. The horizontal coordinate values ​​increase sequentially from left to right, and the vertical coordinate values ​​increase sequentially from bottom to top. Simultaneously, the sensor converts the sensed pressure into a fixed range of pressure values; the greater the pressure, the higher the corresponding pressure value, showing a positive correlation between the pressure value and the actual pressure. During this process, the touch layer continuously monitors the stylus's movement, synchronously collecting the horizontal, vertical, and pressure values ​​of the current contact point between the stylus and the blackboard every 1 millisecond. This data is then linked to the smart blackboard's built-in clock module to record the specific time of each action, forming a unique timestamp accurate to the millisecond level. These timestamps are sequentially incremented according to time. Then, each collected horizontal, vertical, and pressure value, along with its corresponding timestamp, is treated as a complete set of trajectory point data, arranged sequentially according to the collection time. All continuously collected trajectory point data are concatenated and integrated to form a complete original writing trajectory data record of the entire writing process.

[0014] For the coordinate sequence in the original writing trajectory data, a median filter is used to eliminate glitch noise in the coordinate sequence. For trajectory breakpoints caused by data acquisition interruptions or pen lifting during writing, linear interpolation is performed based on the velocity information of the trajectory points before and after the breakpoint to generate continuous transition trajectory points, resulting in a continuous and smooth writing trajectory. Specifically, this involves: firstly, extracting the horizontal and vertical coordinate values ​​of all trajectory points from the original writing trajectory data, arranging them sequentially according to the acquisition time to form complete horizontal and vertical coordinate sequences; then, for both the horizontal and vertical coordinate sequences, using median filtering to process glitch noise. The horizontal coordinate sequence is first divided into small data groups of 5 adjacent trajectory points... Starting with the first trajectory point, the data is divided sequentially, with each small data group containing the horizontal coordinate values ​​of five consecutive trajectory points. The five horizontal coordinate values ​​within each small data group are sorted from smallest to largest. The median coordinate value, which is the third value after sorting, is found and compared with the other four coordinate values ​​in the data group. If the difference between any coordinate value and the median coordinate value exceeds a preset deviation threshold, that coordinate value is determined to be an abnormal coordinate value corresponding to noise, and the abnormal coordinate value is replaced with the median coordinate value. The vertical coordinate sequence is divided into data groups, sorted, and the median value is selected and used to replace abnormal coordinate values ​​in the same way, completing the elimination of noise in the coordinate sequence. Finally, the noise-eliminated data is checked. The horizontal and vertical coordinate sequences are then used to determine if there are any trajectory breakpoints. A preset normal writing time interval threshold of 50 milliseconds is used. The timestamp difference between any two adjacent trajectory points is calculated (the timestamp of the later trajectory point minus the timestamp of the previous trajectory point). If this timestamp difference exceeds 50 milliseconds, a trajectory breakpoint is determined to exist between these two adjacent trajectory points. This breakpoint is caused by an interruption in data acquisition or lifting the pen during writing. For identified trajectory breakpoints, they are filled in as follows: First, the horizontal and vertical coordinate values ​​and timestamp of the last valid trajectory point before the breakpoint (denoted as point A) are obtained, along with the horizontal and vertical coordinate values ​​and timestamp of the next adjacent valid trajectory point before point A (denoted as point B). The timestamps of points A and B are then calculated. The difference in horizontal coordinates (horizontal coordinate value of point A minus horizontal coordinate value of point B) and vertical coordinates (vertical coordinate value of point A minus vertical coordinate value of point B) are calculated. Then, the difference in timestamps between points A and B (timestamp of point A minus timestamp of point B) is calculated. The horizontal movement speed of point A is obtained by dividing the horizontal coordinate difference by the timestamp difference. The vertical movement speed of point A is obtained by dividing the vertical coordinate difference by the timestamp difference. Similarly, the horizontal coordinates, vertical coordinates, and timestamp of the first valid trajectory point after the breakpoint (denoted as point C) and the horizontal coordinates, vertical coordinates, and timestamp of the next adjacent valid trajectory point after point C (denoted as point D) are obtained to calculate the horizontal and vertical movement speeds of point C.

[0015] Next, calculate the lateral distance (lateral coordinate of point C minus lateral coordinate of point A) and longitudinal distance (longitudinal coordinate of point C minus longitudinal coordinate of point A) between points A and C. Add the squares of the lateral and longitudinal distances, then take the square root of the sum to obtain the straight-line distance between points A and C. Set a speed coefficient based on the moving speeds of points A and C (the faster the movement, the larger the speed coefficient). Multiply the straight-line distance by the speed coefficient to obtain the number of transition trajectory points to be inserted (round the result to an integer). Following the principle of uniform distribution, calculate the coordinates of each transition trajectory point. In the lateral direction, divide the lateral distance between points A and C by... The horizontal interval value is obtained by adding 1 to the number of transition trajectory points. Starting from the horizontal coordinate value of point A, the horizontal interval value is added sequentially to obtain the horizontal coordinate value of each transition trajectory point. In the vertical direction, the vertical distance between point A and point C is divided by the number of transition trajectory points plus 1 to obtain the vertical interval value. Starting from the vertical coordinate value of point A, the vertical interval value is added sequentially to obtain the vertical coordinate value of each transition trajectory point. These transition trajectory points are inserted into the breakpoints of the coordinate sequence in sequence, and a corresponding timestamp is assigned to each transition trajectory point (evenly distributed according to the difference between the timestamps of point A and point C), thus forming a continuous and smooth writing trajectory.

[0016] The process involves standardizing and correcting the shape of a continuous, smooth writing trajectory to determine if it forms a closed or nearly closed shape. If it does, the trajectory is matched and fitted with a pre-defined geometric template library to correct its shape, ensuring it conforms to standard geometric shapes and is sized uniformly. If the trajectory does not form a closed shape, its overall size and position are normalized. The final result is a handwriting feature with a standard format. Specifically, this includes extracting the starting point (first trajectory point) and ending point (last trajectory point) of the continuous smooth writing trajectory, obtaining the horizontal and vertical coordinates of the starting point, and the ending point... The horizontal and vertical coordinate values ​​are calculated. The horizontal distance (horizontal coordinate value of the end point minus the horizontal coordinate value of the start point) and the vertical distance (vertical coordinate value of the end point minus the vertical coordinate value of the start point) between the start and end points are calculated. The squares of the horizontal and vertical distances are added together, and the square root of the sum is taken to obtain the straight-line distance between the start and end points. The preset closure threshold is 2 mm. If the straight-line distance is less than 2 mm, and the overall trajectory is observed to show that the trajectory, after starting from the start point, bends and moves around in multiple directions before finally returning to the vicinity of the start point, forming a closed loop, then the continuous smooth writing trajectory is determined to constitute a closed or approximately closed figure. If the straight-line distance between the start and end points is greater than or equal to 2 mm, or the overall trajectory... If the writing trajectory extends unidirectionally without any tendency to loop or close, it is determined that the continuous and smooth writing trajectory does not constitute a closed figure. If it is determined to be a closed or nearly closed figure, the smart blackboard's internal preset basic geometric shape template library is invoked. This template library stores the standard outline coordinate data of basic geometric shapes such as standard circles, equilateral triangles, squares, rectangles, and regular pentagons. The outline coordinate data of a standard circle consists of countless coordinate points distributed at equal angles, with the distance from each coordinate point to the center (i.e., the radius) being completely equal. The outline coordinate data of an equilateral triangle includes the fixed coordinates of its three vertices, with the distance (side length) between the three vertices being completely equal, and the outline coordinates of the three sides connected sequentially by straight lines. The outline coordinate data of a square includes the fixed coordinates of its four vertices. The adjacent distances (side lengths) between vertices are completely equal, and the angles of the four corners are all 90 degrees. Other basic geometric shapes also have corresponding fixed contour coordinate features. All contour coordinate data of the current closed writing trajectory are compared one by one with the standard contour coordinate data of each basic geometric shape in the template library. For each basic geometric shape, the corresponding position coordinate points are selected from the standard contour coordinate data in the same number as the contour coordinate points of the current closed trajectory. The lateral deviation (lateral value of the current trajectory coordinate point minus the lateral value of the standard template coordinate point) and the longitudinal deviation (vertical value of the current trajectory coordinate point minus the vertical value of the standard template coordinate point) of each corresponding position coordinate point are calculated. The lateral deviations and longitudinal deviations of all corresponding positions are added together to obtain the total deviation value.The smaller the total deviation value, the higher the degree of overlap between the current closed trajectory and the outline of the standard geometric figure. The basic geometric figure with the smallest total deviation value is identified and used as the matching template.

[0017] Based on the standard contour coordinate data of the matching template, the contour of the current closed writing trajectory is corrected. Each contour coordinate point of the current trajectory is checked one by one. If the deviation between a coordinate point and the corresponding coordinate point of the matching template exceeds the preset correction threshold, the horizontal and vertical values ​​of the coordinate point are adjusted to the coordinate values ​​of the corresponding position of the matching template. Irregular bends, local protrusions, depressions, or line skew in the trajectory are corrected so that the corrected trajectory perfectly matches the shape characteristics of the matching template. At the same time, according to the preset uniform size specifications, a fixed standard size is set for each basic geometric shape, such as a standard circle with a circumscribed radius of 10 mm, an equilateral triangle with a side length of 15 mm, and a square with a side length of 12 mm. The actual size of the current shape is calculated. The actual size of the closed shape is determined by calculating the circumscribed radius or side length. For example, the actual circumscribed radius of the circle is the distance from the starting point to the farthest point on the trajectory, and the actual side length of the triangle is the distance between the three vertices. The preset standard size is divided by the actual size of the current shape to obtain the size scaling ratio. The horizontal and vertical values ​​of all contour coordinate points of the corrected trajectory are multiplied by the size scaling ratio to make the overall size of the shape conform to the preset uniform size specifications.

[0018] If the shape is determined not to be a closed figure, the following steps are performed for size and position normalization: First, calculate the actual boundary range of the current trajectory. Traverse the horizontal coordinate values ​​of all trajectory points, find the maximum and minimum horizontal coordinate values, and subtract the minimum horizontal coordinate value from the maximum to obtain the actual width of the trajectory. Similarly, traverse the vertical coordinate values ​​of all trajectory points, find the maximum and minimum vertical coordinate values, and subtract the minimum vertical coordinate value from the maximum to obtain the actual height of the trajectory. Second, set a standard size range, preset according to the needs of the teaching scenario, such as a standard width range of 20 mm to 30 mm. The standard height range is 15 mm to 25 mm. Calculate the scaling ratio: if the actual width is greater than the maximum value of the standard width range, the horizontal scaling ratio is the maximum value of the standard width range divided by the actual width; if the actual width is less than the minimum value of the standard width range, the horizontal scaling ratio is the minimum value of the standard width range divided by the actual width; if the actual width is within the standard width range, the horizontal scaling ratio is 1. Calculate the vertical scaling ratio in the same way. Compare the horizontal and vertical scaling ratios, and take the smaller value as the overall scaling ratio. Multiply the horizontal and vertical coordinate values ​​of all trajectory points in the trajectory by this overall scaling ratio. The first step is to ensure that the width and height of the scaled trajectory fall within the preset standard size range. The second step is to adjust the trajectory position, calculate the center coordinates of the scaled trajectory, iterate through the horizontal coordinates of all trajectory points after scaling, find the maximum and minimum horizontal coordinates, add them together and divide by 2 to obtain the horizontal center coordinates. Similarly, iterate through the vertical coordinates of all trajectory points after scaling, find the maximum and minimum vertical coordinates, add them together and divide by 2 to obtain the vertical center coordinates. Finally, preset standard position coordinates are established by setting fixed reference coordinates within the blackboard writing area. For example, the horizontal center reference coordinates are the coordinates of the horizontal midpoint of the blackboard writing area, and the vertical center reference coordinates are... A fixed value is marked slightly below the vertical midpoint of the blackboard writing area. The horizontal translation is calculated by subtracting the horizontal center coordinate and vertical translation of the scaled trajectory from the horizontal coordinate value of the standard position, and subtracting the vertical center coordinate of the scaled trajectory from the vertical coordinate value of the standard position. The horizontal translation is added to the horizontal coordinate value of all scaled trajectory points, and the vertical translation is added to the vertical coordinate value, so that the center coordinate of the scaled trajectory completely coincides with the preset standard position coordinates. This completes the normalization of size and position. Through the above targeted standardization processing of closed and non-closed shapes, the writing handwriting features with standardized shape, uniform size, and standard position are finally obtained.

[0019] By working in tandem with the pressure sensor array and the touch layer, the coordinates of the contact points, pressure values, and timestamps during the writing process are collected, comprehensively capturing every subtle movement and key information during writing. Transitional trajectory points are reasonably inserted based on the movement speed of the trajectory points before and after the breakpoint, ensuring that the overall shape of the trajectory can be fully captured when performing shape recognition and feature extraction, thereby improving the overall teaching experience.

[0020] like Figure 2 As shown, in a preferred embodiment of the present invention, content recognition is performed based on handwriting features to obtain mathematical symbols, graphics, and question text, forming mathematical content, which may include: In this embodiment of the invention, handwriting features are analyzed. Based on the trajectory morphology, stroke characteristics, and spatial distribution characteristics of the handwriting, the handwriting features are classified into symbolic handwriting, graphic handwriting, and textual handwriting. Specifically, this includes: firstly, extracting the trajectory morphology features of the handwriting features, observing the overall outline of each stroke one by one. If the trajectory length of the handwriting is short, the line direction is simple, and there is no obvious combination of multiple strokes or a tendency to wrap around and close, which conforms to the morphological characteristics of mathematical symbols, it is marked as a candidate symbolic handwriting. If the trajectory length of the handwriting is long, the outline shows a wrap-around or multi-segment broken line / curve combination, and the whole occupies an independent writing area, which conforms to the geometric shape... If the morphological characteristics are consistent, it is marked as a candidate graphic handwriting; if the handwriting is composed of multiple consecutive short strokes, with close connections or small gaps between the strokes, and multiple such combined handwritings are distributed horizontally in rows, conforming to the writing form of Chinese characters, letters, numbers, etc., it is marked as a candidate text handwriting; then, the pen stroke characteristics are analyzed, and the writing trend is judged by the timestamp and coordinate changes of the trajectory points. For candidate symbol handwriting, the speed change of its writing process is observed. If the speed of the handwriting is uniform from the start to the end, without obvious pauses or sudden speed changes after the stroke turns, and the overall writing time is short, it is calculated by subtracting the start timetamp from the end timetamp, and it conforms to the... If the writing is rapid and deliberate, it is confirmed as symbolic handwriting. For candidate graphic handwriting, if there is a clear directional change during writing, such as the corner of a broken line or the end of a closed figure, and there is a short pause at the turning point, it is judged by the difference in timestamps between adjacent trajectory points. If the difference is greater than a preset pause threshold, it is considered a pause. If the overall writing rhythm is stable and conforms to the writing style of geometric figures, it is confirmed as graphic handwriting. For candidate text handwriting, if there are multiple strokes with starting, moving, and ending movements, with natural connections or brief intervals between strokes, and the overall writing direction extends horizontally, conforming to the writing style of text, it is confirmed as text handwriting. Finally, spatial analysis is performed. Based on the distribution characteristics, the coordinates of all handwriting on the writing panel were statistically analyzed. Symbolic handwriting is usually distributed around text or graphic handwriting, and the spacing between individual symbolic handwriting is small, mostly used to express mathematical meaning in conjunction with text or graphics. Graphic handwriting occupies independent areas on the writing panel and is spaced further apart from other graphic or text handwriting to avoid overlap and interference. Text handwriting is mostly distributed horizontally in continuous lines, forming text lines with fixed vertical spacing between lines, which conforms to reading habits. Combining the analysis results of the above three major characteristics of trajectory shape, pen strokes and spatial distribution, the handwriting characteristics are finally clearly classified into three categories: symbolic handwriting, graphic handwriting and text handwriting.

[0021] This process extracts key feature vectors from symbolic handwriting and performs feature matching and probability calculations with a pre-trained mathematical symbol feature library to identify specific mathematical symbols and generate corresponding mathematical symbol objects. Specifically, for each symbolic handwriting, key feature vectors are extracted. These features include: total trajectory length (by traversing all trajectory points of the symbolic handwriting), calculating the straight-line distance from the start to the end point, and taking the square root of the sum of the squared horizontal and vertical differences between the start and end points; and the number of direction changes (starting from the first trajectory point, calculating the direction of the line connecting adjacent trajectory points, dividing the vertical difference by the horizontal difference). The direction coefficients are obtained. If the difference between the direction coefficient of the subsequent segment and the direction coefficient of the previous segment exceeds a preset direction threshold, it is counted as a direction change. The number of all direction changes is accumulated. The relative positions of the start and end points are calculated by subtracting the lateral offset of the start point's lateral coordinate from the end point's lateral coordinate, and subtracting the longitudinal offset of the start point's longitudinal coordinate from the end point's longitudinal coordinate. The curvature of the trajectory is determined by iterating through all points on the trajectory, calculating the perpendicular distance from each point to the line connecting the start and end points, multiplying the lateral difference between that point and the start point by the longitudinal difference between the end point and the start point, subtracting the lateral difference multiplied by the lateral difference between the end point and the start point, and then dividing by the absolute value. The curvature is calculated by averaging all perpendicular distances from the starting point to the ending point. The extracted key features (total trajectory length, number of direction changes, lateral offset, longitudinal offset, and curvature) are used as the key feature vector for the handwriting. A pre-trained mathematical symbol feature library in the smart blackboard is then used. This library stores baseline values ​​for key feature vectors corresponding to various standard mathematical symbols. The key feature vector of the current handwriting is matched against the baseline value for each standard mathematical symbol in the feature library. For each feature, the difference between the current feature value and the baseline value is calculated, and this difference is divided by the baseline value to obtain the individual feature. Similarity (the smaller the difference, the closer the similarity is to 1); sum the similarities of all feature items, then divide by the total number of feature items to obtain the overall matching probability between the handwriting of the symbol and the standard mathematical symbol. Traverse all standard mathematical symbols in the feature library, record the matching probability corresponding to each symbol, select the standard mathematical symbol with the highest matching probability that exceeds the preset matching threshold, and determine it as the recognition result of the current handwriting of the symbol. Based on this recognition result, generate the corresponding mathematical symbol object. This object contains information such as the name of the symbol, the corresponding character identifier, the original trajectory features, and the extracted key feature vectors, thus completing the recognition of mathematical symbols and object generation.

[0022] The coordinate sequence of the graphic handwriting is matched with shape determination rules in a pre-defined geometric rule library to identify basic geometric shape types. Based on parameter calculation formulas in the geometric rule library, the geometric parameters of the graphic handwriting are analyzed, including but not limited to the position coordinates of points, the length and endpoint coordinates of line segments, the center coordinates and radius of circles, and the vertex coordinates, side lengths, and angle values ​​of polygons, generating geometric objects. Specifically, this involves: first, performing curve inflection point detection on the coordinate sequence of the graphic handwriting; traversing all trajectory points of the graphic handwriting (excluding the start and end points); and processing each target trajectory point one by one, starting from the second trajectory point and ending at the second-to-last trajectory point, taking the previous phase of the target trajectory point. Consider the adjacent trajectory point (denoted as P1), the target trajectory point itself (denoted as P2), and the next adjacent trajectory point of the target trajectory point (denoted as P3). Calculate the longitudinal difference (vertical coordinate value of P2 minus longitudinal coordinate value of P1) and the lateral difference (lateral coordinate value of P2 minus lateral coordinate value of P1) between P1 and P2. Divide the longitudinal difference by the lateral difference to obtain the initial slope of the line connecting P1 and P2. Calculate the longitudinal difference (vertical coordinate value of P3 minus longitudinal coordinate value of P2) and the lateral difference (lateral coordinate value of P3 minus lateral coordinate value of P2) between P2 and P3. Divide the longitudinal difference by the lateral difference to obtain the subsequent slope of the line connecting P2 and P3. Calculate the initial slope and... The difference in slope (absolute value) is compared with a preset inflection point determination threshold. If the difference is greater than the threshold, P2 is determined to be an inflection point of the curve, and the coordinates of the inflection point are recorded. After traversal, the number of all detected inflection points and the coordinate sequence of each inflection point are counted. A preset geometric rule library is called, which stores the determination rules for basic geometric shapes such as lines, rays, line segments, triangles, rectangles, squares, circles, ellipses, and polygons. These rules include the number of inflection points, inflection point spacing features, and the overall shape of the trajectory. For example, the determination rule for a triangle is that it has 3 inflection points, the lines connecting the 3 inflection points form a closed contour, and the distance between any two inflection points (side length) is specified. The length is not zero; the rule for determining a rectangle is that the number of inflection points is 4, the distance between relative inflection points (diagonal) is equal, and the product of the slopes of the lines connecting adjacent inflection points is -1 (perpendicular); the rule for determining a circle is that the number of inflection points is 0, the trajectory is a continuous closed curve, and the distance from all points on the curve to a certain center point is approximately equal. The number of inflection points and the coordinate sequence obtained by detecting the inflection points of the curve are combined with the overall trajectory shape of the graphic handwriting and matched one by one with the graphic determination rules in the geometric graphic rule library. If 3 inflection points are detected, and the 3 inflection points are connected in sequence to form a closed trajectory, and there are no additional inflection points between any two adjacent inflection points, which meets the determination rules for triangles, then the graphic handwriting is identified as a triangle.If four inflection points are detected, and the straight-line distances between relative inflection points (the square root of the sum of the squared horizontal and vertical differences) are equal, and the product of the slopes of the lines connecting adjacent inflection points is -1 (the product of the previous slope and the next slope equals -1), then it meets the criteria for a rectangle and is identified as a rectangle. If no inflection points are detected, and the trajectory is a closed curve, calculate the distances from all trajectory points on the curve to a certain center point (the average of the horizontal coordinate values ​​of all trajectory points is the horizontal center point, and the average of the vertical coordinate values ​​is the vertical center point). If the difference between all distances is less than a preset uniform threshold, then it meets the criteria for a circle and is identified as a circle. This method completes the identification of basic geometric shape types.

[0023] Next, the geometric parameters are analyzed. For a triangle, the coordinates of the three inflection points (vertices) are recorded. The distance between any two vertices (side length) is calculated by adding the squares of the horizontal and vertical differences between each vertex and taking the square root of the sum. Angle values ​​are calculated using the side lengths, i.e., the angle is determined by the ratio of the lengths of adjacent sides and the side opposite the included angle. For a rectangle, the coordinates of the four inflection points (vertices) are recorded. The distances between adjacent vertices (side length) and the distances between opposite vertices (diagonal length) are calculated. For a circle, the center is obtained by adding the horizontal coordinates of all trajectory points and dividing by the total number of trajectory points. The system calculates the horizontal coordinates of the points; it sums the vertical coordinates of all points and divides the sum by the total number of points to obtain the vertical coordinate of the center; it calculates the distance from the center to any point (square of the horizontal difference plus square of the vertical difference, then takes the square root), sums all such distances and divides the sum by the total number of points to obtain the radius; for line segments, it records the coordinates of the start and end points, calculates the distance between the start and end points (segment length), integrates the identified graphic type and all parsed geometric parameters to generate the corresponding geometric object, which contains information such as graphic name, key coordinates of vertices / center, parameters such as side length / radius / angle, and original trajectory data.

[0024] The handwritten digit recognition engine performs stroke normalization, single-character segmentation and recognition, and context-based semantic error correction on the handwriting. The processed recognition results are then combined according to the writing sequence and spatial location to convert them into a continuous text string. Specifically, this involves: first, performing stroke normalization on the handwriting; traversing all trajectory points of each handwriting stroke; calculating the actual length (straight-line distance from start to end) and actual width (average of the maximum horizontal and vertical differences among all points in the trajectory); pre-setting standard stroke length and width ranges; and calculating the length scaling ratio (median value of the standard length range divided by the actual length) and width scaling ratio (median value of the standard width range divided by the actual width). (Degree); Multiply the horizontal coordinates of all trajectory points of each text stroke by the length scaling factor, and multiply the vertical coordinates by the width scaling factor to unify the length and width of all text strokes to a standard range while preserving the original shape characteristics of the strokes. Then, perform single-character segmentation, traversing all normalized text strokes, and calculating the horizontal spacing (horizontal coordinate of the starting point of the later stroke minus the horizontal coordinate of the ending point of the previous stroke) and vertical spacing (vertical coordinate of the starting point of the later stroke minus the vertical coordinate of the ending point of the previous stroke) between two adjacent text strokes. A preset single-character spacing threshold is set. If the horizontal spacing between two adjacent text strokes is less than the single-character spacing threshold, and the absolute value of the vertical spacing is less than the preset inline deviation threshold, then... If the horizontal spacing is greater than or equal to the single-character spacing threshold, or the absolute value of the vertical spacing is greater than the inline deviation threshold, then the character to which the previous handwriting belongs has ended, and the next handwriting belongs to a new character. Following this rule, all text handwriting is divided into multiple independent single-character handwriting combinations, each combination corresponding to a single character to be identified. Then, single-character recognition is performed, comparing the trajectory features of each single-character handwriting combination, including the number of strokes, stroke direction, stroke order, and relative positional relationships of each stroke, with the preset standard text feature library in the handwritten character recognition engine. For each single-character handwriting combination, the number of strokes (the number of strokes within the combination), the number of directional changes for each stroke, and the distance between strokes are extracted. Features such as intersection coordinates are matched one by one with the corresponding features of each character in the standard text feature library. The matching similarity is calculated, and the degree of matching of each feature is added together and divided by the total number of features. The standard character with the highest similarity and exceeding the recognition threshold is selected as the preliminary recognition result of the single character. Then, error correction processing based on context semantics is performed. The preliminary recognition results of all single characters are arranged according to the writing time sequence and spatial position (horizontal line order) to form a preliminary text sequence. The preliminary text sequence is traversed, and combined with the common vocabulary and semantic logic of the mathematical teaching scenario, it is judged whether there is a recognition error. For example, if the preliminary recognition result is a triangular shape, combined with the context of a right-angled triangular shape, and the similarity of the handwriting features of the solution and the angle is high, it is judged as a recognition error, and the solution is corrected to an angle.If the initial identification result is a function (traditional Chinese), it is corrected to a function according to the preset simplified Chinese conversion rules; if the initial identification result is a meaningless combination of characters, it is replaced with reasonable words that conform to the mathematical teaching scenario, taking into account the semantics of the context. All the corrected characters are then combined sequentially according to their original writing order and spatial position (line order, character order) to form a continuous question text string.

[0025] Based on the spatiotemporal positional relationships of mathematical symbols, geometric shapes, and problem text strings on the writing panel, a logical connection is established between them. This integrates the mathematical symbols, geometric shapes, and problem text strings into structured mathematical content encompassing symbols, graphics, text, and their interrelationships. Specifically, this includes: firstly, extracting the spatial positional information of the mathematical symbols, geometric shapes, and problem text strings, i.e., their coordinate ranges in the global coordinate system of the writing panel, their minimum and maximum horizontal coordinate values, their minimum and maximum vertical coordinate values, and time information, including the start and end timestamps of the corresponding original handwriting. This process is then analyzed. Spatial correlation: If the coordinate range of a mathematical symbol object lies entirely within the coordinate range of two problem text strings, and its horizontal center coordinate approximately coincides with the horizontal center coordinates of these two text strings (the difference is less than a preset alignment threshold), then the mathematical symbol object is determined to have a logical correlation with these two text strings, constituting a complete mathematical expression; if the coordinate range of a geometric object lies below or to the right of a problem text string, and the vertical spacing between them, specifically the difference between the minimum vertical coordinate value of the geometric object and the maximum vertical coordinate value of the text string, is less than a preset correlation spacing threshold, then the geometric object is determined to be a graphical representation of the problem text string; if... If the coordinate ranges of multiple mathematical symbol objects are adjacent (horizontal spacing less than the symbol association threshold) and their timestamps are consecutive, and the difference between the start timestamp of the later symbol and the end timestamp of the earlier symbol is less than a preset continuity threshold, then these symbol objects are determined to constitute a complete mathematical formula. Analyzing the time correlation, if the writing timestamp (start timestamp) of the question text string is earlier than the writing timestamp of a certain mathematical symbol object or geometric figure object, and the difference between their timestamps is less than a preset time sequence threshold, then the symbol or figure is determined to be supplementary explanation or solution content related to the question text; if the writing timestamp of the mathematical symbol object is between the question text and the geometric figure object, then... Symbols serve as the logical link between problems and diagrams. Based on the above analysis of spatiotemporal relationships, a clear logical connection is established. Each problem text string is labeled with a corresponding associated symbol object and graphic object; each mathematical formula (a combination of multiple symbols) is labeled with a corresponding problem text or graphic object; and each geometric figure is labeled with a corresponding problem text and explanatory symbol object. All objects and their logical connections are integrated according to the hierarchical structure of problem text, associated symbols / formulas, and associated graphics to form structured mathematical content that includes symbols, graphics, text, and their mutual logical relationships. This content clearly presents the problem descriptions, mathematical expressions, geometric diagrams, and their inherent connections in teaching.

[0026] By integrating curve inflection point detection into image recognition, key turning points of the image outline can be captured, improving the accuracy of geometric image type identification, facilitating the smooth progress of the teaching process, and enhancing students' understanding of the teaching content.

[0027] In a preferred embodiment of the present invention, based on mathematical content and combined with multiple preset calibration anchor points on the smart blackboard, a writing space relationship model is constructed and structural feature analysis is performed to generate dynamic optimization parameters, which may include: In this embodiment of the invention, the absolute coordinates of all pre-calibrated calibration anchor points on the smart blackboard in the global coordinate system are obtained to form reference coordinate data. Specifically, this includes: multiple calibration anchor points are pre-set in the writing area of ​​the smart blackboard. The anchor points are distributed at the four corners of the writing area, the midpoints of the four borders, and the geometric center of the writing area, totaling nine anchor points. Each anchor point has a physical identifier, which is a white raised dot with a diameter of 1 mm, to facilitate device identification and manual calibration. All anchor points are pre-calibrated before the smart blackboard leaves the factory. The calibration process is as follows: the smart blackboard is fixed at the standard teaching installation height, with the bottom edge of the blackboard 1.1 meters from the ground. A global coordinate system is established, with the lower left corner of the writing area of ​​the smart blackboard as the origin. The rightward direction is the positive direction of the horizontal coordinate axis, and the vertical upward direction is the positive direction of the vertical coordinate axis. Using a high-precision laser rangefinder with an accuracy of 0.01 mm, the horizontal and vertical straight-line distances from each anchor point to the coordinate origin are measured sequentially. The horizontal straight-line distance is the horizontal absolute coordinate value of the anchor point, and the vertical straight-line distance is the vertical absolute coordinate value of the anchor point. Each anchor point is assigned a unique identifier number, numbered sequentially from 1 to 9. The identifier number, horizontal absolute coordinate value, and vertical absolute coordinate value of each anchor point are recorded one-to-one in the data table. After all the corresponding data of the anchor points are fully integrated, the reference coordinate data is formed and stored in the built-in storage unit of the smart blackboard as the reference basis for coordinate transformation.

[0028] Based on the reference coordinate data, transformation parameters from the local coordinate system of the writing acquisition device to the global coordinate system are calculated. Using these transformation parameters, the local coordinates of all handwriting elements in the mathematical content are converted to global coordinates, generating handwriting coordinate data with a unified coordinate reference. Specifically, this involves: first, extracting the identifier numbers, horizontal absolute coordinate values, and vertical absolute coordinate values ​​of all nine calibration anchor points from the reference coordinate data; and simultaneously, acquiring the local coordinates of each calibration anchor point in the device's local coordinate system using the writing acquisition device (touch layer and pressure sensor array). The local coordinate system has its origin at the physical lower left corner of the writing acquisition device, with the horizontal direction (rightward along the device's width) as the positive direction and the vertical direction (upward along the device's height) as the positive direction. The local coordinates are obtained by detecting the position of the physical protrusion of the anchor point using internal sensing elements. That is, the horizontal local coordinate is the horizontal distance from the anchor point to the origin of the local coordinate system, and the vertical local coordinate is the vertical distance from the anchor point to the origin of the local coordinate system. For distance calculation, four non-collinear anchor points with identifiers 1 (top left), 3 (top right), 7 (bottom left), and 9 (bottom right) are selected as reference samples. The transformation parameters from the local coordinate system to the global coordinate system are calculated. These parameters include horizontal scaling, vertical scaling, rotation angle, horizontal translation, and vertical translation. The specific calculation process is as follows: Calculate the scaling: For each reference anchor point, divide its horizontal absolute coordinate value by its horizontal local coordinate value to obtain the horizontal scaling value. Add the horizontal scaling values ​​of the four reference anchor points and divide by 4 to obtain the average horizontal scaling. Similarly, divide the vertical absolute coordinate value of each reference anchor point by its vertical local coordinate value to obtain the vertical scaling value. Add the four vertical scaling values ​​and divide by 4 to obtain the average vertical scaling. If the difference between the average horizontal scaling and the average vertical scaling is less than a preset threshold, it is preset to 0.If the difference is greater than or equal to the preset scaling threshold, then the average horizontal scaling ratio and the average vertical scaling ratio are retained respectively. Calculate the rotation angle by selecting reference sample anchor points 1 (top left) and 3 (top right). In the local coordinate system, calculate the angle between the line connecting the two points and the local horizontal coordinate axis. First, calculate the difference in horizontal local coordinates (the difference between the horizontal local coordinates of anchor point 3 and the horizontal local coordinates of anchor point 1) and the difference in vertical local coordinates (the difference between the vertical local coordinates of anchor point 3 and the vertical local coordinates of anchor point 1). Divide the vertical local coordinate difference by the horizontal local coordinate value to obtain the tangent of the angle. Determine the angle in the local coordinate system based on the tangent value. In the global coordinate system, calculate the angle between the line connecting anchor points 1 and 3 and the global horizontal coordinate axis using the same method. Subtract the angle in the local coordinate system from the angle in the global coordinate system to obtain the final angle. To calculate the translation, taking reference anchor point 7 (lower left corner) as an example, first multiply its horizontal local coordinate value by the average horizontal scaling ratio, then multiply by the cosine of the rotation angle to obtain the horizontal scaling and rotation correction value; multiply its vertical local coordinate value by the average vertical scaling ratio, then multiply by the sine of the rotation angle to obtain the vertical scaling and rotation correction value; subtract the horizontal scaling and rotation correction value from the horizontal absolute coordinate value of anchor point 7, then add the vertical scaling and rotation correction value to obtain the initial horizontal translation of the anchor point; similarly, subtract the vertical scaling and rotation correction value from the vertical absolute coordinate value of anchor point 7, then subtract the horizontal scaling and rotation correction value to obtain the initial vertical translation; calculate the initial horizontal and vertical translations of the remaining three reference anchor points using the same method, add the four initial horizontal translations together and divide by 4 to obtain the final horizontal translation; add the four initial vertical translations together and divide by 4 to obtain the final vertical translation.

[0029] The calculated scaling ratios (horizontal and vertical), rotation angles, and translation amounts (horizontal and vertical) are integrated into complete transformation parameters. Then, all handwriting elements within the mathematical content, including symbolic handwriting, graphic handwriting, and text handwriting, are traversed to obtain the original local coordinates (horizontal and vertical original local coordinate values) of each trajectory point in the local coordinate system for each handwriting element. These are then converted to global coordinates in the following three steps, followed by rotation correction: After horizontal rotation, the coordinate value = the original horizontal local coordinate value multiplied by the cosine of the rotation angle, minus the original vertical local coordinate value multiplied by the sine of the rotation angle; After vertical rotation, the coordinate value = the original horizontal local coordinate value multiplied by the rotation angle. The process involves: 1) The sine of the angle, plus the original vertical local coordinate value multiplied by the cosine of the rotation angle; 2) Scaling: horizontally scaled coordinate value = horizontally rotated coordinate value multiplied by the average horizontal scaling ratio; vertically scaled coordinate value = vertically rotated coordinate value multiplied by the average vertical scaling ratio; 3) Translation: horizontal global coordinate value = horizontally scaled coordinate value plus the final horizontal translation amount; vertical global coordinate value = vertically scaled coordinate value plus the final vertical translation amount. After all trajectory points of all handwriting elements have undergone the above three transformations, each handwriting element corresponds to a set of coordinate data based on the global coordinate system. Integrating all this data generates handwriting coordinate data with a unified coordinate reference.

[0030] Using the global coordinates, geometric attributes, and writing sequence of each element in the handwriting coordinate data, a writing spatial relationship model is constructed. The model is then analyzed to extract the encoded structural features, generating structural feature data, including the syntax tree structure of mathematical formulas, the component topology of geometric figures, and the positional relationships between text and images. Specifically, the system comprehensively collects three core basic information categories for each handwriting element, refining each dimension to ensure no omissions or errors. Global coordinate information not only records the global X-axis and Y-axis coordinates of all trajectory points for each handwriting element but also calculates the bounding box coordinates of each element—the top-left and bottom-right X-axis and Y-axis coordinates of the smallest rectangular area containing all trajectory points of that element—clarifying the element's precise position, coverage, and occupied space on the blackboard display area. Simultaneously, the time interval between each trajectory point is calculated. If the time interval is greater than 100 milliseconds, the handwriting element is determined to consist of two discontinuous writing segments, splitting it into two independent sub-elements, each with its own coordinate information recorded. Geometric attribute information, for line-type handwriting elements, is sequentially recorded according to timestamp order. Connect all trajectory points, calculate the straight-line distance between any two adjacent trajectory points, and sum all adjacent distances to obtain the total length of the line. Simultaneously, analyze the distribution trend of all trajectory points. If the difference in horizontal coordinates between adjacent trajectory points is less than 0.1 mm, it is determined to be a vertical line; if the difference in vertical coordinates is less than 0.1 mm, it is determined to be a horizontal line; if both differences are large and show a regular variation, it is determined to be an inclined line or an arc, and the distance fluctuation from a trajectory point to a fixed point does not exceed 5% of the total length. For graphic handwriting elements, first determine whether it is a closed shape, and then use the last trajectory... If the distance between a point and the first trajectory point is less than 2 mm, and the intermediate trajectory points form a closed area, and it is a closed figure, then the shape type is determined based on the number and distribution characteristics of the trajectory points. If there are 3 obvious turning points and the difference in the length of the three sides does not exceed 10% of the total perimeter, it is determined to be a triangle; if there are 4 obvious turning points and the difference in the length of the opposite sides does not exceed 5%, and the included angle of the adjacent sides is close to 90 degrees (judged by the direction of the sides), it is determined to be a rectangle; if there are a large number of trajectory points and no obvious turning points, it is determined to be a circle or an ellipse (the criteria for determining a circle is that the difference in the length of the major axis and the minor axis does not exceed 5%, otherwise it is an ellipse).

[0031] For symbol and text handwriting elements, the width (lower right X-axis coordinate minus upper left X-axis coordinate) and height (lower right Y-axis coordinate minus upper left Y-axis coordinate) are calculated using bounding box coordinates to determine their size. Simultaneously, the writing order and direction of the trajectory points are analyzed to distinguish similar symbols and record writing timing information. The system synchronously records the writing start time, the timestamp of the stylus first contacting the blackboard with a pressure value greater than 0.5 Newtons, the end time, and the timestamp of the stylus leaving the blackboard with a pressure value less than 0.1 Newtons. Furthermore, each trajectory point is labeled with a writing sequence number (1, 2, 3…) in ascending order of timestamps to clarify the writing order. Additionally, the time interval between two adjacent handwriting elements is recorded. If the interval is less than 500 milliseconds, it is considered continuous writing and marked as a group of related elements; if the interval is greater than 1 second, it is considered independent writing and marked as an independent element. Based on these three types of basic information, the system begins to construct a writing space relationship model. The model construction process proceeds step-by-step in four levels to ensure comprehensive relationships. Node definition and attribute labeling define each independent handwriting element, including its sub-elements, as an independent node in the model. The node ID is consistent with the generation order of the handwriting elements and is numbered in ascending order of the start timestamp. Detailed attribute labels are labeled for each node, including element type (symbol, graphic, text), specific subclass (stress symbol, triangle, Chinese character), and size parameters (width, height, etc.). The system includes parameters such as length, writing time (start time, end time, sequence number), and bounding box coordinates to ensure that the features of each node are clearly identifiable. Temporal associations are constructed by building a temporal association linked list according to the writing start timestamps of all nodes. Each node records the IDs of its predecessor and successor; if it is the first node, there is no predecessor, and if it is the last node, there is no successor. For nodes marked as associated element groups, an additional group sequence number (1, 2, 3, etc.) is added to clarify the writing order of nodes within the group. Simultaneously, the time difference between each node and other nodes is recorded to provide a basis for subsequent judgment of logical associations between elements. Spatial associations are constructed by calculating the bounding box coordinates and global coordinates of any two nodes to establish multi-dimensional spatial relationships. Distance association: Calculate the straight-line distance between the centers of the bounding boxes of two nodes. If the distance is less than 5 mm (small element) or 10 mm (large element), they are considered closely adjacent; if the distance is between 5-15 mm (small element) or 10-30 mm (large element), they are considered generally adjacent; if the distance is greater than 15 mm (small element) or 30 mm (large element), they are considered not adjacent. Orientation association: Using the center of the bounding box of one node as a reference, determine which of the eight directions (above, below, left, right, upper left, lower left, upper right, lower right) the center of the bounding box of another node is located in. For example, if the X-axis coordinate of the center of node A is less than the X-axis coordinate of the center of node B, and the Y-axis coordinate is greater than the Y-axis coordinate of the center of node B, then node A is located to the upper left of node B.For inclusion relationships, if the top-left corner coordinate of one node's bounding box is less than the top-left corner coordinate of another node's bounding box, but the bottom-right corner coordinate is greater than the bottom-right corner coordinate of another node's bounding box, then an inclusion relationship is determined. For preliminary logical relationship determination, combining temporal and spatial relationships, a preliminary logical relationship between nodes is determined. For example, if a text node written earlier is closely adjacent to a formula node written later, and the text node is above the formula node, then the text node is preliminarily determined to be the description of the formula node. If a graphic node written earlier is included in a relationship with a symbol node written later, then the symbol node is preliminarily determined to be the annotation parameter of the graphic node.

[0032] After constructing the spatial relationship model, the system performs hierarchical analysis and extraction of three types of refined structural feature data: the syntax tree structure of mathematical formulas, element filtering (selecting nodes labeled as symbols, operators, and variables from all nodes, excluding text and graphic nodes), forming a set of formula elements, logical hierarchy division, and analysis of the spatial position and temporal relationship of each node in the formula element set, referencing the operation priority rules in primary and secondary school and university engineering mathematics teaching syllabi. If an operator node is located between two symbol / variable nodes with a distance of less than 3 millimeters, it is determined that the operator acts on these two nodes; if a bracket node is located on the left and right sides of a group of elements and contains all elements in that group, it is determined to be an operation group within brackets. The syntax tree is constructed with the highest priority operator as the root node, and the corresponding acting element as a child node. If a child node contains an operator, that child node becomes the parent node of the next level, and its acting element becomes a child node, and so on, forming a multi-level syntax tree structure. For example... +( × The corresponding syntax tree: the root node is +, and the left child node is The right child node is ×; the left child node of × is The right child node is Meanwhile, the bracketed node serves as an auxiliary node in the subtree containing the × symbol, indicating its priority.

[0033] The topological diagram of geometric shapes is generated by component decomposition. Components are broken down into basic parts, such as a rectangle being divided into four sides (top, bottom, left, right) and four vertices (top left, top right, bottom left, bottom right); a triangle into three sides and three vertices; and a circle into arcs and a center point. Each component is treated as an independent topological unit, recording its global coordinates and geometric attributes. Relationship analysis is performed, examining the fixed relationships between topological units, including the relationship between vertices and edges. A vertex is the endpoint of two edges, and the coordinates of the edge endpoints perfectly coincide with the vertex coordinates, with a deviation not exceeding 0.5 mm. Edge-to-edge relationships are also analyzed, such as the relationship between rectangles. For parallel edges, the difference between the vertical coordinates of horizontal edges and vertical edges is less than 0.1 mm, determined by their direction. Adjacent edges are perpendicular, determined by the angle between their directions. For the connection between an arc and its center, the distance difference between all points on the arc's trajectory and the center is no more than 1 mm. A topology diagram is generated using core components of the graphic, such as the four sides of a rectangle or the arc of a circle, as core units. Related components are connected by lines, and the connection type (endpoint connection, parallel, perpendicular, center connection, etc.) is labeled to form a complete component topology diagram, clearly presenting the compositional logic of the graphic and the positional relationships between text and graphics. The system establishes a relationship framework, including candidate filtering for text nodes that are closely adjacent to or contain formula / graphic nodes. Relationship validity is further verified through text content and location. Valid relationships are defined as follows: text content containing keywords such as parameters, labels, edges, and corners, and whose spatial orientation with the formula / graphic node conforms to teaching conventions, are considered valid. If the text content is unrelated to the formula / graphic, it is considered invalid and excluded. The system also records specific information about valid relationships, including text node ID, associated object ID, and relationship type (question description, parameters, etc.). (Annotations, component annotations) - spatial orientation, for example, text node 008 - formula node 015 - problem description - above, text node 010 - graphic node 012 - edge annotation - right side. Finally, the system integrates the parsed syntax tree structure (including hierarchical relationships and priority annotations), component topology diagram (including component splitting and association types), and image-text location association relationship (including valid association list and association attributes) according to the classification format of formula syntax structure - geometric topology structure - image-text association structure, generating structured data containing all refined structural features. Each data item is accompanied by a corresponding node ID and verification identifier.

[0034] Based on structural feature data, dynamic optimization parameters for identification and display optimization are derived and generated. Specifically, this includes: deriving formula structure matching weights; analyzing the importance of each symbol node in the operational logic based on the syntax tree structure of mathematical formulas, with core operators being more important than auxiliary symbols, and variable symbols in formulas being more important than numerical symbols; assigning corresponding weight values ​​to symbol nodes of different importance, with higher importance resulting in larger weight values; integrating these weight values ​​into formula structure matching weights; prioritizing the matching of core symbols with high weight values ​​when matching formula databases to improve matching accuracy; and deriving graphical topological constraint rules; extracting connection constraints for each component based on the component topology diagram of geometric figures, such as the requirement that the three sides of a triangle must be directly connected through endpoints to form a closed figure, and the four sides of a rectangle must be pairwise perpendicular and have opposite sides of equal length; and organizing these constraints into graphical topological constraints. The rules are used to ensure that the connection relationship of graphic components conforms to geometric logic during subsequent graphic recognition verification or graphic generation. Display layout adjustment parameters are derived based on the positional relationship between text and graphics, calculating the optimal display spacing of text, symbols, and graphics. If text and graphics have a descriptive relationship, the vertical spacing between them is adjusted to the preset optimal relationship spacing (ensuring clear distinction and no disconnection). If symbols are logically related symbols, their horizontal position is adjusted to align with the center of the text and graphics. Simultaneously, the display size of symbols is adjusted according to the operational priority of symbols in the syntax tree structure (core operators are slightly larger than auxiliary symbols). These spacing, position, and size adjustment parameters are integrated into display layout adjustment parameters to optimize the display effect of teaching content. Formula structure matching weights, graphic topological constraint rules, and display layout adjustment parameters are integrated to generate complete dynamic optimization parameters, providing a basis for formula matching and display optimization.

[0035] By pre-calibrating anchor points and obtaining their global absolute coordinates, a stable and unified benchmark is provided for the coordinate transformation of all handwriting elements, improving the accuracy of formula matching and the regularity of the display of teaching content, facilitating the smooth conduct of the teaching process, and enhancing the readability and comprehensibility of the teaching content.

[0036] In a preferred embodiment of the present invention, based on the dynamic optimization parameters, a corresponding formula is matched in a preset commonly used formula database. If the match is successful, the corresponding commonly used formula is retrieved and obtained. When the matching result is a stress state expression, the characteristic equation of the stress state matrix is ​​constructed and solved based on the plane stress components, and the values ​​of the two principal stresses and the principal direction angle are calculated. If the match fails, a new formula capture and learning process is initiated, which may include: In this embodiment of the invention, based on dynamic optimization parameters, a matching search is performed in a preset database of commonly used formulas to obtain formula matching results corresponding to the currently written mathematical content. Based on the formula matching results, it is determined whether the matching is successful. Specifically, the dynamic optimization parameters include formula structure matching weights, graphic topology constraint rules, and display layout adjustment parameters. Using these three parameters as the core search basis, a comprehensive and hierarchical search of the preset database of commonly used formulas is initiated. First, according to the formula structure matching weights, a set of candidate formulas that meet the preset standards in terms of symbol composition, operational relationships, and overall structural form matching the currently written mathematical content are selected. Then, according to the graphic topology constraint rules, each formula in the candidate formula set is further filtered to eliminate those that are related to the number of graphic elements in the currently written mathematical content, their positional relationships, and their logical association with the formula. Inconsistent formulas further narrow down the candidate pool. Finally, combining the content presentation logic corresponding to the display layout adjustment parameters, the complete features of the currently written mathematical content, including the arrangement order of mathematical symbols, the vertical / horizontal positional relationship between graphics and text, the sequential order of calculation steps, the representation form of core parameters, and the hierarchical relationship of brackets, are compared point by point and element by element with the filtered candidate formulas. During the comparison process, it is necessary to confirm that the number, type, and arrangement order of symbols are completely consistent, the hierarchical relationship of calculations is completely matched, and the number and positional relationship of graphic elements are consistent with the logical association of the formula. After the comparison is completed, it is checked whether there is a formula that completely matches the features of the currently written mathematical content or has a matching degree exceeding the preset matching degree threshold. If it exists, the matching is considered successful, and the matching formula is the corresponding formula matching result; if it does not exist, the matching is considered unsuccessful.

[0037] If a match is deemed successful, the formula type is further determined based on the formula type corresponding to the matching result. Specifically, this includes: after confirming a successful match, extracting the formula type identifier pre-marked in a pre-defined database of commonly used formulas; simultaneously, deeply analyzing the core features related to the formula in the currently written mathematical content, including whether it contains exclusive symbols for plane stress components, the arrangement logic of these stress components, whether the operational relationships between stress components conform to the basic logic of plane stress analysis, and whether it involves textual descriptions of stress distribution or stress state. The extracted formula type identifier and the analyzed core features are then comprehensively and thoroughly compared with the pre-defined typical features of stress state expressions. These pre-defined typical features include symbols representing normal stresses in two mutually perpendicular directions. , ) and a shear stress characterization symbol ( Furthermore, there are no missing or redundant symbols, and the symbols are arranged in a consistent manner. ; The matrix structure is rudimentary, possessing the basic form of stress state description. The core text description includes exclusive keywords such as plane stress state, principal stress, and stress direction. There are no additional irrelevant operations between stress components, only the arrangement relationship required for matrix construction. If the formula type is clearly identified as a stress state expression, and the core features completely match all preset typical features without any deviation, then the formula type is determined to be a stress state expression. If the formula type is not identified as a stress state expression, or the core features do not match any preset typical features, then the formula type is determined to be a non-stress state expression.

[0038] If the formula type is determined to be a stress state expression, then based on the identified plane stress components, the corresponding stress state matrix is ​​constructed, the characteristic equation of the stress state matrix is ​​solved, and the two principal stress values ​​and principal direction angles are calculated based on the characteristic equation; specifically, this includes: firstly, identifying the specific values ​​of the plane stress components from the currently written mathematical content (such as...). =100MPa =50MPa =30MPa) or standardized characterization symbol ( , , ), clearly define the first normal stress ( The force corresponding to the x-axis direction, the second normal stress ( The shear stress corresponds to the force along the y-axis (where the x-axis and y-axis are perpendicular). The stress corresponds to shear stress in the xy-plane, and the sign of the stress components is clearly defined (e.g., tensile stress is positive, compressive stress is negative). The sign of shear stress is determined according to the right-hand rule. Using these stress components as matrix elements, and strictly following the rules for constructing a plane stress state matrix, a second-order stress state matrix is ​​constructed. The specific form of the matrix is ​​as follows: In this matrix, the element in the first row and first column is fixed as the first normal stress. The element in the first row and second column is fixed as shear stress. The element in the second row and first column is fixed as shear stress. The element in the second row and second column is fixed as the second normal stress. This ensures that the matrix elements are in the correct positions; the construction of the characteristic equation follows the general derivation rules for the characteristic equation of a second-order square matrix, specifically using unknowns. (Characterizing principal stresses) Subtracting each element on the diagonal of the stress state matrix yields a new second-order square matrix. Calculate the determinant of this new square matrix and set it equal to zero. The first step is to construct the new second-order square matrix. The elements in the first row and first column of the new square matrix are ( minus The elements in the first row and second column retain the shear stress of the original matrix. The elements in the second row and first column remain unchanged, maintaining the shear stress of the original matrix. The second row and second column remain unchanged, and the element is ( minus The new square formation is The second step is to calculate the determinant of the new square matrix, following the rule of multiplying the main diagonal elements by subtracting the multiplication of the secondary diagonal elements from the product of the main diagonal elements, i.e. ( ) multiplied by ( ), then subtract ( Multiply The specific calculation process is as follows: × - × - × + × )-( × The third step is to set the determinant to zero, thus obtaining the initial form of the characteristic equation. The fourth step is to expand and rearrange the initial equations to ( )×( Expand as × - × - × + × Subtract × Combine like terms (combine - × and- × Merge into - ( + )× Finally, we obtain the characteristic equation in the form of a quadratic equation. The two principal stress values ​​are calculated by solving the aforementioned quadratic characteristic equation. The specific steps are as follows: First, calculate the discriminant of the quadratic equation. The discriminant follows the discriminant of the quadratic equation ax² + bx + c = 0. =b²-4ac, the general rule, corresponds to a=1 and b=- (in the characteristic equation) + c = () - ²), therefore the discriminant The calculation process is as follows: [-( + )] multiplied by [- ( + ], minus four times 1 multiplied by ( - ²), further expand the calculation [- ( + )]×[-( + )]=( + )×( + )= × +2× × + × ; Four times 1 multiplied by ( - ²) = 4 × ( - ²) = 4 × -4× ², therefore the discriminant The final calculation result is .

[0039] The second step is to solve for the two principal stresses using the quadratic formula. Substituting the parameters a=1 and b=-( into the characteristic equation) + ), Based on the above calculation results, two principal stresses are obtained ( For larger principal stresses, The calculation process for the smaller principal stresses, the first principal stress First calculate -b, that is, -[-( + )]= + In addition to the discriminant The square root (taking non-negative values ​​to ensure numerical validity) gives the sum ( + + Finally, divide the sum by two (2×a=2×1=2), the specific equation is as follows: Second principal stress Similarly, first calculate -b= + Subtract the discriminant The square root (non-negative value) gives the difference ( + - Finally, divide the difference by two; the specific equation is as follows: During the calculation, the units of the stress components must be preserved to ensure the complete physical meaning of the results; calculate the principal direction angle, the principal direction angle ( The angle (2) refers to the angle between the principal stress plane and the positive x-axis. Its calculation follows the derivation rules for the principal direction angle of plane stress. The specific steps are as follows: First, calculate twice the principal direction angle (2...). The tangent value of tan2 is obtained by deriving the formula for the principal direction angle. The calculation process is negative twice the shear stress. Divide by (the first normal stress) Subtract the second normal stress The difference between ) is calculated using the following formula: The second step is to determine the principal direction angle. The specific value is first determined based on the tan2 calculated above. The numerical value, combined with the periodicity of the tangent function, determines 2. If the quadrant in which it is located, tan2 If it is a positive value, then 2 Located in the first or third quadrant, corresponding to The value range is 0° to 45° or 90° to 135°; if tan2 If it is a negative value, then 2 Located in the second or fourth quadrant, corresponding to The value range is 45° to 90° or 135° to 180°, combined with... and Further screening is conducted based on the magnitude relationship and the positive / negative properties of the stress components. Greater than Then the larger principal stress Corresponding principal direction angle Values ​​within the range of 0° to 90° should be used preferentially; if Less than Then the larger principal stress Corresponding principal direction angle Values ​​within the range of 90° to 180° are preferred, and finally, the force analysis requirements in the current teaching scenario are considered. The final value is limited to between -90° and 90°. If it exceeds the range, it is adjusted by adding or subtracting 180° to ensure that the principal direction angle can accurately reflect the actual direction distribution of the stress state and is consistent with the direction definition in teaching.

[0040] If the formula type is determined to be a non-stress state expression, the system directly retrieves and returns the corresponding standard commonly used formula from the database of commonly used formulas based on the formula matching results. Specifically, after determining that the formula type is a non-stress state expression, the system locates the corresponding storage location of the formula in the preset database of commonly used formulas based on the previously obtained formula matching results. The system then extracts the complete standard information of the formula from this storage location, including the standard expression form, clear explanations of each parameter, detailed notes on applicable scenarios, and corresponding teaching application examples. After organizing this extracted standard commonly used formula information, the system directly retrieves and returns it to the display interface of the smart blackboard according to the preset display format, allowing teachers to use it directly during the teaching process.

[0041] If a matching failure is detected, the system will trigger a new formula capture and learning process based on the result. Specifically, when the system determines that a formula matching has failed, it will automatically activate a pre-set new formula capture and learning trigger mechanism. Once activated, the system will continuously collect all handwriting information without omissions, fully recording all handwriting information subsequently written by the teacher for the current mathematical content. This includes the writing trajectory of each mathematical symbol, the order of writing, changes in writing speed, changes in writing pressure, and pause times; the complete trajectory of each calculation step; the writing logic of each derivation step; the spatial relationship of each part of the content on the blackboard; and the teacher's modification marks. During the collection process, the system will continuously monitor the writing actions until the teacher completes the problem-solving derivation of the current mathematical content and forms the final new formula. This ensures that no key problem-solving steps, modification marks, or logical transitions are missed, comprehensively capturing the teacher's personalized problem-solving ideas, derivation logic, step details, and the complete form of the final new formula. This accumulates complete, uninterrupted, and traceable raw data for the recording, logical verification, and database learning of new formulas.

[0042] The hierarchical and precise formula matching and retrieval process, down to the element level, can not only quickly locate commonly used formulas that fit the current teaching content, but also ensure matching accuracy through high fit thresholds and multi-dimensional feature comparisons, enhancing the practicality of intelligent assistance and making the teaching process more efficient, coherent, and logical.

[0043] In a preferred embodiment of the present invention, in the new formula capture and learning process, the complete handwriting of the teacher for the current mathematical content is obtained and recorded as a new problem-solving formula, and logical verification and knowledge fusion processing are performed on the new problem-solving formula, which is then updated to the formula database. This may include: In this embodiment of the invention, when the new formula capture and learning process is triggered, the complete handwriting of the teacher on the smart blackboard for the current mathematical content is continuously acquired and recorded; the complete handwriting is preprocessed and structured to generate structured handwriting data including temporal and spatial structure information; specifically, after the new formula capture process is triggered, the touch layer and pressure sensor array of the smart blackboard enter a high-frequency acquisition mode, with the acquisition frequency increased to 10 times per millisecond to ensure that no writing details are missed. During the acquisition process, the information of each trajectory point written by the teacher is recorded in real time, including the global coordinates of the trajectory point, the contact pressure value between the stylus and the blackboard, and the timestamp corresponding to the trajectory point. The acquisition is terminated under one of two conditions: one is that the teacher clicks on the blackboard interface. The system has two main functions: first, a pre-set virtual button for completing writing; and second, a 30-second period without any new trajectory point collection. After collection, all trajectory points are sorted by timestamp from smallest to largest to form a complete original handwriting dataset, which is stored in a temporary cache. Simultaneously, a data verification code is generated to ensure the handwriting data has not been tampered with or lost. Each trajectory point in the complete original handwriting dataset is iterated through, and the average coordinates of that point and its five adjacent trajectory points are calculated (average X-axis coordinate = X-axis coordinate of the point + sum of X-axis coordinates of the five adjacent points, then divided by 11; the same applies to the average Y-axis coordinate). If the deviation between the current trajectory point's coordinates and the average value exceeds 0.005 mm, it is considered a noise point, and the calculated average value is used to replace the point's coordinates, eliminating jagged edges caused by writing vibration or sensor interference.

[0044] Check the timestamp interval between adjacent trajectory points. If the interval exceeds 50 milliseconds and the straight-line distance between the two points exceeds 3 millimeters, it is determined to be a breakpoint caused by pen lifting during writing. Then, determine whether the writing before and after the breakpoint is continuous writing of the same formula. This is determined by the writing direction and pressure value change trend of the trajectory points before and after the breakpoint. If it is continuous writing, insert transition trajectory points between the breakpoints. Calculate the horizontal distance (X-axis coordinate of the later point - X-axis coordinate of the earlier point) and the vertical distance (Y-axis coordinate of the later point - Y-axis coordinate of the earlier point) between the last valid point before the breakpoint and the first valid point after the breakpoint. Divide the points into several transition points according to the time interval (one every 5 milliseconds). Each transition point... The X-axis coordinate of a point = X-axis coordinate of the previous point + (horizontal distance ÷ number of transition points) × transition point number; the Y-axis coordinate is calculated similarly to ensure the continuity of the trajectory. Using the smallest X-axis and smallest Y-axis coordinates among all trajectory points in the complete handwriting as the origin, the relative coordinates of each trajectory point are recalculated (relative X-axis coordinate = original X-axis coordinate - smallest X-axis coordinate; relative Y-axis coordinate = original Y-axis coordinate - smallest Y-axis coordinate). This eliminates the influence of the writing position on subsequent analysis. Simultaneously, based on the overall size of the handwriting, the relative coordinates of all trajectory points are adjusted proportionally to ensure the overall width and height of the formula fit the system's preset standard size range. The adjustment ratio = standard... The coordinate value is calculated as follows: (Standard width ÷ Current overall width, if the current width exceeds the standard range) = Original relative coordinate × Adjustment ratio. Each trajectory point is labeled with a writing sequence number according to its timestamp, recording the start and end numbers of each trajectory segment to clarify the writing order. Simultaneously, the time interval between adjacent trajectory segments is calculated, and labels are added indicating continuous writing (interval ≤ 500 milliseconds) or interrupted writing (interval > 500 milliseconds) to form a temporal structure data. Cluster analysis is performed on the normalized trajectory points, grouping those with a distance of less than 2 millimeters and consecutive writing sequences into a single independent handwriting unit (corresponding to a symbol, a character, or a line segment). The system calculates the bounding box coordinates (minimum X-axis, maximum X-axis, minimum Y-axis, and maximum Y-axis relative coordinates) of each handwriting unit to determine its spatial position in the overall formula; it calculates the center coordinates of each handwriting unit ((minimum X-axis + maximum X-axis) ÷ 2, (minimum Y-axis + maximum Y-axis) ÷ 2) and marks the spatial orientation relationship between each handwriting unit; it binds the temporal structure data with the spatial structure data, then associates the pressure value information of the original trajectory points, organizes it according to the format of handwriting unit ID - temporal information - spatial information - pressure value sequence, generates complete structured handwriting data, and stores it in the system's structured database.

[0045] The process involves deep analysis of structured handwriting data to identify mathematical symbols, operators, and operational relationships, and to construct corresponding mathematical expression trees. These expression trees are then compared and analyzed against a pre-defined mathematical grammar rule library to verify their mathematical logic correctness and grammatical structure integrity, generating verified formula objects containing the verification conclusions. Specifically, this includes traversing each handwriting unit in the structured handwriting data, extracting the trajectory morphology, size, and pressure variation features of each unit, and comparing these features one by one with pre-defined mathematical symbol feature libraries and operator feature libraries. If a handwriting unit's trajectory morphology is an upper semicircle + lower vertical line with an aspect ratio of approximately 2:3 and stable pressure variation, it is determined to be a symbol. If the trajectory is a horizontal line, its length is 5 times its width, and it lies between two handwriting units, it is identified as the operator "+". After recognition, each handwriting unit is labeled with a symbol type, operator type, or invalid unit label, and invalid units are filtered out. Based on the spatial orientation and temporal information of each handwriting unit, the operational association between the operator and the symbol / number is determined. For example, if the center coordinates of the operator "×" are located at the symbol... 3 millimeters on the right, symbol If the left side is 3 mm and the serial number is written between the two, then the × sign is applied. and ,form × The operational relationship; if a handwriting unit is marked with parentheses "()", its right adjacent unit is + If there is a corresponding set of parentheses “)” on the right, then the set of parentheses is considered a priority operation group, forming ( + The mathematical expression tree is constructed by defining the operational relationships of mathematical symbols and numbers as terminal nodes, operators as non-terminal nodes, and parentheses as auxiliary nodes. Based on the mathematical operation priority rules, the hierarchy of each operator is determined, and a mathematical expression tree is built from bottom to top. The root node is the operator with the highest priority. Each non-terminal node's child node is the symbol, number, or subtree of the next level it operates on. Terminal nodes are located at the bottom level of the tree, ultimately forming a complete mathematical expression tree. The operational logic and hierarchical relationships of each element are clarified. A mathematical syntax rule library is retrieved, which contains the syntax and logic rules of mathematical operations. Each rule is marked with verification standards and exception handling instructions. The mathematical expression tree is compared with the syntax rule library to check whether each operator has a corresponding operand. Check if parentheses appear in pairs; whether the combination of symbols, numbers, and operators conforms to the rules. If there is a case where "+" has only one child node or parentheses are not paired, the syntax structure is considered incomplete. Check if the operation logic of the expression tree conforms to mathematical rules. For example, in a fractional structure, is the value corresponding to the denominator node or the result of the expression zero? Is the radicand in the square root operation a non-negative number? Does the order of operations conform to the priority rules? If the syntax structure is complete and the mathematical logic is correct, a valid verified formula object is generated, which includes the mathematical expression tree, the original structured handwriting data, the recognized complete formula text, and the application scenario label. If there are missing syntax or logical errors, an invalid verified formula object is generated, and the error type and error location are recorded in detail.

[0046] Based on the mathematical semantics expressed by the verified formula objects, a correlation search is performed in the formula database to determine the knowledge category to which the verified formula objects belong and to establish semantic associations between the objects and existing formulas. The verified formula objects, along with the established semantic associations, are then integrated and updated to the corresponding knowledge category in the formula database. Specifically, this includes: semantic extraction of the verified formula objects to clarify the core function, applicable scenarios, parameters involved, and calculation logic of the formulas. For example, the core semantics of the formula Trapezoid Area = (Upper Base + Lower Base) × Height ÷ 2 is to calculate the plane area of ​​the trapezoid using the lengths and heights of the upper and lower bases. The product function is applicable to calculating the area of ​​planar geometric figures. It involves parameters such as the upper base, lower base, and height, and its operational logic is summation, multiplication, and division. For related retrieval and knowledge classification, the core semantics and applicable scenarios are used as search keywords to conduct a comprehensive search in the formula database. Existing formulas with similar semantics and applicable scenarios are found, such as formulas for calculating the area of ​​planar geometric figures (e.g., triangle area = base × height ÷ 2, rectangle area = length × width); formulas for plane stress state analysis (e.g., stress state matrix construction formulas, principal direction angle calculation formulas). Based on the search results and the database's pre-defined knowledge classification system, the category to which the new formula belongs is determined. For example, the trapezoid area formula is classified under the category of geometric formulas - plane figure area formulas, and the new formula for principal stress calculation is classified under the category of mechanics formulas - plane stress state analysis formulas. The semantic association types between the new formula and the retrieved existing formulas are analyzed, including associations based on the same scenario, parameters, logic, and operations. Explicit association descriptions are added for each type of association. For example, the association description between the trapezoid area formula and the triangle area formula is that they both belong to the category of plane figure area calculations, both involve length parameters and multiplication and division operations, and the triangle can be regarded as a special trapezoid with an upper base of 0. Under the corresponding knowledge classification in the formula database, new storage entries are created, and the complete information of the verified formula object is entered, including the formula text, core semantics, applicable scenarios, parameter descriptions, operational logic, and writing trajectory characteristics. The established semantic association relationships are bound to the new formula entries, enabling the new formula to form a semantic network with existing formulas. The database's search index is updated synchronously, adding the core semantics, applicable scenarios, parameters, and other information of the new formula to the index to ensure that the formula can be quickly matched during subsequent searches. At the same time, the update time and source of the formula are recorded to complete the database fusion update.

[0047] The system fully captures teachers' handwriting and preprocesses and structures it to ensure the integrity and standardization of the original data for the new formulas, preventing erroneous knowledge from interfering with teaching and helping to improve teaching efficiency and the quality of knowledge transfer.

[0048] In a preferred embodiment of the present invention, dynamically adjusting display brightness, handwriting contrast, and response sensitivity based on real-time collected ambient light data, screen temperature data, and teacher operation time distribution characteristics to achieve adaptive handwriting recognition may include: The system collects ambient light data, screen temperature data, and teacher operation time distribution characteristics from ambient light sensors, temperature sensors, and an operation timer in real time, and integrates the data and characteristics into an environmental state input set. Specifically, it uses the ambient light sensor built into the smart blackboard to capture real-time light intensity data in the teaching scene at a frequency of 10 times per second. Each capture records the actual light intensity value of the current scene and a timestamp to ensure data timeliness. The collection range covers the core teaching area 0.5 to 3 meters in front of the blackboard, avoiding sensor obstruction or light interference from edge areas to ensure the data accurately reflects the actual visual environment of teachers and students. It uses temperature sensors evenly distributed inside the screen to collect real-time surface temperature data of the display panel at a frequency of 5 times per second. Each capture records the temperature value at the location of each sensor and calculates the average of all sensor temperatures as the final screen temperature data, while also linking the timestamp to ensure time synchronization between temperature and ambient light data. Finally, it uses an operation timer to record all teacher operations on the smart blackboard in real time, including stylus clicks and writing. The start time, end time, and interval duration of operations such as writing, erasing, and annotation are collected at a frequency of 20 times per second, capturing the time node of each operation. Data such as the number of operations per unit time, the average duration of a single operation, the time span of consecutive operations, and the average interval between operations are statistically analyzed to form the teacher's operation time distribution characteristics, such as 15 operations per minute, an average duration of 0.8 seconds per operation, a continuous operation duration of 3 minutes, and an average interval between operations of 2 seconds. Ambient light data, screen temperature data, and teacher operation time distribution characteristics are time-aligned according to the collection timestamp to ensure a one-to-one correspondence among the three types of data at the same time point. For example, the light intensity value, average screen temperature value, and the corresponding operation count statistics collected in the same millisecond are associated. The aligned data and characteristics are then structured and organized into an environmental status input set, constructed according to the field order of collection timestamp - ambient light intensity value - average screen temperature value - number of operations per unit time - average duration of a single operation - continuous operation time span - average interval between operations. Each field is clearly labeled with attribute descriptions to ensure the standardization of the input set data.

[0049] Using ambient light data from the environmental status input set as the processing object, and based on a preset illumination intensity mapping relationship, the target screen brightness parameters required to adapt to the current lighting conditions are determined and obtained. Specifically, this includes: determining the preset illumination intensity mapping relationship, which is based on human visual comfort experimental data, dividing the ambient light intensity into multiple continuous intervals, each interval corresponding to a screen brightness range, with overlapping transition sections between adjacent intervals to avoid abrupt brightness changes. For example, a low-light interval corresponds to a screen brightness range of 30. 0-400 candela per square meter, suitable for dimly lit classrooms; medium lighting range corresponds to 400-550 candela per square meter, suitable for normal indoor natural light environments; high lighting range corresponds to 550-700 candela per square meter, suitable for classrooms with strong light; very high lighting range corresponds to 700-800 candela per square meter, suitable for outdoor or direct sunlight environments near windows; within each range, ambient light intensity and screen brightness are linearly positively correlated, meaning the higher the ambient light intensity, the closer the screen brightness is to the corresponding range. The upper limit of the range is determined; the target screen brightness parameters are determined by extracting the current ambient light intensity value from the environmental state input set and checking the illumination range to which this value belongs. For example, if the current ambient light intensity is 350 lux, it belongs to the medium illumination range. If the ambient light intensity is in the middle area of ​​a certain range, the middle value of the brightness range of that range is taken as the initial brightness value. For example, the initial brightness value corresponding to the middle area of ​​the medium illumination range is 475 candela per square meter. If the ambient light intensity is in the transition area of ​​the range, the transition brightness value is calculated by subtracting the upper limit of the low range from the current ambient light intensity. The difference is calculated by dividing it by the overlap length of the two intervals to obtain a scaling factor. Then, the upper limit of the lower interval brightness is added to the scaling factor and multiplied by the difference between the brightness ranges of the two intervals to obtain the transition brightness value. For example, 500 lux is the overlap point between the upper limit of the middle interval (500 lux) and the lower limit of the high interval (500 lux). The scaling factor is 0.5, and the transition brightness value is 550 candela per square meter. Finally, the initial brightness value or the transition brightness value is determined as the target brightness parameter of the screen to ensure that the screen is neither dazzling nor too bright under the current lighting conditions.

[0050] This method uses screen target brightness parameters and screen temperature data from the environmental input set as processing objects. Based on the joint influence rules of brightness and temperature on display effects, it calculates and obtains the target contrast ratio parameters for optimizing visibility. Specifically, this includes: determining the joint influence rules of brightness and temperature, which are based on screen display characteristics. The core logic is that screen temperature affects the luminous efficiency of the display panel. When the temperature rises, the color saturation at the same brightness will decrease slightly, requiring increased contrast to compensate; when the temperature decreases, the luminous efficiency of the display panel increases, and the contrast ratio can be appropriately reduced to avoid overly sharp images. Simultaneously, the higher the screen brightness, the higher the contrast ratio needs to be to ensure the distinction between handwriting and background. The lower the screen temperature, the lower the contrast ratio should be to avoid eye strain. The default standard reference condition is a screen temperature of 25 degrees Celsius. At this temperature, the base contrast ratios for different screen brightness levels are as follows: 300-400 candela per square meter = 100:1; 400-550 candela per square meter = 120:1; 550-700 candela per square meter = 140:1; 700-800 candela per square meter = 160:1. Temperature adjustment rules: for every 1 degree Celsius the screen temperature exceeds the standard temperature, the contrast ratio increases by 2:1; for every 1 degree Celsius the screen temperature falls below the standard temperature, the contrast ratio decreases by 2:1. Reduce the contrast ratio by 1:1; the upper limit for temperature adjustment is 30% of the base contrast ratio, and the lower limit is 70% of the base contrast ratio to avoid excessive contrast adjustment that could cause display abnormalities; calculate the handwriting target contrast parameters. First, based on the determined screen target brightness parameters, find the corresponding base contrast ratio. For example, if the screen target brightness parameter is 475 candela per square meter, which falls within the 400-550 candela per square meter range, the corresponding base contrast ratio is 120:1. Second, calculate the screen temperature deviation value by subtracting the standard temperature of 25 degrees Celsius from the average screen temperature value in the environmental condition input set. For example, if the current average screen temperature is 28 degrees Celsius, the temperature deviation value is 3 degrees Celsius. If the current average screen temperature is... The temperature is 22 degrees Celsius, with a temperature deviation of -3 degrees Celsius. The third step is to calculate the temperature adjustment contrast ratio by multiplying the temperature deviation value by the corresponding adjustment ratio (2:1 per degree Celsius above the standard temperature, and 1:1 per degree Celsius below the standard temperature). For example, when the temperature deviation is 3 degrees Celsius, the temperature adjustment contrast ratio is 3 multiplied by 2:1, which is 6:1; when the temperature deviation is -3 degrees Celsius, the temperature adjustment contrast ratio is 3 multiplied by 1:1, which is 3:1 (a negative value indicates a reduction). The fourth step is to calculate the handwriting target contrast ratio by adding the temperature adjustment contrast ratio to the base contrast ratio to obtain the final handwriting target contrast ratio parameter. For example, a base contrast ratio of 120:1 plus a temperature adjustment contrast ratio of 6:1 results in a contrast ratio of 126:1.Subtracting the temperature-adjusted contrast ratio of 3:1 from the base contrast ratio of 120:1 yields 117:1. If the calculated result exceeds the 30% upper limit or 70% lower limit of the base contrast ratio, the corresponding upper or lower limit value is taken as the final parameter. For example, the 30% upper limit of the base contrast ratio of 120:1 is 156:1. If the calculated result is 160:1, then 156:1 is taken as the target contrast ratio.

[0051] This approach combines handwriting target contrast parameters with teacher operation time distribution features from the environmental input set as processing objects. Based on handwriting display status and user operation patterns, it dynamically calculates and obtains touch sensitivity parameters to optimize interactive responsiveness, achieving adaptive handwriting recognition. Specifically, this includes analyzing teacher operation time distribution features by extracting key data from the environmental input set, including the number of operations per unit time, the average duration of a single operation, the time span of continuous operations, and the average interval between operations. These data are used to determine the teacher's operation pattern, categorizing it into high-frequency continuous operation patterns and low-frequency intermittent operation patterns. The pattern determination rule is based on the number of operations per unit time... If the number of operations exceeds a preset limit, the continuous operation time span exceeds a preset duration, and the average interval between operations is less than a preset interval, it is determined to be a high-frequency continuous operation mode, such as the operation mode when a teacher writes problem-solving steps in a concentrated manner or makes continuous annotations. If the number of operations per unit time is less than a preset limit, the continuous operation time span is less than a preset duration, and the average interval between operations is greater than a preset interval, it is determined to be a low-frequency intermittent operation mode, such as the operation mode when a teacher occasionally writes on the blackboard or makes sporadic annotations during a lecture. The association rules between handwriting display status and operation mode are determined. The core logic of the association rules is that touch sensitivity determines the response speed when the stylus contacts the screen. Higher sensitivity results in a faster response, but excessive sensitivity may lead to… To prevent accidental touches; lower sensitivity results in a lower probability of accidental touches, but increases response delay. Higher handwriting contrast makes the handwriting clearer on the screen, and teachers are less sensitive to response delay, allowing for a more appropriate increase in sensitivity. Lower contrast results in a softer handwriting display; a balance must be struck between sensitivity and the probability of accidental touches. Preset basic sensitivity parameters, categorizing basic sensitivity levels based on handwriting contrast: a contrast ratio higher than 140:1 corresponds to a high basic sensitivity level with a response threshold of 0.05 seconds (triggering a response 0.05 seconds after screen contact); a contrast ratio between 110:1 and 140:1 corresponds to a medium basic sensitivity level with a response threshold of 0.1 seconds; a contrast ratio lower than 110:1 corresponds to a low basic sensitivity level. The response threshold is 0.15 seconds. The operation mode adjustment rules are as follows: In high-frequency continuous operation mode, teachers need a fast and consistent response, so the basic sensitivity level is increased by one level; in low-frequency intermittent operation mode, teachers have lower requirements for response speed and focus more on avoiding accidental touches, so the basic sensitivity level is decreased by one level; if the basic sensitivity is already at the highest or lowest level, no further adjustment is made, and only the basic level is retained. To calculate the touch sensitivity parameters, the first step is to find the corresponding basic sensitivity level based on the determined handwriting target contrast parameter. For example, if the handwriting target contrast is 126:1, which falls within the 110:1-140:1 range, the corresponding basic sensitivity level is medium, and the response threshold is 0.The first step involves adjusting the sensitivity level based on the teacher's operation time distribution characteristics. The second step is to determine the operation mode, such as a high-frequency continuous operation mode. The third step adjusts the basic sensitivity level according to the operation mode adjustment rules. For example, the basic medium level is increased to high level in the high-frequency continuous operation mode, and the corresponding response threshold is adjusted to 0.05 seconds. If it is determined to be a low-frequency intermittent operation mode, the basic medium level is reduced to low level, and the corresponding response threshold is adjusted to 0.15 seconds. The fourth step involves fine-tuning based on the handwriting display status. If the handwriting target contrast is at the upper limit of the corresponding range, the response threshold is shortened by 0.01 seconds based on the adjusted sensitivity level. If the handwriting target contrast is at the lower limit of the corresponding range, the response threshold is extended by 0.01 seconds to ensure that the sensitivity matches the handwriting display status, without affecting the response speed and reducing accidental touches. Finally, the adjusted response threshold is determined as the touch sensitivity parameter, and the system adjusts the touch response mechanism according to this parameter to achieve adaptive handwriting recognition.

[0052] Real-time and comprehensive collection of environmental and operational data ensures that the adjustment direction matches the actual usage scenario; based on the light intensity mapping relationship, the screen target brightness is matched so that the screen display can remain comfortable and visible under different lighting conditions, effectively protecting the eyesight of teachers and students and helping to improve teaching efficiency and experience.

[0053] Embodiments of the present invention also provide a computer-readable storage medium storing instructions that, when executed on a computer, cause the computer to perform the method described above. All implementations in the above method embodiments are applicable to this embodiment and can achieve the same technical effects.

[0054] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A writing recognition system for an intelligent blackboard, characterized in that, include: The data acquisition module is used to collect teachers' writing operations on the smart blackboard, generate raw writing trajectory data, and perform handwriting smoothing and graphic standardization correction to obtain handwriting features. The recognition module is used to perform content recognition based on handwriting features to obtain mathematical symbols, graphics, and problem text, thus forming mathematical content. The parsing module is used to construct a writing space relationship model based on mathematical content and multiple preset calibration anchor points on the smart blackboard, and to perform structural feature parsing to generate dynamic optimization parameters. The matching module is used to match the corresponding formula in the preset common formula database according to the dynamic optimization parameters. If the match is successful, the corresponding common formula is retrieved and obtained. When the matching result is a stress state expression, the characteristic equation of the stress state matrix is ​​constructed and solved based on the plane stress components, and the values ​​of the two principal stresses and the principal direction angle are calculated. If the matching fails, proceed to the new formula capture and learning process; The fusion module is used in the new formula capture and learning process to obtain the teacher's complete handwriting for the current mathematical content as a new problem-solving formula, record it, perform logical verification and knowledge fusion processing on the new problem-solving formula, and update it to the formula database. The adjustment module is used to dynamically adjust the display brightness, handwriting contrast, and response sensitivity based on real-time collected ambient light data, screen temperature data, and teacher operation time distribution characteristics, so as to achieve adaptive handwriting recognition.

2. The writing recognition system for the intelligent blackboard according to claim 1, characterized in that, The logical verification includes submitting mathematical content and the new problem-solving formula to the background verification service for correctness judgment; the knowledge fusion processing includes extracting application scenario metadata of the new problem-solving formula after the verification is passed, performing structured processing on the metadata based on preset rules, and finally integrating the processed metadata into the updated formula dependency structure.

3. The writing recognition system for the intelligent blackboard according to claim 2, characterized in that, The system collects teachers' writing operations on the smart blackboard, generates raw writing trajectory data, and performs handwriting smoothing and graphic standardization correction to obtain handwriting features, including: The smart blackboard uses a built-in pressure sensor array and touch layer to collect the contact point coordinates, pressure values ​​and timestamp information generated by writing operations in real time, and generates raw writing trajectory data including multiple trajectory points. For the coordinate sequence in the original writing trajectory data, a median filter is used to eliminate the spur noise in the coordinate sequence. For the trajectory breakpoints in the coordinate sequence caused by the interruption of acquisition or the lifting of the pen during writing, linear interpolation is performed based on the velocity information of the trajectory points before and after the breakpoint to generate continuous transition trajectory points, thus obtaining a continuous and smooth writing trajectory. The continuous smooth writing trajectory is subjected to graphic standardization correction to determine whether it constitutes a closed or nearly closed figure. If it does, the trajectory is matched and fitted with a pre-defined basic geometric template library to correct its shape, ensuring it conforms to standard geometry and is sized uniformly. If it does not, the trajectory is normalized in size and position. The final result is a writing feature with a standard format.

4. The writing recognition system for the intelligent blackboard according to claim 3, characterized in that, Content recognition based on handwriting features yields mathematical symbols, graphics, and problem text, forming mathematical content, including: The characteristics of handwriting are analyzed, and based on the trajectory morphology, stroke characteristics, and spatial distribution characteristics of the handwriting, the handwriting characteristics are classified into symbol handwriting, graphic handwriting, and text handwriting. Extract the key feature vectors of symbol handwriting, and perform feature matching and probability calculation with the key feature vectors of symbol handwriting and pre-trained mathematical symbol feature library to identify specific mathematical symbols and generate corresponding mathematical symbol objects; The coordinate sequence of the graphic handwriting is matched with the shape determination rules in the preset geometric rule library to identify the basic geometric shape type. Based on the parameter calculation formula in the geometric rule library, the geometric parameters of the geometric handwriting are parsed, including but not limited to the position coordinates of points, the length and endpoint coordinates of line segments, the center coordinates and radius of circles, the vertex coordinates, side lengths and angle values ​​of polygons, and geometric object is generated. The handwritten character recognition engine performs stroke normalization, single character segmentation and recognition, and context-based semantic error correction on the handwriting. The processed recognition results are combined according to the writing time and spatial position and converted into a continuous question text string. Based on the spatiotemporal positional relationship of mathematical symbol objects, geometric object objects, and problem text strings on the writing panel, establish logical connections between mathematical symbol objects, geometric object objects, and problem text strings, and integrate mathematical symbol objects, geometric object objects, and problem text strings into structured mathematical content that includes symbols, graphics, text, and their interrelationships.

5. The writing recognition system for the intelligent blackboard according to claim 4, characterized in that, Based on mathematical content and combined with multiple preset calibration anchor points on the smart blackboard, a writing space relationship model is constructed and structural feature analysis is performed to generate dynamic optimization parameters, including: Obtain the absolute coordinates of all pre-calibrated anchor points on the smart blackboard in the global coordinate system to form reference coordinate data; Based on the reference coordinate data, the transformation parameters from the local coordinate system of the writing acquisition device to the global coordinate system are calculated; using the transformation parameters, the local coordinates of all handwriting elements in the mathematical content are converted into global coordinates, generating handwriting coordinate data with a unified coordinate reference. Using the global coordinates, geometric attributes, and writing sequence of each element in the handwriting coordinate data, a writing spatial relationship model is constructed; the writing spatial relationship model is analyzed and processed to extract the encoded structural features and generate structural feature data, including the syntax tree structure of mathematical formulas, the component topology diagram of geometric figures, and the positional relationship between text and images; Based on structural feature data, dynamic optimization parameters for identification and display optimization are derived and generated.

6. The writing recognition system for an intelligent blackboard according to claim 5, characterized in that, The dynamic optimization parameters include formula structure matching weights, graphic topology constraint rules, and display layout adjustment parameters.

7. The writing recognition system for an intelligent blackboard according to claim 6, characterized in that, Based on the dynamic optimization parameters, the corresponding formula is matched in the preset common formula database. If the match is successful, the corresponding common formula is retrieved and obtained. When the matching result is a stress state expression, the characteristic equation of the stress state matrix is ​​constructed and solved based on the plane stress components, and the values ​​of the two principal stresses and the principal direction angles are calculated. If the matching fails, the process proceeds to a new formula capture and learning process, including: Based on the dynamic optimization parameters, a matching search is performed in the preset common formula database to obtain the formula matching results corresponding to the currently written mathematical content, and the matching success is determined based on the formula matching results. If the match is successful, then the formula type is further determined to be a stress state expression based on the formula type corresponding to the formula matching result. If the formula type is determined to be a stress state expression, then based on the identified plane stress components, the corresponding stress state matrix is ​​constructed, the characteristic equation of the stress state matrix is ​​solved, and the two principal stress values ​​and principal direction angles are calculated based on the characteristic equation. If the formula type is determined to be a non-stress state expression, then based on the formula matching result, the corresponding standard commonly used formula is directly retrieved from the commonly used formula database and returned. If the match is determined to be unsuccessful, the process of capturing and learning a new formula is triggered based on the result of the unsuccessful match determination.

8. The writing recognition system for the intelligent blackboard according to claim 7, characterized in that, In the new formula capture and learning process, the complete handwriting of the teacher for the current mathematical content is captured and recorded as a new problem-solving formula. Logical verification and knowledge integration are then performed on the new problem-solving formula, and it is updated to the formula database, including: When the new formula capture and learning process is triggered, the system continuously acquires and records the complete handwriting of the teacher on the smart blackboard for the current mathematical content; performs preprocessing and structuring on the complete handwriting to generate structured handwriting data including temporal and spatial structure information; The system performs in-depth analysis of structured handwriting data, identifies mathematical symbols, operators and operational relationships, and constructs corresponding mathematical expression trees. It then compares and analyzes these mathematical expression trees with a pre-defined mathematical grammar rule base to verify the mathematical logic correctness and grammatical structure integrity of the mathematical expression trees, and generates verified formula objects including verification conclusions. Based on the mathematical semantics expressed by the verified formula objects, an association search is performed in the formula database to determine the knowledge category to which the verified formula objects belong and to establish semantic associations between the objects and existing formulas; the verified formula objects, together with the established semantic associations, are integrated and updated to the corresponding knowledge category in the formula database.

9. The writing recognition system for an intelligent blackboard according to claim 8, characterized in that, Based on real-time collected ambient light data, screen temperature data, and teacher operation time distribution characteristics, the system dynamically adjusts display brightness, handwriting contrast, and response sensitivity to achieve adaptive handwriting recognition, including: Real-time acquisition of ambient light data, screen temperature data, and teacher operation time distribution characteristics provided by ambient light sensor, temperature sensor, and operation timer; and integration of data and characteristics into an environmental status input set. Using ambient light data from the environmental status input set as the processing object, and based on the preset light intensity mapping relationship, determine and obtain the screen target brightness parameters required to adapt to the current lighting conditions; The screen target brightness parameter and the screen temperature data in the environmental state input set are used together as the processing object. Based on the joint influence rules of brightness and temperature on display effect, the handwriting target contrast parameter required to optimize visibility is calculated and obtained. By combining the handwriting target contrast parameter with the teacher operation time distribution characteristics in the environmental state input set as the processing object, and dynamically calculating and obtaining the touch sensitivity parameter for optimizing interactive responsiveness based on the handwriting display state and user operation mode, adaptive handwriting recognition is achieved.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program that, when executed by a processor, implements the system as described in any one of claims 1 to 9.

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