Boundary constraint triangulation network measurement system and method suitable for inertial equipment
By collecting and marking boundary points, a triangulation network conforming to boundary constraints is generated using the prediction-correction walking method and the Delaunay method based on concave and convex points. This solves the problem of insufficient boundary processing in traditional methods and improves the accuracy and precision of inertial equipment mapping.
Patent Information
- Application Number
- CN202511059609.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-30
- Publication Date
- 2025-11-21
Smart Images
Figure CN120997442A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of surveying and mapping technology, and specifically to a boundary-constrained triangulation measurement method suitable for inertial equipment. Background Technology
[0002] In the field of surveying and mapping, triangulated irregular networks (TINs), as a form of vector-based digital geographic data, are constructed by assembling a series of vertices (points) into triangles and are often used to represent landforms. There are numerous interpolation methods for forming these triangles, such as the Delaunay triangulation method.
[0003] However, traditional Delaunay triangulation methods, or various improved triangulation methods, only optimize the generation speed of the triangulation mesh, such as point-by-point interpolation and divide-and-conquer methods. They do not effectively handle the boundary conditions of the triangulation mesh, often resulting in the generation of triangles outside the boundaries. While boundary-constrained Delaunay triangulation methods can accurately generate the required triangulation mesh, they require the boundary constraint points to be determined in advance from the 3D point set. However, in reality, it is difficult to automatically and accurately identify boundary points in hundreds or thousands of 3D point clouds, thus making constrained triangulation impossible. Summary of the Invention
[0004] The purpose of this invention is to propose a boundary-constrained triangulation measurement system and method suitable for inertial devices, which can improve the accuracy of inertial device mapping.
[0005] To achieve the above objectives, in a first aspect, the present invention provides a boundary-constrained triangulation measurement method suitable for inertial devices, comprising: Collect measurement points at the outer boundary and inside the target area to obtain a list of measurement points; Mark the boundary points and construct a list of boundary points and a list of constraint edges; Constructing an unconstrained Delaunay triangulation includes: Construct the largest bounding rectangle; construct the upper left and lower right initial triangles within the largest bounding rectangle; Each measurement point Pi is inserted cyclically. The prediction-correction walk method is used to find the triangle in the current triangulation whose circumcircle contains the point Pi. Point Pi is then inserted and the local triangulation is optimized to form a new Delaunay triangle. Insert constraint edges, including: Find intersecting triangles, extract all edges of the intersecting triangles, remove duplicate edges and delete edges that intersect with constraint edges to form influence polygons; starting from the two endpoints of the constraint edges, find edges connected to them in the influence polygons in clockwise and counterclockwise directions respectively to obtain the left influence polygon and the right influence polygon; within the influence polygons, use the Delaunay method based on concave and convex points to regenerate the triangles inside the left and right influence polygons and replace the relevant parts in the original triangulation. Delete all triangles outside the constraint edges to obtain a triangulated mesh that meets the boundary constraints.
[0006] The beneficial effects of the basic scheme are as follows: Collecting measurement points at both the outer and inner boundaries of the target area and constructing a comprehensive list of measurement points lays the data foundation for subsequent triangulation construction, ensuring the integrity of the original data. Marking boundary points and constructing a list of boundary points and constraint edges clarifies the boundary range of the target area, ensuring that the triangulation construction strictly follows the actual boundary and avoids surveying deviations caused by boundary ambiguity. When constructing the unconstrained Delaunay triangulation, by constructing the maximum bounding rectangle and initial triangles, and then iteratively inserting measurement points and optimizing the local triangulation, it ensures that each point can be reasonably integrated into the triangulation, and the resulting triangles conform to the principle of maximizing the minimum angle, avoiding the formation of elongated triangles, thus improving the accuracy of the triangulation from a fundamental structural perspective.
[0007] When iteratively inserting measurement points, a Predict-Correct Walk (PCW) method is proposed to find triangles whose circumcircles contain Pi. Unlike the Walk algorithm in dynamic Delaunay triangulation, this method significantly reduces the number of invalid steps taken from a fixed starting point (such as the boundary or the previous point) to the target region, especially when the point set has strong spatial correlation. Due to the continuity of inertial navigation measurements, the point list is also continuous; adjacent points in the list are adjacent not only in computer memory but also in the real world. Therefore, the PCW method is particularly suitable for point lists acquired by inertial navigation equipment.
[0008] During the process of inserting constraint edges, intersecting triangles are found, edges are extracted, and influence polygons are formed. Then, triangles that satisfy the Delaunay criterion are regenerated to ensure that the constraint edges (i.e., the actual boundaries) are accurately represented in the triangulation network. This ensures that the triangulation network strictly fits the boundary shape of the target area, further improving the accuracy of the survey.
[0009] The constructed unconstrained Delaunay triangulation inherently possesses favorable mathematical properties, with a relatively uniform distribution of triangles, better reflecting the geometric characteristics of the target region. Adding boundary constraints not only retains the advantages of Delaunay triangulation but also adapts to actual boundary conditions, making it more suitable for the geometric model requirements of inertial equipment mapping.
[0010] By traversing the triangulation and deleting triangles that do not meet the constraint conditions, the final triangulation fully complies with the boundary constraints and can accurately delineate the outline of the target area. It has stronger applicability for scenarios where inertial devices need to work based on precise geometric models (such as terrain matching in inertial navigation and spatial positioning of equipment installation).
[0011] As a feasible preferred solution, an inertial device is used to sequentially collect several outer boundary measurement points along the outer boundary of the target area, so that the outer boundary measurement points are evenly distributed and can accurately reflect the shape of the outer boundary of the target area; Connect the outer boundary measurement points sequentially using polylines, and return to the starting point after the data collection is completed. Add the starting point coordinates back to the measurement point set to form a closed set of constraint edges.
[0012] As a feasible preferred solution, for regular rectangular areas, the outer boundary measurement points are set at the four corner points and the midpoint of each side; for irregular areas, measurement points are added at locations with large curvature changes or obvious boundary features.
[0013] As a feasible preferred solution, the inertial device is used to collect internal measurement points within the target area, and the collection density of the internal measurement points is dynamically adjusted according to the complexity and accuracy requirements of the target area.
[0014] As a feasible and preferred approach, boundary points are marked, including the following: Traverse the list of measurement points. If a point that coincides with the coordinates of the starting point is detected, mark the coinciding point and all points in between as boundary points. If no coinciding point is detected, mark all measurement points as boundary points.
[0015] As a feasible and preferred approach, a list of boundary points and a list of constraint edges are constructed, including the following: Copy all marked boundary points to form a boundary point list, and connect adjacent boundary points in sequence to form a constraint edge list.
[0016] As a feasible and preferred solution, the maximum bounding rectangle is constructed, including the following: Find the maximum and minimum values of all measurement points in the x, y, and z directions, and construct a three-dimensional maximum bounding rectangle based on the determined diagonal vertices. In the two-dimensional case, the maximum bounding matrix is determined by the four vertices.
[0017] As a feasible preferred approach, each measurement point Pi is cyclically inserted, and the predictive-corrective walk method is used to find the triangle in the current triangulation whose circumcircle contains that point Pi, including the following: Based on the standard Walk method, the coordinates of the insertion point are additionally recorded to form a historical information list. When the number of points in the historical information list exceeds 3, the initial search position of Pi is predicted by the position weighted average of the historical information list points. The standard Walk is started from the predicted hot spot area. If the prediction is wrong, the distance and direction information between the predicted point and the actual Pi are used to intelligently select to backtrack to the point.
[0018] As a feasible and preferred option, point Pi is inserted and the local triangulation is optimized to form a new Delaunay triangle, including the following: For all triangles whose circumcircles contain Pi, extract the vertices of each triangle and remove duplicates to form enclosing points containing Pi; connect the two enclosing points and Pi in sequence to form a new Delaunay triangle, and replace the found enclosing triangle.
[0019] As a feasible and preferred approach, finding intersecting triangles using the vector cross product method includes the following: Vectors are constructed based on the vertices of the triangle and the endpoints of the constraint edges. The positional relationship between the constraint edges and the triangle is determined by the sign and zero value of the cross product of the vectors.
[0020] As a feasible and preferred approach, the Delaunay method based on concavity and convexity points is used to regenerate the inner triangles of the left and right influencing polygons and replace them in the original triangulation list, including the following: Get the list of vertices affecting the polygon; When the number of vertices is greater than 3, iterate through all vertices. For each vertex, take three adjacent points and determine whether it is a convex vertex. If it is a convex vertex and does not contain other points, record and save the triangle formed by the three points and remove the vertex. For all the new triangles that are saved in the record, restore their Delaunay properties according to the empty circumcircle criterion. If the circumcircle of one triangle contains the opposite vertex of another triangle, then swap the diagonals of the shared sides of the two triangles. Iterate until all triangles satisfy the Delaunay condition.
[0021] Secondly, the present invention also provides a boundary constraint triangulation measurement system suitable for inertial devices, which utilizes the aforementioned boundary constraint triangulation measurement method suitable for inertial devices. Attached Figure Description
[0022] Figure 1This is a logical schematic diagram of a boundary-constrained triangulation measurement method suitable for inertial equipment; Figure 2 A schematic diagram of the architecture of the electronic device provided by the present invention.
[0023] Reference numerals: Electronic device 500, processor 501, communication interface 502, memory 503, bus 504. Detailed Implementation
[0024] To make the technical solution and advantages of this application clearer, the technical solution of the present invention will be further described in detail below with reference to the accompanying drawings. It is understood that the specific embodiments described herein are only some embodiments of the present invention, and are only used to explain this application, not to limit it. It should be noted that the technical features or combinations of technical features described in the following embodiments should not be considered isolated; they can be combined with each other to achieve better technical effects. The same reference numerals appearing in the accompanying drawings of the following embodiments represent the same features or components, and can be applied to different embodiments.
[0025] Furthermore, unless otherwise defined, the technical or scientific terms used in this invention description shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains.
[0026] The present invention will now be described in further detail with reference to the accompanying drawings: Reference Figure 1 A boundary-constrained triangulation measurement method for inertial devices includes the following steps.
[0027] Step S100: Collect measurement points at the outer boundary of the target area, including: Inertial equipment is used to sequentially measure various points along the outer boundary of the target area. During the measurement process, it is ensured that the measurement points are evenly distributed to accurately reflect the shape of the target area's outer boundary. The density of measurement points is determined based on the size of the target area and the complexity of the terrain. For example, for a regular rectangular area, measurement points can be placed at the four corners and the midpoints of each side; for irregular areas, measurement points are added at locations with significant curvature changes or distinct boundary features, based on their shape characteristics. Generally, the collected outer boundary measurement points should fully display the shape characteristics of the outer boundary.
[0028] Connect the measurement points sequentially using a polyline, returning to the starting point after the measurement is complete. Then, add the starting point coordinates to the measurement point set, ensuring that the measurement points on the outer boundary form a closed line segment; this closed line segment is the constraint edge set. For example, measurement points using... This indicates that when the measurement reaches the first... When the time reaches a certain point, return to the starting point, i.e., the starting point. and the end point In reality, the starting and ending points are the same point, but inertial navigation measurements have certain errors, so the coordinates of the starting and ending points are not exactly equal. Therefore, it is stipulated that when the starting point... and the end point The boundary measurement ends when the distance error between the points is less than 0.5% of the total length of the measured broken line segment.
[0029] Assuming a starting point Midpoint End point The total length of the broken line segment is calculated using the two-point distance formula, by summing the results:
[0030] in, For point With point The straight-line distance between them; Let be the total length of the boundary polyline. Then, when:
[0031] The boundary measurement is complete; add the points from the starting point to the measurement point set. Points with the same coordinates These form a closed line segment, which is the set of constraint edges. At this point, the length of the boundary point list is the original length. and add points ,total ,and The set of constraint edges is P0-P1, P1-P2, ..., P. m -P m+1 .
[0032] Step S200: Use an inertial device to collect measurement points within the target area, totaling... The number of internal measurement points can be flexibly adjusted based on the complexity and accuracy requirements of the target area. For complex areas, the number of internal measurement points can be increased to improve the accuracy of the triangulation network; for simple areas, the number of internal measurement points can be reduced to improve measurement efficiency.
[0033] When collecting internal measurement points, care should be taken to avoid the points being too concentrated or too sparse. Internal measurement points can be collected using a uniform or random distribution method, but it is necessary to ensure that the measurement points cover all parts of the target area.
[0034] Step S300: After all measurement points have been collected, obtain a list of all measurement points. , The inertial device transmits the coordinates of all measured points to a computer, creating a list containing the coordinates of all points. Each point in the list includes its number and its corresponding X, Y, and Z three-dimensional coordinates.
[0035] Step S400: Mark boundary points and traverse the obtained list of 3D interest points (i.e., the list of measurement points). , Its length is n+1. If the above measurement mode is followed, points that coincide with the starting point coordinates will inevitably be detected in the list, which are the start and end points of the boundary. Mark all points between the two points as boundary points.
[0036] If no point is detected that coincides with the starting point coordinates, all points are marked as boundary points. This situation may be due to errors during the measurement process or special circumstances that prevent accurate return to the starting point. To ensure the integrity of the generated triangulation network, all points are treated as boundary points.
[0037] Specifically, iterate through the list of points of interest and determine all subsequent points. , In the given information, do there exist points with exactly the same coordinates?
[0038] If the above conditions are met, record the index of this point. Then the index All points in between are boundary points. Design a four-dimensional array to store the three-dimensional coordinates of each point, along with a flag indicating whether it is a boundary point: 1 for boundary points, 0 for interior points. Indicates the boundary point.
[0039] Step S500, construct the boundary point list and constraint edge list, including: copying all boundary points to form the boundary point list, the length of which is... This creates a list of constraint edges formed by adjacent points, with a length of [length missing]. .
[0040] Step S600, construct an unconstrained Delaunay triangulation, including: Step S601: Construct the maximum bounding rectangle, find the maximum and minimum values of all measurement points in the x, y, and z directions, and denote them as follows: , , , , , ;by Constructing a 3D maximum bounding rectangle using the diagonal vertices, in the 2D case (assuming the z-coordinate does not affect the triangulation construction, only considering the x and y coordinates), the maximum bounding matrix is formed by the four vertices. , , , Sure.
[0041] Step S602: Form initial triangles, forming the upper left initial triangle and the lower right initial triangle within the largest bounding rectangle.
[0042] Step S603: Insert all points in a loop, insert all points P in a loop. i (i=0,1,⋯,n), and use the Predict-Correct Walk (PCW) method to find the circumcircle containing P. i The triangle. Unlike the Walk algorithm in dynamic Delaunay triangulation, this method significantly reduces the number of invalid steps taken from a fixed starting point (such as a boundary or the previous point) to the target region, especially when the point set has strong spatial correlation. Due to the continuity of inertial navigation measurements, the point list is also continuous; adjacent points in the point list are adjacent not only in computer memory but also in the real world. Therefore, the PCW method is particularly suitable for point lists acquired by inertial navigation equipment. The PCW method includes the following steps: Step S603-1: Following the standard Walk method, locate the circumcircle and additionally record the coordinates of the insertion point to form a historical information list. ; Step S603-2: When the number of historical information points exceeds 3, the location-weighted average of these historical points can be used for prediction. The initial search location is determined by a standard walk starting from the predicted "hotspot" area.
[0043] Step S603-3: When a prediction error occurs, intelligently select to backtrack using the distance and direction information between the predicted point and the actual Pi. It's about points, not simply starting from the beginning.
[0044] After finding all containing triangles, examine all circumcircles containing triangles. Extract the vertices of the triangle and remove duplicates to form a triangle containing The enclosing points, connecting the two enclosing points and in sequence. This forms a new Delaunay triangle, replacing the found containing triangle. Step S700: Insert constraint edges, ensuring that all constraint edges exist within the existing triangles, including: Step S701: Traverse and find intersecting triangles. Specifically, traverse all triangles and find the constraint edge E that intersects with the inserted triangle. iAll intersecting triangles. The method to determine whether a triangle intersects with a constraint edge can be achieved through the cross product of vectors, that is, by checking whether each of the three sides of the triangle intersects with the constraint edge.
[0045] Assume the three vertices of the triangle are , , The two endpoints of the constraint edge are , Determine the three sides of the triangle respectively. , , Is it related to the constrained edge? intersect.
[0046] For example, judgment Whether or not If they intersect, then the vectors need to be calculated separately. with vector cross product ,vector and cross product ; Calculate vectors with vector cross product ,vector with vector cross product If the cross product result and Different signs and and Opposite signs indicate that the two line segments intersect; Calculate the cross product of vectors: ; ; ; .
[0047] Determine the positional relationship between the constraint edge and the triangle based on the sign and zero value of the cross product. and If the constraint edge intersects the triangle, then record the triangle.
[0048] Step S702, construct the influencing polygon, if E i If a given triangle has a side, insert the next constraint edge and repeat the current operation. When constructing the influence polygon, extract all edges of the intersecting triangles, remove duplicate edges, and delete edges that intersect with the constraint boundaries to obtain the influence polygon.
[0049] Step S703: Locate the edges of the influencing polygon. Starting from the two endpoints of the constraint edge, search for edges in the influencing polygon that are connected to the endpoints in a clockwise and counterclockwise direction until returning to the other endpoint, thus obtaining the left and right influencing polygons. For example, starting from constraint edge E... i Starting from endpoint D, search clockwise for edges connected to D until returning to the other endpoint E. The resulting partial polygon is the left-influenced polygon; the partial polygon obtained by searching counterclockwise is the right-influenced polygon.
[0050] Step S704: Regenerate the inner triangles of the left and right influencing polygons using the Delaunay method based on concave and convex points, and replace them in the original triangulation list. Specifically, this includes: Step S704-1: Obtain the list of vertices affecting the polygon.
[0051] Step S704-2: When the number of vertices is greater than 3, iterate through all vertices. For each vertex... Take three adjacent points , , Judgment point Is it a convex vertex?
[0052] in, , For point The coordinates. If the above expression is true, then it indicates that... If it is a convex dot, then it indicates that if it is false, it means... It is a concave point, and at the same time, it is determined that... , , Does it contain any other vertices? If If it is a convex point and does not include other points, then the record is saved. , , A triangle formed by three points is removed from the vertex list. point.
[0053] Step S704-3: For all the new triangles that are recorded and saved, restore their Delaunay properties according to the empty circumcircle criterion. That is, traverse all adjacent triangle pairs that share a side. If the circumcircle of one triangle contains the opposite vertex of another triangle, then the Delaunay condition is not satisfied. Then swap the diagonals of the shared side of the two triangles and iterate until all triangles satisfy the Delaunay condition.
[0054] In step S800, after all constraint edges have been traversed, delete all triangles outside the constraint edges. By traversing all triangles in the triangulation, determine whether all edges of a triangle are in the constraint edge set. If there is an edge that is not in the constraint edge set, delete the triangle. The final triangulation obtained is the triangulation that satisfies the boundary constraint conditions.
[0055] This application also provides a boundary constraint triangulation measurement system suitable for inertial devices, which utilizes the aforementioned boundary constraint triangulation measurement method suitable for inertial devices.
[0056] This application embodiment also provides an electronic device 500 that utilizes the aforementioned boundary constraint triangulation measurement method for inertial devices. The device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the aforementioned boundary constraint triangulation measurement method for inertial devices. In this application embodiment, the processor is the control center of the computer method and can be a physical machine processor or a virtual machine processor.
[0057] Reference Figure 2 The electronic device 500 includes at least one processor 501, at least one communication interface 502, at least one memory 503, and at least one bus 504. The bus 504 is used for communication between these components, the communication interface 502 is used for signaling or data communication with other node devices, and the memory 503 stores machine-readable instructions executable by the processor 501. When the electronic device 500 is running, the processor 501 communicates with the memory 503 via the bus 504. When the machine-readable instructions are invoked by the processor 501, they execute the steps of the boundary constraint triangulation measurement method for inertial devices described above.
[0058] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor of an electronic device, can implement the steps of a boundary constraint triangulation measurement method for inertial devices as described above.
[0059] Those skilled in the art will understand that implementing all or part of the process in a boundary constraint triangulation measurement method suitable for inertial devices can be accomplished by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium. When executed, the program can include the process of various embodiments of the boundary constraint triangulation measurement method suitable for inertial devices. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.
[0060] This embodiment provides a boundary-constrained triangulation measurement method suitable for inertial devices, specifically addressing the difficulty of boundary identification in topographic mapping scenarios. It achieves efficient and accurate triangulation construction through inertial devices combined with a dynamic insertion algorithm. The following detailed description of the specific implementation steps is provided: The above content is merely an embodiment of the present invention. Commonly known structures and characteristics are not described in detail here. Those skilled in the art are aware of all common technical knowledge in the field prior to the application date or priority date, and are capable of applying conventional experimental methods prior to that date. Those skilled in the art can improve and implement this solution based on the guidance provided in this application and their own capabilities. Typical well-known structures or systems should not be obstacles for those skilled in the art to implement this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the structure of the present invention. These modifications and improvements should also be considered within the scope of protection of the present invention, and will not affect the effectiveness of the invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.
Claims
1. A method for measuring boundary-constrained triangulation networks suitable for inertial devices, characterized in that, include: Collect measurement points at the outer boundary and inside the target area to obtain a list of measurement points; Mark the boundary points and construct a list of boundary points and a list of constraint edges; Constructing an unconstrained Delaunay triangulation includes: Construct the largest bounding rectangle; construct the upper left and lower right initial triangles within the largest bounding rectangle; Each measurement point Pi is inserted cyclically. The prediction-correction walk method is used to find the triangle in the current triangulation whose circumcircle contains the point Pi. Point Pi is then inserted and the local triangulation is optimized to form a new Delaunay triangle. Insert constraint edges, including: Find intersecting triangles, extract all edges of the intersecting triangles, remove duplicate edges and delete edges that intersect with constraint edges to form influence polygons; starting from the two endpoints of the constraint edges, find the edges connected to them in the influence polygons in clockwise and counterclockwise directions respectively to obtain the left influence polygon and the right influence polygon; within the influence polygons, use the Delaunay method based on concave and convex points to regenerate the triangles inside the left and right influence polygons and replace the relevant parts in the original triangulation. Delete all triangles outside the constraint edges to obtain a triangulated mesh that meets the boundary constraints.
2. The boundary-constrained triangulation measurement method for inertial equipment according to claim 1, characterized in that, Using inertial equipment, a number of outer boundary measurement points are collected sequentially along the outer boundary of the target area, so that the outer boundary measurement points are evenly distributed and can accurately reflect the shape of the outer boundary of the target area; Connect the outer boundary measurement points sequentially using polylines, and return to the starting point after the data acquisition is completed. Add the starting point coordinates back to the measurement point set to form a closed set of constraint edges. For regular rectangular areas, the outer boundary measurement points are set at the four corner points and the midpoint of each side; for irregular areas, measurement points are added at locations with large curvature changes or obvious boundary features.
3. The boundary-constrained triangulation measurement method for inertial equipment according to claim 1, characterized in that, The inertial device is used to collect internal measurement points within the target area, and the collection density of the internal measurement points is dynamically adjusted according to the complexity and accuracy requirements of the target area.
4. The boundary-constrained triangulation measurement method for inertial equipment according to claim 1, characterized in that, Mark the boundary points and construct a list of boundary points and a list of constraint edges, including the following: Traverse the list of measurement points. If a point that coincides with the coordinates of the starting point is detected, mark the coinciding point and all points in between as boundary points. If no coincidence point is detected, all measurement points are marked as boundary points; Copy all marked boundary points to form a boundary point list, and connect adjacent boundary points in sequence to form a constraint edge list.
5. The boundary-constrained triangulation measurement method for inertial equipment according to claim 1, characterized in that, Construct the maximum bounding rectangle, including the following: Find the maximum and minimum values of all measurement points in the x, y, and z directions, and construct a three-dimensional maximum bounding rectangle based on the determined diagonal vertices. In the two-dimensional case, the maximum bounding matrix is determined by the four vertices.
6. The boundary-constrained triangulation measurement method for inertial equipment according to claim 1, characterized in that, For each measurement point Pi, iteratively insert the triangle, and use the predictive-corrective walk method to find the triangle in the current triangulation whose circumcircle contains that point Pi, including the following: Based on the standard Walk method, the coordinates of the insertion point are additionally recorded to form a historical information list. When the number of points in the historical information list exceeds 3, the initial search position of Pi is predicted by the position weighted average of the historical information list points. The standard Walk is started from the predicted hot spot area. If the prediction is wrong, the distance and direction information between the predicted point and the actual Pi are used to intelligently select to backtrack to the point.
7. The boundary-constrained triangulation measurement method for inertial equipment according to claim 1, characterized in that, Insert point Pi and optimize the local triangulation to form a new Delaunay triangle, including the following: For all triangles whose circumcircles contain Pi, extract the vertices of each triangle and remove duplicates to form enclosing points containing Pi; connect the two enclosing points and Pi in sequence to form a new Delaunay triangle, and replace the found enclosing triangle.
8. The boundary-constrained triangulation measurement method for inertial equipment according to claim 1, characterized in that, Finding intersecting triangles using the cross product method includes the following: Vectors are constructed based on the vertices of the triangle and the endpoints of the constraint edges. The positional relationship between the constraint edges and the triangle is determined by the sign and zero value of the cross product of the vectors.
9. The boundary-constrained triangulation measurement method for inertial equipment according to claim 1, characterized in that, The left and right inner triangles of the influencing polygons are regenerated using the Delaunay method based on concavity and convexity points, and then replaced in the original triangulation list, including the following: Get the list of vertices affecting the polygon; When the number of vertices is greater than 3, iterate through all vertices. For each vertex, take three adjacent points and determine whether it is a convex vertex. If it is a convex vertex and does not contain other points, record and save the triangle formed by the three points and remove the vertex. For all the new triangles that are saved in the record, restore their Delaunay properties according to the empty circumcircle criterion. If the circumcircle of one triangle contains the opposite vertex of another triangle, then swap the diagonals of the shared sides of the two triangles. Iterate until all triangles satisfy the Delaunay condition.
10. A boundary-constrained triangulation measurement system suitable for inertial devices, characterized in that, The method for measuring boundary-constrained triangulation networks for inertial devices, as described in any one of claims 1-9, is employed.