Flex library

所有粒子和约束以flat-array的形式一次同时传入解算器，使用SOA数据布局。
SOA是什么？

struct {
    uint8_t r, g, b;
} AoS[N];

struct {
    uint8_t r[N];
    uint8_t g[N];
    uint8_t b[N];
} SoA;

Code Demo

#include <NvFlex.h>
NvFlexLibrary* library = NvFlexInit();
NvFlexSolver* solver = NvFlexCreateSolver(library);

// param2:element count
// param3:stride
NvFlexBuffer* particleBuffer = NvlexAllocBuffer(library, n, sizeof(Vec4), eNvFlexBufferHost);

while(true){
    // map buffers for reading / writing
    // get the address whitch can be accessed by CPU
    // this call will be blocked until other transfers
    float4* particles = (float4*)NvlexMap(particles, eNvFlexMapWait);

    // spawn (user method)
    SpawnParticles(particles, velocities, phases);

    // render (user method)
    RenderParticles(particles, velocities, phases);

    // unmap buffers,after CPU has finished writing buffers
    NvFlexUnmap(particleBuffer);

    // write to device (async) 
    NvFlexSetParticles(particleBuffer, n);

    // tick update the solver
    NvFlexUpdateSolver(solver, dt, 1, false);

    // read back (async) retreve data from FLEX
    NvFlexGetParticles(particleBuffer, n);
}
NvFlexFreeBuffer(particleBuffer);
NvFlexDestroySolver(solver);
NvFlexShutdown(library);

Particles

通过位置、速度、质量以及所处阶段来对粒子进行描述。质量存储为质量的倒数，并和位置存储在一起[x, y, z, 1/m]。

spawn particles

for (int i=0; i < n; ++i)
{
        particles[i] = RandomSpawnPosition();
        velocities[i] = RandomSpawnVelocity();
        phases[i] = NvFlexMakePhase(0, eNvFlexPhaseSelfCollide);
}

对数据进行初始化需要按照下图所示的过程：

Radius

使用NvFlexParams::rasius进行设置。

Phase

一个用32位掩码进行表示的量，由组ID和各种粒子标记组成：通过NvFlexMakePhase 设置

eNvFlexPhaseGroupMask 低24位

不同组的粒子总是会进行碰撞解算，而且默认情况下同一组粒子不会进行碰撞。

eFlexPhaseSelfCollide

使同一组的粒子可以进行碰撞 self collision

eNvFlexPhaseFluid

使粒子产生流体物理属性例如：fluid density constraints, cohesion, surface tension effects

粒子的碰撞状态通过NvFlexMakePhase函数设置，可以设置为一下几个：

eNvFlexPhaseSelfCollide：粒子将会与同一组的粒子发生碰撞
eNvFlexPhaseSelfCollideFilter：忽略小于一定半径之内的碰撞
eNvFlexPhaseFluid：生成流体密度约束

Active Set

每一个解算器solver有一个支持粒子的数量上限，可以选择部分粒子处于激活状态，而处于非激活状态的粒子只会消耗很小的计算量。使用NvFlexSetActive(solver, activeBuffer, 10)设置激活组。

运行原理

如何解算
flex中的解算并不是将每个约束单独计算，而是全部设置在NvFlexParams中，再与solver绑定，GPU根据params和分别设置buffer进行解算，例如：

//CPU端写入数据
mapbuffer();
gbuffer.position => set in CPU
unmapbuffer();
//设置进flex
NvFlexSetParticles(g_solver, g_buffers->positions.buffer, NULL);
NvFlexSetVelocities(g_solver, g_buffers->velocities.buffer, NULL);
NvFlexSetPhases(g_solver, g_buffers->phases.buffer, NULL);
NvFlexSetActive(g_solver, g_buffers->activeIndices.buffer, NULL);
NvFlexSetActiveCount(g_solver, g_buffers->activeIndices.size());
//设置状态
NvFlexSetParams(g_solver, &g_params);
//进行FLex模拟
NvFlexUpdateSolver(g_solver, g_dt, g_numSubsteps, g_profile;
//取回数据
NvFlexGetParticles(g_solver, g_buffers->positions.buffer, NULL);		
NvFlexGetVelocities(g_solver, g_buffers->velocities.buffer, NULL);

Constraints

首先需要记住的一点是，FLEX中除了静态碰撞，其余都是粒子，所以position,velocity这些属性是，所有粒子都会记录的，但是还会附加其他的一些buffer来记录部分粒子的特殊性质，这些buffer的标记方式，通过记录粒子的indice来标记。例如之后的rigidbody。

Fluid

设置NvFlexParams::radius和NvFlexParams::fluidRestDistance，保持二者之比为2：1，一下为流体的四个重要属性

Cohesion凝聚力：内部相邻分子之间的相互吸引力
Surface Tension表面张力：由内聚力而产生
Vorticity Confinement向粒子增加旋转力
Adhesion粘着力
Viscosity阻尼
Solid Pressure增加粒子收到的固体表面的力
Surface Drag
Buoyancy浮力
Anisotropy Scale
Smoothing 流体并不需要额外设置参数（在早些版本中可以在NvFlexParams中存在标记fluid的变量，之后的版本中没有了）

如何设置数据

设置粒子的positions,velocities,phases,activeIndices(对应position中粒子的索引，这里所有的buffer相同的索引对应的都是同一个粒子的属性)
获取粒子数目，设置可支持的最大粒子数
设置solverDesc

string

在设置完数据之后设置NvFlexSetSprings

如何设置数据

设置string的索引（两两一对），设置长度和硬度（长度是索引数的0.5倍）
注意设置索引的基础上是position数组已经被设置了
cloth

可以使用string网格完成约束，但是在EXT库中提供了NvFlexExtCreateClothFromMesh进行设置。使用NvFlexSetDynamicTriangles可以增加更多的cloth属性
lift/drag
wind
smooth normal: 可以通过NvFlexGetNormals获得

rigid body

也是通过粒子进行粒子的模拟。可以通过三角网格获取粒子集合（参考函数NvFlexExtCreateRigidFromMesh）。通过NvFlexSetRigids添加rigid粒子约束。
当模拟时间步长过大时，会产生interlocked现象。 PBD则使用SDF来解决这个问题

NvFlexSetRigids(g_solver, 
g_buffers->rigidOffsets.buffer, //记录各个rigid在rigidIndices中的末尾边界
g_buffers->rigidIndices.buffer, //position中对应粒子的索引
g_buffers->rigidLocalPositions.buffer, 
g_buffers->rigidLocalNormals.buffer, 
g_buffers->rigidCoefficients.buffer, 
g_buffers->rigidPlasticThresholds.buffer, //设置plastic 属性
g_buffers->rigidPlasticCreeps.buffer, 
g_buffers->rigidRotations.buffer, 
g_buffers->rigidTranslations.buffer, 
g_buffers->rigidOffsets.size() - 1,     //因为只要存在就会预先push进一个0,所以实际长度要-1
g_buffers->rigidIndices.size());

与其他的效果结合
1.1 在cloth上增加rigid约束
1.2 在fluid上增加rigid约束
在较早版本的flex中，支持从shape创建粒子CreateParticleShape，接受mesh，体素化后转化为粒子。新的版本中也有这样的函数。参数中可以设置是否使其具有rigid的性质，可以设置rigid的rigidStiffness，理解为恢复为原本shape的速度（弹性程度）

collision

Flex支持静态碰撞几何（球，胶囊，平面，凸体，三角网格，有向距离场）

union NvFlexCollisionGeometry
{
        NvFlexSphereGeometry sphere;
        NvFlexCapsuleGeometry capsule;
        NvFlexBoxGeometry box;
        NvFlexConvexMeshGeometry convexMesh;
        NvFlexTriangleMeshGeometry triMesh;
        NvFlexSDFGeometry sdf;
};

通过NvFlexSetShapes生成静态碰撞体。

虽然是静态碰撞体，但是在更新的时候还是可以通过访问

g_buffers->shapeGeometry.buffer,
g_buffers->shapePositions.buffer,
g_buffers->shapeRotations.buffer,
g_buffers->shapePrevPositions.buffer,
g_buffers->shapePrevRotations.buffer,
g_buffers->shapeFlags.buffer,

这些字段来进行位置的修改，修改完成后，一定要再次使用NvFlexSetShapes上传到flex

code demo

//定义四个缓冲
NvFlexCollisionGeometry* geometry = (NvFlexCollisionGeometry*)NvFlexMap(geometryBuffer, 0);
float4* positions = (float4*)NvFlexMap(positionsBuffer, 0);
quat* rotations = (quat*)NvFlexMap(rotationsBuffer, 0);
int* flags = (int*)NvFlexMap(flagsBuffer, 0);

// 第一个缓冲中定义一个球儿
flags[0] = NvFlexMakeShapeFlags(eNvFlexShapeSphere, false);
geometry[0].sphere.radius = radius;
positions[0] = float3(0.0f);
rotations[0] = quat(0.0f);

// 创建一个mesh
NvFlexTriangleMeshId mesh = NvFlexCreateTriangleMesh();
//绑定数据到id
NvFlexUpdateTriangleMesh(lib, mesh, vertices, indices, numVertices, numTriangles, NULL, NULL);

// 在第二个缓冲中创建一个三角网格
flags[1] = NvFlexMakeShapeFlags(eNvFlexShapeTriangleMesh, false);
geometry[1].triMesh.mesh = mesh;
geometry[1].triMesh.scale[0] = 1.0f;
geometry[1].triMesh.scale[1] = 1.0f;
geometry[1].triMesh.scale[2] = 1.0f;
positions[1] = float3(0.0f, 100.0f, 0.0f);
rotations[1] = quat(0.0f);

// unmap buffers
NvFlexUnmap(geometryBuffer, 0);
NvFlexUnmap(positionsBuffer, 0);
NvFlexUnmap(rotationsBuffer, 0);
NvFlexUnmap(flagsBuffer, 0);

// send shapes to Flex
NvFlexSetShapes(solver, geometry, positions, rotation, NULL, NULL, flags, 2);

SDF 有向距离场

通过NvFlexCreateSDF生成。

NvFlexExtAsset

记录了一批粒子和约束信息

struct NvFlexExtAsset
{	
	// particles
	float* particles;				//!< Local space particle positions, x,y,z,1/mass
	int numParticles;				//!< Number of particles
	int maxParticles;				//!< Maximum number of particles, allows extra space for tearable assets which duplicate particles

	// springs
	int* springIndices;				//!< Spring indices
	float* springCoefficients;		//!< Spring coefficients
	float* springRestLengths;		//!< Spring rest-lengths
	int numSprings;					//!< Number of springs

	// shapes
	int* shapeIndices;				//!< The indices of the shape matching constraints
	int numShapeIndices;			//!< Total number of indices for shape constraints	
	int* shapeOffsets;				//!< Each entry stores the end of the shape's indices in the indices array (exclusive prefix sum of shape lengths)
	float* shapeCoefficients;		//!< The stiffness coefficient for each shape
	float* shapeCenters;			//!< The position of the center of mass of each shape, an array of vec3s mNumShapes in length
	int numShapes;					//!< The number of shape matching constraints

	// plastic deformation
	float* shapePlasticThresholds;	//!< The plastic threshold coefficient for each shape
	float* shapePlasticCreeps;		//!< The plastic creep coefficient for each shape

	// faces for cloth
	int* triangleIndices;			//!< Indexed triangle mesh indices for clothing
	int numTriangles;				//!< Number of triangles

	// inflatable params
	bool inflatable;				//!< Whether an inflatable constraint should be added
	float inflatableVolume;			//!< The rest volume for the inflatable constraint
	float inflatablePressure;		//!< How much over the rest volume the inflatable should attempt to maintain
	float inflatableStiffness;		//!< How stiff the inflatable is
};

以rigidbody为例：调用NvFlexExtCreateRigidFromMesh后，shapes 就代表了粒子集合信息（不要和静态碰撞体的shape搞混）。

numShape: rigid的个数
numShapeIndices: rigid代表的粒子索引数组的长度
shapeIndices：存储粒子索引数组的首地址
shapeOffsets：这一个shape占据的偏移量（之后会累加在总粒子数组上，得到这个rigid的粒子数组边界）
shapeCoefficients：物理参数
shapeCenters：中心
以上这些参数，都需要在手动添加到position,rigidOffset,rigidTranslation,等参数中，再调用flexSetRigidBody.

注意

一定要区分rigid body和shape 的关系
向FLEX中设置参数的例子
```c NvFlexSetParams(g_flex, &g_params); NvFlexSetParticles(g_flex, g_buffers->positions.buffer, numParticles); NvFlexSetVelocities(g_flex, g_buffers->velocities.buffer, numParticles); NvFlexSetNormals(g_flex, g_buffers->normals.buffer, numParticles); NvFlexSetPhases(g_flex, g_buffers->phases.buffer, g_buffers->phases.size()); NvFlexSetRestParticles(g_flex, g_buffers->restPositions.buffer, g_buffers->restPositions.size());

NvFlexSetActive(g_flex, g_buffers->activeIndices.buffer, numParticles);

// springs if (g_buffers->springIndices.size()) { assert((g_buffers->springIndices.size() & 1) == 0); assert((g_buffers->springIndices.size() / 2) == g_buffers->springLengths.size());

NvFlexSetSprings(g_flex, g_buffers->springIndices.buffer, g_buffers->springLengths.buffer, g_buffers->springStiffness.buffer, g_buffers->springLengths.size()); }

// rigids if (g_buffers->rigidOffsets.size()) { NvFlexSetRigids(g_flex, g_buffers->rigidOffsets.buffer, g_buffers->rigidIndices.buffer, g_buffers->rigidLocalPositions.buffer, g_buffers->rigidLocalNormals.buffer, g_buffers->rigidCoefficients.buffer, g_buffers->rigidRotations.buffer, g_buffers->rigidTranslations.buffer, g_buffers->rigidOffsets.size() - 1, g_buffers->rigidIndices.size()); }

// inflatables if (g_buffers->inflatableTriOffsets.size()) { NvFlexSetInflatables(g_flex, g_buffers->inflatableTriOffsets.buffer, g_buffers->inflatableTriCounts.buffer, g_buffers->inflatableVolumes.buffer, g_buffers->inflatablePressures.buffer, g_buffers->inflatableCoefficients.buffer, g_buffers->inflatableTriOffsets.size()); }

// dynamic triangles if (g_buffers->triangles.size()) { NvFlexSetDynamicTriangles(g_flex, g_buffers->triangles.buffer, g_buffers->triangleNormals.buffer, g_buffers->triangles.size() / 3); }

// collision shapes if (g_buffers->shapeFlags.size()) { NvFlexSetShapes( g_flex, g_buffers->shapeGeometry.buffer, g_buffers->shapePositions.buffer, g_buffers->shapeRotations.buffer, g_buffers->shapePrevPositions.buffer, g_buffers->shapePrevRotations.buffer, g_buffers->shapeFlags.buffer, int(g_buffers->shapeFlags.size())); } ```

rigidbody约束中，rigidOffsets的数量是rigidbody的数量加一，并且第一个必须是0，每一个表示rigidbody中包含的粒子数。indice数组则记录了所有构成rigidbody的粒子在position中的索引（全局索引）。相当于，offset指定了这个rigidbody的粒子在indice中的区间，再从这个区间中得到在position中的索引，二级索引

FLEX使用教程

Nvidia 位置动力学模拟工具

Flex library

Code Demo

Particles

spawn particles

Radius

Phase

eNvFlexPhaseGroupMask 低24位

eFlexPhaseSelfCollide

eNvFlexPhaseFluid

Active Set

运行原理

Constraints

Fluid

如何设置数据

string

如何设置数据

cloth

rigid body

collision

code demo

SDF 有向距离场

NvFlexExtAsset

注意

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