CN113160413B - Real-time dynamic cloud layer drawing method based on cellular automaton - Google Patents

Abstract

The invention discloses a real-time dynamic cloud layer drawing method based on cellular automata. Judgment rule; 2) The cellular automaton establishes the data structure of the cellular automaton according to the global texture of the input initial low-resolution image, as the cell evolution texture of each frame changing with time sequence; the data structure includes the global array cellMap and each living system. 3) Smooth and interpolate the cell evolution texture of each frame to obtain the large-scale texture of the corresponding frame; 4) The large-scale texture corresponding to each frame is superimposed with fractal noise to generate cloud layer details, and the density field is calculated in each frame. The value of the point corresponding to the texture element; 5) Sampling the volume cloud formed by multiple cloud clusters; 6) Calculate the scattering effect of the point light source on the cloud layer, and finally render the realistic rendering of the cloud layer.

Description

A real-time dynamic cloud layer rendering method based on cellular automata

technical field

The invention belongs to the technical fields of computer graphics, virtual reality technology and software, and relates to a real-time dynamic cloud layer rendering method and system based on cellular automata.

Background technique

Clouds in the natural environment have different shapes and lighting details. How to reasonably model and draw (render) their characteristics has always been a meaningful research topic.

Cellular automata (also translated as cellular automata) is a mathematical model that describes complex patterns and behaviors, in which each cell distributed on an evolving grid is in a certain state in a finite set of discrete states. In each time step, each cell follows the same transition rules and transitions to the next state according to the state distribution of its neighbors. In 1966, von Neumann proposed early cellular automata to study automata systems with organism-general, self-replicating properties. With the deepening of research, cellular automata theory and life games have been widely studied and applied in the fields of physical simulation, sociological simulation, biological research and artificial life. "The Game of Life" is a famous two-dimensional cellular automaton proposed by John Conway in 1970 (Gardner, M. (1970). Mathematical games: The fantastic combinations of John Conway's new solitaire game "life". Scientific American ( Vol.223, pp.120-123).).). This work aims to find simple rules that can generate complex behaviors, his rules use Moore neighborhoods (8-neighborhoods) and binary cell states (life-death), state transitions. The construction of the dynamic cloud of this method is based on the idea that cellular automata carry out morphological evolution over time.

The traditional volume cloud rendering method mostly uses fractal noise to construct the cloud density field.

SUMMARY OF THE INVENTION

In view of the technical problems existing in the prior art, the purpose of the present invention is to provide a real-time dynamic cloud layer rendering method and system based on cellular automata. The present invention introduces a cloud layer distribution texture that can be predefined and interactively operated by a user, and realizes the dynamic change of cloud layer distribution by evolving the texture through cellular automata. The method constructs the cloud density field of the volume cloud by distributing texture and fractal noise, and performs dynamic step ray integration based on the density field envelope to realize volume rendering.

The cloud layer rendering method proposed by the present invention is divided into two parts as a whole: cloud layer distribution and texture evolution driven by cellular automata and cloud layer rendering driven by volume rendering. For the part of cloud layer distribution texture, this system embodies the triviality of distribution texture evolution, and realizes the dynamic change of cloud layer by using general cellular automata without physical features. ) can be combined to generate various special effects. At the same time, the system also has good scalability, and its discrete maintenance and collapse processing of different types of cells makes it possible to use a variety of cloud systems with different laws to evolve simultaneously. In the volume rendering part of the cloud layer, the method uses fractal Brownian noise to obtain the details of the cloud layer, and focuses on optimizing the efficiency of the volume rendering integral, so that the algorithm achieves a certain balance in performance and effect.

The technical scheme of the present invention is:

A real-time dynamic cloud layer rendering method based on cellular automata, the steps of which include:

1) A cellular automaton that generates dynamic clouds. The cellular automaton uses Moore's neighborhood as a dead-alive decision rule for cell neighborhoods and the game of life, that is, for a target cell, different state transition methods are used according to its current state. , where the state transition rule Rule={B0,B1,...,B8,S0,S1,...,S8}, B0-B8 is the state transition rule of a dead cell when the number of live cells in the neighborhood is 0-8, S0- S8 is the state transition rule corresponding to living cells;

2) The cellular automaton establishes the data structure of the cellular automaton according to the global texture of the input initial low-resolution image, as the cell evolution texture of each frame changing with time sequence; the data structure includes the global array cellMap and each life system, different life systems correspond to different regions in the global texture; a set of cell coordinates and vitality information corresponding to each region are determined according to the state transition rules and pixel values, and stored in the life system corresponding to each region; Each pixel corresponds to a cell, and the pixel value corresponds to the vitality of the cell; the global array cellMap stores the cell state information corresponding to each pixel in the current frame; wherein the cellular automaton is based on the state transition rule Rule corresponding to each living system Calculate the cell changes in the next frame of the corresponding life system; when all the life systems are calculated, update the global array cellMap according to the current cell information of the next frame, and then traverse all the life systems to obtain the living cells owned by each life system and record and store them into cellList;

3) smooth and interpolate the cell evolution texture of each frame obtained in step 2) to obtain a large-size texture of the corresponding frame;

4) superimposing the large-size texture corresponding to each frame and fractal noise to generate cloud layer details, and calculating the value of the density field at the corresponding point of each texture element;

5) Sampling a volume cloud formed by a plurality of cloud clusters through a step-by-step state transition method of a variable-length integral state machine;

6) Calculate the scattering effect of the point light source on the cloud layer through Beer's law and the Henyey-Greenstein image function, and finally render the realistic rendering of the cloud layer.

f为任意形式的转移函数。Further, the state transition rule refers to determining the state transition function of the state of cell i at the next moment according to the current state of cell i and the state of cell j in its neighborhood; the state transition function is:

f is a transfer function of any form.

Further, a boundary constraint is set for the living system, and the boundary constraint is: according to the distance between the cells in the living system and the center of the living system, the cells are isolated or linearly attenuated.

Further, the living system supports random "seeding" within a certain radius, that is, new cells with a certain vitality are directly generated at random positions of the living system.

Further, in step 3), the image obtained by smoothing the cell evolution texture of each frame obtained in step 2) and the image obtained by interpolation and amplification processing are fused with the image obtained by interpolating and smoothing a prefabricated high-resolution image to obtain a corresponding image. Large size texture for frames.

其中，D_g为噪声全局卷动,W_i为第i层噪声的振幅，F_i为第i层噪声的频率，m为层数，Noise()为用噪声纹理形式表示的噪声函数，x为位置作为噪声函数的变量。Further, the fractal noise is

Among them, D _g is the noise global scroll, Wi is the amplitude of the noise of the _i -th layer, F _i is the frequency of the noise of the i-th layer, m is the number of layers, Noise() is the noise function expressed in the form of noise texture, and x is the position as a variable of the noise function.

Further, in step 4), the method for calculating the value of the density field at the point corresponding to each texture element is:

1-1) The cloud layer constructed by volume rendering is modeled as a hemisphere with a flat bottom and an enlarged top. Set the cloud layer base plane height to 0, and calculate the cloud layer at this point P according to the actual thickness value p of the point P on the cloud layer distribution texture. The top P _Upper and the bottom P _Lower of the density field;

1-2) For the point at the position of point P and the height is h, first calculate its relative height ratio t; then calculate the cloud layer density P _den of this point according to the ratio t;

1-3) Multiply the density P _den by the overall transmittance constant transmittance to obtain the actual scattering rate α of the point.

Further, the method for drawing a volume cloud is: firstly, a cloud layer envelope grid is generated according to the cloud layer distribution texture, and then starting from the cloud layer envelope grid, the volume cloud is drawn based on a step-by-step state transition method of a variable-length integral state machine; wherein, The step-by-step state transition method based on the variable-length integral state machine is:

2-1) Divide the step of the integral position into a large step FAST_STEP and a small step SLOW_STEP; set state 0 to mean that no cloud is encountered, and perform FAST_STEP with a large step at this time; set state 1 to the previous step FAST_STEP encounters a cloud , then perform small step SLOW_STEP; set state 2 to be already in the cloud, then perform small step SLOW_STEP; set state 3 to reach the upper limit of the number of small steps, then only perform FAST_STEP until all steps are exhausted;

2-2) When the current new position cloud density field after FAST_STEP is not 0, the state machine transfers from state 0 to state 1; when it is in state 1 and the current new position density field after the last SLOW_STEP is not 0, Transfer from state 1 to state 2; when it is in state 2, and the current new position density field after the last SLOW_STEP is 0, it is considered that it has left the cloud layer, and it transfers from state 2 to state 0; when the number of SLOW_STEP reaches the upper limit, unconditional Transition to state 3.

Further, for each sampling point P on the integration path, the scattering rate α of the point P is calculated as the opacity of the point P; then the color of the point P is premultiplied by the opacity of the point P, and then the The transparency blending mode is blended as RGB color values.

Compared with the prior art, the positive effects of the present invention are:

Different from the traditional method, this method introduces a cloud layer distribution texture that can be defined and interactively operated by the user, and fuses fractal noise on the basis of the texture to generate a cloud layer density field. In order to realize the changing effects of different types of clouds, this method uses cellular automata to dynamically evolve the above-mentioned cloud distribution textures. Therefore, the method of the present invention has the advantages of strong controllability, and can realize the changing effects of various types of cloud layers, and the effects of real-time rendering are rich and diverse.

Compared with the traditional static sky cloud layer representation and rendering method, the present invention has the advantages of the cloud layer volume rendering method, that is, it has the ability of dynamic evolution: through the evolution of the cellular automaton and the multi-level translation of the cloud layer distribution texture, the method And the system can freely evolve cloud distribution and achieve better dynamic effects. In this process, adjusting the rules of cellular automata can obtain rich evolutionary law effects. In addition, the volume rendering method proposed in the present invention has stronger expressiveness for the volume sense of mid- and low-altitude cloud layers, can dynamically change illumination, and can realize continuous and seamless weather and time change by dynamically adjusting the color of the light source and the base color.

Compared with the traditional volume rendering method, the cloud layer distribution of the present invention has higher controllability, and the flexible combination of cellular automata, pre-rendered texture and post-processing can realize special dynamics and different types of cloud layer effects that cannot be reflected by simple noise.

Description of drawings

FIG. 1 is a flow chart of the method of the present invention.

Figure 2 is a structural diagram of the cellular automata system.

Figure 3 is an example of fixed-step ray marching (Ray Marching) sampling.

Figure 4 is a grid diagram of the cloud envelope.

Figure 5 is a variable-length integration state machine.

Detailed ways

The present invention will be described in further detail below through specific embodiments and accompanying drawings.

The basic flow of this method is shown in Figure 1:

1. Cellular automata generation of dynamic clouds

For the evolution of cloud layer distribution texture, the present invention proposes a compound cellular automaton that can simultaneously evolve different rule systems and maintain their interactions (corresponding to the "life system" and "time evolution" modules in the flowchart). It is worth noting that the architecture of the cellular automaton is not limited to a specific evolutionary rule, and multiple systems evolving in the same rule space can have completely different characteristics.

1.1 Rule Definition

Although the evolution process of "Game of Life" has good chaotic characteristics, its "dead or alive" cell transformation makes the local features of the overall image change drastically and has poor stability, which is not suitable for direct use as a cloud layer distribution texture. The basic rule proposed by the present invention is an improvement of the basic rule of "Game of Life". The rule continues to use the classic Moore neighborhood (8-neighborhood) as the cell neighborhood and the dead-alive decision rule of the game of life, that is, for a specific cell, different state transition methods are used according to its current dead/alive state. A state transition rule of the present invention can be represented by the following set of values:

即一个细胞在t+1时刻的状态为t时刻的邻域状态组合，称为细胞自动机的局部映射或局部规则。在本发明中，状态转移规则可以为任意定义的规则，即f可以为任意形式的转移函数。Rule={B0,B1,…,B8,S0,S1,…,S8}, where B0-B8 is the state transition rule of a dead cell when the number of live cells in the neighborhood is 0-8, and S0-S8 is a live cell corresponding state transition rules. The state transition rule refers to the state transition function that determines the state of the cell at the next moment according to the current state of the cell and the state of the cells in its neighborhood; the state transition rule can be written as

That is, the state of a cell at time t+1 is the neighborhood state combination at time t, which is called the local map or local rule of cellular automata. In the present invention, the state transition rule can be an arbitrarily defined rule, that is, f can be a transition function in any form.

In the method of the present invention, the binary dead/live (0/1) of each cell is replaced by "vitality" represented by 0-255, which corresponds to the luminance value range of one channel in the 8-bit image. In the present invention, all cells with "vitality" (that is, the brightness value in the cloud layer distribution texture) greater than zero are regarded as "live", and the "dead/live" in the above cell state transition rules are also transformed into cells within the range of -255 to 255. Integer. The cellular automata designed in this way can obtain more detailed and controllable evolution by adjusting a wider range of parameters. For image processing, the cells here correspond to the pixels in the image, that is, each pixel is a cell, and the pixel value corresponds to the vitality of the cell.

1.2 Organization of cells and living systems

Traditional cellular automata are implemented by directly storing the cell state in the global grid array. This implementation is simple and simple, but it is difficult to deal with the simultaneous evolution of cells with different rules. The method proposed in the present invention stores the coordinates and vitality information of a group of cells with the above state transition rules in a specific "life system", and the entire cellular automata system represented by the global texture (global array cellMap) is composed of several "life systems". The system” simultaneously evolves and superimposes. The overall logic of the system is shown in Figure 2.

The input data of this system is a low-resolution grayscale image (global texture). The resolution of the texture image is usually 128*128. The data structure of the cellular automaton established based on this grayscale image includes the global array cellMap and Each life system, each life system can divide the entire grayscale image into different areas, the areas can overlap, and all areas can not completely cover the entire image. Each region can be used as the original cell data for the evolution of a lifesystem. Each living system that may have different rules stores the living cells owned by that system in its variable-length array cellList. The stepping cycle of each living system consists of the following two steps:

1) At the beginning of each frame, the global cellMap stores the cell dead/live information of each point on the global regular grid of this frame. First, for each living system, the next frame of cell changes is calculated according to the state transition rule. This calculation will traverse the 8-neighborhood of all living cells in the living system at this moment and obtain the number of living cells in the neighborhood from the global cellMap.

2) When all the living systems are calculated, refresh and write the global cellMap according to the cell information of the next frame just calculated, traverse all the living systems again, obtain the living cells owned by each living system, and store the records in the cellList. This process can get the cell dead/live information on the global regular grid in the next frame.

This calculation preserves the interaction between different regular cells, and does not need to traverse the entire regular grid when the number of cells is small. In addition, "living systems" that encapsulate cell communities with different evolution rules can provide us with more specific means of cell control; the evolution rules (state transfer functions, rules) used by each living system are different. The present invention firstly introduces a system boundary constraint that cuts off or linearly decays according to the distance between cells and the center of the living system. The system using the boundary constraint can dynamically simulate a "piece of cloud" within a certain radius, and the center of such a living system can be translated. Manually control the movement trend of this cloud. The living system also supports random "seeding" within a certain radius, that is, new cells with a certain vitality are directly generated at random positions in the living system. For some rules with weak expansion characteristics, this design can maintain the vitality of the entire system; to an empty system Seeding cells in the medium can also achieve the generation of new cloud sources at specified locations. The design of this part is scalable, and users can write corresponding seeding and attenuation rules according to actual needs to achieve specific needs.

2. Image post-processing and interactive evolution

The present invention is a method and system proposed for the dynamic change process and rendering of dynamically changing cloud layers (corresponding to the "high-resolution interpolation smoothing" and "interactive image overlay and fusion" modules in the flowchart). The resolution of the 128*128 cell evolution texture obtained by the cellular automaton evolution is low. The system first blurs the image, smoothes it, and interpolates it to a large-scale texture of 512*512. At this moment and the previous moment ( frame) to obtain the actual cloud distribution texture used by volume rendering. It is worth noting that modifying the number of iterations and sampling radius of the blur can adjust the sharpness and radian of the cloud boundary, which will be further detailed in the volume rendering section.

The smooth 512*512 texture of dynamic interpolation can be used in volume rendering as cloud layer distribution texture, but the present invention considers higher controllability of cloud layer configuration, and additionally introduces the following two post-processing and interactive evolution steps:

1) Start the evolution from the prefabricated distribution texture of the shape: the user can prefabricate a 128*128 initial state of the cellular automaton, and completely customize the shape of the cloud layer at the beginning of the evolution. This method traverses all the pixels of the 128*128 prefab texture at the beginning of evolution, adding all pixels with non-zero brightness to a special starting life system. The system can use certain cellular automata rules, or it can use completely different special rules to treat each cell as just a "pixel" for digital image processing such as point processing. These "pixels" will still be regarded as living cells by other living systems and normally undergo mixed evolution, and the flexible application of the various schemes described above can achieve several different effects. After the low-resolution image of 128*128 is evolved by cellular automata, the high-resolution image of 512*512 is obtained by high-resolution interpolation smoothing operation.

2) Directly process the final texture: the user can directly perform interactive drawing overlay on the smoothed 512*512 texture, and use the interactive image overlay fusion operation to achieve the fusion with the 512*512 image obtained by high-resolution interpolation and smoothing. These processes do not affect the actual behavior of cellular automata, and are very effective in realizing effects that are relatively "independent" from cloud evolution, such as aircraft wake clouds and the generation of "holes" in clouds.

The above interaction and post-processing steps further illustrate the realization of the “ordinary” cellular automaton of the present invention—evolution pays more attention to cloud layers with strong controllability and customizable evolution rules, rather than relying on specific physical properties or cell behavior.

3. Construction of cloud volume density field

This part corresponds to the "Superimposed Fractal Noise" and "Cloud Density Field Construction" modules in the flowchart. Before obtaining the path integral required for volume rendering, the cloud density at any coordinate in the integral space needs to be described first. This calculation starts from the 512*512 cloud layer distribution texture obtained in the previous step. First, the 512*512 texture and fractal noise are superimposed to generate cloud layer details, and then the value of the density field at the corresponding point of each texture element is calculated accordingly.

3.1 Fractal noise calculation

The edge details of the cloud layer are obtained by superimposing the noise texture through fractal Brownian motion, that is, more and more fractal details are obtained by superimposing multiple layers of basic noise textures with frequency multiplication and decreasing amplitude:

Among them, D _g is the noise global scroll, Wi is the amplitude of the _i -th layer of noise, F _i is the frequency of the i-th layer of noise, Noise() is the noise function, and x is the position as a function variable.

The present invention realizes that four layers of fractal noise are superimposed in total:

F _i takes 1, 3, 9, and 27 in turn.

Wi takes 0.5, 0.25, 0.125, and _0.0625 in turn.

For each position in space, its 3D coordinates are split and summed to get the UV coordinates sampled on the 2D texture. In cloud evolution, the present system scrolls noise along three dimensions to achieve changes in cloud detail beyond cellular automata evolution. After obtaining the fractal noise intensity N, the actual thickness p of the cloud layer at any point P on the cloud layer distribution texture can be calculated:

p= _plum ·N

where p _lum is the brightness of any pixel point P of the cloud layer distribution texture calculated in the previous step.

3.2 Density field calculation

According to the morphological characteristics of clouds in nature, the present invention will model the clouds constructed by volume rendering as a hemisphere with a flat bottom and an enlarged top. It is advisable to specify that the height of the cloud layer reference plane is 0, and calculate the top P _Upper and bottom P _Lower of the cloud layer density field at this point P according to the actual thickness value p of the point P on the cloud layer distribution texture:

P _Upper =C·p

P _Lower =-0.3C·p

Among them, C is the cloud layer thickness parameter, and -0.3 is the shrinkage coefficient of the bottom surface compared with the top surface. Modifying these constants controls the overall top and bottom thickness of the cloud layer.

P _Upper and P _Lower describe the upper and lower bounds of the cloud density field at the point P. It is generally believed that the density at the edge of the cloud layer is lower and the density at the center is higher. For a point located at the position of point P and the height is h, first calculate its relative height ratio t:

Then calculate the cloud density of the point according to the ratio t:

where smoothstep is a cubic interpolation function:

smoothstep(min, max, p)=-2t ³ +3t ² ,

For the cloud layer with small difference between P _Upper and P _Lower , and the overall thin cloud layer, perform another interpolation to smooth the rendering effect of thin cloud:

P _den =P _den ·smoothstep(0, 1.8, P _Upper -P _Lower ), if(P _Upper -P _Lower )≤18

The 1.8 in the formula is the threshold for the thin cloud layer.

Finally, multiply the density P _den by the overall transmittance constant to obtain the actual scattering rate α at that point:

α=P _den ·transmittance

The overall opacity of the cloud layer can be adjusted by adjusting the overall transmittance constant transmittance. The selection of this parameter transmittance will be discussed further in the path integration strategy in the next step.

4 Cloud Volume Rendering Credits

This section corresponds to the Building Envelope Mesh, Variable Length Integral with Step State Transition, and Transparency Calculation and Blending modules in the flowchart. The volume cloud effect uses the Ray Marching algorithm to draw clouds with a strong sense of volume, such as stratus, cumulus, and cumulonimbus. These clouds are relatively low in height and mostly in the form of clumps, with well-defined boundaries and striking contrast between light and dark.

4.1 Overview of Basic Path Integral Methods

The basis of the Ray Marching algorithm for volume rendering is to start from the viewpoint and gradually sample and accumulate the calculation results along the line of sight. Figure 3 depicts a typical simple Ray Marching algorithm. This method starts from a plane in front of the viewpoint. The color calculation of each fragment is obtained by the path integration with a fixed number of times. Yuan's light path.

The simple Ray Marching algorithm of fixed degree is easy to implement, but has a series of problems:

1) Inefficiency. All sampling along the light path not covered by clouds in the screen is invalid, as is the bulk sampling between two clouds.

2) The aliasing is obvious. The potential consequence of wasting a large number of samples is that the actual effective number of samples is not enough to generate a smooth high-quality image, resulting in banding and aliasing, and for thin clouds, visual errors such as cloud disconnection and disappearance may occur.

Using the full-screen Ray Marching algorithm with a fixed number of steps, when the cloud layer area is large, even if the entire optical path is sampled 256 times per fragment, banding and aliasing caused by obvious uneven sampling can still be observed.

4.2 Integral strategy of the present invention

In order to solve many problems of full-screen path integration with a fixed number of steps, the present invention mainly proposes two methods: firstly, a cloud layer envelope grid is constructed, and then a variable-length strategy is used to carry out the integration from the envelope.

4.2.1 Building an envelope mesh

The path integration from the viewpoint may waste a large number of sampling points before reaching the cloud area, and it is completely ineffective for the sampling in the area without cloud layer. After the cloud envelope mesh is constructed, the starting point of the path integration from the fragments on the mesh will only fall near the cloud layer. The system constructs the envelope mesh through the 512*512 cloud layer distribution texture generated in the previous steps. Since the brightness of the superimposed fractal noise and the distribution texture is always less than or equal to the distribution texture itself, the texture actually describes the possible envelope area of the cloud layer.

The envelope uses a 129*129 square grid with a cloud distribution texture downscaled to 128*128. First traverse the texture after post-processing, find all pixels with brightness greater than zero, record the generated vertices corresponding to these pixels, and then generate the corresponding vertex index and triangle index. For each square area, its opposite sides always connect the two vertices with the largest height interpolation.

The cloud envelope mesh generated according to the cloud layer distribution texture is shown in Figure 4.

4.2.2 Variable length integral and step state transition

When doing path integration, we want to reduce unnecessary sampling as much as possible. Since volume clouds are mostly aggregated into cloud clusters and cloud bands, the idea of variable-length integration is to increase the step size when the integration path is outside the cloud, and reduce the step size and accurately accumulate the results when the integration path is outside the cloud. Envelope grid representation, determined to be inside/outside the cloud by judging inside/outside the envelope grid). The present invention proposes a step-by-step state transition method based on a variable-length integral state machine, which is the state machine and state transition shown in FIG. 5 .

The step of the integral position is divided into a large step (FAST_STEP) and a small step (SLOW_STEP).

Status 0: Cloud not encountered. At this point, a FAST_STEP with a large step size is performed.

State 1: The previous step FAST_STEP encountered a cloud. At this time, a small step SLOW_STEP is performed.

Status 2: Already in the cloud. At this time, a small step SLOW_STEP is performed.

Status 3: The maximum number of small steps has been reached. At this time, the cloud conditions on the route are no longer considered, and only FAST_STEP is performed until all steps are exhausted.

The key state transition timings are:

A: When the cloud density field at the current new position after FAST_STEP is not 0, the state machine transitions from state 0 to state 1. Since the previous FAST_STEP step size is large, in order to ensure that the next SLOW_STEP captures all the details of the cloud layer, at this time, take a step back FAST_STEP on the integration path.

B: When in state 1 and the current new position density field after the last SLOW_STEP is not 0, transition from state 1 to state 2.

C: When it is in state 2, and the current new position density field after the last SLOW_STEP is 0, it is considered that it has left the cloud layer, and it is transferred from state 2 to state 0.

D: When the number of SLOW_STEP reaches the upper limit, unconditionally transfer to state 3.

The variable-step path integral designed in this way can better capture the details of various cloud layers. Even with very thin clouds, as soon as one step of FAST_STEP hits any area where the density field is not 0, the algorithm switches to SLOW_STEP to sample all areas with high precision.

4.2.3 Transparency calculation and blending

Before introducing the lighting model, we first describe how to accumulate transparency in the cloud density field. For a fragment, its color and transparency are achieved by computing and blending all sample points along the integration path. For each sampling point on the integration path, calculate the scattering rate α of the point (as described in 3.2) as the opacity of the point, and the result calculated according to the lighting model as the RGB color value. The blending between sampling points includes two parts: color value blending and transparency blending. For the sampling point P, the color calculation and transparency calculation value of this point are recorded as:

P _sample =(P _rgb ,P _a )

Among them, P _rgb is the color of the point, and _Pa is the opacity of the point.

For each fragment, color and opacity accumulation starts from the initial value (0,0,0,0).

For the accumulated color S and the new sample point P _sample , use alpha pre-multiplied (pre-multipliedalpha) for mixing:

S' _rgb =S _rgb +(1.0-S _a )·P _rgb ·P _a

S' _a =S _a +(1.0-S _a )·P _a

The above formula can also be written in a unified form:

S'=S+(1.0-S _a )·P _{pre-mult; plied}

That is, the color of P is first multiplied by the opacity of P, and then mixed using the premultiplied opacity blending mode. This blending is done on every sample, and the final result is a premultiplied alpha fragment color that is blended with the sky background in the same way (Add, One OneMinusSrcAlpha). At the same time, once the opacity Sa of _a certain fragment reaches 1 (that is, it is completely opaque), the path integration can be terminated in advance, and the cloud volume rendering integration is completed.

4.2.4 Parameter selection and optimization

For several parameters mentioned above, the value selection has the following characteristics:

Overall transmittance transmittance: The larger the value is without affecting the visual effect, the more likely the integration will end earlier, but if the value is too large, the cloud layer will be too stiff.

大步长FAST_STEP：次数过少可能使稀薄的云层断开，若步长过大，在SLOW_STEP用尽后视觉效果下降明显。

Large step size FAST_STEP: If the number of times is too small, the thin clouds may be disconnected. If the step size is too large, the visual effect will drop significantly after the SLOW_STEP is exhausted.

小步长SLOW_STEP：次数过少、提前切换至大步长对视觉效果影响较大。

Small step size SLOW_STEP: Too few times and switching to a large step size in advance will have a greater impact on the visual effect.

光照采样次数LSTEP：该采样将在下一步骤中详细介绍。由于该采样位于内层循环中，次数稍多便会显著影响性能。

Lighting Sampling LSTEP: This sampling will be detailed in the next step. Since this sampling is in an inner loop, a little more can significantly impact performance.

The path integral is expected to end as early as possible to reduce the amount of loops. After debugging and weighing, the effect of the present invention uses an overall light transmittance of 0.22, a maximum of 64 FAST_STEP, a maximum of 64 SLOW_STEP, and 4 lighting samples per sampling point.

5. Lighting model and lighting calculation

This section describes how to calculate the light color value at each sampling time (each sampling point on the integration path), corresponding to the "light calculation" module in the flowchart. When a specific light enters the cloud (the cloud represented by the cloud envelope grid), after multiple scattering by water droplets and ice crystals, some of the light is absorbed by the cloud, some of the light is scattered to other directions, and some of the light is scattered in other directions. The scattering part of the added to its light path. In non-real-time fields such as film and television special effects, some methods are used to accurately calculate the multiple scattering that occurs in the cloud, but the calculation amount that increases exponentially with the number of scattering is difficult to meet the real-time requirements. The illumination model used in the present invention uses Beer's law and the Henyey-Greenstein image function to calculate the single scattering effect of the point light source on the cloud layer.

5.1 Beer's Law

Beer's law describes the relationship between the absorbance and the thickness and concentration of the medium when light passes through an absorbing medium. It is expressed as:

为透过介质的光通量，

为抵达介质的光通量，τ为光深度(optical depth)。本方法中，通过在每个采样点额外做一组朝向光源的路径积分，并将该路径积分上的散射率α求和作为该采样点的光深度τ：where T is the transmittance,

is the luminous flux through the medium,

is the luminous flux reaching the medium, τ is the optical depth. In this method, an additional set of path integrals toward the light source is performed at each sampling point, and the scattering rate α on the path integral is summed as the optical depth τ of the sampling point:

Beer's Law states that as the depth of light increases, the intensity of light transmitted through the sampling point decreases exponentially. In the above integral, y describes the integral distance towards the light source. Bringing the result obtained by this integration into the luminance calculation, the path integral equation can be expressed as:

This set of additional path integrals is called Lighting Samples (LSTEP). The integral is used to determine what thickness of cloud layer the light source passes through before reaching the sampling point, and correspondingly attenuate the light intensity according to Beer's law. Due to being in the inner layer of the path integration loop, this sampling is performed only a few times (4 times in the present invention), and is terminated as soon as it leaves the cloud layer (the sampled scattering rate α is zero).

5.2 Henyey-Greenstein phase function

Beer's law can better calculate the influence of light received by clouds of different thicknesses, but its scattering calculation is isotropic, and the Mie Scattering mainly occurs in water droplets and ice crystals in clouds has significant anisotropic characteristics, Many meteorological phenomena, such as fog bows and solar rings, are related to the anisotropic characteristics of Mie scattering. A more common phenomenon is silver lining around the edges of backlit clouds.

This phenomenon is caused by the dominant forward scattering peak in Mie scattering: the cloud layer is thinner at the edge of the cloud layer, and the strong forward scattering makes the light path direction almost unchanged and the intensity attenuation is small. Since the phase function of Mie scattering is relatively complex, the Henyey-Greenstein phase function is usually used in applications to approximate its scattering distribution, which is expressed as:

Where g is the anisotropy coefficient, θ is the angle between the incident light and the outgoing light, the larger the value of g, the more concentrated the distribution of the phase function is in the forward scattering part where the angle θ is 0.

When calculating the light color at each sampling point, the influence of the Henyey-Greenstein phase function is calculated according to the angle between the line of sight vector (that is, the integration direction) of the point and the light source vector, and multiplied with the color value of Beer's law, the path integral equation changes for:

Illumination calculations using the Henyey-Greenstein phase function, notice a significant silver lining phenomenon at the edge of the cloud near the light source.

5.3 Lighting parameter adjustment

The cloud layer color input from the outside of the system includes two parts, the environment color BaseColor of the cloud layer and the light source color LightColor before the lighting calculation is performed. The final color of each sampling point is obtained by adding the base color and the light source color, and the part not affected by the light source (such as the back of a thick cloud) is the ambient color. By adjusting the color of the environment and the color of the light source, the system can realize various weather effects with different colors in different periods of the day.

The above embodiments are only used to illustrate the technical solutions of the present invention rather than limit them. Those of ordinary skill in the art can modify or equivalently replace the technical solutions of the present invention without departing from the spirit and scope of the present invention. The scope of protection shall be subject to what is stated in the claims.

Claims (9)

1. A real-time dynamic cloud layer drawing method based on a cellular automaton comprises the following steps:

1) generating a cellular automaton of a dynamic cloud layer, wherein the cellular automaton adopts a Moore neighborhood as a dead-live judgment Rule of a cell neighborhood and a life game, namely different state transition modes are used for a target cell according to different current states of the target cell, wherein the state transition Rule is { B0, B1, …, B8, S0, S1, … and S8}, B0-B8 is a state transition Rule of a dead cell when the number of the living cells in the neighborhood is 0-8, and S0-S8 are state transition rules corresponding to the living cells;

2) the cellular automaton establishes a data structure of the cellular automaton according to the input global texture of the initial low-resolution image, and the data structure is used as the cellular evolution texture of each frame which changes along with the sequence; the data structure comprises a global array cellMap and various life systems, wherein different life systems correspond to different areas in the global texture; determining a group of cell coordinates and vitality information corresponding to each area according to the state transition rule and the pixel value, and storing the cell coordinates and the vitality information into a life system corresponding to each area; each pixel in the image corresponds to a cell, and the pixel value corresponds to the vitality of the cell; the global array cellMap stores cell state information corresponding to each pixel in the current frame; the cellular automaton calculates the cell change of the next frame of the corresponding life system according to the state transition Rule corresponding to each life system; after all the life systems are calculated, updating the global array cellMap according to the next frame of cell information obtained currently, then traversing all the life systems, obtaining the living cells owned by each life system, and recording and storing the living cells into the cellList;

3) smoothing and interpolating the cell evolution texture of each frame obtained in the step 2) to amplify to obtain a large-size texture of the corresponding frame;

4) superposing the large-size texture corresponding to each frame with fractal noise to generate cloud layer details, and calculating the value of a density field at a point corresponding to each texture element;

5) sampling a volume cloud formed by a plurality of cloud clusters through a stepping state transition method of a variable-length integrating state machine;

6) and calculating the scattering effect of the point light source on the cloud layer through the beer law and a Henyey-Greenstein image function, and rendering a realistic effect graph of the cloud layer.

2. The method of claim 1, wherein the state transition rule is a state transition function for determining the state of the cell i at the next time according to the current state of the cell i and the states of the cells j in the neighborhood of the cell i; a state transfer function of

f is a transfer function of any form.

3. The method of claim 1, wherein a boundary constraint is set for the living system, the boundary constraint being: the cells are isolated or linearly attenuated according to the distance from the cells in the living system to the center of the living system.

4. The method of claim 1, wherein the life system supports random "seeding" within a set radius, i.e., the direct generation of viable new cells at random locations of the life system.

5. The method as claimed in claim 1, wherein in step 3), the image obtained by smoothing the cell evolution texture of each frame obtained in step 2) and performing interpolation and amplification processing is fused with the image obtained by performing interpolation and smoothing on a pre-prepared high resolution image to obtain the large-size texture of the corresponding frame.

6. The method of claim 1, in which the fractal noise is

Wherein D is_gFor global scrolling of noise, W_iAmplitude of layer i noise, F_iM is the number of layers, Noise () is a Noise function expressed in the form of a Noise texture, and x is a variable of the Noise function.

7. The method according to claim 1 or 6, wherein in step 4), the method for calculating the value of the corresponding point of the density field at each texture element comprises:

1-1) modeling a cloud layer constructed for volume rendering into a hemisphere with a flat bottom end and an enlarged top end, setting the height of a cloud layer reference plane as 0, and calculating the top end P of a cloud layer density field of a point P according to the actual thickness value P of the point P on the cloud layer distribution texture_UpperAnd bottom end P_Lower；

1-2) for a point with the height h and at the position of the point P, firstly calculating the relative height ratio t of the point; then calculating the cloud layer density P of the point according to the proportion t_den；

1-3) reduction of the density P_denThe actual scattering ratio a at this point is obtained by multiplying the overall transmission constant transmittince.

8. The method of claim 1 or 6, wherein the method of rendering the volume cloud is: firstly, generating a cloud layer envelope grid according to cloud layer distribution textures, and then drawing a volume cloud based on a stepping state transfer method of a variable-length integral state machine from the cloud layer envelope grid; the stepping state transition method based on the variable length integral state machine comprises the following steps:

2-1) dividing the stepping of the integral position into a large STEP FAST _ STEP and a small STEP SLOW _ STEP; setting the state 0 as not meeting the cloud, and performing FAST _ STEP with a large STEP size at the moment; setting a state 1 as that the last STEP FAST _ STEP meets the cloud, and then performing small STEP SLOW _ STEP; setting a state 2 as being in the cloud, and performing small STEP length SLOW _ STEP at the moment; setting a state 3 as that the upper limit of the small STEP size number is reached, and only performing FAST _ STEP till all the STEP sizes are exhausted;

2-2) when the current new position cloud layer density field after FAST _ STEP is not 0, the state machine is transferred from state 0 to state 1; when the current new position density field is not 0 after last SLOW _ STEP and is in the state 1, the state is transferred to the state 2 from the state 1; when the current new position density field is 0 after last SLOW _ STEP in the state 2, the cloud layer is considered to be left, and the state 2 is transferred to the state 0; when the SLOW _ STEP number reaches the upper limit, the system unconditionally transitions to state 3.

9. The method according to claim 8, wherein for each sampling point P on the integral path, the scattering rate α of the point P is calculated as the opacity of the point P; the color of point P is then pre-multiplied by the opacity of point P and then blended using a blend mode of pre-multiplying opacity as the RGB color value.

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