An ellipse pattern generation method and system based on three-dimensional camera view angle

Abstract

The application provides a three-dimensional camera perspective-based ellipse pattern generation method and system. The method according to the application comprises: transforming a three-dimensional curved surface to a local coordinate system of an elliptic cylinder to obtain a converted three-dimensional curved surface; obtaining user input, defining an elliptic cylinder based on the user input and a three-dimensional camera perspective; performing intersection detection calculation on the converted three-dimensional curved surface and the elliptic cylinder, and visually outputting the intersection result to obtain a final ellipse pattern; the method further comprises: dynamically adjusting an intersection condition in the intersection detection calculation process according to user demand; wherein the intersection condition comprises a value range of an intersection region. That is, the application provides a three-dimensional elliptic cylinder surface intersection detection method based on coordinate transformation. Points in a world coordinate system are converted to a local coordinate system of an elliptic cylinder, and an elliptic equation is combined for judgment, thereby realizing high-precision and high-efficiency geometric recognition and pattern generation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer, and in particular to an ellipse figure generation method and system based on three-dimensional camera view angle. BACKGROUND

[0002] In three-dimensional figure interface drawing, the traditional ellipse generation method is mainly based on two-dimensional plane coordinate system, and is realized through parameter equation or scanning line algorithm. However, when the three-dimensional camera view angle transformation is introduced, the method has the following significant defects:

[0003] 1. Visual deviation problem: the ellipse drawn on the two-dimensional plane does not consider the perspective projection transformation, resulting in geometric distortion when observed in three-dimensional space, such as the projection of the center and the center of the ellipse not coinciding, the ratio of the major axis and the minor axis deviating from the actual view angle effect;

[0004] 2. High computational complexity: directly solving the ellipse equation in three-dimensional space requires complex matrix operations (such as inverse transformation of view matrix and projection matrix), and the time complexity of calculating the ellipse boundary condition pixel by pixel can reach O(n 2 ), which is difficult to meet the real-time rendering requirements;

[0005] 3. Strong coupling of coordinate system: the existing method depends on the screen coordinate system or the local coordinate system, and cannot adapt to the arbitrary angle change of the camera and the spatial dynamic adjustment of the three-dimensional interface.

[0006] Although there have been attempts to solve the ellipse through three-dimensional geometric projection, there is still no standardized pixel-level judgment process, and there is a lack of effective optimization of the figure rendering efficiency. The traditional method is to use triangular mesh to approximate the elliptical cylinder, but this method still has the following problems:

[0007] 1. Limited accuracy: the coarser the mesh division, the greater the fitting error;

[0008] 2. High performance overhead: fine mesh brings a large number of vertex calculations, affecting the rendering efficiency;

[0009] 3. Complex interactive judgment: collision detection needs to be processed triangle by triangle, with high algorithm complexity;

[0010] 4. Difficult to dynamically control: the ellipse parameters need to be regenerated when the mesh is changed.

[0011] Therefore, it is urgent to propose an ellipse drawing method that can accurately map the three-dimensional view angle projection relationship and efficiently realize pixel-level figure generation. SUMMARY

[0012] The present application aims to provide an ellipse figure generation method and system based on three-dimensional camera view angle, which aims to solve the above problems in the prior art.

[0013] The embodiment of the present application provides an elliptical pattern generation method based on a three-dimensional camera perspective, comprising:

[0014] transforming a three-dimensional curved surface to a local coordinate system of an elliptical cylinder to obtain a converted three-dimensional curved surface;

[0015] acquiring user input, and defining an elliptical cylinder based on the user input and a three-dimensional camera perspective;

[0016] performing intersection detection calculation on the converted three-dimensional curved surface and the elliptical cylinder, and performing visual output on an intersection result to obtain a final elliptical pattern.

[0017] The embodiment of the present application provides an elliptical pattern generation system based on a three-dimensional camera perspective, comprising:

[0018] a coordinate system conversion module, configured to transform a three-dimensional curved surface to a local coordinate system of an elliptical cylinder to obtain a converted three-dimensional curved surface;

[0019] an elliptical cylinder definition module, configured to acquire user input, and define an elliptical cylinder based on the user input and a three-dimensional camera perspective;

[0020] an elliptical pattern generation module, configured to perform intersection detection calculation on the converted three-dimensional curved surface and the elliptical cylinder, and perform visual output on an intersection result to obtain a final elliptical pattern.

[0021] The embodiment of the present application further provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the computer program, when executed by the processor, implements the steps of the elliptical pattern generation method based on a three-dimensional camera perspective.

[0022] The embodiment of the present application further provides a computer readable storage medium, wherein the computer readable storage medium stores an implementation program of information transmission, and the program, when executed by a processor, implements the steps of the elliptical pattern generation method based on a three-dimensional camera perspective.

[0023] The embodiment of the present application can have the following beneficial effects: the embodiment of the present application provides a three-dimensional elliptical cylinder surface intersection detection method based on coordinate transformation, points in a world coordinate system are transformed to a local coordinate system of an elliptical cylinder, and an elliptical equation is combined for judgment, so that high-precision and high-efficiency geometric recognition and pattern generation are realized. BRIEF DESCRIPTION OF DRAWINGS

[0024] In order to make one or more embodiments of the present specification or the prior art clearer, the drawings needed in the embodiment or prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments described in the specification, and other drawings can be obtained by those skilled in the art without creative labor.

[0025] Figure 1 is the flow chart of the ellipse generation method based on the three-dimensional camera view angle of the embodiment of the application;

[0026] Figure 2 is the coordinate conversion flow chart of the inverse projection transformation of the display pixel point from the screen coordinate system to the three-dimensional world coordinate system of the embodiment of the application;

[0027] Figure 3 is the intersection detection algorithm logic diagram for detailing the intersection judgment process of the three-dimensional point and the elliptical cylinder surface of the embodiment of the application;

[0028] Figure 4 is the schematic diagram of the ellipse generation system based on the three-dimensional camera view angle of the embodiment of the application;

[0029] Figure 5 is the GPU rendering pipeline schematic diagram for explaining the parallel processing mechanism of the shader program in the graphic rendering pipeline of the embodiment of the application. DETAILED DESCRIPTION

[0030] In order to make one or more embodiments of the present specification or the prior art clearer, the drawings needed in the embodiment or prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments described in the specification, and other drawings can be obtained by those skilled in the art without creative labor.

[0031] Method embodiment

[0032] According to the embodiment of the present application, a method for generating an ellipse based on a three-dimensional camera view angle is provided, Figure 1 is the flow chart of the ellipse generation method based on the three-dimensional camera view angle of the embodiment of the application, as Figure 1 shown, the ellipse generation method based on the three-dimensional camera view angle according to the embodiment of the present application specifically includes:

[0033] Step S101, transform the three-dimensional surface to the local coordinate system of the elliptical cylinder, and obtain the converted three-dimensional surface;

[0034] In step S102, a user input is acquired, and an elliptic cylinder is defined based on the user input and a three-dimensional camera perspective, specifically including:

[0035] A 2D screen point of the user input is acquired by using an OpenGL graphics library, the 2D screen point is converted into a three-dimensional world coordinate, elliptic parameters are calculated according to the three-dimensional world coordinate, a center point, a major semi-axis and a minor semi-axis of the ellipse are obtained, and the elliptic cylinder is defined along the center point of the ellipse and a three-dimensional camera perspective point.

[0036] In step S103, intersection detection calculation is performed on the converted three-dimensional curved surface and the elliptic cylinder, and an intersection result is visualized and output to obtain a final elliptic graph, specifically including:

[0037] The intersection part of the converted three-dimensional curved surface and the elliptic cylinder is calculated to obtain an intersection vertex set, and pixel points of the intersection are real-time colored and rendered to obtain the final elliptic graph.

[0038] The method further includes:

[0039] The intersection condition in the intersection detection calculation process is dynamically adjusted according to user needs.

[0040] The intersection condition includes a value range of an intersection region.

[0041] The above technical solutions of the embodiments of the present application are described in detail in combination with the specific conditions of the elliptic graph generation method based on a three-dimensional camera perspective of the embodiments of the present application.

[0042] The embodiments of the present application provide a method for generating an elliptic graph by an elliptic cylinder and an interface intersection pixel processing mode in a three-dimensional space based on a three-dimensional camera perspective, which is suitable for various application scenarios such as three-dimensional modeling, virtual simulation, real-time rendering, engineering modeling, game development, accurate drawing, collision detection, object picking and the like. Specifically, the method for drawing an ellipse on a three-dimensional curved surface provided by the embodiments of the present application includes the following steps:

[0043] I. Coordinate system conversion: the three-dimensional curved surface is rotated and translated, and then transformed to a local coordinate system of the elliptic cylinder.

[0044] 1. Three-dimensional transformation basis

[0045] (1) Translation

[0046] Translation refers to moving an object along a certain direction by a certain distance. Given a translation vector t = (t x ,t y ,t z), the translation transformation matrix T is:

[0047]

[0048] For a point p = (x, y, z), the new coordinates p' after translation are:

[0049] p' = T - p = (x + t x , y + t y , z + t z ) (2).

[0050] (2) Rotation

[0051] Rotation is usually represented using a rotation matrix or quaternions, here we take the Euler angle rotation matrix (rotation around x, y, z axes) as an example.

[0052] A. Rotation around x axis

[0053] Rotation angle θ x , transformation matrix R x :

[0054]

[0055] B. Rotation around y axis

[0056] Rotation angle θ y , transformation matrix R y :

[0057]

[0058] C. Rotation around z axis

[0059] Rotation angle θ z , transformation matrix R z :

[0060]

[0061] D. Combined rotation (order R z · R y · R x ):

[0062] R = R z · R y · R x (6).

[0063] II. User input acquisition: use OpenGL graphics library to get two three-dimensional points specified by the user;

[0064] 1. From screen coordinates to world coordinates, as shown in Figure 2 ​

[0065] OpenGL mouse click returns screen coordinates (2D), but the embodiment of the application needs three-dimensional world coordinates (3D), and the conversion process is as follows:

[0066] Screen coordinates -> normalized device coordinates (NDC) -> view space -> world space.

[0067] (1) Screen coordinates -> NDC

[0068] Screen coordinates (x screen ,y screen ) range: (0, 0) to (width, height).

[0069] Convert to NDC (x ndc ,y ndc ):

[0070]

[0071] Where the NDC range of OpenGL is [-1, 1], and the y-axis is reversed.

[0072] (2) NDC -> View Space

[0073] Use the inverse projection matrix P -1 Convert to view space:

[0074]

[0075] Where z ndc Usually take the near plane (-1) or the far plane.

[0076] (3) View Space -> World Space

[0077] Use the inverse view matrix V -1 Convert to world coordinates:

[0078]

[0079] Three, Ellipse parameter calculation: calculating the center point, major axis and minor axis of the ellipse according to the two three-dimensional points;

[0080] 1. Calculate the center point, major axis and minor axis of the ellipse according to two three-dimensional points

[0081] In three-dimensional space, given two points p1 = (x1, y1, z1) and P2 = (x2, y2, z2), the center point, major axis and minor axis of an ellipse (or ellipsoid) can be calculated, and the calculation method is as follows:

[0082] (1) Center point

[0083] The center point c of the ellipse is the midpoint of the two points:

[0084]

[0085] (2) long semi-axis

[0086] The long semi-axis a is half the distance between two points:

[0087]

[0088] (3) short semi-axis

[0089] The short semi-axis b is usually specified by the user, or calculated from the flattening of the ellipse:

[0090]

[0091] where e is the eccentricity of the ellipse (0 ≤ e < 1), and if e is not given, we can set b = k · a, k is a scale factor (e.g. 0.5).

[0092] 2. Special case: 2D ellipse

[0093] If the ellipse lies in a certain plane (e.g. z = 0), then:

[0094] Center point:

[0095]

[0096] Long semi-axis:

[0097]

[0098] Short semi-axis:

[0099] b = k · a (e.g. k = 0.5) (16).

[0100] Four, Elliptic Cylinder Definition: Determine an elliptic cylinder along the center point of the ellipse and the direction of the camera view; 1, define an elliptic cylinder along the center point of the ellipse and the camera view point

[0101] Given:

[0102] Ellipse center point c = (c x , c y , c z ) (calculated from two three-dimensional points);

[0103] Camera position v = (v x , v y , v z ) (view point);

[0104] Ellipse cylinder parameters: long semi-axis a, short semi-axis b, height h.

[0105] Then define an elliptic cylinder whose axis is directed from c to v and calculate its geometric parameters.

[0106] 2. Calculation formula

[0107] (1) The direction of the elliptic cylinder's axis

[0108] The direction vector of the axis d:

[0109] d = v - c (17);

[0110] The unit direction vector:

[0111]

[0112] (2) The local coordinate system of the elliptic cylinder

[0113] Define the local coordinate system:

[0114] Z-axis: (the direction of the axis).

[0115] X-axis: an optional vector perpendicular to (such as (1, 0, 0) projected onto the perpendicular direction).

[0116] Y-axis: Orthogonalize the x-axis:

[0117]

[0118] (3) The transformation matrix of the elliptic cylinder

[0119] Transform the local coordinate system to the world coordinate system:

[0120]

[0121] The final transformation matrix:

[0122]

[0123] (4) The parametric equation of the elliptic cylinder

[0124] In the local coordinate system, the equation of the elliptic cylinder is:

[0125]

[0126] Transform to the world coordinate system:

[0127] p world = M · p local (23);

[0128] where p world represents the coordinates of the point in the world coordinate system, and p local ​(x, y, z) represents the coordinates of a point in the local coordinate system.

[0129] V. Intersection detection calculation, such as Figure 3 computing the intersection of an elliptic cylinder and a three-dimensional surface;

[0130] Given a point (a point on the surface) The elliptic cylinder is defined by the following parameters:

[0131] Center point: Rotation matrix: R; major semi-axis: a; minor semi-axis: b; tolerance length: len;

[0132] Then do the following:

[0133] 1. Transform the point to the local coordinate system:

[0134]

[0135] Let the transformed point be (x', y', z').

[0136] 2. Determine whether the point is on the side of the elliptic cylinder (ignore the z' coordinate and only look at the cross section):

[0137] The implicit equation of the side of the elliptic cylinder is:

[0138]

[0139] In order to consider the tolerance, a certain error range e = 0.004 + len is allowed:

[0140]

[0141] where len represents the width parameter and ε represents the tolerance.

[0142] Equivalent to:

[0143]

[0144] 3. Final mathematical formula

[0145] Let the transformed point be:

[0146]

[0147] The judgment condition is:

[0148]

[0149] If it is true, then the point is considered to be on the side of the elliptic cylinder or within its tolerance range, i.e.:

[0150]

[0151] Six, width range setting: set the value range of the intersection region, used to determine the display width of the ellipse line.

[0152] Seven, pixel coloring output: set the intersecting pixel points to red to visualize the ellipse contour.

[0153] System embodiment

[0154] According to the embodiment of the present application, a three-dimensional camera perspective-based ellipse figure generation system is provided, Figure 4 is a three-dimensional camera perspective-based ellipse figure generation system schematic diagram of the embodiment of the present application, as Figure 4 shown, the three-dimensional camera perspective-based ellipse figure generation system according to the embodiment of the present application specifically comprises:

[0155] The coordinate system conversion module 40 is used to transform the three-dimensional surface to the local coordinate system of the elliptical cylinder to obtain the converted three-dimensional surface.

[0156] The elliptical cylinder definition module 42 is used to obtain the user input and define the elliptical cylinder based on the user input and the three-dimensional camera perspective, specifically used for:

[0157] The OpenGL graphics library is used to obtain the 2D screen point of the user input, the 2D screen point is converted into the three-dimensional world coordinates, the elliptic parameters are calculated according to the three-dimensional world coordinates, the center point, the major semi-axis and the minor semi-axis of the ellipse are obtained, and the elliptical cylinder is defined along the center point of the ellipse and the three-dimensional camera perspective point.

[0158] The ellipse figure generation module 44 is used to perform intersection detection calculation on the converted three-dimensional surface and the elliptical cylinder, and visually output the intersection result to obtain the final ellipse figure, specifically used for:

[0159] The intersection part of the converted three-dimensional surface and the elliptical cylinder is calculated to obtain the intersection vertex set, and the intersecting pixel points are real-time colored and rendered to obtain the final ellipse figure.

[0160] The system further comprises:

[0161] The adaptive adjustment module is used to dynamically adjust the intersection condition in the intersection detection calculation process according to the user demand.

[0162] The intersection condition comprises the value range of the intersection region.

[0163] The embodiment of the present application is a system embodiment corresponding to the above-mentioned method embodiment, and the specific operation of each module can be understood with reference to the description of the method embodiment, which will not be repeated here.

[0164] Compared with the prior art, the embodiments of the present application have the following beneficial effects:

[0165] 1. Strong universality: supports the determination of ellipsoidal cylinders in any rotation and translation state, suitable for complex animations or interactive scenes;

[0166] 2. Controllable accuracy: set the len parameter to flexibly adjust the determination area, balancing accuracy and performance;

[0167] 3. High efficiency of calculation: only basic matrix operations and vector transformations are involved, suitable for GPU parallel execution, as shown in the following formula: Figure 5

[0168] 4. Strong anti-interference ability: the error tolerance mechanism is introduced to effectively avoid false positives caused by floating-point precision problems;

[0169] 5. Strong scalability: can be extended to the determination logic of ellipsoids, parabolic surfaces and other quadratic surfaces.

[0170] That is, through the embodiments of the present application, accurate and efficient drawing of ellipses in three-dimensional perspective can be realized, solving the core problem of traditional methods in visual accuracy and calculation efficiency, and having significant technical progress and application value. The embodiments of the present application can be widely applied in the following fields: geometric figure drawing in three-dimensional modeling software, 3D face measurement and detection (such as marking feature points), virtual reality (VR) and augmented reality (AR) interface element rendering, accurate drawing in scientific computing visualization (such as ellipse region labeling in medical images), dynamic figure generation in real-time game engines, and interactive functions such as collision detection and object picking, etc.

[0171] Device embodiment one

[0172] The embodiments of the present application provide an electronic device, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the computer program is executed by the processor to realize the steps as described in the method embodiments.

[0173] Device embodiment two

[0174] The embodiments of the present application provide a computer readable storage medium, wherein the computer readable storage medium stores an implementation program of information transmission, and the program is executed by a processor to realize the steps as described in the method embodiments.

[0175] The computer readable storage medium described in the embodiments includes but is not limited to ROM, RAM, magnetic or optical disks, etc.

[0176] ​It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions recorded in the above embodiments can be modified, or some or all of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for generating an elliptical pattern based on a three-dimensional camera view, characterized by The method comprises the following steps: transforming a three-dimensional curved surface to a local coordinate system of an elliptic cylinder to obtain a converted three-dimensional curved surface; obtaining user input, and defining an elliptic cylinder based on the user input and a three-dimensional camera perspective, specifically comprising: obtaining a 2D screen point input by the user by using an OpenGL graphics library, converting the 2D screen point into a three-dimensional world coordinate, calculating elliptic parameters according to the three-dimensional world coordinate, obtaining a center point, a major semi-axis and a minor semi-axis of the ellipse, and defining the elliptic cylinder along the center point of the ellipse and a three-dimensional camera perspective point; performing intersection detection calculation on the converted three-dimensional curved surface and the elliptic cylinder, and visually outputting an intersection result to obtain a final elliptic graph, specifically comprising: transforming a point on the three-dimensional curved surface to the local coordinate system of the elliptic cylinder by using Formula 1, and judging whether the transformed point is located within a tolerance range of a side surface of the elliptic cylinder in the local coordinate system; wherein an expression of a judgment condition is shown in Formula 2; if the judgment condition is established, the point is determined as an intersection point; Formula 1 ; Formula 2; wherein, denotes a point on a three-dimensional curved surface, R denotes a rotation matrix of an elliptic cylinder, denotes a center point, denotes a transformed point, the transformed point coordinates are , denotes a width parameter, a and b are a long semi-axis and a short semi-axis of the elliptic cylinder, respectively.

2. The method of claim 1, wherein, the method further comprises: dynamically adjusting an intersection condition in the intersection detection calculation process according to user demand; wherein the intersection condition comprises a value range of an intersection region.

3. The method of claim 1, wherein, performing intersection detection calculation on the converted three-dimensional curved surface and the elliptic cylinder, and visually outputting an intersection result to obtain a final elliptic graph, specifically comprising: calculating an intersection part of the converted three-dimensional curved surface and the elliptic cylinder to obtain an intersection vertex set, and performing real-time coloring and rendering on a pixel point of the intersection to obtain a final elliptic graph.

4. A three-dimensional camera view-based ellipse pattern generation system, comprising: The system comprises: a coordinate system conversion module configured to transform a three-dimensional curved surface to a local coordinate system of an elliptic cylinder to obtain a converted three-dimensional curved surface; an elliptic cylinder definition module configured to obtain user input, and define an elliptic cylinder based on the user input and a three-dimensional camera perspective, specifically configured to: obtain a 2D screen point input by the user by using an OpenGL graphics library, convert the 2D screen point into a three-dimensional world coordinate, calculate elliptic parameters according to the three-dimensional world coordinate, obtain a center point, a major semi-axis and a minor semi-axis of the ellipse, and define the elliptic cylinder along the center point of the ellipse and a three-dimensional camera perspective point; an elliptic graph generation module configured to perform intersection detection calculation on the converted three-dimensional curved surface and the elliptic cylinder, and visually output an intersection result to obtain a final elliptic graph, specifically configured to: transform a point on the three-dimensional curved surface to the local coordinate system of the elliptic cylinder by using Formula 1, and judge whether the transformed point is located within a tolerance range of a side surface of the elliptic cylinder in the local coordinate system; wherein an expression of a judgment condition is shown in Formula 2; if the judgment condition is established, the point is determined as an intersection point; Formula 1 ; Formula 2: wherein, denotes a point on a three-dimensional curved surface, R denotes a rotation matrix of an elliptic cylinder, denotes a center point, denotes a transformed point, the transformed point coordinates are , denotes a width parameter, a and b are a long semi-axis and a short semi-axis of the elliptic cylinder, respectively.

5. The system of claim 4, wherein, the system further comprises: an adaptive adjustment module configured to dynamically adjust an intersection condition in the intersection detection calculation process according to user demand; wherein the intersection condition comprises a value range of an intersection region.

6. The system of claim 4, wherein, the elliptic graph generation module is specifically configured to: The intersection part of the converted three-dimensional curved surface and the elliptic cylinder is calculated to obtain an intersection vertex set, and the intersected pixel points are real-time colored and rendered to obtain a final elliptic graph.

7. An electronic device, comprising: The application relates to a three-dimensional camera perspective-based elliptic graph generation method. The application relates to a three-dimensional camera perspective-based elliptic graph generation method.

8. A computer-readable storage medium, characterized in that, The computer readable storage medium stores an information transmission implementation program, and the program is executed by the processor to implement the steps of the three-dimensional camera perspective-based elliptic graph generation method.

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