softbody_pbd_cuda.cu

#include "cuda_runtime.h"
#include "device_launch_parameters.h"

#include <iostream>
#include <vector>
#include <fstream>
#include <string>
#include <sstream>
#include <cassert>
#include <set>

template <typename T>
struct Vec2 {
	T x, y;
	__host__ __device__ Vec2() :x(0), y(0) {}
	__host__ __device__ Vec2(T x, T y) : x(x), y(y) {}
	__host__ __device__ T operator[](int idx) { if (idx == 0)return x; else return y; }
	__host__ __device__ Vec2 operator+(const Vec2& v) const { return Vec2(x + v.x, y + v.y); }
	__host__ __device__ Vec2 operator-(const Vec2& v) const { return Vec2(x - v.x, y - v.y); }
	__host__ __device__ Vec2& operator+=(const Vec2& v) { x += v.x; y += v.y; return *this; }
	__host__ __device__ Vec2& operator-=(const Vec2& v) { x -= v.x; y -= v.y; return *this; }
	__host__ __device__ Vec2& operator*=(T s) { x *= s; y *= s; return *this; }
	__host__ __device__ Vec2& operator/=(T s) { x /= s; y /= s; return *this; }
	__host__ __device__ T dot(const Vec2& v) const { return x * v.x + y * v.y; }
	__host__ __device__ T cross(const Vec2& v) const { return x * v.y - y * v.x; }
	__host__ __device__ T norm() const { return sqrt(x * x + y * y); }
	__host__ __device__ T square_norm() const { return x * x + y * y; }
	__host__ __device__ Vec2 normalized() const { return *this / norm(); }
};

template <typename T>
__host__ __device__ Vec2<T> operator*(T s, const Vec2<T>& v) { return Vec2<T>(v.x * s, v.y * s); }
template <typename T>
__host__ __device__ Vec2<T> operator/(T s, const Vec2<T>& v) { return Vec2<T>(v.x / s, v.y / s); }

template <typename T>
struct Vec3 {
	T x, y, z;
	__host__ __device__ Vec3() :x(0), y(0), z(0) {}
	__host__ __device__ Vec3(T x, T y, T z) : x(x), y(y), z(z) {}
	__host__ __device__ T operator[](int idx) { if (idx == 0)return x; else if (idx == 1) return y; else return z; }
	__host__ __device__ Vec3 operator+(const Vec3& v) const { return Vec3(x + v.x, y + v.y, z + v.z); }
	__host__ __device__ Vec3 operator-(const Vec3& v) const { return Vec3(x - v.x, y - v.y, z - v.z); }
	__host__ __device__ Vec3& operator+=(const Vec3& v) { x += v.x; y += v.y; z += v.z; return *this; }
	__host__ __device__ Vec3& operator-=(const Vec3& v) { x -= v.x; y -= v.y; z -= v.z; return *this; }
	__host__ __device__ Vec3& operator*=(T s) { x *= s; y *= s; z *= s; return *this; }
	__host__ __device__ Vec3& operator/=(T s) { x /= s; y /= s; z /= s; return *this; }
	__host__ __device__ T dot(const Vec3& v) const { return x * v.x + y * v.y + z * v.z; }
	__host__ __device__ Vec3 cross(const Vec3& v) const { return Vec3(y * v.z - z * v.y, z * v.x - x * v.z, x * v.y - y * v.x); }
	__host__ __device__ T norm() const { return sqrt(x * x + y * y + z * z); }
	__host__ __device__ T square_norm() const { return x * x + y * y + z * z; }
	__host__ __device__ Vec3 normalized() const { return *this / norm(); }
};
template <typename T>
__host__ __device__ Vec3<T> operator*(const Vec3<T>& v, T s) { return Vec3<T>(v.x * s, v.y * s, v.z * s); }
template <typename T>
__host__ __device__ Vec3<T> operator/(const Vec3<T>& v, T s) { return Vec3<T>(v.x / s, v.y / s, v.z / s); }
template <typename T>
__host__ __device__ Vec3<T> operator*(T s, const Vec3<T>& v) { return Vec3<T>(v.x * s, v.y * s, v.z * s); }
template <typename T>
__host__ __device__ Vec3<T> operator/(T s, const Vec3<T>& v) { return Vec3<T>(v.x / s, v.y / s, v.z / s); }


template <typename T>
struct Vec4 {
	int x, y, z, w;
	__host__ __device__ Vec4() :x(0), y(0), z(0), w(0) {}
	__host__ __device__ Vec4(int x, int y, int z, int w) : x(x), y(y), z(z), w(w) {}
};


using Real = float;
using Vec4i = Vec4<int>;
using Vec3f = Vec3<Real>;
using Vec3i = Vec3<int>;
using Vec2i = Vec2<int>;


class Softbody {
private:
	std::vector<Vec3f> pos_;
	std::vector<Vec3f> old_pos_;
	std::vector<Vec3f> predict_pos_;
	std::vector<Vec3f> vel_;
	std::vector<Real> w_;

	std::vector<Vec3i> faces_;
	std::vector<Vec2i> edges_;
	std::vector<Vec4i> tets_;

	std::vector<Real> rest_length_;
	std::vector<Real> rest_volume_;

	int num_vertices_{ 0 };
	int num_edges_{ 0 };
	int num_faces_{ 0 };
	int num_tets_{ 0 };

public:
	Real* d_pos;
	Real* d_old_pos;
	Real* d_predict_pos;
	Real* d_vels;
	Real* d_w;
	int* d_edges;
	int* d_tets;
	Real* d_rest_length;
	Real* d_rest_volume;

private:
	void read_node_file(const std::string node_file) {
		std::ifstream infile(node_file);
		std::string line;
		std::getline(infile, line);
		std::stringstream ss(line);
		int tmp1, tmp2, temp3;
		ss >> num_vertices_ >> tmp1 >> tmp2 >> temp3;
		while (std::getline(infile, line)) {
			if (line[0] == '#') continue;
			std::stringstream ss(line);
			int idx;
			Real a, b, c;
			ss >> idx >> a >> b >> c;
			pos_.push_back(Vec3f(a, b, c));
		}
		assert(pos_.size() == num_vertices_);
		infile.close();
	}
	void read_ele_file(const std::string ele_file) {
		std::ifstream infile(ele_file);
		std::string line;
		std::getline(infile, line);
		std::stringstream ss(line);
		int tmp1, tmp2;
		ss >> num_tets_ >> tmp1 >> tmp2;
		while (std::getline(infile, line)) {
			if (line[0] == '#') continue;
			std::stringstream ss(line);
			int idx, a, b, c, d;
			ss >> idx >> a >> b >> c >> d;
			tets_.push_back(Vec4i(a, b, c, d));
		}
		assert(num_tets_  == tets_.size());
		infile.close();
	}
	void read_face_file(const std::string face_file) {
		std::ifstream infile(face_file);
		std::string line;
		std::getline(infile, line);
		std::stringstream ss(line);
		int tmp1, tmp2;
		ss >> num_faces_ >> tmp1 >> tmp2;
		while (std::getline(infile, line)) {
			if (line[0] == '#') continue;
			std::stringstream ss(line);
			int idx, a, b, c;
			ss >> idx >> a >> b >> c;
			faces_.push_back(Vec3i(a, b, c));
		}
		assert(num_faces_ == faces_.size());
		infile.close();
	}
	void extract_edges() {
		std::set<std::pair<int, int>> edges;
		for (int i = 0; i < num_tets_; i++)
		{
			int dix0 = tets_[i].x, idx1 = tets_[i].y,  idx2 = tets_[i].z,  idx3 = tets_[i].w;
			edges.insert(std::make_pair(std::min(dix0, idx1), std::max(dix0, idx1)));
			edges.insert(std::make_pair(std::min(dix0, idx2), std::max(dix0, idx2)));
			edges.insert(std::make_pair(std::min(dix0, idx3), std::max(dix0, idx3)));
			edges.insert(std::make_pair(std::min(idx1, idx2), std::max(idx1, idx2)));
			edges.insert(std::make_pair(std::min(idx1, idx3), std::max(idx1, idx3)));
			edges.insert(std::make_pair(std::min(idx2, idx3), std::max(idx2, idx3)));
		}
		for (auto e = edges.begin(); e != edges.end(); e++)
		{
			edges_.push_back(Vec2i(e->first, e->second));
		}
		num_edges_ = (int)edges.size();
	}
public:
	Softbody(const std::string node_file, const std::string ele_file, const std::string face_file)
	{
		read_node_file(node_file);
		read_ele_file(ele_file);
		read_face_file(face_file);
		extract_edges();
	}

	void init_physical_data() {
		old_pos_ = pos_;
		predict_pos_ = pos_;
		vel_.resize(num_vertices_, Vec3f(0.0f, 0.0f, 0.0f));
		w_.resize(num_vertices_, 1.0f);
	}
	void init_constraints() {
		rest_length_.resize(num_edges_);
		for (int i = 0; i < num_edges_; i++)
		{
			int idx0 = edges_[i].x, idx1 = edges_[i].y;
			rest_length_[i] = (pos_[idx0] - pos_[idx1]).norm();
		}
		rest_volume_.resize(num_tets_);
		for (int i = 0; i < num_tets_; i++)
		{
			int idx0 = tets_[i].x, idx1 = tets_[i].y, idx2 = tets_[i].z, idx3 = tets_[i].w;
			Vec3f p10 = pos_[idx1] - pos_[idx0];
			Vec3f p20 = pos_[idx2] - pos_[idx0];
			Vec3f p30 = pos_[idx3] - pos_[idx0];
			rest_volume_[i] = p30.dot(p10.cross(p20)) / 6.0f;
		}
	}

	void init_gpu_data() {
		cudaMalloc((void**)&d_pos, sizeof(Real) * 3 * num_vertices_);
		cudaMalloc((void**)&d_old_pos, sizeof(Real) * 3 * num_vertices_);
		cudaMalloc((void**)&d_predict_pos, sizeof(Real) * 3 * num_vertices_);
		cudaMalloc((void**)&d_vels, sizeof(Real) * 3 * num_vertices_);
		cudaMalloc((void**)&d_w, sizeof(Real) * num_vertices_);
		cudaMalloc((void**)&d_edges, sizeof(int) * 2 * num_edges_);
		cudaMalloc((void**)&d_tets, sizeof(int) * 4 * num_tets_);
		cudaMalloc((void**)&d_rest_length, sizeof(Real) * num_edges_);
		cudaMalloc((void**)&d_rest_volume, sizeof(Real) * num_tets_);

		cudaMemcpy(d_pos, pos_.data(), sizeof(Real) * 3 * num_vertices_, cudaMemcpyHostToDevice);
		cudaMemcpy(d_old_pos, old_pos_.data(), sizeof(Real) * 3 * num_vertices_, cudaMemcpyHostToDevice);
		cudaMemcpy(d_predict_pos, predict_pos_.data(), sizeof(Real) * 3 * num_vertices_, cudaMemcpyHostToDevice);
		cudaMemcpy(d_vels, vel_.data(), sizeof(Real) * 3 * num_vertices_, cudaMemcpyHostToDevice);
		cudaMemcpy(d_w, w_.data(), sizeof(Real) * num_vertices_, cudaMemcpyHostToDevice);
		cudaMemcpy(d_edges, edges_.data(), sizeof(int) * 2 * num_edges_, cudaMemcpyHostToDevice);
		cudaMemcpy(d_tets, tets_.data(), sizeof(int) * 4 * num_tets_, cudaMemcpyHostToDevice);
		cudaMemcpy(d_rest_length, rest_length_.data(), sizeof(Real) * num_edges_, cudaMemcpyHostToDevice);
		cudaMemcpy(d_rest_volume, rest_volume_.data(), sizeof(Real) * num_tets_, cudaMemcpyHostToDevice);
	}
	void data2cpu() {
		cudaMemcpy(pos_.data(), d_pos, 3 * sizeof(Real) * num_vertices_, cudaMemcpyDeviceToHost);
	}

	void init_static_points(const std::vector<int> &static_points) {
		for (auto p : static_points)
			w_[p] = 0.0f;
	}

	void semi_euler(Real h) {
		old_pos_ = pos_;
		for (int i = 0; i < num_vertices_; i++)
		{
			if (w_[i] != 0.0f)
			{
				vel_[i] += h * Vec3f(0.0f, -9.8f, 0.0f);
				pos_[i] += h * vel_[i];
			}
		}
		predict_pos_ = pos_;
	}
	void solve_distance_constraints() {
		for (int i = 0; i < num_edges_; i++)
		{
			int idx0 = edges_[i].x, idx1 = edges_[i].y;
			Real w0 = w_[idx0], w1 = w_[idx1];
			Real w_sum = w0 + w1;
			if (w_sum == 0.0) continue;

			Vec3f p0p1 = predict_pos_[idx0] - predict_pos_[idx1];
			Real constraint = p0p1.norm() - rest_length_[i];
			Vec3f normal = p0p1.normalized();
			Real delta_lambda = constraint / w_sum;
			Vec3f corr = - 0.4f * delta_lambda *  normal;
			if (w0 != 0.0)
			{
				pos_[idx0] += w0 * corr;
			}
			if (w1 != 0.0)
			{
				pos_[idx1] -= w1 * corr;
			}
		}
	}
	void solve_volume_constraints() {
		for (int i = 0; i < num_tets_; i++)
		{
			int idx0 = tets_[i].x, idx1 = tets_[i].y, idx2 = tets_[i].z, idx3 = tets_[i].w;

			Vec3f p0 = pos_[idx0];
			Vec3f p1 = pos_[idx1];
			Vec3f p2 = pos_[idx2];
			Vec3f p3 = pos_[idx3];
			Real w0 = w_[idx0];
			Real w1 = w_[idx1];
			Real w2 = w_[idx2];
			Real w3 = w_[idx3];

			Real volume = (1.0f / 6.0f) * (p1 - p0).cross(p2 - p0).dot(p3 - p0);

			Vec3f grad0 = (p3 - p1).cross(p2 - p1);
			Vec3f grad1 = (p2 - p0).cross(p3 - p0);
			Vec3f grad2 = (p3 - p0).cross(p1 - p0);
			Vec3f grad3 = (p1 - p0).cross(p2 - p0);

			Real lambda = w0 * grad0.square_norm() + w1 * grad1.square_norm() + w2 * grad2.square_norm() + w2 * grad3.square_norm();

			if (fabs(lambda) < 1e-6) continue;

			lambda = (volume - rest_volume_[i]) / lambda;
			Real stiffness = 0.5f;
			if (w0 != 0.0f)
				pos_[idx0] -= stiffness * grad0 * lambda * w0;
			if (w1 != 0.0f)
				pos_[idx1] -= stiffness * grad1 * lambda * w1;
			if (w2 != 0.0f)
				pos_[idx2] -= stiffness * grad2 * lambda * w2;
			if (w3 != 0.0f)
				pos_[idx3] -= stiffness * grad3 * lambda * w3;
		}
	}
	void update_velocity(Real h) {
		for (int i = 0; i < num_vertices_; i++)
		{
			if (w_[i] != 0.0f)
			{
				vel_[i] = (pos_[i] - old_pos_[i]) / h;
			}
		}
	}
	void update(Real h, int maxIte) {
		semi_euler(h);
		for (int ite = 0; ite < maxIte; ite++)
		{
			solve_distance_constraints();
			solve_volume_constraints();
			predict_pos_ = pos_;
		}
		update_velocity(h);
	}
	void write_obj(const std::string obj_file) {
		std::ofstream outfile(obj_file);
		for (int i = 0; i < num_vertices_; i++)
		{
			outfile << "v " << pos_[i].x << " " << pos_[i].y << " " << pos_[i].z << std::endl;
		}
		for (int i = 0; i < num_faces_; i++)
		{
			outfile << "f " << faces_[i].x + 1 << " " << faces_[i].y + 1 << " " << faces_[i].z + 1 << std::endl;
		}
		outfile.close();
	}


	int get_num_vertices() { return num_vertices_; }
	int get_num_edges() { return num_edges_; }
	int get_num_faces() { return num_faces_; }
	int get_num_tets() { return num_tets_; }
};


__global__ void semi_euler(int num_vertices, Real* w, Real h, Real* pos, Real* vels) {
	int idx = threadIdx.x + blockDim.x * blockIdx.x;
	if (idx < num_vertices)
	{
		if (w[idx] == 0.0) return;
		vels[3 * idx + 1] += h * -9.8;
		pos[3 * idx + 0] += h * vels[3 * idx + 0];
		pos[3 * idx + 1] += h * vels[3 * idx + 1];
		pos[3 * idx + 2] += h * vels[3 * idx + 2];
	}
}

__global__ void solve_distance_constraint(int num_edges, Real* w, Real* predic_pos, Real* pos, int* edges, Real* rest_length)
{
	int idx = threadIdx.x + blockDim.x * blockIdx.x;
	if (idx < num_edges)
	{
		int idx0 = edges[2 * idx], idx1 = edges[2 * idx + 1];
		Vec3f p0(predic_pos[3 * idx0 + 0], predic_pos[3 * idx0 + 1], predic_pos[3 * idx0 + 2]);
		Vec3f p1(predic_pos[3 * idx1 + 0], predic_pos[3 * idx1 + 1], predic_pos[3 * idx1 + 2]);
		Vec3f normal = p0 - p1;
		Real dis = normal.norm() - rest_length[idx];
		Vec3f n = normal.normalized();
		Real sum_inv_mass = w[idx0] + w[idx1];
		if (sum_inv_mass == 0.0) return;
		Real deltaLambda = -dis / sum_inv_mass;
		Vec3f corr = 0.3f * deltaLambda * n;
		if (w[idx0] != 0.0)
		{
			atomicAdd(&pos[3 * idx0 + 0], w[idx0] * corr.x);
			atomicAdd(&pos[3 * idx0 + 1], w[idx0] * corr.y);
			atomicAdd(&pos[3 * idx0 + 2], w[idx0] * corr.z);
		}
		if (w[idx1] != 0.0)
		{
			atomicAdd(&pos[3 * idx1 + 0], -w[idx1] * corr.x);
			atomicAdd(&pos[3 * idx1 + 1], -w[idx1] * corr.y);
			atomicAdd(&pos[3 * idx1 + 2], -w[idx1] * corr.z);
		}
	}
}

__global__ void solve_volume_constraint(int num_tets, Real* w, Real* predic_pos, Real* pos, int* tets, Real* rest_volume)
{
	int idx = threadIdx.x + blockDim.x * blockIdx.x;
	if (idx < num_tets)
	{
		int idx0 = tets[4 * idx], idx1 = tets[4 * idx + 1], idx2 = tets[4 * idx + 2], idx3 = tets[4 * idx + 3];
		Vec3f p0(predic_pos[3 * idx0 + 0], predic_pos[3 * idx0 + 1], predic_pos[3 * idx0 + 2]);
		Vec3f p1(predic_pos[3 * idx1 + 0], predic_pos[3 * idx1 + 1], predic_pos[3 * idx1 + 2]);
		Vec3f p2(predic_pos[3 * idx2 + 0], predic_pos[3 * idx2 + 1], predic_pos[3 * idx2 + 2]);
		Vec3f p3(predic_pos[3 * idx3 + 0], predic_pos[3 * idx3 + 1], predic_pos[3 * idx3 + 2]);

		Real w0 = w[idx0], w1 = w[idx1], w2 = w[idx2], w3 = w[idx3];

		Real volume = (1.0f / 6.0f) * (p1 - p0).cross(p2 - p0).dot(p3 - p0);

		Vec3f grad0 = (p3 - p1).cross(p2 - p1);
		Vec3f grad1 = (p2 - p0).cross(p3 - p0);
		Vec3f grad2 = (p3 - p0).cross(p1 - p0);
		Vec3f grad3 = (p1 - p0).cross(p2 - p0);

		Real lambda = w0 * grad0.square_norm() + w1 * grad1.square_norm() 
					+ w2 * grad2.square_norm() + w2 * grad3.square_norm();

		if (fabs(lambda) < 1e-6) return;

		lambda = (volume - rest_volume[idx]) / lambda;

		Real stiffness = 0.5f;
		if (w[idx0] != 0.0)
		{
			atomicAdd(&pos[3 * idx0 + 0], -stiffness * lambda * w[idx0] * grad0.x);
			atomicAdd(&pos[3 * idx0 + 1], -stiffness * lambda * w[idx0] * grad0.y);
			atomicAdd(&pos[3 * idx0 + 2], -stiffness * lambda * w[idx0] * grad0.z);
		}
		if (w[idx1] != 0.0)
		{
			atomicAdd(&pos[3 * idx1 + 0], -stiffness * lambda * w[idx1] * grad1.x);
			atomicAdd(&pos[3 * idx1 + 1], -stiffness * lambda * w[idx1] * grad1.y);
			atomicAdd(&pos[3 * idx1 + 2], -stiffness * lambda * w[idx1] * grad1.z);
		}
		if (w[idx2] != 0.0)
		{
			atomicAdd(&pos[3 * idx2 + 0], -stiffness * lambda * w[idx2] * grad2.x);
			atomicAdd(&pos[3 * idx2 + 1], -stiffness * lambda * w[idx2] * grad2.y);
			atomicAdd(&pos[3 * idx2 + 2], -stiffness * lambda * w[idx2] * grad2.z);
		}
		if (w[idx3] != 0.0)
		{
			atomicAdd(&pos[3 * idx3 + 0], -stiffness * lambda * w[idx3] * grad3.x);
			atomicAdd(&pos[3 * idx3 + 1], -stiffness * lambda * w[idx3] * grad3.y);
			atomicAdd(&pos[3 * idx3 + 2], -stiffness * lambda * w[idx3] * grad3.z);
		}
	}
}


__global__ void update_vel(int num_vertices, Real h, Real* pos, Real* old_pos, Real* vel, Real* w)
{
	int idx = threadIdx.x + blockDim.x * blockIdx.x;
	if (idx < num_vertices) {
		if (w[idx] != 0.0) {
			for (int i = 0; i < 3; i++)
				vel[3 * idx + i] = (pos[3 * idx + i] - old_pos[3 * idx + i]) / h;
		}
	}
}



void simulate_on_gpu() {
	Softbody softbody("../model/torus.node", "../model/torus.ele", "../model/torus.face");
	softbody.init_physical_data();
	softbody.init_static_points({ 0, 1, 2 });
	softbody.init_constraints();
	softbody.init_gpu_data();
	Real h = 0.01f;
	int maxIte = 10;
	int max_frame = 100;

	int nv = softbody.get_num_vertices();
	int ne = softbody.get_num_edges();
	int nt = softbody.get_num_tets();
	int nthreads = 256;
	int nblocks = (nv + nthreads - 1) / nthreads;
	int ndcblocks = (ne + nthreads - 1) / nthreads;
	int ntcblocks = (nt + nthreads - 1) / nthreads;
	for (int frame = 0; frame < max_frame; frame++) {

		cudaMemcpy(softbody.d_old_pos, softbody.d_pos, sizeof(Real) * 3 * nv, cudaMemcpyDeviceToDevice);
		semi_euler << <nblocks, nthreads >> > (nv, softbody.d_w, h, softbody.d_pos, softbody.d_vels);
		cudaError error = cudaGetLastError();
		if (error != cudaSuccess)
			std::cout << "Failed to run semi-euler integrator " << std::endl;
		cudaMemcpy(softbody.d_predict_pos, softbody.d_pos, sizeof(Real) * 3 * nv, cudaMemcpyDeviceToDevice);

		for (int i = 0; i < maxIte; i++)
		{
			solve_distance_constraint << <ndcblocks, nthreads >> > (ne, softbody.d_w, softbody.d_predict_pos, softbody.d_pos, softbody.d_edges, softbody.d_rest_length);
			solve_volume_constraint<<< ntcblocks, nthreads>>> (ne, softbody.d_w, softbody.d_predict_pos, softbody.d_pos, softbody.d_tets, softbody.d_rest_volume);
			cudaMemcpy(softbody.d_predict_pos, softbody.d_pos, sizeof(Real) * 3 * nv, cudaMemcpyDeviceToDevice);
		}
		update_vel << <nblocks, nthreads >> > (nv, h, softbody.d_pos, softbody.d_old_pos, softbody.d_vels, softbody.d_w);
		softbody.data2cpu();
		softbody.write_obj("../output/frame" + std::to_string(frame) + ".obj");
	}
}

void simulate_on_cpu() {
	Softbody softbody("../model/torus.node", "../model/torus.ele", "../model/torus.face");
	softbody.init_physical_data();
	softbody.init_static_points({ 0, 1, 2 });
	softbody.init_constraints();
	int max_frame = 100;
	for (int frame = 0; frame < max_frame; frame++) {
		softbody.update(0.01f, 10);
		softbody.write_obj("../output/frame" + std::to_string(frame) + ".obj");
	}
}
int main() {
	simulate_on_gpu();
	return 0;
}

torus.ele

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torus.face

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torus.node

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