improve mpcg
This improved performance significantly in some small test systems.
This commit is contained in:
Irlan
parent
b202988d82
commit
079e6eddca
@ -124,8 +124,7 @@ struct b3SpringClothStep
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u32 iterations;
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};
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// This class implements a cloth. It treats cloth as a collection
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// of masses connected by springs.
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// A cloth it treats cloth as a collection of masses connected by springs.
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// Large time steps can be taken.
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// If accuracy and stability are required, not performance,
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// you can use this class instead of using b3Cloth.
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@ -177,7 +176,7 @@ public:
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// Return the kinetic (or dynamic) energy in this system.
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float32 GetEnergy() const;
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// Return the tension forces (due to springs) of each point mass.
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// Return the tension forces (due to springs) acting at each point mass.
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// Units are kg * m / s^2
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void GetTension(b3Array<b3Vec3>& tensions) const;
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@ -222,6 +221,8 @@ protected:
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float32* m_m;
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float32* m_inv_m;
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b3Vec3* m_y;
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b3Vec3* m_z;
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b3Vec3* m_x0;
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b3MassType* m_types;
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u32 m_massCount;
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@ -28,6 +28,7 @@ class b3SpringCloth;
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class b3StackAllocator;
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struct b3DenseVec3;
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struct b3DiagMat33;
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struct b3SparseMat33;
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struct b3MassContact;
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@ -58,15 +59,15 @@ private:
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// Compute A and b in Ax = b
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void Compute_A_b(b3SparseMat33& A, b3DenseVec3& b) const;
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// Compute the initial guess for the iterative solver.
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void Compute_x0(b3DenseVec3& x0);
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// Compute S.
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void Compute_S(b3DiagMat33& S);
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// Compute the constraint projection matrix S.
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void Compute_S(b3Mat33* S);
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// Compute z.
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void Compute_z(b3DenseVec3& z);
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// Solve Ax = b.
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// Output x and the residual error f = Ax - b ~ 0.
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void Solve(b3DenseVec3& x0, b3DenseVec3& f, u32& iterations, const b3SparseMat33& A, const b3DenseVec3& b, const b3Mat33* S) const;
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void Solve(b3DenseVec3& x, b3DenseVec3& f, u32& iterations, const b3SparseMat33& A, const b3DenseVec3& b, const b3DiagMat33& S, const b3DenseVec3& z, const b3DenseVec3& y) const;
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b3SpringCloth * m_cloth;
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float32 m_h;
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@ -82,6 +83,8 @@ private:
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float32* m_m;
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float32* m_inv_m;
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b3Vec3* m_y;
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b3Vec3* m_z;
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b3Vec3* m_x0;
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b3MassType* m_types;
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u32 m_massCount;
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@ -43,6 +43,8 @@ b3SpringCloth::b3SpringCloth()
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m_v = nullptr;
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m_f = nullptr;
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m_y = nullptr;
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m_z = nullptr;
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m_x0 = nullptr;
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m_m = nullptr;
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m_inv_m = nullptr;
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m_types = nullptr;
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@ -67,6 +69,8 @@ b3SpringCloth::~b3SpringCloth()
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b3Free(m_inv_m);
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b3Free(m_m);
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b3Free(m_y);
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b3Free(m_z);
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b3Free(m_x0);
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b3Free(m_types);
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b3Free(m_contacts);
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b3Free(m_springs);
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@ -212,6 +216,8 @@ void b3SpringCloth::Initialize(const b3SpringClothDef& def)
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m_m = (float32*)b3Alloc(m_massCount * sizeof(float32));
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m_inv_m = (float32*)b3Alloc(m_massCount * sizeof(float32));
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m_y = (b3Vec3*)b3Alloc(m_massCount * sizeof(b3Vec3));
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m_z = (b3Vec3*)b3Alloc(m_massCount * sizeof(b3Vec3));
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m_x0 = (b3Vec3*)b3Alloc(m_massCount * sizeof(b3Vec3));
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m_types = (b3MassType*)b3Alloc(m_massCount * sizeof(b3MassType));
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m_contacts = (b3MassContact*)b3Alloc(m_massCount * sizeof(b3MassContact));
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@ -230,6 +236,8 @@ void b3SpringCloth::Initialize(const b3SpringClothDef& def)
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m_m[i] = 0.0f;
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m_inv_m[i] = 0.0f;
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m_y[i].SetZero();
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m_z[i].SetZero();
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m_x0[i].SetZero();
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m_types[i] = b3MassType::e_staticMass;
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}
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@ -615,7 +623,6 @@ void b3SpringCloth::Step(float32 dt)
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}
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// Integrate
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b3SpringSolverDef solverDef;
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solverDef.cloth = this;
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solverDef.dt = dt;
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@ -19,12 +19,17 @@
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#include <bounce/dynamics/cloth/spring_solver.h>
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#include <bounce/dynamics/cloth/spring_cloth.h>
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#include <bounce/dynamics/cloth/dense_vec3.h>
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#include <bounce/dynamics/cloth/diag_mat33.h>
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#include <bounce/dynamics/cloth/sparse_mat33.h>
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#include <bounce/dynamics/shapes/shape.h>
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#include <bounce/common/memory/stack_allocator.h>
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// Here, we solve Ax = b using the Modified Conjugate Gradient method.
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// This work is based on the paper "Large Steps in Cloth Simulation - David Baraff, Andrew Witkin".
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// Here, we solve Ax = b using the Modified Preconditioned Conjugate Gradient (MPCG) algorithm.
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// described in the paper:
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// "Large Steps in Cloth Simulation - David Baraff, Andrew Witkin".
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// Some improvements for the original MPCG algorithm are described in the paper:
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// "On the modified conjugate gradient method in cloth simulation - Uri M. Ascher, Eddy Boxerman".
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b3SpringSolver::b3SpringSolver(const b3SpringSolverDef& def)
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{
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@ -42,6 +47,8 @@ b3SpringSolver::b3SpringSolver(const b3SpringSolverDef& def)
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m_m = m_cloth->m_m;
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m_inv_m = m_cloth->m_inv_m;
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m_y = m_cloth->m_y;
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m_z = m_cloth->m_y;
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m_x0 = m_cloth->m_x0;
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m_types = m_cloth->m_types;
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m_massCount = m_cloth->m_massCount;
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@ -58,8 +65,27 @@ b3SpringSolver::~b3SpringSolver()
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}
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static B3_FORCE_INLINE b3SparseMat33 b3AllocSparse(b3StackAllocator* allocator, u32 M, u32 N)
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{
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u32 size = M * N;
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b3Mat33* elements = (b3Mat33*)allocator->Allocate(size * sizeof(b3Mat33));
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u32* cols = (u32*)allocator->Allocate(size * sizeof(u32));
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u32* row_ptrs = (u32*)allocator->Allocate((M + 1) * sizeof(u32));
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return b3SparseMat33(M, N, size, elements, row_ptrs, cols);
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}
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static B3_FORCE_INLINE void b3FreeSparse(b3SparseMat33& matrix, b3StackAllocator* allocator)
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{
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allocator->Free(matrix.row_ptrs);
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allocator->Free(matrix.cols);
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allocator->Free(matrix.values);
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}
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void b3SpringSolver::Solve(b3DenseVec3& f)
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{
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B3_PROFILE("Solve");
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//
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m_Jx = (b3Mat33*)m_allocator->Allocate(m_springCount * sizeof(b3Mat33));
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m_Jv = (b3Mat33*)m_allocator->Allocate(m_springCount * sizeof(b3Mat33));
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@ -73,34 +99,42 @@ void b3SpringSolver::Solve(b3DenseVec3& f)
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// A = M - h * dfdv - h * h * dfdx
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// b = h * (f0 + h * dfdx * v0 + dfdx * y)
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// Allocate matrix memory for the worst case.
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u32 nzCount = m_massCount * m_massCount;
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b3Mat33* nzElements = (b3Mat33*)m_allocator->Allocate(nzCount * sizeof(b3Mat33));
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u32* nzColumns = (u32*)m_allocator->Allocate(nzCount * sizeof(u32));
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u32* rowPtrs = (u32*)m_allocator->Allocate((m_massCount + 1) * sizeof(u32));
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{
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b3SparseMat33 A(m_massCount, m_massCount, nzCount, nzElements, rowPtrs, nzColumns);
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// A
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b3SparseMat33 A = b3AllocSparse(m_allocator, m_massCount, m_massCount);
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//
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// b
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b3DenseVec3 b(m_massCount);
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// A, b
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Compute_A_b(A, b);
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// S
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b3DiagMat33 S(m_massCount);
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Compute_S(S);
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// z
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b3DenseVec3 z(m_massCount);
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Compute_z(z);
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// x0
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b3DenseVec3 x0(m_massCount);
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for (u32 i = 0; i < m_massCount; ++i)
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{
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x0[i] = m_x0[i];
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}
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// x
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b3DenseVec3 x(m_massCount);
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// x0
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Compute_x0(x);
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// S
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b3Mat33* S = (b3Mat33*)m_allocator->Allocate(m_massCount * sizeof(b3Mat33));
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Compute_S(S);
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// Solve Ax = b
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Solve(x, f, m_iterations, A, b, S);
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Solve(x, f, m_iterations, A, b, S, z, x0);
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// Store x0
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for (u32 i = 0; i < m_massCount; ++i)
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{
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m_x0[i] = x[i];
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}
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// Update state
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for (u32 i = 0; i < m_massCount; ++i)
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{
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@ -113,13 +147,9 @@ void b3SpringSolver::Solve(b3DenseVec3& f)
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m_x[i] += m_h * m_v[i] + m_y[i];
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}
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m_allocator->Free(S);
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b3FreeSparse(A, m_allocator);
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}
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m_allocator->Free(rowPtrs);
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m_allocator->Free(nzColumns);
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m_allocator->Free(nzElements);
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m_allocator->Free(m_Jv);
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m_allocator->Free(m_Jx);
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m_Jv = nullptr;
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@ -128,6 +158,7 @@ void b3SpringSolver::Solve(b3DenseVec3& f)
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#define B3_INDEX(i, j, size) (i + j * size)
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//
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static void b3SetZero(b3Vec3* out, u32 size)
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{
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for (u32 i = 0; i < size; ++i)
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@ -136,23 +167,16 @@ static void b3SetZero(b3Vec3* out, u32 size)
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}
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}
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//
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static void b3SetZero(b3Mat33* out, u32 size)
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{
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for (u32 i = 0; i < size * size; ++i)
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for (u32 i = 0; i < size; ++i)
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{
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out[i].SetZero();
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}
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}
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static void b3SetZero_Jacobian(b3Mat33* out, u32 springCount)
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{
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for (u32 i = 0; i < springCount; ++i)
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{
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out[i].SetZero();
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}
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}
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// J = dfdx or dvdx
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//
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static void b3Mul_Jacobian(b3Vec3* out, const b3Vec3* v, u32 massCount,
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const b3Mat33* J_ii, const b3Spring* springs, u32 springCount)
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{
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@ -177,8 +201,8 @@ static void b3Mul_Jacobian(b3Vec3* out, const b3Vec3* v, u32 massCount,
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void b3SpringSolver::ApplySpringForces()
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{
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// Zero Jacobians
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b3SetZero_Jacobian(m_Jx, m_springCount);
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b3SetZero_Jacobian(m_Jv, m_springCount);
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b3SetZero(m_Jx, m_springCount);
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b3SetZero(m_Jv, m_springCount);
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// Compute spring forces and Jacobians
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for (u32 i = 0; i < m_springCount; ++i)
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@ -249,10 +273,10 @@ void b3SpringSolver::Compute_A_b(b3SparseMat33& SA, b3DenseVec3& b) const
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{
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// Compute dfdx, dfdv
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b3Mat33* dfdx = (b3Mat33*)m_allocator->Allocate(m_massCount * m_massCount * sizeof(b3Mat33));
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b3SetZero(dfdx, m_massCount);
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b3SetZero(dfdx, m_massCount * m_massCount);
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b3Mat33* dfdv = (b3Mat33*)m_allocator->Allocate(m_massCount * m_massCount * sizeof(b3Mat33));
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b3SetZero(dfdv, m_massCount);
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b3SetZero(dfdv, m_massCount * m_massCount);
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for (u32 i = 0; i < m_springCount; ++i)
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{
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@ -286,14 +310,14 @@ void b3SpringSolver::Compute_A_b(b3SparseMat33& SA, b3DenseVec3& b) const
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// A = 0
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b3Mat33* A = (b3Mat33*)m_allocator->Allocate(m_massCount * m_massCount * sizeof(b3Mat33));
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b3SetZero(A, m_massCount);
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b3SetZero(A, m_massCount * m_massCount);
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// A += M
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for (u32 i = 0; i < m_massCount; ++i)
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{
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A[B3_INDEX(i, i, m_massCount)] += b3Diagonal(m_m[i]);
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}
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// A += - h * dfdv - h * h * dfdx
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for (u32 i = 0; i < m_massCount; ++i)
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{
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@ -359,12 +383,15 @@ void b3SpringSolver::Compute_A_b(b3SparseMat33& SA, b3DenseVec3& b) const
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m_allocator->Free(dfdx);
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}
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void b3SpringSolver::Compute_x0(b3DenseVec3& x0)
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void b3SpringSolver::Compute_z(b3DenseVec3& z)
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{
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x0.SetZero();
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for (u32 i = 0; i < m_massCount; ++i)
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{
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z[i] = m_z[i];
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}
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}
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void b3SpringSolver::Compute_S(b3Mat33* out)
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void b3SpringSolver::Compute_S(b3DiagMat33& out)
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{
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for (u32 i = 0; i < m_massCount; ++i)
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{
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@ -410,80 +437,58 @@ void b3SpringSolver::Compute_S(b3Mat33* out)
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}
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}
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// S * v
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static void b3Filter(b3DenseVec3& out,
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const b3DenseVec3& v, const b3Mat33* S, u32 massCount)
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void b3SpringSolver::Solve(b3DenseVec3& x, b3DenseVec3& f, u32& iterations,
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const b3SparseMat33& A, const b3DenseVec3& b, const b3DiagMat33& S, const b3DenseVec3& z, const b3DenseVec3& y) const
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{
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for (u32 i = 0; i < massCount; ++i)
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{
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out[i] = S[i] * v[i];
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}
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}
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void b3SpringSolver::Solve(b3DenseVec3& dv, b3DenseVec3& e, u32& iterations, const b3SparseMat33& A, const b3DenseVec3& b, const b3Mat33* S) const
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{
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b3DenseVec3 P(m_massCount);
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b3DenseVec3 inv_P(m_massCount);
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// Compute P, P^-1
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// P = diag(A)^-1
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// diag(A)
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b3Mat33* diagA = (b3Mat33*)m_allocator->Allocate(m_massCount * sizeof(b3Mat33));
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A.AssembleDiagonal(diagA);
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// P = diag(A)
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b3DiagMat33 inv_P(m_massCount);
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A.AssembleDiagonal(inv_P);
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// Invert
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for (u32 i = 0; i < m_massCount; ++i)
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{
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b3Mat33 D = diagA[i];
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b3Mat33& D = inv_P[i];
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// Sylvester Criterion to ensure PD-ness
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B3_ASSERT(b3Det(D.x, D.y, D.z) > B3_EPSILON);
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B3_ASSERT(D[0][0] != 0.0f);
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B3_ASSERT(D[1][1] != 0.0f);
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B3_ASSERT(D[2][2] != 0.0f);
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B3_ASSERT(D.x.x != 0.0f);
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float32 xx = 1.0f / D.x.x;
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P[i] = b3Vec3(1.0f / D[0][0], 1.0f / D[1][1], 1.0f / D[2][2]);
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inv_P[i] = b3Vec3(D[0][0], D[1][1], D[2][2]);
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B3_ASSERT(D.y.y != 0.0f);
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float32 yy = 1.0f / D.y.y;
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B3_ASSERT(D.z.z != 0.0f);
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float32 zz = 1.0f / D.z.z;
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D = b3Diagonal(xx, yy, zz);
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}
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m_allocator->Free(diagA);
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// I
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b3DiagMat33 I(m_massCount);
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I.SetIdentity();
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// delta0 = dot(filter(b), P * filter(b))
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b3DenseVec3 S_b(m_massCount);
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b3Filter(S_b, b, S, m_massCount);
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// x = S * y + (I - S) * z
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x = (S * y) + (I - S) * z;
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// P * filter(b)
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b3DenseVec3 P_S_b(m_massCount);
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for (u32 i = 0; i < m_massCount; ++i)
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{
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P_S_b[i][0] = P[i][0] * S_b[i][0];
|
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P_S_b[i][1] = P[i][1] * S_b[i][1];
|
||||
P_S_b[i][2] = P[i][2] * S_b[i][2];
|
||||
}
|
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// b^ = S * (b - A * (I - S) * z)
|
||||
b3DenseVec3 b_hat = S * (b - A * ((I - S) * z));
|
||||
|
||||
float32 delta0 = b3Dot(S_b, P_S_b);
|
||||
// b_delta = dot(b^, P^-1 * b_^)
|
||||
float32 b_delta = b3Dot(b_hat, inv_P * b_hat);
|
||||
|
||||
// r = filter(b - Adv)
|
||||
b3DenseVec3 r = b - A * dv;
|
||||
b3Filter(r, r, S, m_massCount);
|
||||
// r = S * (b - A * x)
|
||||
b3DenseVec3 r = S * (b - A * x);
|
||||
|
||||
// c = filter(P^-1 * r)
|
||||
b3DenseVec3 c(m_massCount);
|
||||
for (u32 i = 0; i < m_massCount; ++i)
|
||||
{
|
||||
c[i][0] = inv_P[i][0] * r[i][0];
|
||||
c[i][1] = inv_P[i][1] * r[i][1];
|
||||
c[i][2] = inv_P[i][2] * r[i][2];
|
||||
}
|
||||
b3Filter(c, c, S, m_massCount);
|
||||
// p = S * (P^-1 * r)
|
||||
b3DenseVec3 p = S * (inv_P * r);
|
||||
|
||||
// deltaNew = dot(r, c)
|
||||
float32 deltaNew = b3Dot(r, c);
|
||||
// deltaNew = dot(r, p)
|
||||
float32 deltaNew = b3Dot(r, p);
|
||||
B3_ASSERT(b3IsValid(deltaNew));
|
||||
|
||||
// Tolerance.
|
||||
// This is the main stopping criteria.
|
||||
// [0, 1]
|
||||
const float32 epsilon = 10.0f * B3_EPSILON;
|
||||
|
||||
@ -492,50 +497,41 @@ void b3SpringSolver::Solve(b3DenseVec3& dv, b3DenseVec3& e, u32& iterations, con
|
||||
|
||||
// Main iteration loop.
|
||||
u32 iter = 0;
|
||||
while (iter < maxIters && deltaNew > epsilon * epsilon * delta0)
|
||||
while (iter < maxIters && deltaNew > epsilon * epsilon * b_delta)
|
||||
{
|
||||
// q = filter(A * c)
|
||||
b3DenseVec3 q = A * c;
|
||||
b3Filter(q, q, S, m_massCount);
|
||||
// s = S(A * p)
|
||||
b3DenseVec3 s = S * (A * p);
|
||||
|
||||
// alpha = deltaNew / dot(c, q)
|
||||
float32 alpha = deltaNew / b3Dot(c, q);
|
||||
float32 alpha = deltaNew / b3Dot(p, s);
|
||||
|
||||
// dv = dv + alpha * c
|
||||
dv = dv + alpha * c;
|
||||
// x = x + alpha * p
|
||||
x = x + alpha * p;
|
||||
|
||||
// r = r - alpha * q
|
||||
r = r - alpha * q;
|
||||
|
||||
// s = inv_P * r
|
||||
b3DenseVec3 s(m_massCount);
|
||||
for (u32 i = 0; i < m_massCount; ++i)
|
||||
{
|
||||
s[i][0] = inv_P[i][0] * r[i][0];
|
||||
s[i][1] = inv_P[i][1] * r[i][1];
|
||||
s[i][2] = inv_P[i][2] * r[i][2];
|
||||
}
|
||||
// r = r - alpha * s
|
||||
r = r - alpha * s;
|
||||
|
||||
// h = inv_P * r
|
||||
b3DenseVec3 h = inv_P * r;
|
||||
|
||||
// deltaOld = deltaNew
|
||||
float32 deltaOld = deltaNew;
|
||||
|
||||
// deltaNew = dot(r, s)
|
||||
deltaNew = b3Dot(r, s);
|
||||
// deltaNew = dot(r, h)
|
||||
deltaNew = b3Dot(r, h);
|
||||
B3_ASSERT(b3IsValid(deltaNew));
|
||||
|
||||
// beta = deltaNew / deltaOld
|
||||
float32 beta = deltaNew / deltaOld;
|
||||
|
||||
// c = filter(s + beta * c)
|
||||
c = s + beta * c;
|
||||
b3Filter(c, c, S, m_massCount);
|
||||
// p = S * (h + beta * p)
|
||||
p = S * (h + beta * p);
|
||||
|
||||
++iter;
|
||||
}
|
||||
|
||||
iterations = iter;
|
||||
|
||||
// Residual error
|
||||
// f = A * x - b
|
||||
e = A * dv - b;
|
||||
// Residual
|
||||
f = A * x - b;
|
||||
}
|
||||
Loading…
x
Reference in New Issue
Block a user