CN101149841A - Tri-dimensional application program convex mirror effect simulation method - Google Patents
Tri-dimensional application program convex mirror effect simulation method Download PDFInfo
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Abstract
A method for simulating convex lens effect in a 3-D application program is disclosed. Grains are dynamically applied to a frame buffer and mapped onto a mirror surface using grain mapping technology to form mirror surface effect; the program calculates the view point in a virtual scene symmetric to the mirror surface so as to get a new visual body symmetrical to the original visual body; all scene is drawn according to the new visual body; then a part of the drawn picture is mapped onto the mirror surface through grain mapping. In the course of grain mapping, normal vector of the mirror surface is used for correcting the calculation of grain coordinate so as to gain the aim of simulating the effect of convex lens. Advantage: directly drawing picture on mirror surface onto a virtual mirror surface without an extra display to simulate mirror surface effect.
Description
Technical Field
The invention relates to a virtual reality technology, in particular to a convex mirror simulation method for a three-dimensional application program, which can provide real-time convex mirror effect support for the three-dimensional application program, especially a driving simulator.
Background
The convex mirror effect refers to a convex mirror effect generated in real time in a three-dimensional scene. The effect is mainly used for driving a simulator to simulate the effect of a real vehicle rearview mirror, so that a user can see more scenery from a virtual rearview mirror. The simulation of the rearview mirror is an important link of the design of a driving simulator, and is mainly used for enabling a user to judge the posture of a virtual vehicle in a virtual scene through scenery in a mirror surface and relative positions of the scenery and the virtual vehicle besides generating a simulation effect close to a real vehicle.
Many rear view mirror simulation methods for driving simulators have been proposed:
1. method of adding additional display device: the method is characterized in that a miniature display device, such as a miniature liquid crystal display, is arranged in a position, corresponding to a real vehicle rearview mirror, of a virtual driving machine, and the scene which should appear in a mirror surface is directly rendered in the display.
2. Method of real specular reflection projection onto a scene behind: the scene that can see with the mirror surface is the complete projection to the screen behind the driving simulator, and the rear-view mirror is the mirror the same as real car rearview mirror, and the screen can see through the rear-view mirror, and its shortcoming is that projection equipment is expensive, and when the observation position moved, if the equipment that does not catch the observation position was caught to the observation position, the visual scene body of using of observing can not be adjusted, and this can reduce the degree of reality of the scenery of observing through the mirror.
The invention aims to provide a rearview mirror simulation method for a driving simulator, which can provide real-time convex mirror effect support for a three-dimensional application program, particularly the driving simulator.
Disclosure of Invention
The invention aims to provide a method for realizing the convex mirror effect in virtual driving simulation.
The method for realizing the convex mirror effect in the virtual driving simulation comprises the following steps:
(1) And (3) leading a perpendicular line to the mirror plane through the observation position, extending the perpendicular line, finding a point with the same distance between the observation position and the plane at the other end of the extension line, and calculating to obtain the symmetrical position of the observation position relative to the mirror plane, wherein the known positions are as follows: the coordinate of the observation position C is (x) c ，y c ，z c ) The symmetry point position C' of the mirror plane m equation Ax + By + Cz + D =0,C with respect to m is calculated By:
wherein, A, B, C and D are four parameters of a plane equation;
(2) Generating a new mirror image scene body with the same parameters as the original scene body on the basis of the mirror image symmetrical position, and mapping the scene image to an observation plane to form a scene image through the mirror image scene body, wherein the mirror image scene body and the original scene body are symmetrical about the mirror plane;
(3) Rendering the whole scene through the mirror image scene body, calculating a corresponding projection matrix according to the setting parameters of the mirror image scene body, wherein the rendering result is to project points on a scene object onto an observation plane, and the projection result is also clipped in a clipping window in the process, and the clipping result is used as a result image for texture mapping of the next step; when a cutting window is used for cutting in the process of rendering through the mirror image view, if the mirror image view is not a symmetrical view, the cutting window is not symmetrical;
(4) Then according to the mirror surface range mapping the scene image which should be appeared in the mirror surface to the mirror surface by means of texture, firstly calculating new scene image on the basis of mirror image viewpoint CModel viewpoint matrix M ModelView Then calculating a projective transformation matrix M corresponding to the mirror view pers The parameters of a symmetric view volume are known as follows: the viewing point being at a distance-z from the viewing plane vp Length and width of clipping window, projection transformation matrix M pers Expressed as:
wherein s is z ，t z The method is characterized in that a z coordinate projection value is normalized by a proportion and a translation factor, projection transformation is carried out in a standard coordinate system with a mirror image observation position as an origin and a mirror image observation direction as a positive z-axis direction, the form of a projection transformation matrix obtained through calculation is only related to the distance between the mirror image observation position and a mirror image observation plane, the length and the width do not influence the projection transformation matrix and are used for limiting the range of a clipping window, and the two matrixes are multiplied and combined to obtain a reflection transformation matrix M reflect ：
M reflect ＝M pers ·M ModelView 3
Next, the coordinate of any point P (x, y, z, l) on the observation plane on the mirror surface can be calculated by using the reflection transformation matrix, and P' (x, y, z, h) is obtained by first performing perspective transformation on the point P:
P′M reflect ·P 4
and then perspective removal is carried out on P':
UV＝P′(x，y)/h 5
where h is the homogeneous coordinate term of P' and UV is the preliminary texture coordinate. When the mirror surface is positioned in the view body, the point on the mirror surface is converted by the reflection and then is always appeared in the cutting window, the point becomes a number between 0 and 1 after the size of the cutting window is normalized, and then the surface normal line of the convex mirror is utilized to correct the texture coordinate:
wherein UV final Is the final texture coordinate value, f is a two-dimensional vector (x, y), where x, y are both floating point numbers between-1 and 1,
is the surface normal of a point on the mirror surface, when the mirror surface is flat
(5) Given the surface curvature equation f (x, y), the calculation of the convex mirror surface normal in the above step is performed by:
dividing the surface into grids on the basis of the two-dimensional area, calculating corresponding normal vectors by grid points, wherein the normal line of the surface of the convex mirror is calculated by a script offline rather than in real time, and for all the grid points, substituting x and y coordinates of the grid points into a formula 7 to calculate and obtain the surface normal line corresponding to the grid point
The results are saved in a file for use by the driving simulator or the three-dimensional application.
The calculation yields the symmetry position of the viewing position with respect to the mirror plane: if the mirror plane is perpendicular to the coordinate axis, directly translating the one-dimensional coordinate value corresponding to the observation position coordinate by a certain length to obtain the coordinate of the symmetrical position of the observation position relative to the mirror plane, wherein the translation length is equal to the distance from the observation position to the mirror plane.
The whole scene is rendered through the mirror image view: in the process of rendering through the mirror image view, the view behind the mirror needs to be removed from the scene, and the mirror plane is defined as a clipping plane in the scene:
double clip_plane[4]＝{A，B，C，D)；
wherein, A, B, C, D are plane parameters of the mirror plane, and in OpenGL:
glClipPlane(GL_CLIP_PLANE0,equation1)；
glEnable(GL_CLIP_PLANE0)；
the cutting result keeps the scenery which is close to one side of the observation position and is divided by the mirror plane in the scene, and the scenery which is intersected with the cutting plane can be cut.
The calculation of the surface normal of the convex mirror is as follows: the surface of the convex mirror is an elliptic paraboloid,
f(x，y)＝z＝-ax 2 -by 2 +h 8
the elliptic paraboloid is characterized in that any plane vertical to the x and y axes is intersected with the curved surface to obtain a curve which is a parabola.
Compared with the prior art, the invention has the advantages that:
1. the invention directly renders the simulation effect of the convex mirror on the microcomputer screen without adding additional display equipment;
2. the invention can simulate the effect of the convex mirror, and increases the visual range of the rearview mirror in the driving simulator for the simulation of the convex mirror provided in the driving simulator;
3. in the invention, in the simulation of the convex mirror, the expense of one rendering process is additionally added for all rearview mirrors positioned on the same plane;
4. the invention uses dynamic texture mapping technology to solve the simulation problem of the convex mirror in the three-dimensional program, realizes the simulation by the programmable shader supported by modern graphics hardware, and only needs to make a small amount of changes in the three-dimensional program needing to use the programmable shader.
Drawings
FIG. 1 is an implementation schematic;
fig. 2 (a) is a texture image of a mirror image scene obtained after the rendering in step 5) is finished;
FIG. 2 (b) is a diagram of the simulated effect of the virtual convex mirror;
FIG. 3 is a model of a car and mirror created using 3Ds Max;
FIG. 4 is a schematic illustration of materials associated with the mirror surface model in 3Ds Max;
FIG. 5 is an image that stores surface normal information for a convex mirror;
Detailed Description
The implementation principle of the convex mirror for virtual driving is as follows: firstly, according to an observation position and a mirror plane equation, the symmetrical position of the observation position relative to a mirror plane and a mirror image visual body corresponding to the symmetrical position are solved, a scene is dynamically rendered into a texture through the visual body, then a part of image of a rendering result is mapped to the mirror plane through texture mapping, in the mapping process, the texture coordinate of each point on the mirror plane is firstly calculated, the texture coordinate is used for sampling on the rendering result image, and finally a scene appears in the mirror plane displayed on a screen.
The implementation steps of the method are shown in figure 1:
1) And (3) leading a perpendicular line to the mirror plane through the observation position, extending the perpendicular line, finding a point with the same distance between the observation position and the plane at the other end of the extension line, and obtaining the symmetrical position of the observation position relative to the mirror plane, wherein the known positions are as follows: the coordinate of the observation position C is (x) c ，y c ，z c ) The equation of the mirror plane m is Ax + By + Cz + D =0,C, and the symmetrical point position C' of m is represented By the formula
Calculating to obtain the position of C' for generating a mirror image scene body;
2) The direction of symmetry of the viewing direction with respect to the mirror plane is calculated: the viewing direction is determined by two parameters, one being the viewing position C and the other being the position O at which the viewer is gazing, and is calculated by:
in step 1), the symmetric position C 'of the observation position C is calculated, and in this step, the symmetric position O' of the position O at which the observer gazes is calculated by the same method, and the symmetric direction can be calculated by the following formula:
3) The mirror image symmetrical position and the observation direction jointly generate a new mirror image scene body with the same parameters as the original scene body, and the mirror image scene body and the original scene body are symmetrical about a mirror plane;
4) Generating a new mirror image scene body which is completely the same as the original scene body parameter on the basis of the mirror image symmetrical position, and setting the scene body parameter in OpenGL by the following codes:
gluLookAt(C′x，C′y，C′z，O′x，O′y，O′z，0，1，0)
wherein, C 'x, C' y, C 'z are three coordinate components of C' respectively, O 'x, O' y, O 'z are three coordinate components of O' respectively, through this step of transformation, establish and regard observation position as the center, observe the coordinate system of the z axle in the direction:
order:
the results were normalized:
let s = f × [0 10 ], u = s × f, resulting in a matrix:
this is equivalent to using both in OpenGL:
glMultMatrixf(M)；
glTranslated(-eyex，-eyey，-eyez)；
5) Rendering a mirror image scene in a three-dimensional application program through the mirror image view, rendering a rendering result image into a texture, wherein the result is shown in fig. 2 (a), the process utilizes the support of the technology of rendering the texture by a modern GPU, firstly, a texture object used for storing the rendering result is set in the application program, then, a rendering target is set as the texture object, and fig. 2 (a) is the texture image of the mirror image scene obtained after rendering is finished;
6) Creating a three-dimensional model of the convex mirror, and creating a three-dimensional model of the convex mirror in 3Ds Max as shown in fig. 4, wherein the three-dimensional model of the convex mirror is a simple plane, and different shapes are set for the mirror surface according to the placement position of the convex mirror in the three-dimensional model of the whole automobile: rectangular, circular, etc.;
7) Associating a corresponding DirectX9 material for the three-dimensional model of the convex mirror, as shown in fig. 5, wherein the material editing panel is an operation panel of a material editor of 3Ds Max, firstly, selecting an fx effect file for the DirectX9 material, where the fx effect file is a core component of the DirectX9 material, and includes a plurality of colorizers, which are divided into two types: a vertex shader and a pixel shader, wherein the vertex shader and the pixel shader include a core algorithm of the present invention, when a three-dimensional model of a convex mirror is rendered, an fx effect file of a material associated with the convex mirror is enabled, wherein the algorithm is executed, the texture image is mapped to a surface of the three-dimensional model after execution, when the fx effect file is set, a setting parameter provided by the fx effect file appears on a material editing panel, wherein a position of an image file on a disk, in which normal information of the surface of the convex mirror is stored, is set, when a three-dimensional application is executed, the normal information of the surface of the convex mirror stored therein can be read according to the position, and finally, on the material editing panel, one of a plurality of shaders provided in the fx effect file is selected to map the texture image of a mirror image scene to the surface of the three-dimensional model of the convex mirror, and only the selected shader is executed;
8) The texture coordinates are calculated for the points of the convex mirror surface, this is done in the vertex shader contained in the fx effects file associated with DirectX9 material as described above: firstly, a new model viewpoint matrix M is calculated on the basis of a mirror image viewpoint C ModelView Then, a projective transformation matrix M corresponding to the mirror view volume is calculated pers The parameters of a symmetric view volume are known as follows: the viewing point being at a distance-z from the viewing plane vp The length and width of the cutting window and a projection transformation matrix M pers Expressed as:
wherein s is z ，t z The projection transformation is carried out in a standard coordinate system with a mirror image observation position as an original point and a mirror image observation direction as a positive z-axis direction, the calculated projection transformation matrix form is only related to the distance between the mirror image observation position and a mirror image observation plane, and the length and the width are in pairsThe projective transformation matrix has no influence and is used for limiting the range of the clipping window, and then the two matrixes are multiplied and combined to obtain the reflection transformation matrix M reflect ：
M reflect ＝M pers ·M ModelView 3
Next, the coordinates of any point P (x, y, z, l) on the mirror surface on the observation plane are calculated using the reflection transformation matrix:
(1) Performing perspective transformation on the point P to obtain P' (x, y, z, h),
P′＝M reflect ·P 4
(2) And (3) performing perspective removal on P':
UV＝P′(x，y)/h 5
wherein h is a homogeneous coordinate item of P', UV is a coordinate of P (x, y, z, l) on an observation plane, when the convex mirror is positioned in a visual scene, a point on the mirror surface is converted by the reflection and then is definitely appeared in a clipping window, the number is normalized to be a number between 0 and 1 according to the size of the clipping window, when a plane mirror is simulated, UV is a texture coordinate of a point on the plane mirror, and finally the texture coordinate is corrected by using a surface normal of the convex mirror:
wherein UV final Is the final texture coordinate value, f is a two-dimensional vector (x, y), where x, y are both floating point numbers between-1 and 1,
is the surface normal of one point on the mirror surface, the surface normal is obtained by sampling 7) the image file storing the surface normal information of the convex mirror, when the mirror surface is a plane
9) Performing texture sampling on the scene image obtained in the step 5) according to the texture coordinates of the point P (x, y, z, l) on the convex mirror calculated in the step 8), wherein the texture sampling is performed in a pixel shader included in the fx effect file associated with the DirectX9 material, the texture image of the scene is mapped onto the convex mirror surface in the pixel shader, and an object in the scene is rendered on the convex mirror surface, as shown in fig. 2 (b);
10 Before the program is run, calculating 7) the image file storing the surface normal information of the convex mirror, and knowing a surface curved surface equation f (x, y), wherein the calculation of the surface normal of the convex mirror is performed according to the following formula:
wherein x, y ∈ D, D is a two-dimensional region, and when calculating, firstly, the surface is divided into grids according to a fixed distance Δ x, Δ y on the basis of the two-dimensional region, the fixed distance is set to Δ x, Δ y =0.1, then, a corresponding normal vector is calculated for each grid point according to formula 7, and finally, the result is stored in an image file, and the calculation of the surface normal of the convex mirror is performed offline through a script instead of real-time: for all the grid points, the x and y coordinates are substituted into equation 7, and the surface normal corresponding to the grid point is calculated
The result is saved in a file for use by a driving simulator or a three-dimensional application, and the resulting image file storing the normal information of the surface of the convex mirror is shown in fig. 3.
Claims (4)
1. A method for simulating the effect of a convex mirror in a three-dimensional application program is characterized by comprising the following steps:
(1) And (3) leading a perpendicular line to the mirror plane through the observation position, extending the perpendicular line, finding a point with the same distance between the observation position and the plane at the other end of the extension line, and calculating to obtain the symmetrical position of the observation position relative to the mirror plane, wherein the known positions are as follows: the coordinate of the observation position C is (x) c ，y c ，z c ) The symmetry point position C' of the mirror plane m equation Ax + By + Cz + D =0,C with respect to m is calculated By:
wherein, A, B, C and D are four parameters of a plane equation;
(2) Generating a new mirror image scene body with the same parameters as the original scene body on the basis of the mirror image symmetrical position, and mapping the scene image to an observation plane to form a scene image through the mirror image scene body, wherein the mirror image scene body and the original scene body are symmetrical about the mirror plane;
(3) Rendering the whole scene through the mirror image scene body, calculating a corresponding projection matrix according to the setting parameters of the mirror image scene body, wherein the rendering result is to project points on a scene object onto an observation plane, and the projection result is also clipped in a clipping window in the process, and the clipping result is used as a result image for texture mapping of the next step; when a cutting window is used for cutting in the process of rendering through the mirror image view, if the mirror image view is not a symmetrical view, the cutting window is not symmetrical;
(4) Then according to the mirror surface range mapping the scene image which should appear in the mirror surface to the mirror surface by texture, firstly calculating out new model viewpoint matrix M on the basis of mirror image viewpoint C ModelView Then, a projective transformation matrix M corresponding to the mirror view volume is calculated pers The parameters of a symmetric view volume are known as follows: the viewing point being at a distance-z from the viewing plane vp Length and width of clipping window, projection transformation matrix M pers Is shown as
Wherein s is z ，t z The method is characterized in that a z coordinate projection value is normalized by a proportion and a translation factor, projection transformation is carried out in a standard coordinate system with a mirror image observation position as an origin and a mirror image observation direction as a positive z-axis direction, the form of a projection transformation matrix obtained through calculation is only related to the distance between the mirror image observation position and a mirror image observation plane, the length and the width do not influence the projection transformation matrix and are used for limiting the range of a clipping window, and the two matrixes are multiplied and combined to obtain a reflection transformation matrix M reflect ：
M reflect ＝M pers ·M ModelView 3
Next, the coordinate of any point P (x, y, z, l) on the observation plane on the mirror surface can be calculated by using the reflection transformation matrix, and P' (x, y, z, h) is obtained by first performing perspective transformation on the point:
P′＝M reflect ·P 4
and then perspective removal is carried out on P':
UV＝P′(x，y)/h 5
where h is the homogeneous coordinate term of P' and UV is the preliminary texture coordinate. When the mirror surface is positioned in the view body, the point on the mirror surface is converted by the reflection and then is always appeared in the cutting window, the point is normalized according to the size of the cutting window and becomes a number between 0 and 1, and then the surface normal of the convex mirror is utilized to correct the texture coordinate:
wherein UV final Is the final texture coordinate value, f is a two-dimensional vector (x, y), where x, y are both floating point numbers between-1 and 1,
is the surface normal of a point on the mirror surface, when the mirror surface is flat
(5) Knowing the surface equation f (x, y), the calculation of the convex mirror surface normal in the above step is performed by:
wherein, x, y belongs to D, D is a two-dimensional area, the surface is divided into grids on the basis of the two-dimensional area, corresponding normal vectors are calculated by grid points, the calculation of the surface normal of the convex mirror is performed by a script offline instead of real time, and the calculation is performed on the surface normal of the convex mirror in real timeWith the grid points, the x, y coordinates of the grid points are substituted into formula 7, and the surface normal corresponding to the grid points is calculated
And the results are saved in a file for use by the driving simulator or the three-dimensional application program.
2. A method according to claim 1, wherein said calculating yields a symmetry position of the viewing position with respect to the mirror plane: if the mirror plane is perpendicular to the coordinate axis, directly translating the one-dimensional coordinate value corresponding to the observation position coordinate by a length to obtain the coordinate of the symmetrical position of the observation position relative to the mirror plane, wherein the translation length is equal to the distance from the observation position to the mirror plane.
3. The method of claim 1, wherein the entire scene is rendered by the mirror view: in the process of rendering through the mirror image view, the view behind the mirror needs to be removed from the scene, and the mirror plane is defined as a clipping plane in the scene:
double clip_plane[4]＝{A，B，C，D)；
wherein, A, B, C, D are plane parameters of the mirror plane, in OpenGL:
glClipPlane(GL_CLIP_PLANE0，equation1)；
glEnable(GL_CLIP_PLANE0)；
the cutting result keeps the scenery which is close to one side of the observation position and is divided by the mirror plane in the scene, and the scenery which is intersected with the cutting plane can be cut.
4. The method according to claim 1, wherein the calculation of the normal of the convex mirror surface is performed by: the surface of the convex mirror is an elliptic paraboloid,
z＝f(x，y)＝-ax 2 -by 2 +h 8
the elliptic paraboloid is characterized in that any plane vertical to the x and y axes is intersected with the curved surface to obtain a curve which is a parabola.
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN102831632A (en) * | 2012-07-24 | 2012-12-19 | 上海晨思电子科技有限公司 | Mirror image texture generating method, device and computer |
| CN103096134A (en) * | 2013-02-08 | 2013-05-08 | 广州博冠信息科技有限公司 | Data processing method and data processing equipment based on live video and game |
| CN103354616A (en) * | 2013-07-05 | 2013-10-16 | 南京大学 | Method and system for realizing three-dimensional display on two-dimensional display |
| CN105374065A (en) * | 2014-08-08 | 2016-03-02 | 想象技术有限公司 | Local irradiance estimation for use in rendering an image |
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| CN111369655A (en) * | 2020-03-02 | 2020-07-03 | 网易（杭州）网络有限公司 | Rendering method and device and terminal equipment |
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| CN102831632A (en) * | 2012-07-24 | 2012-12-19 | 上海晨思电子科技有限公司 | Mirror image texture generating method, device and computer |
| CN103096134A (en) * | 2013-02-08 | 2013-05-08 | 广州博冠信息科技有限公司 | Data processing method and data processing equipment based on live video and game |
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| CN103354616A (en) * | 2013-07-05 | 2013-10-16 | 南京大学 | Method and system for realizing three-dimensional display on two-dimensional display |
| CN105374065B (en) * | 2014-08-08 | 2020-09-11 | 想象技术有限公司 | Relightable textures for use in rendering images |
| CN105374065A (en) * | 2014-08-08 | 2016-03-02 | 想象技术有限公司 | Local irradiance estimation for use in rendering an image |
| CN109621415A (en) * | 2018-12-26 | 2019-04-16 | 网易（杭州）网络有限公司 | Display control method and device in 3D game, computer storage medium |
| CN111369655A (en) * | 2020-03-02 | 2020-07-03 | 网易（杭州）网络有限公司 | Rendering method and device and terminal equipment |
| CN112686948A (en) * | 2020-12-25 | 2021-04-20 | 北京像素软件科技股份有限公司 | Editor operation method and device and electronic equipment |
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| CN113570696A (en) * | 2021-09-23 | 2021-10-29 | 深圳易帆互动科技有限公司 | Mirror image processing method and device of dynamic model and readable storage medium |
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