Elliptical graph generation method and system based on visual angle of three-dimensional camera

Abstract

The invention provides an elliptic graph generation method and system based on a visual angle of a three-dimensional camera, and the method comprises the steps: converting a three-dimensional curved surface into a local coordinate system of an elliptic cylinder, and obtaining a converted three-dimensional curved surface; acquiring user input, and defining an elliptic cylinder based on the user input and the visual angle of the three-dimensional camera; performing intersection detection calculation on the converted three-dimensional curved surface and the elliptic cylinder, and performing visual output on an intersection result to obtain a final elliptic graph; the method further comprises the following steps: dynamically adjusting intersection conditions in an intersection detection calculation process according to user requirements; wherein the intersection condition comprises a value domain range of the intersection area. According to the coordinate transformation-based three-dimensional elliptic cylinder surface intersection detection method provided by the invention, points in a world coordinate system are converted into a local coordinate system of an elliptic cylinder, and judgment is carried out in combination with an elliptic equation, so that high-precision and high-efficiency geometric recognition and graph generation are realized.

Description

Technical Field

[0001] The present invention relates to the field of computer technology, and in particular to a method and system for generating elliptical graphics based on a three-dimensional camera viewing angle. Background Art

[0002] In the rendering of 3D graphical interfaces, traditional ellipse generation methods are mainly based on 2D coordinate systems and implemented through parametric equations or scanline algorithms. However, when 3D camera perspective transformation is introduced, these methods have the following significant drawbacks:

[0003] 1. Visual deviation: The ellipse drawn on a two-dimensional plane does not take into account perspective projection transformation, resulting in geometric distortion when viewed in three-dimensional space. For example, the center of the circle does not coincide with the center of the ellipse, and the ratio of the major axis to the minor axis deviates from the actual viewing angle.

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

[0005] 3. Strong coupling of coordinate systems: Existing methods mostly rely on the screen coordinate system or the local coordinate system, and cannot adapt to arbitrary angle changes of the camera and the spatial dynamic adjustment of the three-dimensional interface.

[0006] Although some studies have attempted to solve ellipses through 3D geometric projection, a standardized pixel-level determination process has not yet been established, and there is a lack of effective optimization for graphics rendering efficiency. The traditional approach is to use triangular meshes to approximate the elliptical cylinder, but this method still has the following problems:

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

[0008] 2. High performance overhead: Fine meshes require a large number of vertex calculations, affecting rendering efficiency;

[0009] 3. Complex interaction judgment: Collision detection needs to be processed triangle by triangle, and the algorithm complexity is high;

[0010] 4. Difficult to control dynamically: The mesh needs to be regenerated when the ellipse parameters change.

[0011] Therefore, it is urgent to propose an ellipse drawing method that can accurately map the three-dimensional perspective projection relationship and efficiently realize pixel-level graphics generation. Summary of the Invention

[0012] The purpose of the present invention is to provide a method and system for generating elliptical graphics based on a three-dimensional camera viewing angle, aiming to solve the above-mentioned problems in the prior art.

[0013] An embodiment of the present invention provides a method for generating an elliptical graphic based on a three-dimensional camera viewing angle, comprising:

[0014] Transform the three-dimensional surface into the local coordinate system of the elliptical cylinder to obtain a transformed three-dimensional surface;

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

[0016] An intersection detection calculation is performed on the converted three-dimensional surface and the elliptical cylinder, and the intersection result is output visually to obtain a final elliptical figure.

[0017] An embodiment of the present invention provides a system for generating an elliptical graphic based on a three-dimensional camera viewing angle, comprising:

[0018] A coordinate system conversion module is used to convert the three-dimensional surface into the local coordinate system of the elliptical cylinder to obtain the converted three-dimensional surface;

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

[0020] The elliptical graphic generation module is used to perform intersection detection calculation on the converted three-dimensional surface and the elliptical cylinder, and output the intersection result in a visual format to obtain a final elliptical graphic.

[0021] An embodiment of the present invention also provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is executed by the processor, the steps of the above-mentioned method for generating an elliptical graphic based on a three-dimensional camera perspective are implemented.

[0022] An embodiment of the present invention further provides a computer-readable storage medium storing an information transmission implementation program, which, when executed by a processor, implements the steps of the above-mentioned method for generating an elliptical graphic based on a three-dimensional camera perspective.

[0023] The use of the embodiments of the present invention can include the following beneficial effects: The embodiments of the present invention provide a three-dimensional elliptical cylinder surface intersection detection method based on coordinate transformation, which transforms the points in the world coordinate system to the local coordinate system of the elliptical cylinder and makes judgments based on the elliptical equation, thereby achieving high-precision and high-efficiency geometric recognition and graphics generation. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate one or more embodiments of this specification or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments recorded in this specification. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0025] Figure 1 This is a flow chart of a method for generating an elliptical graphic based on a three-dimensional camera viewing angle according to an embodiment of the present invention;

[0026] Figure 2 This is a coordinate conversion flow chart showing the inverse projection transformation of a pixel point from a screen coordinate system to a three-dimensional world coordinate system according to an embodiment of the present invention;

[0027] Figure 3 This is a logic diagram of an intersection detection algorithm for detailing the intersection determination process between a three-dimensional point and an elliptical cylinder surface according to an embodiment of the present invention;

[0028] Figure 4 Schematic diagram of an elliptical graphic generation system based on a three-dimensional camera viewing angle according to an embodiment of the present invention;

[0029] Figure 5 This is a schematic diagram of a GPU rendering pipeline for illustrating a parallel processing mechanism of a shader program in a graphics rendering pipeline according to an embodiment of the present invention. DETAILED DESCRIPTION

[0030] In order to enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below in conjunction with the drawings in one or more embodiments of this specification. Obviously, the described embodiments are only part of the embodiments of this specification, not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of this document.

[0031] Method Example

[0032] According to an embodiment of the present invention, a method for generating an ellipse graphic based on a three-dimensional camera viewing angle is provided. Figure 1 FIG is a flow chart of a method for generating an elliptical graphic based on a three-dimensional camera viewing angle according to an embodiment of the present invention. Figure 1 As shown, the method for generating an elliptical graphic based on a three-dimensional camera viewing angle according to an embodiment of the present invention specifically includes:

[0033] Step S101, transforming the three-dimensional surface into the local coordinate system of the elliptical cylinder to obtain a transformed three-dimensional surface;

[0034] Step S102, obtaining user input, and defining an elliptical cylinder based on the user input and the three-dimensional camera viewing angle, specifically includes:

[0035] Using the OpenGL graphics library to obtain a 2D screen point input by the user, the 2D screen point is converted into a 3D world coordinate, ellipse parameters are calculated based on the 3D world coordinate to obtain the center point, major semi-axis, and minor semi-axis of the ellipse, and an elliptical cylinder is defined along the center point of the ellipse and the viewpoint of the 3D camera;

[0036] Step S103, performing intersection detection calculation on the converted three-dimensional surface and the elliptical cylinder, visually outputting the intersection result, and obtaining a final elliptical figure, specifically includes:

[0037] Calculating the intersection of the converted three-dimensional surface and the elliptical cylinder to obtain an intersection vertex set, and performing real-time coloring and rendering on the intersecting pixel points to obtain a final elliptical figure;

[0038] The method further comprises:

[0039] Dynamically adjust the intersection conditions during intersection detection calculations based on user needs;

[0040] The intersection condition includes a value range of the intersection area.

[0041] The above technical solution of the embodiment of the present invention is described in detail below in conjunction with the specific situation of the method for generating an elliptical graphic based on a three-dimensional camera viewing angle according to the embodiment of the present invention.

[0042] The present invention provides a method for generating an elliptical graphic in three-dimensional space by processing pixels at the intersection of an elliptical cylinder and an interface based on a three-dimensional camera perspective. The method is suitable for a variety of application scenarios, including three-dimensional modeling, virtual simulation, real-time rendering, engineering modeling, game development, precision drawing, collision detection, and object picking. Specifically, the present invention provides a method for drawing an ellipse on a three-dimensional surface, including the following steps:

[0043] 1. Coordinate system conversion: After rotating and translating the three-dimensional surface, transform it into the local coordinate system of the elliptical cylinder;

[0044] 1. Three-dimensional transformation basics

[0045] (1) Translation

[0046] Translation means moving an object a certain distance in a certain direction. 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 coordinate p′ after translation is:

[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 quaternion. Here we use the Euler angle rotation matrix (rotation around the x, y, and z axes) as an example.

[0052] A. Rotation around the x-axis

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

[0054]

[0055] B. Rotation around the y-axis

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

[0057]

[0058] C. Rotation around the z axis

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

[0060]

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

[0062] R=R z ·R y ·R x (6).

[0063] 2. User input acquisition: Use the OpenGL graphics library to obtain two 3D points specified by the user;

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

[0065] OpenGL mouse clicks return screen coordinates (2D), but the present invention requires three-dimensional world coordinates (3D). 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] Among them, the NDC range of OpenGL is [-1, 1], and the y-axis is reversed.

[0072] (2) NDC → Observation Space

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

[0074]

[0075] Among them, z ndc Usually the near plane (-1) or the far plane is used.

[0076] (3) Observation space → World space

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

[0078]

[0079] 3. Ellipse parameter calculation: Calculate the center point, major semi-axis and minor semi-axis of the ellipse based on the two three-dimensional points;

[0080] 1. Calculate the center point, major semi-axis and minor semi-axis of the ellipse based on two 3D points

[0081] In three-dimensional space, given two points p1 = (x1, y1, z1) and p2 = (x2, y2, z2), we can calculate the center point, major semi-axis, and minor semi-axis of an ellipse (or ellipsoid) as follows:

[0082] (1) Center point

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

[0084]

[0085] (2) Semi-major axis

[0086] The semimajor axis a is half the distance between the two points:

[0087]

[0088] (3) Semi-minor axis

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

[0090]

[0091] Where e is the eccentricity of the ellipse (0≤e<1). If e is not given, b=k·a can be set, and k is a scaling factor (such as 0.5).

[0092] 2. Special case: two-dimensional ellipse

[0093] If the ellipse is located in a plane (such as z = 0), then:

[0094] Center Point:

[0095]

[0096] Semimajor axis:

[0097]

[0098] Semi-minor axis:

[0099] b=k·a (e.g. k=0.5) (16).

[0100] 4. Elliptical cylinder definition: Determine an elliptical cylinder along the center point of the ellipse and the direction of the camera's view; 1. Define an elliptical cylinder along the center point of the ellipse and the camera's view point

[0101] Given:

[0102] Ellipse center c=(c x ,c y ,c z )(calculated from two 3D points);

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

[0104] Elliptical cylinder parameters: major semi-axis a, minor semi-axis b, height h.

[0105] Then define an elliptical cylinder with its axis pointing from c to v, and calculate its geometric parameters.

[0106] 2. Calculation formula

[0107] (1) Axis direction of the elliptical cylinder

[0108] Axis direction vector d:

[0109] d=vc(17);

[0110] Unit direction vector:

[0111]

[0112] (2) Local coordinate system of elliptical cylinder

[0113] Define the local coordinate system:

[0114] Z-axis: (Axis direction).

[0115] X-axis: Choose one A vertical vector (e.g., (1, 0, 0) projected to the vertical direction).

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

[0117]

[0118] (3) Transformation matrix of elliptical cylinder

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

[0120]

[0121] Final transformation matrix:

[0122]

[0123] (4) Parametric equations of elliptical cylinders

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

[0125]

[0126] Transform to world coordinate system:

[0127] p world =M·p local (twenty three);

[0128] Among them, p world Represents the coordinates of the point in the world coordinate system, p localRepresents the coordinates of a point in the local coordinate system.

[0129] 5. Intersection detection calculation, such as Figure 3 Shown: Calculate the intersection of the elliptical cylinder and the three-dimensional surface;

[0130] Given a point (surface point) An elliptical 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] The transformed point is recorded as (x′, y′, z′).

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

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

[0138]

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

[0140]

[0141] Among them, len represents the width parameter and ε represents the tolerance.

[0142] is equivalent to:

[0143]

[0144] 3. Final mathematical formula

[0145] Let the transformed point be:

[0146]

[0147] The judgment conditions are:

[0148]

[0149] If it holds, then the point On the side of the elliptical cylinder or within its tolerance, that is:

[0150]

[0151] 6. Width range setting: Set the value range of the intersection area to determine the display width of the ellipse line.

[0152] 7. Pixel shading output: Set the intersecting pixels to red to visualize the ellipse outline.

[0153] System Example

[0154] According to an embodiment of the present invention, a system for generating elliptical graphics based on a three-dimensional camera perspective is provided. Figure 4 FIG is a schematic diagram of an elliptical graphic generation system based on a three-dimensional camera viewing angle according to an embodiment of the present invention. Figure 4 As shown, the elliptical graphic generation system based on the three-dimensional camera viewing angle according to an embodiment of the present invention specifically includes:

[0155] A coordinate system conversion module 40 is used to convert the three-dimensional surface into the local coordinate system of the elliptical cylinder to obtain a converted three-dimensional surface;

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

[0157] Using the OpenGL graphics library to obtain a 2D screen point input by the user, the 2D screen point is converted into a 3D world coordinate, ellipse parameters are calculated based on the 3D world coordinate to obtain the center point, major semi-axis, and minor semi-axis of the ellipse, and an elliptical cylinder is defined along the center point of the ellipse and the viewpoint of the 3D camera;

[0158] The elliptical graphic 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 elliptical graphic, specifically for:

[0159] Calculating the intersection of the converted three-dimensional surface and the elliptical cylinder to obtain an intersection vertex set, and performing real-time coloring and rendering on the intersecting pixel points to obtain a final elliptical figure;

[0160] The system further comprises:

[0161] Adaptive adjustment module, used to dynamically adjust the intersection conditions in the intersection detection calculation process according to user needs;

[0162] The intersection condition includes a value range of the intersection area.

[0163] The embodiment of the present invention is a system embodiment corresponding to the above-mentioned method embodiment. The specific operations of each module can be understood by referring to the description of the method embodiment, which will not be repeated here.

[0164] In summary, compared with the prior art, the embodiments of the present invention have the following beneficial effects:

[0165] 1. Strong versatility: supports elliptical cylinder determination under arbitrary rotation and translation states, suitable for complex animation or interactive scenes;

[0166] 2. Controllable accuracy: By setting the len parameter, the judgment area can be flexibly adjusted to balance accuracy and performance;

[0167] 3. Efficient calculation: It only involves basic matrix operations and vector transformations, which is suitable for GPU parallel execution, such as Figure 5 As shown;

[0168] 4. Strong anti-interference ability: The introduction of error tolerance mechanism effectively avoids misjudgment caused by floating-point precision issues;

[0169] 5. Strong scalability: The judgment logic can be extended to other quadratic surfaces such as ellipsoids and paraboloids.

[0170] Specifically, the present invention enables accurate and efficient rendering of elliptical shapes in three-dimensional perspectives, resolving the core issues of traditional methods in visual accuracy and computational efficiency, demonstrating significant technological advancement and application value. The present invention is widely applicable in the following fields: geometric figure rendering in three-dimensional modeling software, 3D face measurement and detection (such as marking feature points), rendering of interface elements in virtual reality (VR) and augmented reality (AR), precise rendering in scientific computing visualization (such as elliptical region annotation in medical images), dynamic graphics generation in real-time game engines, and interactive functions such as collision detection and object picking.

[0171] Device Example 1

[0172] An embodiment of the present invention provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program implements the steps described in the method embodiment when executed by the processor.

[0173] Device Example 2

[0174] An embodiment of the present invention provides a computer-readable storage medium, on which a program for implementing information transmission is stored. When the program is executed by a processor, the steps described in the method embodiment are implemented.

[0175] The computer-readable storage medium in this embodiment includes, but is not limited to, ROM, RAM, magnetic disk, or optical disk.

[0176] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for generating elliptical graphics based on a three-dimensional camera viewing angle, characterized in that include: Transform the three-dimensional surface into the local coordinate system of the elliptical cylinder to obtain a transformed three-dimensional surface; Obtaining user input, and defining an elliptical cylinder based on the user input and a three-dimensional camera perspective; An intersection detection calculation is performed on the converted three-dimensional surface and the elliptical cylinder, and the intersection result is output visually to obtain a final elliptical figure.

2. The method according to claim 1, characterized in that The method further comprises: Dynamically adjust the intersection conditions during intersection detection calculations based on user needs; The intersection condition includes a value range of the intersection area.

3. The method according to claim 1, characterized in that Obtaining user input and defining an elliptical cylinder based on the user input and the three-dimensional camera viewing angle specifically includes: The OpenGL graphics library is used to obtain the 2D screen point input by the user, and the 2D screen point is converted into a 3D world coordinate. The ellipse parameters are calculated based on the 3D world coordinate to obtain the center point, major semi-axis and minor semi-axis of the ellipse. The ellipse cylinder is defined along the center point of the ellipse and the 3D camera viewpoint.

4. The method according to claim 3, characterized in that Performing intersection detection calculation on the converted three-dimensional surface and the elliptical cylinder, visually outputting the intersection result, and obtaining the final elliptical figure specifically includes: The intersection of the converted three-dimensional surface and the elliptical cylinder is calculated to obtain an intersection vertex set, and the intersecting pixel points are colored and rendered in real time to obtain a final elliptical figure.

5. A system for generating elliptical graphics based on a three-dimensional camera perspective, characterized in that include: A coordinate system conversion module is used to convert the three-dimensional surface into the local coordinate system of the elliptical cylinder to obtain the converted three-dimensional surface; an elliptical cylinder definition module, configured to obtain user input and define an elliptical cylinder based on the user input and a three-dimensional camera viewing angle; The elliptical graphic generation module is used to perform intersection detection calculation on the converted three-dimensional surface and the elliptical cylinder, and output the intersection result in a visual format to obtain a final elliptical graphic.

6. The system according to claim 5, characterized in that The system further comprises: Adaptive adjustment module, used to dynamically adjust the intersection conditions in the intersection detection calculation process according to user needs; The intersection condition includes a value range of the intersection area.

7. The system according to claim 5, characterized in that The elliptical cylinder definition module is specifically used for: The OpenGL graphics library is used to obtain the 2D screen point input by the user, and the 2D screen point is converted into a 3D world coordinate. The ellipse parameters are calculated based on the 3D world coordinate to obtain the center point, major semi-axis and minor semi-axis of the ellipse. The ellipse cylinder is defined along the center point of the ellipse and the 3D camera viewpoint.

8. The system according to claim 7, characterized in that The ellipse graphic generation module is specifically used for: The intersection of the converted three-dimensional surface and the elliptical cylinder is calculated to obtain an intersection vertex set, and the intersecting pixel points are colored and rendered in real time to obtain a final elliptical figure.

9. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is executed by the processor, the steps of the method for generating an elliptical graphic based on a three-dimensional camera perspective as described in any one of claims 1 to 4 are implemented.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores an information transmission implementation program, and when the program is executed by the processor, the steps of the elliptical graphic generation method based on the three-dimensional camera perspective as described in any one of claims 1 to 4 are implemented.

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