[graphics] hair simulation in tressfx

reference：《GPU Pro5》Hair Simulation in TressFX

        The hair of the character is about 120000 root , Due to the high cost of rendering and the lack of real-time simulation technology , Presenting human hair in real-time video games has always been a challenge . therefore , Many artists and game developers have to choose other methods , For example, use simple polygons and textures .

        In this chapter , I will explain TressFX Hair simulation method in , This method has been used in recent Tomb Raider and AMD Rudy Use... In the demonstration .

        At the high end GPU in , It can simulate about... In less than a millisecond 19000 Contains 22 A line of ten thousand vertices .TressFX Designed for video games (video game) The development of , therefore , Performance is the highest concern of physical accuracy .

Simulation overview

        Developing TressFX When simulating , The main focus is to simulate molded hair , It's much harder than straight hair , Because he needs more powerful bending and twisting effects . No matter what kind of hairstyle , The hair of characters should be considered as non expandable . To simulate these three effects , There are usually two ways to express them , That is, rigid springs or constraints .

        stay VFX in , Rigid springs are commonly used in various simulations , Such as hair or clothes . however , For real-time physical simulation , The actual effect of rigid spring is poor , Because the integration of strong spring force is easy to make the mass spring damper system unstable , Unless you use a complex integration scheme , For example, implicit backward integrator （implicit backward integrator）. and , Stretching is difficult to handle in the same solver 、 Bend and twist the spring , Especially in GPU in . stay Tress in , All springs are replaced by hard constraints and soft constraints . For non scalability , We use a simple position based iterative distance constraint . For the sake of simplicity , Bending and twisting are seen as a single effect , Therefore, local and global shape constraints are used . Sometimes , We also use special constraints （ad-hoc） To handle fast-moving characters .

        In addition to bending and twisting effects , Other hair simulations are similar to cloth simulations . however , If you use GPU Calculation , Better for hair , Because there are many bunches , If the collision between hair bundles is not considered , They are independent of each other . And the topological order of vertex connection is direct . By using these points ,TressFX Can achieve hair bundles / Vertex level parallelism , Without complex data structures .

Definition

        Basically , Every hair is a polygonal line . When interpreting local shape constraints , Local and global terms are often used . The overall situation lies in the world framework , The part is located in the local frame , This area is attached to the starting point of the line segment .

        The vertex index starts from the root of the hair bundle attached to the scalp . Is the vertex in the current time step i The location of . The first 0 Time is static , We use the right superscript to make it clear （ namely ). ad locum , When we explain the algorithm , We only focus on one set of hair bundles . therefore , Vertex Index i Always unique .

        If you need to specify which coordinate system we use , You can use the left superscript to specify it （ namely It means a vertex i In local frame i-1 The position in the current time step defined in ）. After defining the position in the world coordinate system , We can delete the frame index （ namely ）

        In terms of transformation , We Defined as including rotation Move peacefully Complete transformation of . It is from Convert to , In order to make

        Because the vertices in the hair bundle are carefully indexed , Therefore, the following equation holds ：

        

        In this chapter , We call For local transformation , For global transformation . At the top 0 For example , Local transformation and global transformation are the same , namely

        In the figure 1.2 in , Local frames are defined on each vertex . vector and Is the vertex under the current time step i The base vector of the local frame . It is simply defined as The normalized vector of . More specifically ,.

        In the figure 1.3 in , The base vector is displayed in red 、 Yellow and blue .

        To describe the head transformation , We use , It turns its head from idle State transition to current state , As input of user or preset animation .

        

        

integral

        In order to integrate the motion of hair dynamics , We use Verlet Integral scheme , Because it is related to explicit Euler The method is relatively simple and shows good numerical stability . In this step, an external force will be applied , Such as gravity . The damping effect can be simulated by multiplying the damping coefficient by the speed . We only integrate particles with non-zero inverse mass . If the inverse mass is zero , We think it is immovable , Please attach an object to it （ For example, head ） Then update its location , Then skip the rest of these particles . We are the apex 0 and 1 Zero inverse masses are assigned , So they can animate as the head moves .

constraint

        There are three constraints .

       ELC（ Edge length constraint ） Is a hard constraint that simulates non stretchable hair ;

        LSC( Local shape constraints ） It is a soft constraint of bending and twisting ;

        GSC( Global shape constraints ） yes LSC A supplement to , And it helps to retain the initial hair shape at a very low computational cost ;

Length constraint

       ELC Force the edge to keep it idle Length in state . chart 1.4 Shows how to calculate the position correction for each edge . For the sake of simplicity , We set equal mass for the first two vertices . To apply this constraint in parallel , We created two batches , Each batch is processed independently , Therefore, the vertex position can be updated safely without conflict .

        

        In the hair , It is easy to create two batches as even edge index groups and odd edge index groups . We run the first batch , Then run the second batch . This method provides us with good parallelism . Unfortunately , The compromise scheme has poor convergence , So we iterate it many times , So that all edges reach their rest length .

        stay Tomb Raider in , The protagonist can move and turn quickly . Basically , Users can generate strong acceleration , This leads to long hair elongation .

        under these circumstances , Even if the iteration exceeds 20 Time ,ELC It can't converge well . By measuring the length of the first movable edge and comparing it with the rest length , Convergence can be easily checked .

        To solve this problem , Let's switch to abhocyu constraint , This constraint updates only one vertex position , Pictured 1.4 Medium pi+. By updating a vertex position of each edge starting from the root of the hair clump , We can simply satisfy ELC.

        however , This method will add extra energy to the system , And lead to unnatural simulation results , To eliminate this excess energy , We added high damping . therefore , We only use this method when we really need it , Interested readers can refer to Muller, In order to have a deeper understanding of this problem and different solutions .

Global constraints

        GSC The main idea is simple . We take the initial hair shape as the target , And try to move the vertex to the shape , It is similar to shape matching .

        The easiest way to understand is to think of the initial hair shape as a cage , and GSC Forced to trap hair .

        Before the simulation starts , We save vertices P The rest of the position . take idle Position is used as the target position , To apply global shape constraints .

        In the formula 1.1 in ,SG Is the rigid body coefficient of the overall shape constraint , Range from 0 To 1. If SG by 0, It doesn't work , If 1, The hair becomes completely stiff , And freeze to initial shape .

         

        in many instances , We are in part of the hair band （ For example, close to the root ） Apply global shape constraints on . We can also gradually reduce from the root to the end of the hair SG. This is because the hair seems to be stiffer near the root . Again , It can maintain the hair style more effectively , It will not bring unnecessary additional stiffness to the whole hair simulation .

        The benefits of global shape constraints are , It keeps the overall shape at the minimum cost . Combine local shape constraints , It takes almost no time to complete the simulation , And there will be no visual interference at the beginning of the simulation .

        Designers can expect that the hair shape they create will be the initial shape .

        The overall shape limit can also ensure that during the fast-moving game , Hair will not tangle into strange shapes .

Local constraints

        Even if GSC Can effectively manage hair shape , We still need a method to simulate the bending and twisting forces of a single hair bundle . In real-time cloth simulation , The bending effect is usually expressed as a soft distance constraint connecting two vertices across the curved edge . You can also use the same method to produce a bending effect on your hair , But twisting is not easy .

        For simplicity and high performance , We combine bending and twisting effects into a soft distance constraint . To define this constraint , Pictured 1.2 and 1.3 Shown , Use the local frame to calculate the target location .

        The formula （1.2） Because its subscripts and superscripts may look complex , But the concept is different from ELC identical . The first equation calculates i-1di, It is the distance between the current position and its target position . Left superscript i-1 Indicates that those positions are defined in the local frame .

        Last , When we calculate the position correction , We actually use world space , But the equation （1.2） Written in local space to simplify it ：

       

        Such as ELC Described in , We divide the position correction by the mass ratio , And apply it to two connected vertices （i-1Pi-1 and i-1Pi）. ad locum , We have assumed that all masses are equal , So the ratio is 1/2.

Wind and collision

        Wind is an important part of simulation , Because it makes the hair interact with the environment , Even in idle It can also give the game characters a sense of dynamics in the state . In order to produce more random effects and prevent caking , Convert a single wind input to four conical directions , As shown in the figure ：

        

        Modulate the size of the wind by using the sine function and the number of frames , As shown below ：

        

        The formula shows how to calculate the wind force and apply it to the location update .W1,W2,W3 and W4 It's four wind vectors , And for more randomization ：

       

        In the first equation 20 It's an arbitrary choice ,W Is one of the four wind vectors a Interpolated wind vector ,Δt It's the time step .

        Wind is imposed after shape constraints , Not part of the integral , Because the shape constraint is too strong and if it is applied as an external force in the integration process , May offset its impact . The key to calculating wind is to create random directions and periods . therefore , It is more like an empirical parameter than physically correct .

assets

        After creating the hair clump as a spline , Customize python The script will export it as a polyline . stay TressFX In the demonstration , Hair is divided into front , Top , Side and ponytail four groups , Each group is saved as a separate file .

      

GPU Realization

        TressFX stay DirectX 11 Calculation shaders are used in GPU Run hair simulation in .

        There are five computational shader cores . detailed list 1.1 Shows Simulate Hair_A kernel , The kernel handles integration and GSC. The kernel calculates a vertex for each thread . because GROUP_SIZE Defined as 64, therefore , If a thread group has 16 vertices , Then a thread group can calculate four hairs . Use maxPossibleVertsInStrand, You can control how many lines can be calculated in a thread group . because GROUP_SIZE by 64, So the maximum number of vertices in a harness is 64. By way of GROUP_SIZE Change to 128 or 256, We can have more vertices . however , More vertices may take longer to execute ELC and LSC. therefore , It is recommended to use 16 or 32 vertices .

        

        detailed list 1.2 Shows SimulateHair_A kernel , It performs LSC. The kernel calculates one thread for each thread , So there is a for loop . strandType It's a variable , Display the group to which the chain belongs . such , We can assign different simulation parameters to hair groups , Such as stiffness or damping .

       SimulateHair_C The kernel calculates a vertex for each thread , perform ELC And apply wind . Last ,SimulateHair_D Be responsible for collision and calculate the tangent of the segment of the rendering pipeline .

        If you should ignore the hair simulation ,SkipSimulateHair The kernel implements this . This can also be done by setting 1.0 Of GSC Stiffness to complete , But this will waste a lot of unnecessary operations .SkipSimulateHair The kernel only applies the head transform to vertices , And make the hair move rigidly .

summary

       TressFX Hair simulation of has been optimized for the implementation of the game in many aspects , For example, use shape constraints , And the limit on the number of vertices of each hair bundle . therefore , Need to understand the basic method , To maximize its performance and quality .