CN104463943A - Multi-light-source acceleration method for programmable shader - Google Patents

Abstract

The present invention provides a programmable shader-oriented multi-light source acceleration method, realizes the Lightcuts algorithm in the programmable shader environment, clusters the light sources into a tree structure, and then cuts the light source tree to reduce actual rendering The number of light sources can reduce the relationship between rendering time and the number of light sources to sub-linear, and the stability is relatively good, and in most cases, it can have a good acceleration effect. Secondly, the experiment found that for the rendering of the shadow part in the scene, the acceleration effect of the algorithm is not ideal, and it is optimized for this problem. Finally, the present invention groups similar points on the same object for rendering, further improving efficiency.

Description

A Multi-Light Acceleration Method for Programmable Shader

technical field

The invention relates to the field of graphics realistic rendering, in particular to a typical multi-light source acceleration method based on hierarchical structure.

Background technique

In the rendering of large-scale scenes, the increase in the number of light sources will lead to a linear increase in rendering time. For some complex lighting effects, such rendering time is unacceptable. The present invention belongs to the research and development part of the rendering engine in the realistic rendering system. When the engine renders a multi-light source scene, it does not optimize the multi-light source, resulting in unacceptable rendering speed. In order to save costs and improve efficiency, the present invention implements an acceleration scheme for multi-light source scenes for a rendering engine based on the Renderman specification.

There are many ways to optimize the rendering of multi-light source scenes. In the article [A general version of crow's shadow volumes], Bergeron proposed a method of setting a radius of influence for the light source. Objects within the radius of influence will be illuminated by the light source. Otherwise, it will not be considered. The influence of the light source, which will cause the lighting effect produced by a large number of low-brightness light sources to be ignored; in the article [Adaptive shadow testing for ray tracing], Ward proposed to establish a contribution table for all light sources, and only consider light sources with relatively large contributions. When the number of light sources is large, it will take a lot of time to calculate the contribution value; in the article [Monte carlo techniques for direct lighting calculation], Shirley divides the light sources into important and unimportant categories according to the radius of influence, and samples the two types of light sources separately, but An inappropriate number of samples will cause aliasing problems; in the article [A light hierarchy for fast rendering of scenes with many lights], Paquette proposed an optimization algorithm based on a tree-like hierarchy, but it does not support shadow effects, which greatly limits its scope of use.

In the article [Lightcuts in blender], Davide gave a brief introduction to the implementation and scope of application of the Lightcuts algorithm in the Blender engine. But the shaders of the Blender engine are built-in, not as flexible and easy to use as programmable shaders. No implementation of the algorithm in the context of programmable shaders is proposed in the literature. Moreover, the literature also pointed out that the acceleration effect of the Lightcuts algorithm implemented in Blender is not as obvious as expected in practical applications.

After analyzing and comparing various multi-light source optimization algorithms, the present invention selects the Lightcuts algorithm based on the hierarchical structure as the research basis. This algorithm is a light source clustering optimization method based on a binary tree structure, which has a good acceleration effect, and the algorithm has strong universality, and can be optimized for rendering of most scenes. The algorithm can control the degree of optimization through the adjustment of error threshold parameters, which is convenient for practical engineering use.

The Lightcuts algorithm is based on Weber's principle, that is, the smallest brightness change that humans can perceive is about 1% of the current brightness. In the algorithm, 0.02 is generally selected as the parameter of the error threshold, and the light generated by the light source set is less than 0.02 times the total brightness. can simplify calculations. The algorithm calculates a weight between every two light sources, which is related to the distance and brightness of the two light sources. Then the light sources are clustered into a binary tree according to the weights. When rendering a point, start from the root node of the light source tree, and judge whether to split the node according to Weber's principle: if the contribution value of the current node to the brightness of the rendering point is greater than the error threshold and there is a leaf node, the node will be down Split into two child nodes, otherwise stop splitting. When all paths stop splitting, the set of all nodes obtained is a light source cut. Subsequent rendering passes use the light source cut instead of the original light source for rendering.

Contents of the invention

The purpose of the present invention is to solve the above-mentioned problems, and proposes a multi-light source acceleration method for programmable shaders. The method first realizes the Lightcuts algorithm in the programmable shader environment, and clusters the light sources into a tree structure. Then cut the light source tree to reduce the number of light sources actually rendered, which can reduce the relationship between rendering time and the number of light sources to sub-linear, and the stability is relatively good, and in most cases, it can have a good acceleration effect.

In order to achieve the above object, the present invention adopts the following technical solutions:

A multi-light source acceleration method for programmable shaders, including:

(1) The rendering engine reads the light source information in the scene file, extracts the lighting parameters required by the Lightcuts algorithm, and stores them in the light source linked list;

(2) Before rendering the scene, use the Lightcuts algorithm to cluster the light sources, traverse the light source linked list, and build a global light source tree for each type of light source;

(3) During the rendering process, place the points to be rendered on the geometric surface in the buffer; cluster the rendering points in the buffer: similar points on the same object have the same material and are affected by the same light source, so the next step is to A group of similar rendering points on the same object find a common light source cut for rendering;

(4) For each group of rendering points, use the global light source tree to group the rendering points to calculate the light source cut;

(5) Set the value of the shadow domain parameter and the background brightness parameter, if the current light source node brightness L _c is smaller than the shadow domain parameter value, then take the background brightness parameter value as the estimated value of the current light source node brightness, and calculate the light source cut ;

(6) The rendering engine recognizes the shader file in this light source cut, and uses the light source cut instead of the original light source for lighting;

(7) The rendering process is repeated until all rendering points are rendered, and the rendering result image is output.

In the step (3), the specific method for seeking common light source cuts for similar rendering points on the same object is as follows:

a. Each group of rendering points shares a stack for storing light source cuts; set the flag bit to mark whether the executed point is the first point of the group of rendering points;

b. If the first point is executed, the light source cut is performed normally, and the result is stored in the stack; if it is not the first point, the light source cut of the current point is executed starting from the last calculated light source cut in the stack process, the result is still stored on the stack;

c. Execute step b continuously until the group of rendering points are all executed, and the result in the stack is the common light source cut of the group of rendering points.

In the step (4), the specific method for grouping the rendering points to calculate the light source cut is:

1) Estimate the two values of the light source node in the light source tree: L _c and upperbound; the L _c represents the estimation of the brightness of a light source cluster actually irradiated to the rendering point; upperbound represents the theoretical light source cluster represented by the light source node The expected maximum value of the brightness produced by the class shining on the rendering point;

2) If maxupperbound<0.02*∑L _c , it means that the upperbound values of all light source nodes in the stack meet the condition of less than 0.02*∑L _c , then the light source node in the stack is the last obtained light source node, and the calculation is completed; among them, maxupperbound is the maximum value of the upperbound of all nodes in the stack, and 0.02 is the Weber parameter;

Otherwise, split the light source node, pop the split node out of the stack, and push its child nodes into the stack; calculate the upperbound and L _c of the newly added node.

In the step (5), if the background brightness is used, in the subsequent calculation process, when the estimated light source node brightness L _c value is greater than or equal to the shadow domain parameter value, the estimated light source node brightness will be used again L _c is used to calculate the cut of the light source.

The shadow domain parameter defaults to the median value of the absolute sensory threshold of 0.05, and the background brightness parameter is greater than or equal to the value of the shadow domain parameter, and the default absolute sensory threshold is 0.1.

The method for clustering the rendering points in the buffer in the step (3) is:

Step 1: For the set of the same group of light sources, find the two light sources with the smallest weight;

Step 2: Construct a parent node for the two light sources with the smallest weight, randomly select a light source from the two light sources as its representative light source, and record the bounding box information and total brightness value;

Step 3: Add the parent node to the light source collection, and delete the two child nodes from the light source collection;

Step 4: Skip to step 1 until there is only one node left in the group of light sources, that is, the root node, and the light source tree is constructed; the leaf nodes are the actual light sources, and the internal nodes are representative light sources.

The calculation method of the weight in the first step is shown in the following formula:

W＝I _c (a _c ² +c ² (1–cosβ _c ) ² )

Among them, I _c is the sum of the brightness of the two light sources, a _c is the diagonal length of the axis-aligned bounding box of the two light sources; for the point light source and parallel light, the value of c is 0, and for the spotlight, c is a connection space size and the spotlight A constant of the direction, related to the diagonal length of the bounding box of the scene; β _c is 1/2 of the binding angle of the two light sources.

Beneficial effects of the present invention

1. The present invention analyzes and improves the algorithm for the problem that the rendering acceleration effect of the shadow part in the Lightcuts algorithm is unsatisfactory, and proposes two parameters of the shadow domain and background brightness to control the rendering process of the shadow part to avoid Some unnecessary calculations speed up the rendering efficiency of shadows.

2. The present invention adopts the method of rendering point clustering to obtain Lightcuts for a group of rendering points of the same material and close spatial distance, which reduces the construction time of light source cuts and improves rendering efficiency.

3. In order to enable the algorithm to support the rendering process under the programmable shader, the present invention designs related interfaces so that it supports the programmable shader commonly used in commercial rendering and improves the usability of the algorithm.

Description of drawings

Figure 1 is a schematic diagram of the clustering process of four light sources;

Fig. 2 is the schematic diagram of the light source cutting process for four light sources;

FIG. 3 is a histogram of rendering time comparison according to an embodiment of the present invention.

Detailed ways

The present invention will be further described below in combination with specific embodiments and accompanying drawings.

The Lightcuts algorithm is mainly divided into two parts: light source clustering and light source cut calculation.

a. Light source clustering:

The light source clustering process clusters the light sources in the scene into a binary tree, as shown in Figure 1. Proceed as follows:

1) For the set of all light sources of the same type, find the two light sources with the smallest weight. The weight calculation method is shown in formula (1):

W＝I _c (a _c ² +c ² (1–cosβ _c ) ² ) Formula (1)

Among them, I _c is the sum of the brightness of the two light sources, and a _c is the diagonal length of the axis-aligned bounding box of the two light sources. The value of c is 0 for point lights and parallel lights. For spotlights, c is a constant that connects the size of the space and the direction of the spotlight, and is related to the diagonal length of the bounding box of the scene, and β _c is 1/2 of the binding angle of the two light sources.

2) Construct a parent node for the two light sources with the smallest weight, randomly select one of the two light sources as its representative light source, and record the bounding box information and total brightness value. The bounding box means to approximately replace complex geometric objects with slightly larger and simple geometric objects.

3) Add the parent node to the light source collection, and delete the two child nodes from the light source collection.

4) Jump to the first step and execute until there is only one node left in the light source collection, that is, the root node, and the light source tree is constructed. The leaf nodes are actual light sources, and the internal nodes are representative light sources.

b. Find the cut of the light source:

To simplify multi-light sources while ensuring the quality of rendering results, it is necessary to split nodes according to Weber's principle in the process of solving light source cuts. During the splitting process, for the representative light source node in the light source tree, there are two values: L _c and upperbound. These two values are only calculated when a node is found:

L _c represents an estimate of the brightness of a light source cluster that actually illuminates the rendering point. Its calculation formula (2) is as follows:

L _c (x,w)≈M _j (x,w)G _j (x)V _j (x)∑ _i∈C I _i formula (2)

The set C represents a light source cluster, x represents the rendering point (including position, normal and other information), w represents the viewpoint direction, M represents the material factor, G represents the geometric factor, V represents the visibility, and I represents the brightness of the light source. i represents the actual light source, and j is the representative light source of the current cluster. upperbound represents theoretically the estimated maximum value of the brightness generated by the light source cluster represented by the node irradiating the rendering point (assuming that all light sources are visible). Its calculation formula is the same as that of _Lc , except that the material factor M, geometric factor G and visibility factor V need to take the upper limit value during the calculation process.

The specific process of calculating the light source cut is shown in Figure 2, including:

1) Set up a stack to store the results. First push the root node into the stack, and calculate the upperbound and L _c of the root node.

2) If maxupperbound<0.02*∑L _c (maxupperbound is the maximum value of the upperbound of all nodes in the stack, and 0.02 is the Weber parameter), it means that the upperbound values of all nodes in the stack meet the condition of less than 0.02*∑L _c , then the stack The inner node is the last obtained node, and the calculation is completed. Otherwise, split the node (if there are child nodes), pop the split node out of the stack, and push its child nodes into the stack. Calculate the upperbound and L _c of the newly pushed node.

What is stored in the final stack is the simplified result of the Lightcuts algorithm, that is, a light cut.

The original Lightcuts algorithm is relatively inefficient in places with many shadows in the scene. In the shadows where a large number of light sources are blocked, the number of light sources in the light cut is basically equal to the actual number of light sources. The estimated brightness L _c of these shadows is very small (possibly 0), so the product of the Weber parameter 0.02 and L _c is also very small, and the estimated value upperbound representing the light source is generally greater than 0.02*L _c because occlusion is not considered. . As a result, the nodes continue to split during the process of seeking light source cuts until the leaf nodes.

In order to speed up the actual rendering efficiency, the present invention proposes two optional empirical parameters of shadow domain and background brightness. When calculating the executed light source, when the estimated total illumination value L _c is less than the shadow domain parameter value (in order to ensure the rendering effect and neutralize the error caused by the estimated total illumination, the median value of the absolute sensory threshold is taken as 0.05 by default) When , it is considered that the rendering point is in the shadow, and the value of the background brightness parameter (generally greater than or equal to the parameter value of the shadow domain, the default is the absolute threshold of perception 0.1) is taken as the value of the current estimated brightness L _c to calculate the light source cut. calculate. If the estimated total illumination value is greater than or equal to the value of the shadow domain parameter in the subsequent calculation process after using the background brightness, then restore the calculation using the estimated brightness L _c to ensure accuracy.

By appropriately increasing the estimated brightness of the rendering points in the shadow area, the total number of light sources in the light source cut can be reasonably reduced, and the rendering efficiency of the shadow area can be improved. The actual rendering results are also in line with expectations, and the image quality can be guaranteed.

In order to improve efficiency, similar points on the same object are grouped for rendering, and only need to execute the material shader once to render up to 256 points. The normal direction and position of similar points are generally not much different, and the calculated light source cuts are also roughly the same. Therefore, according to this feature, the method of incremental calculation of common light source cuts is used to adapt to the engine's process of grouping rendering points, and speed up the calculation process. The speed at which the light cuts.

Programmable shaders are widely used in rendering, but traditional Lightcuts algorithms generally do not support light sources described by programmable shaders. The invention extracts the necessary parameters of the Lightcuts algorithm from the shader for extracting the light source and transmits them, thereby supporting the programmable shader. The extracted information mainly includes: light source type, light source brightness, attenuation mode, light source position, direction, and irradiation range.

To implement the Lightcuts algorithm in the rendering engine, it is first necessary to obtain light source information to build a light source tree. Moreover, the process of building a light source tree must be performed before rendering each point. The tree building process can be regarded as a kind of preprocessing, which is only executed once globally. The rendering engine traverses all light sources to calculate the lighting value at the rendering point. To apply the Lightcuts algorithm for acceleration, it is necessary to add the process of finding the light source cut before traversing, and use the obtained light cut to replace the original light source for rendering to achieve the purpose of acceleration.

The multi-light source acceleration method for programmable shaders of the present invention comprises the following steps:

1) The rendering engine reads the light source information in the scene file, Lightcuts parses and extracts the required lighting parameters, and stores them in the light source linked list.

2) Before rendering the scene, the Lightcuts algorithm clusters the light sources, traverses the light source linked list, and constructs a global light source tree for each type of light source.

3) During the rendering process, when the rendering engine calculates the lighting of a point, it executes the Lightcuts algorithm:

3.1) When rendering a point, place the point to be rendered in the buffer.

3.2) Cluster the rendering points in the buffer. Similar points on the same object have the same material and are affected by the same light source. Cluster them for rendering.

3.3) A group of 256 rendering points, using the global light source tree, solves a light source cut.

3.4) Traversing the light sources in the light source cut, estimating the influence of the light source on the scene according to the shadow domain or background brightness parameters, and ignoring the non-affecting light sources. Submit rendering to execute light shader

4) The rendering engine executes the corresponding light source shader to calculate the lighting result. Select the next batch of points, repeat step 2 until the rendering is completed, and output the rendered image.

Implementation details:

1) The light source shader and material shader defined by the programmable shader have great flexibility, and it is necessary to define the interface matching the Lightcuts algorithm for constraints. When the interface is designed, only the necessary parameters are extracted for transmission, avoiding redundant calculations, and at the same time preventing the interface parameters from constraining the shader too much and affecting the flexibility of the programmable shader.

In the above-mentioned design scheme, calculating the light source cut needs to estimate the value of direct illumination (L _c ), which is repeated with the calculation of the direct illumination part in the material, and the two-pass calculation leads to a decrease in efficiency. Experiments show that more than 90% of the workload in repeated calculations comes from the solution of visibility V. The calculation of visibility involves the intersection of shadow lines and the entire scene (trace function), which is related to the number of patches in the scene, and the complexity is very high. Therefore, the trace_reuse interface parameter is designed, and the intersection result obtained during the calculation of Lc by the rendering engine is passed to the material shader for reuse to improve the acceleration effect.

2) In the engine rendering process, in order to improve efficiency, similar points on the same object are grouped for rendering, so that a maximum of 256 points can be rendered only by executing the material shader once. The normal direction and position of similar points are generally not much different, and the calculated light source cuts are also roughly the same. According to this characteristic, the present invention adopts the method of incrementally calculating the common light source cut, and calculates the light source cut by grouping the rendering points, which speeds up the speed of calculating the light source cut. The calculation method is as follows:

1. A set of points share a stack that stores light source cuts. Set the flag bit to mark whether the execution is the first point of a set of points.

2. If the execution is the first point, execute the light source cut normally, and store the result in the stack. If it is not the first point, start from the light source cut calculated last time in the stack, execute the light source cut process of the current point, and the result is still stored in the stack.

3. The second step is executed in a loop until all the points in a group are executed, and the result in the stack is the common light source cut of this group of points.

For a rendering algorithm, it is the process of converting a three-dimensional scene into a picture, and the scene includes information such as cameras, geometry, light sources, materials, and map textures. Before the rendering task starts, the expression of a three-dimensional scene in the modeling software is converted into a data expression that can be read and recognized by the rendering engine. In the conversion program, Lightcuts is implemented in the programmable shader according to the present invention. Algorithms and related improvements. After the user submits a scene data file package containing complete information, the rendering engine can identify the camera, geometry, light source and other information described in these files. After the entire scene data is read in, the rendering starts, the algorithm is executed during the shading process, and the image is output.

The Pudong night scene is a rendering example. The scene contains 110,000 triangular patches and 724 light sources. All geometry, light sources, and materials conform to the Renderman specification. The light sources and materials are described by programmable shaders. The specific scene information data is shown in Table 1.

Table 1

Lightcuts algorithm integrated rendering engine of the present invention carries out following steps processing:

1) The user submits the rendering scene data, the rendering engine reads the scene data, and Lightcuts analyzes and extracts the required lighting parameters, stores them in a light source list composed of 724 light sources, and analyzes the empirical parameter estimation of the user's background brightness.

2) Before rendering the scene, the Lightcuts algorithm clusters the light sources, traverses the light source linked list, and constructs a global light source tree composed of 724 light sources, which is used to solve the light source cut.

3) During the rendering process, when the rendering engine calculates the material of a certain patch, it needs to calculate the lighting of the patch, then execute the Lightcuts algorithm:

3.1) Place all the points on the patch in the buffer.

3.2) Cluster the rendering points in the buffer. Similar points on the same object have the same material and are affected by the same light source. Cluster them for rendering.

3.3) A group of 256 rendering points, using the global light source tree, solves a light source cut.

3.4) Traversing the light sources in the light source cut, estimating the influence of the light source on the scene according to the shadow domain or background brightness parameters, and ignoring the non-affecting light sources. Submit rendering to execute light shader

4) The rendering engine executes the corresponding light source shader to calculate the lighting result. Select the next batch of points, repeat step 2 until the rendering is completed, and output the rendered image.

In the Pudong night scene, with the traditional rendering method, the average number of light sources processed at each rendering point is 724. Using the article [Lightcuts: a scalable approach to illumination], the original method processes an average of 275 light sources. The average number of light sources processed by this method is 149. Compared with the original multi-light optimization algorithm, the speedup percentage is about 30% to 40%. The specific statistical data comparison between the original algorithm and the improved algorithm of the present invention is shown in Table 2. The comparison of rendering time without acceleration, accelerated by the original algorithm and accelerated by the improved method of the present invention is shown in Fig. 3 .

Table 2

Although the specific implementation of the present invention has been described above in conjunction with the accompanying drawings, it does not limit the protection scope of the present invention. Those skilled in the art should understand that on the basis of the technical solution of the present invention, those skilled in the art do not need to pay creative work Various modifications or variations that can be made are still within the protection scope of the present invention.

Claims (7)

1. A multi-light source acceleration method for programmable shaders, characterized in that it comprises: (1) The rendering engine reads the light source information in the scene file, extracts the lighting parameters required by the Lightcuts algorithm, and stores them in the light source linked list; (2) Before rendering the scene, use the Lightcuts algorithm to cluster the light sources, traverse the light source linked list, and build a global light source tree for each type of light source; (3) During the rendering process, place the points to be rendered on the geometric surface in the buffer; cluster the rendering points in the buffer: similar points on the same object have the same material and are affected by the same light source, so the next step is to A group of similar rendering points on the same object find a common light source cut for rendering; (4) For each group of rendering points, use the global light source tree to group the rendering points to calculate the light source cut; (5) Set the value of the shadow domain parameter and the background brightness parameter, if the current light source node brightness L _c is smaller than the shadow domain parameter value, then take the background brightness parameter value as the estimated value of the current light source node brightness, and calculate the light source cut ; (6) The rendering engine recognizes the shader file in this light source cut, and uses the light source cut instead of the original light source for lighting; (7) The rendering process is repeated until all rendering points are rendered, and the rendering result image is output. 2. a kind of programmable shader-oriented multi-light source acceleration method as claimed in claim 1, it is characterized in that, in described step (3), the specific method for seeking common light source cut to similar rendering points on the same object is as follows : a. Each group of rendering points shares a stack for storing light source cuts; set the flag bit to mark whether the executed point is the first point of the group of rendering points; b. If the first point is executed, the light source cut is performed normally, and the result is stored in the stack; if it is not the first point, the light source cut of the current point is executed starting from the last calculated light source cut in the stack process, the result is still stored on the stack; c. Execute step b continuously until the group of rendering points are all executed, and the result in the stack is the common light source cut of the group of rendering points. 3. a kind of programmable shader-oriented multi-light source acceleration method as claimed in claim 1, is characterized in that, in described step (4), the specific method of grouping calculation light source cut to rendering point is: 1) Estimate the two values of the light source node in the light source tree: L _c and upperbound; the L _c represents the estimation of the brightness of a light source cluster actually irradiated to the rendering point; upperbound represents the theoretical light source cluster represented by the light source node The expected maximum value of the brightness produced by the class shining on the rendering point; 2) If maxupperbound<0.02*∑L _c , it means that the upperbound values of all light source nodes in the stack meet the condition of less than 0.02*∑L _c , then the light source node in the stack is the last obtained light source node, and the calculation is completed; among them, maxupperbound is the maximum value of the upperbound of all nodes in the stack, and 0.02 is the Weber parameter; Otherwise, split the light source node, pop the split node out of the stack, and push its child nodes into the stack; calculate the upperbound and L _c of the newly added node. 4. A kind of programmable shader-oriented multi-light source acceleration method as claimed in claim 1, it is characterized in that, in said step (5), if after using the background brightness, in the subsequent calculation process, estimate When the brightness L _c value of the light source node is greater than or equal to the parameter value of the shadow domain, the calculation of the light source cut is resumed using the estimated brightness L _c of the light source node. 5. A method for accelerating multi-light sources oriented to programmable shaders according to claim 4, wherein the shadow domain parameter defaults to a median value of 0.05 of the absolute perception threshold, and the background brightness parameter is greater than or equal to The parameter value of the shadow domain, the absolute sensory threshold is 0.1 by default. 6. a kind of programmable shader-oriented multi-light source acceleration method as claimed in claim 1, is characterized in that, in described step (3), the method for the rendering point clustering in buffer is: Step 1: For the set of the same group of light sources, find the two light sources with the smallest weight; Step 2: Construct a parent node for the two light sources with the smallest weight, randomly select a light source from the two light sources as its representative light source, and record the bounding box information and total brightness value; Step 3: Add the parent node to the light source collection, and delete the two child nodes from the light source collection; Step 4: Skip to step 1 until there is only one node left in the group of light sources, that is, the root node, and the light source tree is constructed; the leaf nodes are the actual light sources, and the internal nodes are representative light sources. 7. A kind of programmable shader-oriented multi-light source acceleration method as claimed in claim 6, is characterized in that, the calculation method of weight in the described 1st step is as follows: W＝I _c (a _c ² +c ² (1–cosβ _c ) ² ) Among them, I _c is the sum of the brightness of the two light sources, a _c is the diagonal length of the axis-aligned bounding box of the two light sources; for the point light source and parallel light, the value of c is 0, and for the spotlight, c is a connection space size and the spotlight A constant of the direction, related to the diagonal length of the bounding box of the scene; β _c is 1/2 of the binding angle of the two light sources.