CN101271588B - Reconstructable Geometry Shadow Map Method - Google Patents

Abstract

The invention provides a method capable of reconstructing a geometric shadow map. Standard shadow maps provide a fast and appropriate way to draw shadows in a scene. The present invention provides a new algorithm: the present invention achieves this by using depth values that are actually reconstructed from the geometric surface instead of sampling from the depth map points. At the same time, this reconstructable geometric shadow map algorithm can produce correct images without false "self-shadows" or false "no-shadows" using smaller depth offset values than most shadow map techniques, which can set constant offset values. The method for reconstructing the geometric shadow map can generate accurate shadow edges by reducing perspective saw teeth and projection saw teeth.

Description

Reconstructable Geometry Shadow Map Method

technical field

The present invention relates to graphics processing, and more particularly to shaded drawing.

Background technique

In computer graphics, shadow mapping and shadow volumes are two commonly used real-time shadowing techniques. The shadow cone is a technique proposed by Frank Crow in 1977, which uses geometric methods to calculate the shading area of 3-dimensional (3-D) objects. This algorithm uses the stencil buffer to calculate whether a certain pixel (test pixel) is in shadow. The main advantage of shadow cones is that they are pixel accurate, whereas the accuracy of shadow maps depends on the size of texture memory and how shadows are cast. The shadow cone technique requires a lot of hardware rendering time, and its execution speed is often slower than the shadow map technique, especially when dealing with large-scale and complex geometric scenes.

Shadow maps are a technique for adding shadows to 3-D computer images, proposed by Lance Williams in 1978. This algorithm is widely used in pre-rendered scenes and real-time applications. The depth of the shading object and the test pixel is compared through the light source observation point, that is, it is tested whether a certain test pixel is visible to the light source, so as to establish the shadow of the shading object. Shadow maps are a simple and effective image space method. Shadow map is one of the shadow representation methods, which is often applied to high-speed requirements. However, shadow maps suffer from aliasing errors and depth bias issues. Addressing these two shortcomings is a research topic in the field of shadow representation techniques.

Aliasing errors in shadow maps can be divided into two categories: perspective aliasing errors and projective aliasing errors. Perspective aliasing occurs when zooming in on shadow edges. Projection aliasing occurs when rays are nearly parallel to a geometric surface and extend beyond the depth range. Another problem with most shadow map techniques is the problem of depth offset. To avoid false "seld-shadowing" problems, William discloses a constant depth offset technique that adds the offset value to the depth samples before comparing with the true surface. Unfortunately, too much offset can lead to false "non-shadowing" (looks like the occluder is floating above the light receiver) causing shadows to recede too far. In practice, it is very difficult to directly determine the offset value, and it is impossible to find a universally acceptable value in every scene.

Contents of the invention

The present invention provides a method for reconstructing geometric shadow maps to reduce the two kinds of aliasing errors of "perspective aliasing" and "projective aliasing", and solve the error "self-shadowing" caused by depth offset (false self-shadowing) and false "no shadow" (false non-shadowing) issues.

The present invention proposes a method for reconstructing geometric shadow maps. Firstly, with the light source as the observation point, the geometric information of multiple shading triangles on the front surface (fonrt-face) of the object is stored. Consistency testing is performed on the test pixel, so as to find the shading triangle corresponding to the test pixel from the plurality of shading triangles. The shading triangle corresponding to the test pixel has a shading point; the test pixel overlaps the shading point with the light source as the observation point. Using the geometric information of the shading triangle and the position information of the test pixel, the depth value of the shading point is reconstructed. Finally, compare the depth value of the shading point with the depth value of the test pixel to complete the shadow judgment of the test pixel; wherein, the coordinates of the test pixel are (px, py, pz), and the consistency test includes: selecting the plurality of One of the shading triangles; read the geometric information of the selected shading triangle, which includes the vertex coordinates of the selected shading triangle (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); computing the equation $\left[\begin{array}{ccc}p.x& p.\mathrm{the\; <figure-callout\; id="1"\; label="y"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">y</figure-callout>}& 1\end{array}\right]=\left[\begin{array}{ccc}{w}_1& w_2& w_3\end{array}\right]*\left[\begin{array}{ccc}{v}_0.x& v_0.\mathrm{the\; y}& 1\\ v_1.x& v_1.\mathrm{the\; y}& 1\\ v_2.x& v_2.\mathrm{the\; <figure-callout\; id="1"\; label="y"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">y</figure-callout>}& 1\end{array}\right],$ To obtain the barycentric coordinates (w ₁ , w ₂ , w ₃ ) of the shading point; judge whether the selected shading triangle is consistent according to the barycentric coordinates (w ₁ , w ₂ , w ₃ ) of the shading point and if the selected shading triangle judgment result is consistent, then the selected shading triangle is the shading triangle corresponding to the test pixel; rebuilding the depth value of the shading point includes: calculating the equation $T.z=[{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">w</figure-callout>}}_1,w_2,w_3]\left[\begin{array}{c}{v}_0.z\\ v_1.z\\ v_2.z\end{array}\right],$ In order to obtain the depth value Tz of the shading point.

In one embodiment of the present invention, instead of calculating the equation $T.z=[{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">w</figure-callout>}}_1,w_2,w_3]\left[\begin{array}{c}{v}_0.z\\ v_1.z\\ v_2.z\end{array}\right],$ while computing the equation $T.z=[w_1,w_2,w_3]*\left[\begin{array}{ccc}{v}_0.x& v_0.\mathrm{the\; y}& 1\\ v_1.x& v_1.\mathrm{the\; y}& 1\\ v_2.x& v_2.\mathrm{the\; <figure-callout\; id="1"\; label="y"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">y</figure-callout>}& 1\end{array}\right]*{\left[\begin{array}{ccc}{v}_0.x& v_0.\mathrm{the\; y}& 1\\ v_1.x& v_1.\mathrm{the\; y}& 1\\ v_2.x& v_2.\mathrm{the\; y}& 1\end{array}\right]}^{-1}*\left[\begin{array}{c}{v}_0.z\\ v_1.z\\ v_2.z\end{array}\right]=$ $\left[\begin{array}{ccc}p.x& p.\mathrm{the\; <figure-callout\; id="1"\; label="y"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">y</figure-callout>}& 1\end{array}\right]*{\left[\begin{array}{ccc}{v}_0.x& v_0.\mathrm{the\; y}& 1\\ v_1.x& v_1.\mathrm{the\; y}& 1\\ v_2.x& v_2.\mathrm{the\; y}& 1\end{array}\right]}^{-1}*\left[\begin{array}{c}{v}_0.\mathrm{<figure-callout\; id="1"\; label="z\; v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">z</figure-callout>}& \\ v_{}{}_1.z\\ v_2.z\end{array}\right],$ In order to obtain the depth value Tz of the shading point.

In one embodiment of the present invention, instead of calculating the equation $T.z=[{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">w</figure-callout>}}_1,w_2,w_3]\left[\begin{array}{c}{v}_0.\mathrm{<figure-callout\; id="1"\; label="z\; v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">z</figure-callout>}& \\ v_{}{}_1.z\\ v_2.z\end{array}\right],$ while computing the equation $T.z=v_0.z+\frac{\&PartialD;z}{\&PartialD;x}(p.x-v_0.x)+\frac{\&PartialD;z}{\&PartialD;\mathrm{the\; y}}(p.\mathrm{the\; y}-v_0.\mathrm{the\; y})=$ $v_0.z+\left(\begin{array}{cc}p.x-v_0.x& p.\mathrm{the\; y}-v_0.\mathrm{the\; y}\end{array}\right)*{\left(\begin{array}{cc}{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">v</figure-callout>}}_1.x-v_0.\mathrm{<figure-callout\; id="1"\; label="x\; v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">x</figure-callout>}& v_{}{}_1.\mathrm{the\; y}-v_0.\mathrm{the\; y}\\ v_2.x-v_0.x& v_2.\mathrm{the\; y}-v_0.\mathrm{the\; y}\end{array}\right)}^{-1}*\left(\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">v</figure-callout>}}_1.z-v_0.z\\ v_2.z-v_0.z\end{array}\right),$ In order to obtain the depth value Tz of the shading point.

The present invention uses the light source as the observation point to store the geometric information of multiple triangles on the front surface of the object, so 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 value of the shading point and the test pixel can be compared to complete the shadow judgment of the test pixel.

The reconstructable geometric shadow map method described in the present invention can generate accurate shadow edges by reducing perspective aliasing and projection aliasing.

Description of drawings

FIG. 1 is a flowchart illustrating a method for reconstructing a geometric shadow map according to an embodiment of the present invention.

FIG. 2 illustrates the spatial relationship among shadow maps, object surfaces (parts) and test pixels according to an embodiment of the present invention.

FIG. 3A illustrates two adjacent triangles TR0 and TR1.

FIG. 3B illustrates rasterized areas AR0 and AR1 of triangles TR0 and TR1 in FIG. 3A.

FIG. 3C is an example of patterns illustrating two sampling templates according to the present invention.

Figure 4A illustrates projection aliasing errors produced by standard shadow maps.

FIG. 4B illustrates the projection aliasing results generated by the reconstructable geometric shadow map according to an embodiment of the present invention.

FIG. 5A illustrates a test scene generated by a standard shadow map with a constant depth offset technique (depth offset value 1e-3).

FIG. 5B illustrates a test scene generated by a standard shadow map with a constant depth offset technique (depth offset value 1e-6).

FIG. 5C is a graph illustrating a depth migration test scene generated by a reconstructable geometric shadow map (depth migration value 1e-6) according to an embodiment of the present invention.

Detailed ways

In order to make the above-mentioned features and advantages of the present invention more comprehensible, preferred embodiments will be described in detail below together with the accompanying drawings.

Those skilled in the art can realize the present invention with reference to the following embodiments. Of course, the following embodiments can also be implemented in the form of a computer program, and a computer-readable storage medium is used to store the computer program, so that the computer can execute the method for reconstructing a geometric shadow map.

FIG. 1 is a flowchart illustrating a method for reconstructing a geometric shadow map according to an embodiment of the present invention. This embodiment can handle multiple light sources. In order to describe this embodiment simply and clearly, a single light source will be taken as an example below to describe a method for reconstructing a geometric shadow map. In graphics drawn by a computer, the surface of an object may be composed of multiple geometric shapes (such as triangles or other geometric shapes). In this embodiment, it is assumed that the surface of the object is composed of multiple triangles. A person of ordinary skill in the art may render the surface of the above-mentioned object by any technique.

FIG. 2 illustrates the spatial relationship among shadow maps, object surfaces (parts) and test pixels according to an embodiment of the present invention. A scene can be drawn from the light's point of view. In the case of a point light source, this observer point may be a perspective projection. For directional light, an orthographic projection can be used. As shown in FIG. 2 , the surface of the shading object includes triangles TR0 , TR1 , TR2 and TR3 . From the above drawing, the information of each occluding triangles TR0-TR3 will be extracted and stored in geometry shadow maps. That is, the geometric information of a plurality of geometric shapes on the front surface of an object is stored by taking the light source as the observation point (step S110 ). In this embodiment, the above-mentioned geometric information may include vertex coordinates of each geometric shape, for example, vertex coordinates of the light-shielding triangles TR0 - TR3 , or include graphic indexes of each geometric shape. The linearity of this triangle allows us to reconstruct these shading triangles for point lights (and directional lights as well) in the light canonical view volume of the light observer and in the light view space.

Next, step S120 is performed to perform a consistency test on the test pixels to find a shading geometric shape from all the geometric shapes. Wherein, the shading geometry has a shading point Pd (the test pixel P overlaps with the shading point Pd in the geometric shadow diagram with the light source as the observation point). Step S120 may apply geometry shadowmaps to draw the scene from the camera viewpoint. This process has three main building blocks. For each testing pixel (testing pixel, such as the testing pixel P in FIG. 2 ) of the object, it is first necessary to find out the coordinates (p.x, p.y, p.z) of the pixel seen from the light source. The x and y values of the coordinates (p.x, p.y, p.z) correspond to positions in the geometry map texture and are used in triangle consistency tests to find shading triangles.

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

Next, step S140 is performed to compare the depth value of the shading point Pd with the depth value of the test pixel P, so as to complete the shadow determination of the test pixel P. Compared with the reconstructed depth value of the shading triangle TR0, the z value (depth value, obtained from the light canonical view volume of the light source observation point) of the test pixel P is tested to complete the shadow judgment of the test pixel P. Finally, the tested pixel is drawn either in shadow or in light. If there are multiple lights, use a separate geometric shadow map for each light.

Those skilled in the art can implement this embodiment according to the above description. A detailed implementation example of each step in FIG. 1 will be described below, but the implementation of the present invention should not be limited thereto. Figure 2 illustrates the conversion from a point source of light in the view view space of light to a directional light source in the canonical view volume of the view point of the light source. Assume that the scene in the canonical viewing volume of the light source observer is composed of four adjacent triangles TR0, TR1, TR2 and TR3.

First (step S110 ), the triangles TR0 - TR3 are respectively projected and rasterized to their corresponding regions AR0 , AR1 , AR2 and AR3 in the geometric shadow map. Each texel in each area AR0-AR3 contains the geometric information (vertex coordinates in this embodiment) of its corresponding triangle, for example, the texel in the area 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). Except that the geometry information is stored in the shadow map in step S110 (in the prior art, depth values are stored in the shadow map instead of geometry information), the operation of step S110 is almost identical to the standard shadow map. For point lights, transforms the scene to the light canonical view volume of the light's observer point, then stores the coordinates of the triangle's three vertices in a rasterized region of its shadow map. Another way is to get coordinate vertices from adjacent triangles. For example, in FIG. 2 , the coordinates of the six vertices of the triangles TR1 , TR2 and TR3 adjacent to the triangle TR0 are all stored in the rasterization area of the triangle TR0 . For directional lights, stores the vertex coordinates of the canonical view volume space specifying the "processing"light's observer point whose rays are parallel to the z-axis.

Next, a visible pixel (visible pixel) P in eye space is transformed to the canonical view volume coordinates (px, py, pz) of the light source observer point. The consistency test in 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 geometric shape (for example, if the triangle TR0 is selected, reading the geometric information of the area AR0 from the geometric shadow map). The above geometric information may include the vertex coordinates of geometric shapes, for example, the vertex coordinates (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 two-dimensional (2-D) coordinates (px, py), the corresponding sampling point T in the geometric shadow map can be found. At this step S120 may include calculating Equation 1:

$\left[\begin{array}{ccc}p.x& p.\mathrm{the\; <figure-callout\; id="1"\; label="y"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">y</figure-callout>}& 1\end{array}\right]=\left[\begin{array}{ccc}{w}_1& w_2& w_3\end{array}\right]*\left[\begin{array}{ccc}{v}_0.x& v_0.\mathrm{the\; y}& 1\\ {\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">v</figure-callout>}}_1.\mathrm{<figure-callout\; id="1"\; label="x\; v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">x</figure-callout>}& v_{}{}_1.\mathrm{the\; y}& 1\\ v_2.x& v_2.\mathrm{the\; y}& 1\end{array}\right]$ (equation 1)

To obtain the three-dimensional (3-D) barycentric coordinates (w ₁ , w ₂ , w ₃ ) of the shading point Pd corresponding to the apex of the triangle TR0. According to the barycentric coordinates (w ₁ , w ₂ , w ₃ ) of the shading point Pd, it is judged whether the selected geometry (triangle TR0) is consistent.

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 the so-called triangle "conformance test". However, sampling texture maps with test pixel coordinates (x, y) may not necessarily return information about the triangle TR0 occluding the test pixel P. If the three center-of-gravity coordinates (w ₁ , w ₂ , w ₃ ) calculated from Equation 1 are in the range [0, 1] (meaning the triangle blocks the test pixel), it is called the triangle test is consistent. Otherwise the test is inconsistent. If the selected geometric shapes are consistent, the geometric shape (triangle TR0 ) is the shading geometric shape of the test pixel P.

Due to the limited resolution of the shadow map, this can lead to inconsistent results for triangle tests. Lower resolution texture maps are more likely to make triangle test results inconsistent. FIG. 3A illustrates two adjacent triangles TR0 and TR1 , and the triangles TR0 and TR1 are limited resolution. FIG. 3B illustrates rasterized areas AR0 and AR1 of triangles TR0 and TR1 in FIG. 3A. Under limited resolution, area AR0 is the rasterized area of triangle TR0 and area AR1 is the rasterized area of triangle TR1. Point T is a sampled point which has the same (x, y) coordinates as visible pixel P under test. However, through the sampling point T, the object accessed in this embodiment is the texel A with the geometric information of the triangle TR0. As shown in Figure 3B, the sampling point T should be in the rasterization area of the triangle TR1, but the information of the triangle TR0 may cause wrong depth value reconstruction due to the limited resolution (the sampling point T is mistakenly regarded as the shading of the triangle TR0 point). The sampling point T' in Fig. 3B also has a similar problem.

With the geometric information of the adjacent triangles, by sampling the corresponding point T, the shading triangle that blocks the pixel P under test can be found. However, when two adjacent regions are rasterized, the geometric information of adjacent triangles may not be available. In order to solve this problem, this embodiment increases sampling points to include more geometric information of triangles, thus increasing the chance of finding consistent triangle tests. FIG. 3C is an example diagram illustrating two sampling kernels T and T' according to the present invention. If the tested pixel P is blocked by multi-layer geometric surfaces, this template can also sort the depth results of all consistent triangle tests, and take the minimum value as the final depth value of the shading point. Taking the pattern of the sampling template T as an example, in addition to accessing the texel with area AR0 information to calculate the sampling point T, it also accesses the texel with area AR0 information to calculate the depth value of the sampling point T2. The texel with the information of the area AR2 is used to calculate the depth value of the sampling point T1, and the texel with the information of the area AR1 is accessed to calculate the depth values of the sampling points T3 and T4. Next, sort the depth results of all consistent triangle tests (the depth values of T, T1, T2, T3 and T4), and take the minimum value as the final depth value of the shading point Pd.

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

For the tested pixel P, when the texture resolution is subcritical (which will cause some shading triangles to fail to be stored in the shadow map), the corresponding triangles must be tested inconsistently. Based on this, the triangle tests are sorted in order of weighted distance to the central triangle for reconstruction using the triangle information corresponding to the "closest-distance" weight value. When it is reasonable to assume that the reconstructed shading point is on the same plane as the "closest distance" triangle, the calculated weighted distance can be calculated in Euclidean geometry.

After obtaining the correct triangle information, the shading point depth value of the tested pixel can be reconstructed. Through triangle interpolation, the depth value of the shading point Pd in the shading triangle TR0 can be reconstructed. After calculating the above weight value from Equation 1, the depth value T.z of the shading point Pd in step S130 can be reconstructed using the following equation:

$T.z=[{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">w</figure-callout>}}_1,w_2,w_3]\left[\begin{array}{c}{v}_0.\mathrm{<figure-callout\; id="1"\; label="z\; v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">z</figure-callout>}& \\ v_{}{}_1.z\\ v_2.z\end{array}\right]$ (equation 2)

Alternatively, combining Equation 1 and Equation 2, Equation 3 can be obtained:

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="w"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">w</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; *</span>\left[\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; x</span>}& {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">v</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="x\; v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">x</figure-callout></span><figure-callout\; id="1"\; label="x\; v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">\; </figure-callout>}& {\mathrm{<span\; class="notranslate">\; </span>}}_{}{\mathrm{<span\; class="notranslate">v</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; x</span>}& {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="1"\; label="y"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">y</figure-callout></span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; *</span>{\left[\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; x</span>}& {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">v</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="x\; v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">x</figure-callout></span><figure-callout\; id="1"\; label="x\; v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">\; </figure-callout>}& {\mathrm{<span\; class="notranslate">\; </span>}}_{}{\mathrm{<span\; class="notranslate">v</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; x</span>}& {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; *</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="z\; v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">z</figure-callout></span><figure-callout\; id="1"\; label="z\; v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">\; </figure-callout>}& \\ {\mathrm{<span\; class="notranslate">\; </span>}}_{}{\mathrm{<span\; class="notranslate">v</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; z</span>}\\ {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; z</span>}\end{array}\right]$

$=\left[\begin{array}{ccc}p.x& p.\mathrm{the\; <figure-callout\; id="1"\; label="y"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">y</figure-callout>}& 1\end{array}\right]*{\left[\begin{array}{ccc}{v}_0.x& v_0.\mathrm{the\; y}& 1\\ {\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">v</figure-callout>}}_1.\mathrm{<figure-callout\; id="1"\; label="x\; v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">x</figure-callout>}& v_{}{}_1.\mathrm{the\; y}& 1\\ v_2.x& v_2.\mathrm{the\; y}& 1\end{array}\right]}^{-1}*\left[\begin{array}{c}{v}_0.\mathrm{<figure-callout\; id="1"\; label="z\; v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">z</figure-callout>}& \\ v_{}{}_1.z\\ v_2.z\end{array}\right]$ (equation 3)

The depth value T.z of the shading point Pd in step S130 can be reconstructed using Equation 3. In Equation 3 above, an inverse operation of the 3*3 matrix must be performed. Currently, Graphics Processing Unit (GPU) hardware does not directly support the inverse operation of a 3×3 matrix. So we have to break it down into some usual arithmetic and logic unit (ALU) instructions. However, the ALU instruction set does not guarantee accuracy, and may introduce more related errors to the inversion result and affect the final reconstructed depth value.

In order to improve the above problems, this embodiment rewrites Equation 3 into the following equivalent equation:

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; z</span>}{<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; +</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; z</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; z</span>}}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>$

$=v_0.z+\left(\begin{array}{cc}p.x-v_0.x& p.\mathrm{the\; y}-v_0.\mathrm{the\; y}\end{array}\right)*{\left(\begin{array}{cc}{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">v</figure-callout>}}_1.x-v_0.\mathrm{<figure-callout\; id="1"\; label="x\; v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">x</figure-callout>}& v_{}{}_1.\mathrm{the\; y}-v_0.\mathrm{the\; y}\\ v_2.x-v_0.x& v_2.\mathrm{the\; y}-v_0.\mathrm{the\; y}\end{array}\right)}^{-1}*\left(\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="S2008100961357E00012.png"\; state="\{\{state\}\}">v</figure-callout>}}_1.z-v_0.z\\ v_2.z-v_0.z\end{array}\right)$ (equation 4)

Therefore, the depth value T.z of the shading point Pd in step S130 can also be reconstructed using Equation 4.

Finally, by comparing the shading point Pd with the canonical volume depth values of the pixel P, that is, comparing T.z and p.z, the shadow judgment of the pixel P can be completed (step S140).

Figure 4A illustrates projection aliasing errors produced by standard shadow maps. The scene shown in Fig. 4A is a quadrilateral plate floating above the bottom plane, so the quadrilateral plate forms a strip shadow on the bottom plane. The lower left corner of Figure 4A shows a partially enlarged view of the banded shadow. It can be clearly seen from FIG. 4A that the projection aliasing error produced by the traditional standard shadow map is very obvious. Compared with FIG. 4A , FIG. 4B illustrates the projection aliasing result generated by the reconstructable geometric shadow map according to an embodiment of the present invention. That is, FIG. 4B uses the new algorithm described in the above-mentioned embodiments of the present invention: Reconstructable Geometry Shadow Map (RGSM), as a solution to the aliasing problem. Figure 4B shows the same scene as Figure 4A. It can be clearly seen from FIG. 4B that the projection aliasing error generated by the RGSM algorithm used in the embodiment of the present invention is significantly improved.

Another problem with most shadow map techniques is the problem of depth offset. 5A, 5B and 5C have the same scene for the graphics depth migration test, which are houses and railings. FIG. 5A illustrates a test scene generated by a standard shadow map with a constant depth offset technique (depth offset value 1e-3) to avoid false self-shadowing problems. That is, it adds the depth offset value to the depth sample before comparing it to the true surface. Because the depth offset value in FIG. 5A is too large, it causes false "non-shadowing" (it looks like the shading object is floating above the light receiving object) phenomenon and the shadow recedes too far. In practice, it is very difficult to directly determine the offset value, and it is impossible to find an acceptable value in every scene. For example, FIG. 5B illustrates a test scene generated by a standard shadow map with a constant depth offset technique (depth offset value 1e-6). In order to improve the false "no shadow" phenomenon, a small depth offset value (1e-6) is used. Although the "no shadow" phenomenon is improved, the false "self-shadowing" problem (such as Figure 5B). FIG. 5C is a graph illustrating a depth migration test scene generated by a reconstructable geometric shadow map according to an embodiment of the present invention. That is, FIG. 5C uses the RGSM algorithm introduced in the above embodiments of the present invention as a solution to the depth migration problem. The depth offset value of FIG. 5C is the same as that of FIG. 5B, which is 1e-6. It can be clearly seen from FIG. 5C that the RGSM algorithm used in the embodiment of the present invention can use a very small depth offset value without causing false "self-shadowing" problems.

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

1. By reducing perspective aliasing and projection aliasing, it can produce accurate shadow edges. It also removes shadow edge "jittering" in dynamic scenes.

2. Compared with other shadow map techniques, this embodiment can have a small depth offset value. By setting a single and fixed offset value, programmers using RGSM can meet the needs of most applications and produce correct images without false self-shadowing or false "no shadows". "(falsenon-shadowing) problem.

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

The above description is only a preferred embodiment of the present invention, but it is not intended to limit the scope of the present invention. Any person familiar with this technology can make further improvements on this basis without departing from the spirit and scope of the present invention. Improvements and changes, so the protection scope of the present invention should be defined by the claims of the present application.

A brief description of the symbols in the drawings is as follows:

A, B: texture elements

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

P: test pixel

Pd: shading point

S110-S140: According to the embodiment of the present invention, each step of the method for reconstructing the geometric shadow map is described

TR0, TR1, TR2, TR3: triangles on the surface of the shading object

T, T': sampling point.

Claims (17)

1. a Recreatable geometric shade pattern method is characterized in that, comprising:

With a light source is observation point, stores the leg-of-mutton geological information of a plurality of shadings of an object front surface;

One test pixel is carried out uniformity test, from said a plurality of shading triangles, to find out a shading triangle that corresponds to this test pixel;

Reconstruction corresponds to the depth value of a chopping point of this test pixel; And

Carrying out the shade of this test pixel judges;

Wherein, the coordinate of this test pixel be (p.z), and this uniformity test comprises for p.x, p.y:

Select said a plurality of shading triangle one of them;

Read the leg-of-mutton geological information of selected shading, comprise this selected shading vertex of a triangle coordinate (v in the leg-of-mutton geological information of this selected shading 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);

Calculation equation $\left[\begin{array}{ccc}p.x& p.y& 1\end{array}\right]=\left[\begin{array}{ccc}{w}_1& w_2& w_3\end{array}\right]*\left[\begin{array}{ccc}{v}_0.x& v_0.y& 1\\ v_1.x& v_1.y& 1\\ v_2.x& v_2.y& 1\end{array}\right],$ To ask for the barycentric coordinates value (w of this chopping point ₁, w ₂, w ₃);

(w1, w2 w3) judge whether this selected shading triangle is consistent according to the barycentric coordinates value of this chopping point; And

If this selected shading triangle judged result is consistent, then this selected shading triangle is the shading triangle that corresponds to this test pixel;

The depth value of rebuilding this chopping point comprises:

Calculation equation $T.z=[w_1,w_2,w_3]\left[\begin{array}{c}{v}_0.z\\ v_1.z\\ v_2.z\end{array}\right],$ To ask for the depth value T.z of this chopping point.

2. Recreatable geometric shade pattern method according to claim 1 is characterized in that, the leg-of-mutton geological information of said a plurality of shadings comprises said a plurality of shading vertex of a triangle coordinate or how much index.

3. Recreatable geometric shade pattern method according to claim 1 is characterized in that,

Replace calculation equation $T.z=[w_1,w_2,w_3]\left[\begin{array}{c}{v}_0.z\\ v_1.z\\ v_2.z\end{array}\right],$ And calculation equation $T.z=[w_1,w_2,w_3]*\left[\begin{array}{ccc}{v}_0.x& v_0.y& 1\\ v_1.x& v_1.y& 1\\ v_2.x& v_2.y& 1\end{array}\right]*{\left[\begin{array}{ccc}{v}_0.x& v_0.y& 1\\ v_1.x& v_1.y& 1\\ v_2.x& v_2.y& 1\end{array}\right]}^{-1}*\left[\begin{array}{c}{v}_0.z\\ v_1.z\\ v_2.z\end{array}\right]=$ $\left[\begin{array}{ccc}p.x& p.y& 1\end{array}\right]*{\left[\begin{array}{ccc}{v}_0.x& v_0.y& 1\\ v_1.x& v_1.y& 1\\ v_2.x& v_2.y& 1\end{array}\right]}^{-1}*\left[\begin{array}{c}{v}_0.z\\ v_1.z\\ v_2.z\end{array}\right],$ To ask for the depth value T.z of this chopping point.

4. Recreatable geometric shade pattern method according to claim 1 is characterized in that,

Replace calculation equation $T.z=[w_1,w_2,w_3]\left[\begin{array}{c}{v}_0.z\\ v_1.z\\ v_2.z\end{array}\right],$ And calculation equation $T.z=$ $v_0.z+\frac{\&PartialD;z}{\&PartialD;x}(p.x-v_0.x)+\frac{\&PartialD;z}{\&PartialD;y}(p.y-v_0.y)=$ $v_0.z+\left(\begin{array}{cc}p.x-v_0.x& p.y-v_0.y\end{array}\right)*{\left(\begin{array}{cc}{v}_1.x-v_0.x& v_1.y-v_0.y\\ v_2.x-v_0.x& v_2.y-v_0.y\end{array}\right)}^{-1}*\left(\begin{array}{c}{v}_1.z-v_0.z\\ v_2.z-v_0.z\end{array}\right),$ To ask for the depth value T.z of this chopping point.

5. Recreatable geometric shade pattern method according to claim 1 is characterized in that, the shading triangle that corresponds to this test pixel has this chopping point; With this light source is observation point, and this test pixel and this chopping point are overlapping.

6. Recreatable geometric shade pattern method according to claim 1 is characterized in that, the depth value of rebuilding this chopping point need utilize the positional information of the leg-of-mutton geological information of the shading that corresponds to this test pixel and this test pixel.

7. Recreatable geometric shade pattern method according to claim 1 is characterized in that, the shade of carrying out this test pixel judges it is through the relatively depth value of this chopping point and the depth value of this test pixel.

8. a method of rebuilding the geometrical shadow figure of a viewing area is characterized in that, comprises:

Determine the test pixel in this viewing area;

Determine among the geometrical shadow figure of this viewing area a chopping point corresponding to this test pixel;

Calculate the weighted value of this chopping point according to the planimetric coordinates value of covering a shading vertex of a triangle of this test pixel in the planimetric coordinates value of this test pixel and this viewing area;

Decide the depth value of this chopping point according to the depth value of the weighted value of this chopping point and this shading vertex of a triangle; And

Relatively the depth value of the depth value of this chopping point and this test pixel should be illustrated in light or the shade to determine this test pixel.

9. the method for the geometrical shadow figure of reconstruction according to claim 8 one viewing area is characterized in that, more comprises when this viewing area has multiple-level surface, repeats institute in steps.

10. the method for the geometrical shadow figure of reconstruction according to claim 9 one viewing area is characterized in that, more comprises to select that the depth value reckling is the depth value of this chopping point in the multiple-level surface.

11. the method for the geometrical shadow figure of reconstruction according to claim 8 one viewing area is characterized in that, the depth value of this weighted value and this chopping point be according to this shading triangle with and the summit of adjacent triangle calculate.

12. the method for the geometrical shadow figure of reconstruction according to claim 11 one viewing area is characterized in that, each leg-of-mutton resolution is different.

13. the method for the geometrical shadow figure of reconstruction according to claim 8 one viewing area is characterized in that this test pixel decides with respect to a light source.

14. the method for the geometrical shadow figure of reconstruction according to claim 8 one viewing area is characterized in that the planimetric coordinates of this chopping point is identical with the planimetric coordinates of this test pixel.

15. the method for the geometrical shadow figure of reconstruction according to claim 8 one viewing area; It is characterized in that the weighted value of this chopping point is to calculate according to following formula: the planimetric coordinates of this weighted value and this shading vertex of a triangle multiplies each other and equals the planimetric coordinates of this test pixel.

16. the method for the geometrical shadow figure of reconstruction according to claim 8 one viewing area; It is characterized in that the depth value of this chopping point is to calculate according to following formula: the depth value that the depth value of this chopping point equals this weighted value and this shading vertex of a triangle multiplies each other.

17. the method for the geometrical shadow figure of reconstruction according to claim 8 one viewing area is characterized in that, the calculating of the depth value of this chopping point is that matrix inversion operation is decomposed into a plurality of arithmetic logical unit instructions.

Images