TWI417808B - Reconstructable geometry shadow mapping method - Google Patents

Description

Method for reconstructing geometric shadow maps

This invention relates to a graphics process and, more particularly, to a shadow plot.

In computer graphics, shadow mapping and shadow volumes are two common real-time shadow techniques. The shadow cone is a technique proposed by Frank Crow in 1977 to calculate the 3D (3-D) object shading area using geometric methods. This algorithm uses a stencil buffer to calculate whether a pixel (test pixel) is in the shadow. The main advantage of the shadow cone is that it is accurate for the pixel, whereas the accuracy of the shadow map depends on the size of the texture memory and how the shadow is projected. The shadow cone technique requires a lot of hardware fill time, and its execution speed tends to be slower than the shadow map technique, especially when dealing with large and complex geometric scenes.

The shadow map is a technique for adding shadows to 3-D computer images, which was proposed by Lance Williams in 1978. This algorithm is widely used in pre-rendered scenarios, as well as in real-time applications. The depth of the shade and the test pixel are compared against the source observation point, that is, whether a test pixel is visible to the light source to establish a shadow of the shade. The shadow map is a simple and effective image space method. Shadow maps are one of the shadow representation methods that are often used in high speed requirements. However, the shadow map will encounter aliasing errors. And depth bias issues. Solving these two shortcomings is a research topic in the field of shadow representation technology.

The jagged errors in the shadow map can be divided into two categories: perspective aliasing errors and projective aliasing errors. A see-through error occurs when zooming in on the edge of the shadow. Projection aliasing errors occur when the light is nearly parallel to the geometric surface and extends beyond a certain depth range. Another problem with most shadow map techniques is the depth offset problem. To avoid erroneous "self-shadowing" problems, William exposes a constant depth migration technique that adds an offset value to the depth sample before it is deeper than the true surface. Unfortunately, too many offsets can cause false "non-shadowing" (which looks like the shade floats above the light receiver) and the shadows move back too far. In fact, it is very difficult to determine the offset value directly, and it is not possible to find a universally acceptable value in each scene.

The invention provides a method for reconstructing a geometric shadow map, which reduces two kinds of sawtooth errors of "perspective aliasing" and "projective aliasing", and solves the error "self shadow" caused by depth deviation ( False self-shadowing) and the problem of false "non-shadowing".

The invention proposes a method for reconstructing geometric shadow maps. First, the light source is used as an observation point to store geometric information of a plurality of shading geometries of the front-face of the object. A conformance test is performed on the test pixels to find the shading geometry corresponding to the test pixels from each of the geometries. Reconstruction correspondence The depth value of the shading point of the test pixel. Finally, the shadow judgment of the test pixel is performed.

In an embodiment of the invention, the geometric information may include vertex coordinates or a graphical index of the geometric shapes. The above conformance test can include the following steps. First select one of the geometric shapes, and then read the geometric information of the selected geometry, and the geometric information includes the vertex coordinates of the geometry ( v ₀ . x , v ₀ . y , v ₀ . z ), ( v ₁ . x , v ₁ . y , v ₁ . z ) and ( v ₂ . x , v ₂ . y , v ₂ . z ). Next calculate the equation To obtain the center of gravity coordinate value ( w ₁ , w ₂ , w ₃ ) of the shading point; wherein ( p . x , p . y , p . z ) is the coordinate of the test pixel. Whether the selected geometry is consistent according to the center of gravity coordinate value ( w ₁ , w ₂ , w ₃ ) of the shading point. If the selected geometry is judged to be consistent, the geometry is a shading geometry.

In an embodiment of the invention, the step of reconstructing the shading point depth value comprises: calculating an equation In order to obtain the depth value Tz of the shading point.

In an embodiment of the invention, the step of reconstructing the shading point depth value comprises: calculating the equation Tz = In order to obtain the depth value Tz of the shading point.

In an embodiment of the invention, the step of reconstructing the shading point depth value comprises: calculating an equation In order to obtain the depth value Tz of the shading point.

The invention stores geometric information of a plurality of geometric shapes on the front surface of the object by using the light source as an observation point. Therefore, the position information of the test pixel and the stored geometric information can be used to reconstruct the depth value of the shading point. After obtaining the depth value of the shading point, the depth values of the shading point and the test pixel can be compared to complete the shadow judgment of the test pixel.

The above described features and advantages of the present invention will be more apparent from the following description.

Those skilled in the art can implement the present invention with reference to the following examples. Of course, the following embodiments can also be implemented in the form of a computer program, and the computer can be used to read the storage medium to store the computer program, so that the computer can perform the method of reconstructing the geometric shadow map.

1 is a flow chart illustrating a method of reconstructing a geometric shadow map in accordance with an embodiment of the present invention. This embodiment can process a plurality of light sources. In order to explain the present embodiment in a simple and clear manner, a method of reconstructing a geometric shadow map will be described below by taking a single light source as an example. In graphics drawn by a computer, the surface of an object can be made up of multiple geometries (such as triangles or other geometric shapes). This embodiment will assume that the surface of the object is composed of a plurality of triangles. Those skilled in the art can draw the surface of the above object by any technique.

2 is a block diagram showing the spatial relationship between a shadow map, an object surface (portion), and a test pixel, in accordance with an embodiment of the present invention. The scene can be drawn from the light's point of view. In the case of a point light source, this observation point can be a perspective projection. For directional light, orthographic projection can be used. As shown in FIG. 2, the surface of the light-shielding object includes triangles TR0, TR1, TR2, and TR3. From the above drawing, the information of each occluding triangles TR0~TR3 is taken and stored in the geometric shadow maps. That is, using the point source as the observation point, geometric information of a plurality of geometric shapes of the front surface of an object is stored (step S110). In this embodiment, the geometric information may include vertex coordinates of each geometry, such as vertex coordinates of the shading triangles TR0~TR3, or include a graphical index of each geometry. In the light canonical view volume of the source observation point and the light view space, the linear nature of the triangle allows us to reconstruct these shading triangles for point sources (the same for directional sources).

Next, in step S120, the test pixels are subjected to a consistency test to find a consistency test from all the geometric shapes. Wherein, the shading geometry has a light-shielding point Pd (in the geometric shadow diagram with the light source as the observation point, the test pixel overlaps with the shading point Pd). Step S120 may apply geometric shadow maps to draw a scene from a camera viewpoint. This process has three main components. For each test pixel of the object (such as test pixel P in Figure 2), first find the coordinates ( px , py , pz ) of the pixel seen from the light source. The x and y values of the coordinates ( px , py , pz ) correspond to locations in the geometry map texture and are used in triangle consistency tests to find the shading triangles.

The above step S120 can find that the shading triangle of the test pixel P is TR0. Next, in step S130, the depth information of the shading point Pd is reconstructed using the geometric information of the shading geometry and the position information of the test pixel P. That is, the geometrical information stored in step S110 is used to reconstruct the shading point depth value of the pixel P (for example, the depth value of the shading point Pd in FIG. 2).

Next, in step S140, the depth value of the light-shielding point Pd and the depth value of the test pixel P are compared to complete the shadow determination of the test pixel P. The depth value reconstructed by the shading triangle TR0 is compared with the z value of the test pixel P (the depth value, which is obtained from the light canonical view volume of the light source observation point to complete the shadow judgment of the test pixel P. Finally, the drawing is performed. The pixel being tested in the shadow or in the light. If there are multiple sources, use a different geometric shadow map for each source.

Those skilled in the art can implement the present embodiment in accordance with the above description. Detailed implementation examples of the steps in FIG. 1 will be described below, but the implementation of the present invention should not be limited thereto. Figure 2 illustrates a directional light source that is converted from a point source in the viewing field of light to a specular field of view of the source viewing point. It is assumed that the scene in the canonical space of the light source observation point is composed of four adjacent triangles TR0, TR1, TR2 and TR3.

First (step S110), the triangles TR0 to TR3 are respectively projected and rasterized to their corresponding regions AR0, AR1, AR2 and AR3 in the geometric shadow map. Each texel in each of the regions AR0~AR3 contains geometric information of its corresponding triangle (the vertex coordinates in this embodiment), for example, the texel in the region AR0 contains the vertex coordinates of the triangle TR0 ( v ₀ . x , v ₀ . y , v ₀ . z ), ( v ₁ . x , v ₁ . y , v ₁ . z ) and ( v ₂ . x , v ₂ . y , v ₂ . z ). In step S110, except that the geometric information is stored in the shadow map (the conventional technique stores the depth value in the shadow map instead of the geometric information), the operation of step S110 is almost equivalent to the standard shadow map. For a point source, the scene is converted to a light canonical view volume of the source observation point, and then the three vertex coordinates of the triangle are stored in the rasterized area of the shadow map. Another way is to get the coordinate vertices from adjacent triangles. For example, in FIG. 2, the six vertex coordinates of the triangles TR1, TR2, and TR3 adjacent to the triangle TR0 are stored in the rasterized region of the triangle TR0. For directional light sources, the vertex coordinates of the canonical field of view specifying the "in process" source observation point are stored, and the light in this observation point space is parallel to the z-axis.

Next, the visible pixel P in the eye space is converted to the canonical field of view coordinates (px, py, pz) of the source observation point. The conformance test of step S120 may include selecting one of the geometric shapes (eg, triangles TR0~TR3). Step S120 may include reading the geometric information of the selected geometry (eg, if the triangle TR0 is selected, the geometric information of the region AR0 is read from the geometric shadow map). The geometric information may include vertex coordinates of the geometric shape, such as the vertex coordinates of the triangle TR0 ( v ₀ . x , v ₀ . y , v ₀ . z ), ( v ₁ . x , v ₁ . y , v ₁ . z And ( v ₂ . x , v ₂ . y , v ₂ . z ). With the two-dimensional (2-D) coordinates (px, py), you can find the corresponding sampling point T in the geometric shadow map. At this step S120, it may include calculating Equation 1: The three-dimensional (3-D) center-of-gravity coordinates ( w ₁ , w ₂ , w ₃ ) corresponding to the shading point Pd of the vertices of the triangle TR0 are obtained. It is judged whether or not the selected geometry (triangle TR0) is uniform according to the centroid coordinate value ( w ₁ , w ₂ , w ₃ ) of the shading point Pd.

For each visible pixel P, the shading triangle TR0 needs to be correctly positioned so that the depth value of this shading point Pd can be reconstructed from the geometric information stored in the geometric shadow map. This process is called the triangle "conformance test". However, sampling texture maps with test pixel coordinates (x, y) may not necessarily return information about the triangle TR0 blocking the test pixel P. If the three centroid values ( w ₁ , w ₂ , w ₃ ) obtained from Equation 1 are in the range [0, 1] (meaning that the triangle blocks the test pixel), the triangle test is called It is consistent. Otherwise the test is inconsistent. If the selected geometry determination result is consistent, the geometry (triangle TR0) is the shading geometry of the test pixel P.

Due to the limited resolution of the shadow map, it may lead to inconsistent results of the triangle test. If the resolution of the texture map is low, it is more likely to make the triangle test results inconsistent. Figure 3A illustrates two adjacent triangles TR0 and TR1, while triangles TR0 and TR1 have a finite resolution. Figure 3B illustrates the rasterized regions AR0 and AR1 of triangles TR0 and TR1 in Figure 3A. Under the limited resolution, the region AR0 is a grating of the triangle TR0. The area AR1 is the rasterized area of the triangle TR1. Point T is a sampled point having the same (x, y) coordinates as the visible pixel P being tested. However, by sampling point T, the accessor in this embodiment is texel A with triangular TR0 geometric information. As shown in FIG. 3B, the sampling point T should originally be in the rasterized region of the triangle TR1, but the information of the triangle TR0 may result in erroneous depth value reconstruction due to limited resolution (wrongly consider the sampling point T as the shading of the triangle TR0). point). The sampling point T' in Fig. 3B also has similar problems.

By tiling the geometrical information of the adjacent triangles, the light-shielding triangle that blocks the tested pixel P can be found by sampling the corresponding point T. However, when two adjacent regions are rasterized, the geometric information of adjacent triangles may not be available. In order to solve this problem, the present embodiment increases the sampling point to contain geometric information of more triangles, thus also increasing the chance of finding a consistent triangle test. Figure 3C is a diagram showing an example of a pattern of two sampling kernels T and T' in accordance with the present invention. If the tested pixel P is blocked by the multi-layer geometry surface, the template can also sort the depth results of all consistent triangle tests and take the minimum value as the final depth value of the blackout point. Taking the pattern of the sampling template T as an example, in addition to accessing the texel with the area AR0 information to calculate the sampling point T, the texel with the area AR0 information is accessed to calculate the depth value of the sampling point T2, and access is performed. A texel with area AR2 information is used to calculate the depth value of the sample point T1, and a texel with area AR1 information is accessed to calculate the depth values of the sample points T3 and T4. Next, sort the depth results of all consistent triangle tests (T, T1, T2) The depth value of T3 and T4), and the minimum value thereof is taken as the final depth value of the light-shielding point Pd.

For accuracy, it is important to choose the appropriate template pattern. Larger template patterns often provide higher accuracy than smaller template patterns. However, larger templates containing many sampling points may be detrimental to performance. The special template pattern shown in Figure 3C can achieve similar accuracy with less sampling. By setting the total amount of triangle conformance test for a test pixel, the number of samples can be reduced.

For the pixel P tested, when the texture resolution is critical (subcritical, which will cause some shading triangles to not be stored in the shadow map), these corresponding triangle tests must be inconsistent. Based on this, these triangle tests are ordered in the order of the weighted distances to the central triangle to reconstruct using the triangle information corresponding to the "closest-distance" weight value. When it is reasonable to assume that the reconstructed shading point is in the same plane of the "nearest distance" triangle, the calculated weighted distance can be Euclidean's calculation method.

After the correct triangle information is obtained, the shading point depth value of the tested pixel can be reconstructed. The depth value of the shading point Pd in the shading triangle TR0 can be reconstructed via a triangle interpolation. After calculating the above weight value from Equation 1, the depth value Tz of the light-shielding point Pd in step S130 can be reconstructed by the following formula:

Alternatively, in conjunction with Equation 1 and Equation 2, Equation 3 can be obtained: The depth value Tz of the light-shielding point Pd in step S130 can be reconstructed using Equation 3. The inverse of the 3x3 matrix must be performed in Equation 3 above. At present, the graphics processing unit (GPU) hardware does not directly support the inverse of the 3x3 matrix. So we have to break it down into some common arithmetic and logic unit (ALU) instructions. However, the ALU instruction set does not guarantee accuracy, and may introduce more relevant errors to the inverse operation results and affect the final reconstruction depth value.

In order to improve the above problem, the present embodiment rewrites Equation 3 into the following equivalent equation: Therefore, the depth value Tz of the light-shielding point Pd in step S130 can also be reconstructed by using Equation 4.

Finally, by comparing the light-shielding point Pd with the light source specification of the pixel P, the canonical volume depth values, that is, comparing Tz and pz , the shadow determination of the pixel P can be completed (step S140).

Figure 4A illustrates a projection sawtooth error produced by a standard shadow map. The scene shown in Fig. 4A is a quadrilateral plate suspended above the bottom plane, so that the quadrilateral plate forms a strip shadow on the bottom plane. A partial enlarged view of the strip shadow is shown in the lower left corner of Fig. 4A. As is apparent from Fig. 4A, the projection sawtooth error produced by the conventional standard shadow map is obvious. In contrast to FIG. 4A, FIG. 4B illustrates projection jagged results produced by reconstructable geometric shadow maps in accordance with an embodiment of the present invention. That is, FIG. 4B uses the new algorithm described in the above embodiment of the present invention: Reconstructable Geometry Shadow Map (RGSM) as a solution to the sawtooth problem. The scene shown in Fig. 4B is the same as Fig. 4A. As is apparent from Fig. 4B, the projection sawtooth error produced by the RGSM algorithm used in the embodiment of the present invention is significantly improved.

Another problem with most shadow map techniques is the depth offset problem. The scenes of the graphical depth shift test of Figures 5A, 5B and 5C are the same, both houses and railings. Figure 5A illustrates a test scenario generated by a standard shadow map with a constant depth offset technique (depth offset value 1e-3) to avoid erroneous self-shadowing problems. That is, it adds the depth offset value to the depth sample before comparing it to the true surface. Since the depth offset value of FIG. 5A is too large, the erroneous "non-shadowing" (which looks like the shade floats above the light receiving object) causes the shadow to retreat too far. In fact, it is very difficult to determine the offset value directly, and it is not possible to find an acceptable value in each scene. For example, Figure 5B illustrates a test scenario resulting from a standard shadow map with a constant depth offset technique (depth offset value 1e-6). Used to improve the wrong "no shadow" phenomenon The small depth offset value (1e-6), although improving the "no shadow" phenomenon, produces the wrong "self-shadowing" problem (as shown in Figure 5B). FIG. 5C is a diagram illustrating a graphics depth shift test scenario generated by reconstructing a geometric shadow map in accordance with an embodiment of the present invention. That is, FIG. 5C uses the RGSM algorithm described in the above embodiment of the present invention as a solution to the depth offset problem. The depth offset value of FIG. 5C is the same as that of FIG. 5B, and both are 1e-6. As is apparent from Fig. 5C, the RGSM algorithm used in the embodiment of the present invention can use a very small depth offset value without causing an erroneous "self-shadow" problem.

In summary, the present embodiment can ensure pixel-level depth accuracy, and has the following advantages:

1. By reducing the perspective sawtooth and projection sawtooth, it produces precise shadow edges. It can also remove the "jittering" phenomenon of shadow edges in dynamic scenes.

2. This embodiment can have a small depth offset value compared to other shadow map techniques. By setting a single and fixed offset value, programmers using RGSM can meet the needs of most applications and produce correct images to avoid false "self-shadowing" or "false" errors. "false non-shadowing" problem.

3. On the premise of the same output shadow quality and high speed execution, it uses only a small amount of memory space of the standard shadow map.

Although the present invention has been disclosed in the above preferred embodiments, it is not intended to limit the invention, and any one of ordinary skill in the art can make some modifications and refinements without departing from the spirit and scope of the invention. , Therefore, the scope of the invention is defined by the scope of the appended claims.

A, B‧‧‧Texture elements

Corresponding regions in the geometric shadow map of AR0, AR1, AR2, AR3‧‧

P‧‧‧ test pixels

Pd‧‧‧ shading point

S110~S140‧‧‧ steps of a method for reconstructing a geometric shadow map according to an embodiment of the invention

TR0, TR1, TR2, TR3‧‧‧ triangular shape on the surface of the light-shielding object

T, T’‧‧‧ sampling points

1 is a flow chart illustrating a method of reconstructing a geometric shadow map in accordance with an embodiment of the present invention.

2 is a block diagram showing the spatial relationship between a shadow map, an object surface (portion), and a test pixel, in accordance with an embodiment of the present invention.

Figure 3A illustrates two adjacent triangles TR0 and TR1.

Figure 3B illustrates the rasterized regions AR0 and AR1 of triangles TR0 and TR1 in Figure 3A.

3C is a diagram showing an example of a pattern of two sampling templates in accordance with the present invention.

Figure 4A illustrates a projection sawtooth error produced by a standard shadow map.

4B is a diagram showing projection jagged results produced by reconstructing a geometric shadow map in accordance with an embodiment of the present invention.

Figure 5A illustrates a test scenario resulting from a standard shadow map with a constant depth offset technique (depth offset value 1e-3).

Figure 5B illustrates a test scenario resulting from a standard shadow map with a constant depth offset technique (depth offset value 1e-6).

5C is a graph depth shift test scenario generated by a reconfigurable geometric shadow map (depth offset value 1e-6) in accordance with an embodiment of the present invention.

S110~S140‧‧‧ steps of a method for reconstructing a geometric shadow map according to an embodiment of the invention

Claims (9)

A method for reconstructing a geometric shadow map, comprising: storing a geometric information of a plurality of shading geometric shapes on a front surface of an object by using a light source as an observation point; performing consistency testing on a test pixel to find from the geometric shapes And a shading geometry corresponding to the test pixel; reconstructing a depth value corresponding to a shading point of the test pixel; and performing a shadow determination of the test pixel, where the coordinates of the test pixel are ( px , py , pz ), The consistency test includes: selecting one of the geometric shapes; reading the selected geometric information of the geometric shape, and the geometric information includes the vertex coordinates of the geometric shape ( v ₀ . x , v ₀ . y , v ₀ . z ), ( v ₁ . x , v ₁ . y , v ₁ . z ) and ( v ₂ . x , v ₂ . y , v ₂ . z ); , In order to obtain the coordinate value of the center of gravity of the light shading dot _{(w 1, w 2, w} 3); according to the light shading dot centroid coordinates _{(w 1, w 2, w} 3) determining the geometry consistent whether the selected And if the selected geometric shape judgement result is consistent, the geometric shape is the shading geometry. A method of reconstructing a geometric shadow map as described in claim 1 wherein the geometric shapes comprise triangles. The method of reconstructing a geometric shadow map as described in claim 1, wherein the geometric information includes vertex coordinates or geometric indexes of the geometric shapes. The method for reconstructing a geometric shadow map as described in claim 1, wherein reconstructing the depth value of the shading point comprises: calculating an equation In order to obtain the depth value Tz of the shading point. The method for reconstructing a geometric shadow map as described in claim 1, wherein reconstructing the depth value of the shading point comprises: calculating an equation In order to obtain the depth value Tz of the shading point. The method for reconstructing a geometric shadow map as described in claim 1, wherein reconstructing the depth value of the shading point comprises: calculating an equation In order to obtain the depth value Tz of the shading point. The method of reconstructing a geometric shadow map as described in claim 1, wherein the shading geometry has the shading point; and the light source is an observation point, the test pixel overlaps the shading point. The method for reconstructing a geometric shadow map as described in claim 1, wherein reconstructing the depth value of the shading point requires utilizing geometric information of the shading geometry and position information of the test pixel. The method for reconstructing a geometric shadow map as described in claim 1, wherein performing the shadow determination of the test pixel is by comparing a depth value of the light-shielding point with a depth value of the test pixel.