Method and device for visualizing streamline for Anti-aliasing

Abstract

The present invention relates to a method and device for visualizing streamlines for anti-aliasing. The method for visualizing streamlines according to the present invention comprises the steps of: generating a first streamline by applying a Runge-Kutta method to vector field data; calculating an equation of a first parameter curve on the basis of a plurality of points included in a first streamline, and generating a second streamline along the first parameter curve; and selecting, as essential points, points at both ends of each vector group composed of vectors having continuously similar directions in the second streamline, and generating a third streamline by calculating an equation of a second parameter curve on the basis of the coordinates of the essential points.

Description

Streamline visualization method and device for anti-aliasing

[0001] The present invention relates to image generation technology in the field of computer graphics. Specifically, the present invention relates to a technology for visualizing streamlines based on vector fields.

[0002] In the visualization technology of streamlines, existing streamline visualization methods (hereinafter referred to as "existing techniques") that solely use the Runge-Kutta ordinary differential equation solution method (hereinafter referred to as "existing techniques") can cause aliasing (staircase effect) in fine parts of the vector field because vectors are connected by straight lines. Aliasing can distort visualization results, hindering accurate interpretation of data, and degrades the visual quality of streamlines, especially in complex three-dimensional vector fields.

[0003] Furthermore, existing techniques generate a lot of unnecessary computation because they construct streamlines using all vectors within a vector field. This is particularly problematic when processing large vector fields, where the computational load increases dramatically, resulting in excessive consumption of computing resources. This significantly reduces efficiency when processing real-time visualization or large data sets.

[0004] Furthermore, existing technologies suffer from the problem of inefficient vector usage. Specifically, they fail to distinguish between vectors that convey important information and those that do not, resulting in inefficient streamlines containing unnecessary vectors. This reduces the clarity of visualization results and complicates user understanding.

[0005] Furthermore, existing techniques have limitations in representing smooth curves. Because the connections between vectors are linear, the curved shapes of streamlines can appear angular rather than smooth. In other words, existing techniques have limitations in visualizing the natural flow of vector fields, and in complex fields, streamlines are often inaccurately represented.

[0006] Meanwhile, existing technologies rely on fixed algorithms and procedures, making it difficult to flexibly adapt to diverse requirements. In particular, they face limitations in balancing visual quality and performance, limiting their ability to provide optimized visualizations for specific situations.

[0007] The purpose of the present invention is to provide a streamline visualization method and device that generates an initial streamline within a three-dimensional vector field based on a Runge-Kutta ordinary differential equation solution method, and additionally uses a Bezier curve equation to smoothly connect each vector, thereby improving the visualization quality of the streamline, and at the same time optimizing the use of computing resources by removing unnecessary vectors.

[0008] The purpose of the present invention is not limited to the purposes mentioned above, and other purposes not mentioned will be clearly understood by those skilled in the art from the description below.

[0009] A streamline visualization method according to one embodiment of the present invention comprises: (a) a step in which a streamline visualization device receives vector field data; (b) a step in which the streamline visualization device generates a first streamline by applying a Runge-Kutta method to the vector field data; and (c) a step in which the streamline visualization device samples a plurality of points included in the first streamline, calculates a formula for a first parameter curve based on coordinates for the plurality of points, and generates a second streamline along the first parameter curve.

[0010] In one embodiment of the present invention, the first parameter curve may be a Bezier curve.

[0011] In one embodiment of the present invention, the streamline visualization method may further include the steps of (d) extracting a vector corresponding to the second streamline from the vector field data, grouping continuous vectors having a direction difference within a set error range from the extracted vectors to generate one or more vector groups, extracting a line segment of the second streamline corresponding to the vector group, selecting points at both ends of each extracted line segment as essential points, calculating a formula for a second parameter curve based on coordinates for the essential points, and generating a third streamline along the second parameter curve.

[0012] In one embodiment of the present invention, the second parameter curve may be a Bezier curve.

[0013] In one embodiment of the present invention, the streamline visualization method may further include: (e) calculating an error rate of the third streamline based on an error of the third streamline compared to the first streamline; (f) comparing the error rate with a set threshold value; and (g) adjusting the error range by applying a set ratio to the error range when the error rate is greater than or equal to the threshold value.

[0014] In one embodiment of the present invention, the streamline visualization method may further include the step of performing (d) by applying the error range adjusted in (g).

[0015]

[0016] A streamline visualization device according to one embodiment of the present invention includes a storage device storing vector field data; a memory storing computer-readable commands; and at least one processor configured to execute the commands.

[0017] The at least one processor is configured to, by executing the instructions, receive the vector field data from the storage device, apply the Runge-Kutta method to the vector field data to generate a first streamline, sample a plurality of points included in the first streamline, derive a formula for a first parameter curve based on coordinates for the plurality of points, and generate a second streamline along the first parameter curve.

[0018] In one embodiment of the present invention, the first parameter curve may be a Bezier curve.

[0019] In one embodiment of the present invention, the at least one processor may be configured to extract a vector corresponding to the second streamline from the vector field data, group continuous vectors having a direction difference within a set error range from the extracted vectors to generate one or more vector groups, extract a line segment of the second streamline corresponding to the vector group, select points at both ends of each extracted line segment as essential points, calculate a formula for a second parameter curve based on coordinates for the essential points, and generate a third streamline along the second parameter curve.

[0020] In one embodiment of the present invention, the second parameter curve may be a Bezier curve.

[0021] In one embodiment of the present invention, the at least one processor may be configured to calculate an error rate of the third streamline based on an error of the third streamline compared to the first streamline, compare the error rate with a set threshold value, and adjust the error range by applying a set ratio to the error range when the error rate is greater than or equal to the threshold value.

[0022] According to the present invention, by constructing streamlines using Bézier curves, the curves are expressed more smoothly and continuously. In other words, the present invention has the effect of minimizing the aliasing phenomenon inherent in existing techniques, thereby improving the visual quality of streamlines. In particular, it has the effect of enabling more accurate visualization of the shape of streamlines in complex three-dimensional vector fields.

[0023] Furthermore, the present invention reduces computational complexity by eliminating unnecessary vectors within a set error range. Therefore, the present invention optimizes the use of computing resources, enabling faster and more efficient visualization.

[0024] Furthermore, the present invention has the advantage of being able to flexibly set the error range. Specifically, the present invention can adjust the error range according to user or system requirements. Therefore, the present invention can generate streamlines optimized for specific visual quality or performance requirements. For example, when high-quality visualization is required, setting the allowable error range small allows more vectors to be used to generate precise streamlines. When performance is critical, setting the allowable error range large allows for a reduction in the number of vectors required for streamlines, thereby reducing processing time. Therefore, the present invention can be applied to a variety of fields. For example, the present invention can be utilized in various fields such as fluid dynamics, meteorology, and engineering applications.

[0025] In short, the present invention provides high quality and efficiency in visualization tasks of various vector fields by combining Bezier curves and vector optimization techniques.

[0026] The effects that can be obtained from the present invention are not limited to the effects mentioned above, and other effects not mentioned can be clearly understood by a person having ordinary skill in the art to which the present invention belongs from the description below.

[0027] Fig. 1 is a block diagram showing the configuration of a streamline visualization device according to an embodiment of the present invention.

[0028] FIG. 2 is a flowchart for explaining a streamline visualization method according to one embodiment of the present invention.

[0029] Figures 3a to 3c are drawings comparing the two-dimensional curve processing effects of the existing technology and the present invention.

[0030] Figures 4a to 4c are drawings comparing the three-dimensional curve processing effects of the existing technology and the present invention.

[0031] The present invention relates to a technique for visualizing streamlines based on vector fields. In particular, the present invention relates to a method for minimizing aliasing and optimizing computing resource utilization using numerical solutions of ordinary differential equations and Bézier curves.

[0032] The advantages and features of the present invention, and the methods for achieving them, will become clear with reference to the embodiments described in detail below together with the accompanying drawings. However, the present invention is not limited to the embodiments disclosed below, but may be implemented in various different forms, and these embodiments are provided only to make the disclosure of the present invention complete and to fully inform those skilled in the art of the scope of the invention, and the present invention is defined only by the scope of the claims. Meanwhile, the terminology used in this specification is for the purpose of describing the embodiments and is not intended to limit the present invention. In this specification, the singular also includes the plural unless specifically stated in the phrase. The terms "comprises" and / or "comprising" as used in the specification do not exclude the presence or addition of one or more other components, steps, operations, and / or elements mentioned.

[0033] While terms like "first" and "second" may be used to describe various components, these components should not be limited by these terms. These terms may be used to distinguish one component from another. For example, without departing from the scope of the present invention, a first component could be referred to as a "second component," and similarly, a second component could also be referred to as a "first component."

[0034] When a component is referred to as being "connected" or "connected" to another component, it should be understood that it may be directly connected or connected to that other component, but that there may be other components in between. Conversely, when a component is referred to as being "directly connected" or "directly connected" to another component, it should be understood that there are no other components in between. Other expressions that describe the relationship between components, such as "between" and "directly between" or "adjacent to" and "directly adjacent to", should be interpreted similarly.

[0035] In this specification, vector field data refers to a set of points in Euclidean space and their corresponding vectors. In this specification, a streamline is constructed by sequentially connecting some points or surrounding points included in the vector field data. Reducing the number of vectors (vector samples) in a streamline means reducing the number of corresponding points. Furthermore, removing a point from a streamline means removing its corresponding vector.

[0036] In describing the present invention, if it is determined that a detailed description of a related known technology may unnecessarily obscure the gist of the present invention, the detailed description is omitted.

[0037] Hereinafter, embodiments of the present invention will be described in detail with reference to the attached drawings. In order to facilitate an overall understanding in describing the present invention, the same reference numbers will be used for the same means regardless of the drawing numbers.

[0038]

[0039] Fig. 1 is a block diagram showing the configuration of a streamline visualization device according to an embodiment of the present invention.

[0040] A streamline visualization device (1000) according to one embodiment of the present invention is a device for visualizing a streamline of two or more dimensions. The streamline visualization device (1000) is a device that performs the streamline visualization method according to the present invention. The streamline visualization device (1000) can be implemented in the form of the computer system of FIG. 1.

[0041] Referring to FIG. 1, the streamline visualization device (1000) may include at least one processor (1010), memory (1030), input interface device (1050), output interface device (1060), and storage device (1040) that communicate via a bus (1070). The streamline visualization device (1000) may further include a communication device (1020) coupled to a network.

[0042] The streamline visualization device (1000) illustrated in FIG. 1 is according to one embodiment, and the components of the streamline visualization device (1000) according to the present invention are not limited to the embodiment illustrated in FIG. 1, and may be added, changed, or deleted as needed.

[0043] The processor (1010) may be a central processing unit (CPU) or a semiconductor device that executes computer-readable instructions stored in the memory (1030) or the storage device (1040). The memory (1030) and the storage device (1040) may include various types of volatile or non-volatile storage media. For example, the memory (1030) may include read-only memory (ROM) and random access memory (RAM). In the embodiment of the present disclosure, the memory (1030) may be located inside or outside the processor (1010), and the memory (1030) may be connected to the processor (1010) via various known means. The memory (1030) may be various types of volatile or non-volatile storage media. For example, the memory (1030) may include read-only memory (ROM) or random access memory (RAM).

[0044] Accordingly, embodiments of the present invention may be implemented as a computer-implemented method or as a non-transitory computer-readable medium storing computer-executable instructions. In one embodiment, when executed by a processor (1010), the computer-readable instructions may perform a method according to at least one aspect of the present disclosure.

[0045] The communication device (1020) can transmit or receive wired or wireless signals.

[0046] In addition, the streamline visualization method according to an embodiment of the present invention can be implemented in the form of program commands that can be performed through various computer means and recorded on a computer-readable medium.

[0047] The computer-readable medium may include program commands, data files, data structures, etc., either singly or in combination. The program commands recorded on the computer-readable medium may be specially designed and configured for embodiments of the present invention, or may be known and usable by those skilled in the art of computer software. The computer-readable recording medium may include a hardware device configured to store and execute the program commands. For example, the computer-readable recording medium may be a magnetic medium such as a hard disk, a floppy disk, and a magnetic tape, an optical medium such as a CD-ROM or a DVD, a magneto-optical medium such as a floptical disk, a ROM, a RAM, a flash memory, etc. The program commands may include not only machine language codes such as those generated by a compiler, but also high-level language codes that can be executed by a computer through an interpreter, etc.

[0048] The processor (1010) receives vector field data stored in the memory (1030) or the storage device (1040) by executing computer-readable instructions stored in the memory (1030) or the storage device (1040), and applies the Runge-Kutta method to the vector field data to generate a first streamline.

[0049] The processor (1010) is configured to sample a plurality of points included in the first streamline, calculate a formula for a first parameter curve based on coordinates for the plurality of points, and generate a second streamline along the first parameter curve.

[0050] The above first parameter curve may be a Bezier curve.

[0051] The processor (1010) may be configured to extract a vector corresponding to the second streamline from the vector field data, group continuous vectors having a direction difference within a set error range from the extracted vectors to generate one or more vector groups, extract a line segment of the second streamline corresponding to the vector group, select points at both ends of each extracted line segment as essential points, calculate a formula for a second parameter curve based on coordinates for the essential points, and generate a third streamline along the second parameter curve.

[0052] The above second parameter curve may be a Bezier curve.

[0053] The processor (1010) may be configured to calculate an error rate of the third streamline based on an error of the third streamline compared to the first streamline, compare the error rate with a set threshold value, and adjust the error range by applying a set ratio to the error range when the error rate is greater than or equal to the threshold value.

[0054]

[0055] FIG. 2 is a flowchart for explaining a three-dimensional streamline visualization method according to one embodiment of the present invention.

[0056] Referring to FIG. 2, a streamline visualization method according to an embodiment of the present invention comprises steps S100 to S700. The streamline visualization method illustrated in FIG. 2 is according to one embodiment, and the steps of the streamline visualization method according to the present invention are not limited to the embodiment illustrated in FIG. 2, and may be added, changed, or deleted as needed.

[0057] For convenience of explanation, it is assumed that the streamline visualization method of FIG. 2 is performed by a streamline visualization device (1000).

[0058] Step S100 is the step where vector field data is input.

[0059] The streamline visualization device (1000) receives vector field data from an external computational fluid dynamics (CFD) system. The vector field data may be two-dimensional or three-dimensional vector field data.

[0060] For example, the streamline visualization device (1000) can receive vector field data through a communication device (1020). The processor (1010) stores the vector field data in a memory (1030) or a storage device (1040).

[0061]

[0062] Step S200 is a step for generating a first streamline using the Runge-Kutta method. The processor (1010) reads vector field data from the memory (1030) or the storage device (1040). The processor (1010) applies the Runge-Kutta method to the vector field data to generate the first streamline.

[0063] The present invention uses the Runge-Kutta ordinary differential equation solving method (referred to herein as the "Runge-Kutta method") to generate a first streamline within a vector field. The Runge-Kutta method is a widely used numerical technique for generating streamlines by calculating the movement path between points included in vector field data based on the direction of the vector. The processor (1010) forms the first streamline by moving each point included in the vector field data along the flow of the vector field using the Runge-Kutta method.

[0064]

[0065] Step S300 is a step of generating a second streamline using a parameter curve based on the first streamline. The processor (1010) samples a plurality of points included in the first streamline, calculates a formula for the first parameter curve based on the coordinates of the plurality of points, and generates a second streamline along the first parameter curve.

[0066] For example, the parametric curve used in the present invention may be any one of a Bezier curve, a spline, a Bezier spline, a Hermite spline, a Catmull-Rom spline, and a Cardinal spline. The present invention is not limited to the types of parametric curves described above. However, for convenience of explanation, the present specification is described mainly on the case where the parametric curve is a Bezier curve.

[0067] After the first streamline is generated, the processor (1010) connects each point of the first streamline using a Bezier curve equation. That is, the processor (1010) collects the coordinates of each point of the first streamline and generates a Bezier curve based on the collected coordinates. The processor (1010) generates a second streamline along the generated Bezier curve.

[0068] Bézier curves are curves that smoothly connect points, allowing them to naturally express the curvature of streamlines. Applying Bézier curves to streamline generation allows for smooth visualization of streamlines and minimizes aliasing.

[0069] For example, the formula for a quadratic Bezier curve is as shown in Formula 1.

[0070]

[0071] In Equation 1, t is a parameter, and P0, P1, and P2 are control points that constitute the Bezier curve.

[0072] Step S400 is the step of generating the third streamline by selecting essential points (hereinafter referred to as essential points) based on the pre-set error range based on the second streamline.

[0073] The processor (1010) extracts the positions of each point constituting the second streamline from vector field data and the vectors corresponding thereto. The number of extracted points and the number of vectors corresponding thereto may be determined according to a preset sampling number.

[0074] And the processor (1010) analyzes the direction of the extracted vector to generate a vector group. Specifically, the processor (1010) groups consecutive vectors having a direction difference within a set error range among the extracted vectors to generate one or more vector groups.

[0075] And the processor (1010) removes intermediate points from among the points corresponding to the grouped vectors, leaving only essential points. That is, the processor (1010) extracts line segments (sets of points) of the second streamline corresponding to the vector group, and selects points at both ends of each extracted line segment as essential points.

[0076] And the processor (1010) calculates a formula for a second parameter curve based on coordinates for the selected essential points, and generates a third streamline along the second parameter curve.

[0077] The streamline visualization device (1000) according to the present invention sets an error range to optimize essential points that constitute a streamline. The error range refers to the range within which vectors can be determined to have similar directions. For example, the error range can be expressed as a cosine similarity value (e.g., 0.8 or greater or 0.9 or greater). The error range can be set by an external device or user input.

[0078] The streamline visualization device (1000) groups consecutive vectors with similar directions within a set error range from vectors corresponding to a second streamline, and eliminates unnecessary vectors from each vector group, thereby reducing the amount of computation and optimizing computing resources. The above-described method can improve the efficiency of streamline visualization while maintaining visualization quality.

[0079]

[0080] Steps S500 to S700 correspond to the steps for adjusting the error range based on aesthetic judgment or performance requirements. The error range applied to the third streamline generation in Step S400 can be adjusted through Steps S500 to S700 based on aesthetic judgment or specific performance requirements. For example, if high-quality visualization is required, the error range can be adjusted to a smaller value to increase the required points. If performance is critical, the error range can be adjusted to a larger value to reduce the required points.

[0081] In steps S500 and S600, the streamline visualization device (1000) evaluates the visualization result (third streamline) derived in step S400 to determine whether quality and performance are balanced, and in step S700, the streamline visualization device (1000) adjusts the error range if the visualization result does not meet specific requirements. The streamline visualization device (1000) applies the adjusted error range and performs step S400 again to generate an optimized streamline.

[0082] Below, each step from step S500 to step S700 is described in detail.

[0083]

[0084] Step S500 is a step for calculating the error rate of the third streamline. The processor (1010) calculates the error rate of the third streamline based on the error of the third streamline compared to the first streamline.

[0085] When generating the third streamline at step S400, errors may occur compared to the first streamline because the curve was generated by reducing the number of vector samples (required points). Various methods may be used to calculate the error rate of the third streamline. For example, the processor (1010) may calculate the error rate of the third streamline according to Equations 2 to 5.

[0086] First, Equation 2 is the equation for calculating the error between streamlines.

[0087]

[0088] E(t) represents the error between streamlines, r(t) represents the third streamline (or second parameter curve), r b (t) represents the first streamline (base curve).

[0089] Next, the processor (1010) calculates the sum of the errors. Equation 3 is the equation for calculating the sum of the errors.

[0090]

[0091] Next, the processor (1010) calculates the length of the third streamline. Equation 4 is an equation for calculating the length of the streamline.

[0092]

[0093] In addition, the processor (1010) can obtain the error rate of the third streamline by calculating the ratio of the total error compared to the length of the third streamline. Equation 5 is an equation expressing the error rate of the third streamline as a percentage.

[0094]

[0095] Step S600 compares the error rate of the third streamline with a threshold. The threshold can be set differently depending on specific requirements. For example, if high-quality visualization is required, the threshold may be set low, while if high performance is required, the threshold may be set high.

[0096] The processor (1010) compares the error rate of the third streamline calculated in step S500 with a set threshold value, and if the error rate is less than the threshold value, terminates the process, and if the error rate is greater than the threshold value, performs step S700.

[0097]

[0098] Step S700 is a step for adjusting the error range. The processor (1010) adjusts the error range by applying a set ratio to the error range applied in step S400. For example, the processor (1010) can adjust the error range by multiplying the existing error range (cosine similarity 0.8 or higher) by 1.05 (a 5% increase) (adjusted error range: cosine similarity 0.84 or higher). As another example, the processor (1010) can adjust the error range based on the difference between the error rate and the threshold value. That is, if the error rate significantly exceeds the threshold value, the error range decreases significantly.

[0099] After step S700, the processor (1010) optimizes the streamline by performing step S400 again with the adjusted error range applied.

[0100]

[0101] The aforementioned streamline visualization method has been described with reference to the flowchart presented in the drawings. For simplicity, the method has been depicted and described as a series of blocks. However, the present invention is not limited to the order of the blocks. Some blocks may occur in a different order or concurrently with other blocks than depicted and described herein, and various other branches, flow paths, and block orders that achieve the same or similar results may be implemented. Furthermore, not all depicted blocks may be required to implement the method described herein.

[0102]

[0103] Meanwhile, in the description referring to FIG. 2, each step may be further divided into additional steps or combined into fewer steps, depending on the implementation of the present invention. Furthermore, some steps may be omitted as needed, and the order of steps may be changed. Furthermore, even if other details are omitted, the content of FIG. 1 may be applied to the content of FIG. 2. Furthermore, the content of FIG. 2 may be applied to the content of FIG. 1.

[0104]

[0105]

[0106] Hereinafter, the results of testing the streamline visualization method and device according to the present invention will be described.

[0107] Table 1 shows the results of testing the streamline visualization method and device according to the present invention on one curve sample.

[0108]

[0109] When the number of vectors in the discrete vector field data was 5000, an error rate of 2.3% was observed even for 10% sampling.

[0110]

[0111] Additionally, the processing time for extracting vector data from a Computational Fluid Dynamics (CFD) system varies depending on the number of vectors used. Reducing the number of vector samples used can reduce the processing time required for extraction. Table 2 shows a test environment to which the present invention is applied, and Table 3 shows the extraction processing time for different numbers of sampled vectors.

[0112]

[0113]

[0114] When 10% of the vectors were sampled, it was confirmed that the processing time was approximately 15% of the time required to process 5000 vectors.

[0115]

[0116] And, the anti-aliasing effect of the present invention is explained.

[0117] FIGS. 3a to 3c are drawings comparing the two-dimensional curve processing effects of the existing technology and the present invention, and FIGS. 4a to 4c are drawings comparing the three-dimensional curve processing effects of the existing technology and the present invention.

[0118] FIGS. 3A and 4A illustrate streamlines generated by applying 100 vector samples based on existing technology. FIGS. 3B and 4B illustrate streamlines generated by applying 10 vector samples based on existing technology. FIGS. 3C and 4C illustrate streamlines according to Bézier curves by applying 10 vector samples based on the present invention. When a Bézier curve is processed by the method proposed in the present invention, it can be confirmed that a visually stair-stepping phenomenon does not occur even with a relatively small number of vectors, as shown in FIGS. 3C and 4C. In addition, the present invention can form an error rate within an error rate (threshold value) desired by a user through accurate error rate calculation. In other words, the present invention can secure a processing time and curve error rate at a level desired by the user by automating the task of reaching the error rate desired by the user.

[0119]

[0120] Although the present invention has been described above with reference to preferred embodiments thereof, it will be understood by those skilled in the art that various modifications and changes may be made to the present invention without departing from the spirit and scope of the present invention as set forth in the claims below.

Claims

1. (a) A streamline visualization device, a step of receiving vector field data; (b) a step in which the streamline visualization device generates a first streamline by applying the Runge-Kutta method to the vector field data; and (c) a step of the streamline visualization device sampling a plurality of points included in the first streamline, calculating a formula of a first parameter curve based on coordinates of the plurality of points, and generating a second streamline along the first parameter curve; A streamline visualization method including .

2. In paragraph 1, The above first parameter curve is a Bezier curve In-streamline visualization method.

3. In paragraph 1, (d) a step of extracting a vector corresponding to the second streamline from the vector field data, grouping continuous vectors having a direction difference within a set error range from the extracted vectors to create one or more vector groups, extracting a line segment of the second streamline corresponding to the vector group, selecting points at both ends of each extracted line segment as essential points, calculating a formula for a second parameter curve based on the coordinates for the essential points, and creating a third streamline along the second parameter curve; A streamline visualization method that further includes .

4. In paragraph 3, (e) a step of calculating an error rate of the third streamline based on an error of the third streamline compared to the first streamline; (f) a step of comparing the above error rate with a set threshold value; and (g) a step of adjusting the error range by applying a ratio set in the error range when the error rate is greater than or equal to the threshold value; A streamline visualization method that further includes .

5. In paragraph 4, (h) performing (d) by applying the error range adjusted in (g); A streamline visualization method that further includes .

6. A storage device that stores vector field data; A memory that stores computer-readable instructions; and comprising at least one processor implemented to execute the above instructions, At least one processor, by executing the instructions, Reading the vector field data from the storage device, The first streamline is generated by applying the Runge-Kutta method to the above vector field data, A method configured to sample a plurality of points included in the first streamline, calculate a formula for a first parameter curve based on coordinates for the plurality of points, and generate a second streamline along the first parameter curve. In-streamline visualization device.

7. In paragraph 6, The above first parameter curve is a Bezier curve In-streamline visualization device.

8. In the 6th paragraph, the at least one processor, A method for extracting a vector corresponding to the second streamline from the vector field data, grouping continuous vectors having a direction difference within a set error range from the extracted vectors to generate one or more vector groups, extracting a line segment of the second streamline corresponding to the vector group, selecting points at both ends of each extracted line segment as essential points, calculating a formula for a second parameter curve based on coordinates for the essential points, and generating a third streamline along the second parameter curve. In-streamline visualization device.

Images