[opengl]弹簧质点法模拟柔性布料以及椭球碰撞的opengl实现

代码大体与http://bbezxcy.iteye.com/blog/2204322相同，修改了部分不稳定的bug，增加了椭球碰撞以及旋转观察的实现

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#ifndef GLUT_DISABLE_ATEXIT_HACK
#define GLUT_DISABLE_ATEXIT_HACK
#endif
#define GLEW_STATIC
#include <GL/glew.h>
#include <GL/wglew.h>
#include <GL/freeglut.h>
#include <vector>
#include<cstring>
#include <glm/glm.hpp>
#include <glm/gtc/matrix_transform.hpp> //for matrices
#include <glm/gtc/type_ptr.hpp>
//undefine if u want to use the default bending constraint of pbd
#include<iostream>
using namespace std;
//using namespace glm;

GLfloat rtx = 0.0f, rty = 0.0f, rtz = 0.0;

glm::vec3 Up=glm::vec3(0,1,0), Right, viewDir;
const int GRID_SIZE=10;  //地板砖边长
GLdouble MV[16];
GLint viewport[4];
GLdouble PP[16];
bool isfix[1000];
int dist = -23;

//椭球参数
int iStacks = 30;
int iSlices = 30;
float fRadius = 1;
float radius = 1;					 //object space radius of ellipsoid
//float exp1 = 1e-3;

const int numX = 20, numY=20; //一行有numx+1个点
const int total_points = (numX+1)*(numY+1); //总点数
//布料顶点位置 速度

glm::vec3 Pos[total_points];
glm::vec3 Veloc[total_points];
glm::vec3 force[total_points];
glm::mat4 ellipsoid,invreseEllipsoid;

int size = 4;
float hsize = size/2.0f;
const float frameTime = 1.0f/60.0f;

const float mass = 1.0/total_points;
const float globalDamp = 0.98;  //速度衰减参数
const glm::vec3 gvat = glm::vec3(0,-9.8,0);  //重力加速度
const float Spring_K = 2.5;  //弹性系数
const float len0 = 4.0/numX; //单边长度
const float tolera = 1.08;   //弹性限度
float fuck;//球体运动

//视角问题
int oldX=0, oldY=0;
const int width = 1024, height = 1024;
GLdouble P[16];
int selected_index = -1;
int state =1 ;
float rX=15, rY=0;


void initGL()
{
    //初始化顶点位置
	memset(Pos,0,sizeof(Pos));
	memset(Veloc,0,sizeof(Veloc));
	memset(force,0,sizeof(force));
    //fill in positions
    int count1 = 0;
    int u = numX + 1;
    int v = numY + 1;
	for(int j=0;j<=numY;j++) {
		for(int i=0;i<=numX;i++) {
            Pos[count1++] = glm::vec3( ((float(i)/(u-1)) *2-1)* hsize, size+1, ((float(j)/(v-1) )* size));
			printf("(%.1lf ,%.1lf)",((float(i)/(u-1)) *2-1)* hsize,((float(j)/(v-1) )* size));
		}printf("\n");
		//悬挂点为X[0] 和 X[numX]
	}
	memset(isfix,0,sizeof(isfix));
	isfix[0] = isfix[numX] = 1;
	fuck = 0;


}
void DrawEllipsoid(){//画绿色椭球
    //设置椭球
    ellipsoid = glm::translate(glm::mat4(1),glm::vec3(0,fuck,0));
    fuck += 0.01;
	if(fuck>=4.0)fuck = -1;
	ellipsoid = glm::rotate(ellipsoid, 45.0f ,glm::vec3(1,0,0));
	ellipsoid = glm::scale(ellipsoid, glm::vec3(fRadius,fRadius,fRadius/2));
	invreseEllipsoid = glm::inverse(ellipsoid);

	fuck +=0.005;

    //画出椭球
    glColor3f(0,1,0);
	glPushMatrix();
		glMultMatrixf(glm::value_ptr(ellipsoid));
        //半径，经线条数，维线条数
        glutWireSphere(fRadius, iSlices, iStacks);
	glPopMatrix();
}
void DrawGrid()  //画地板
{
	glBegin(GL_LINES);
	glColor3f(0.5f, 0.5f, 0.5f);
	for(int i=-GRID_SIZE;i<=GRID_SIZE;i++)
	{
		glVertex3f((float)i,0,(float)-GRID_SIZE);
		glVertex3f((float)i,0,(float)GRID_SIZE);

		glVertex3f((float)-GRID_SIZE,0,(float)i);
		glVertex3f((float)GRID_SIZE,0,(float)i);
	}
	glEnd();
}

void drawTextile(){  //画布料
	//draw polygons
	int k = 0;
    glBegin(GL_LINES);
    glColor3f(1,1,1);
	for(int i = 0;i <= numX;i ++){
        for(int j = 0;j <= numY;j ++){
//                cout<<i<<" "<<j<<";";
            if(j != numX){
                glm::vec3 p1 = Pos[k];
                glm::vec3 p2 = Pos[k+1];
                glVertex3f(p1.x,p1.y,p1.z);
                glVertex3f(p2.x,p2.y,p2.z);
//                printf("add %d %d\n",k,k+1);
            }
            if(i != numY){
                glm::vec3 p1 = Pos[k];
                glm::vec3 p2 = Pos[k+numX+1];
                glVertex3f(p1.x,p1.y,p1.z);
                glVertex3f(p2.x,p2.y,p2.z);
            }
            k++;
        }
//        cout<<endl;
	}
    glEnd();

    glPointSize(3);
    glBegin(GL_POINTS);
    glColor3f(1,0,0);
	for(size_t i = 0;i < total_points;i ++){
        glm::vec3 p = Pos[i];
		glVertex3f(p.x,p.y,p.z);
	}
    glEnd();
}

void OnRender(void)
{
    glClear(GL_COLOR_BUFFER_BIT| GL_DEPTH_BUFFER_BIT);
    glLoadIdentity();
    //设置视角
	glTranslatef(0,0,dist);
//	glRotatef(15,1,0,0);
	glRotatef(rX,1,0,0);
	glRotatef(rY,0,1,0);
    glGetDoublev(GL_MODELVIEW_MATRIX, MV);
	viewDir.x = (float)-MV[2];
	viewDir.y = (float)-MV[6];
	viewDir.z = (float)-MV[10];
	Right = glm::cross(viewDir, Up);
	//做出地面
    DrawGrid();
    drawTextile();
    DrawEllipsoid();
//    drawblock();
    glutSwapBuffers();
}
//求出b点对a点的作用力
glm::vec3 SpringForce(int a, int b, int is){
    float inilen;
    if(is == 1)inilen = len0;
    if(is == 2) inilen = len0 * 2;
    if(is == 3) inilen = len0 * 1.414213;
    glm::vec3 res = glm::vec3(0);
    glm::vec3 tmp = Pos[b] - Pos[a];
    float dis = glm::length(tmp);
    res = tmp/dis;
    res *= (dis - inilen);
    res *= Spring_K;
    return res;
}
void ComputeForces(){
    //重力
	for(size_t i=0;i<total_points;i++) {
		force[i] = glm::vec3(0);
		if(!isfix[i])
            force[i] += mass * gvat;
	}
	int i,j,k = 0;
    //结构弹簧 上下左右
    for(i = 0;i <= numY;i++){
        for(j = 0;j <= numX;j ++){
            if(i!=0){//上
                force[k] += SpringForce(k, k - numX - 1, 1);
            }
            if(j!=numX){//右
                force[k] += SpringForce(k, k+1, 1);
            }
            if(i!=numY){//下
                force[k] += SpringForce(k, k + numX + 1, 1);
            }
            if(j!=0){//左
                force[k] += SpringForce(k, k - 1, 1);
            }
            k++;
        }
    }
    //柔性弹簧
    k = 0;
    for(i = 0;i <= numY;i++){
        for(j = 0;j <= numX;j ++){
            if(i>1){//上
                force[k] += SpringForce(k, k - 2*numX - 2, 2);
            }
            if(j<numX-1){//右
                force[k] += SpringForce(k, k+2, 2);
            }
            if(i<numY-1){//下
                force[k] += SpringForce(k, k + 2*numX + 2, 2);
            }
            if(j>1){//左
                force[k] += SpringForce(k, k - 2, 2);
            }
            k++;
        }
    }
    //剪切弹簧
    k = 0;
    for(i = 0;i <= numY;i ++){
        for(j = 0;j <= numX;j ++){
            if(i>0&&j>0){  //左上
                force[k] += SpringForce(k, k - numX - 2, 3);
            }
            if(i>0&&j<numX){  //右上
                force[k] += SpringForce(k, k - numX, 3);
            }
            if(i<numY&&j<numX){  //右下
                force[k] += SpringForce(k, k + numX + 2, 3);
            }
            if(i<numY&&j>0){   //坐下
                force[k] += SpringForce(k, k + numX, 3);
            }
            k ++;
        }
    }
}

void EllipsoidCollision() { //检测与处理布料和椭球之间的碰撞
	for(size_t i=0;i<total_points;i++) {
        glm::vec3 tPos(Pos[i]);
		glm::vec4 X_0 = (invreseEllipsoid*glm::vec4(tPos,1));
		glm::vec3 delta0 = glm::vec3(X_0.x, X_0.y, X_0.z);
		float distance = glm::length(delta0);
		if (distance < 1.0f) {
			delta0 = (radius - distance) * delta0 / distance;
			// Transform the delta back to original space
			glm::vec3 delta;
			glm::vec3 transformInv;
			transformInv = glm::vec3(ellipsoid[0].x, ellipsoid[1].x, ellipsoid[2].x);
			transformInv /= glm::dot(transformInv, transformInv);
			delta.x = glm::dot(delta0, transformInv);
			transformInv = glm::vec3(ellipsoid[0].y, ellipsoid[1].y, ellipsoid[2].y);
			transformInv /= glm::dot(transformInv, transformInv);
			delta.y = glm::dot(delta0, transformInv);
			transformInv = glm::vec3(ellipsoid[0].z, ellipsoid[1].z, ellipsoid[2].z);
			transformInv /= glm::dot(transformInv, transformInv);
			delta.z = glm::dot(delta0, transformInv);
			tPos +=  delta ;
            Veloc[i] += (tPos - Pos[i])/frameTime;
            Veloc[i] *= globalDamp;
            Pos[i] = tPos;
		}
	}
}

void CalcPos(){  //计算新的位置
//	frameTime/=1000;
//	printf("%.3lf\n",frameTime);
	glm::vec3 acc = glm::vec3(0);
    //得到的frame就是间隔时间 毫秒
    for(size_t i = 0;i < total_points;i ++){
        if(isfix[i])continue;
        acc = force[i] / mass;  //得到加速度向量
        Veloc[i] = Veloc[i] + acc*frameTime;  //得到新的速度值
        Veloc[i] *= globalDamp;
        Pos[i] = Pos[i] + Veloc[i] * frameTime;
    }
}

void StepPhysics(){
    ComputeForces();
    CalcPos();
    EllipsoidCollision();
    glutPostRedisplay();
    Sleep(5);
}


void OnReshape(int nw, int nh) {
	glViewport(0,0,nw, nh);
	glMatrixMode(GL_PROJECTION);
	glLoadIdentity();
	gluPerspective(60, (GLfloat)nw / (GLfloat)nh, 1.f, 100.0f);

	glGetIntegerv(GL_VIEWPORT, viewport);
	glGetDoublev(GL_PROJECTION_MATRIX, PP);

	glMatrixMode(GL_MODELVIEW);
}

void OnMouseDown(int button, int s, int x, int y)
{
	if (s == GLUT_DOWN)
	{
		oldX = x;
		oldY = y;
		int window_y = (height - y);
		float norm_y = float(window_y)/float(height/2.0);
		int window_x = x ;
		float norm_x = float(window_x)/float(width/2.0);

		float winZ=0;
		glReadPixels( x, height-y, 1, 1, GL_DEPTH_COMPONENT, GL_FLOAT, &winZ );
		if(winZ==1)
			winZ=0;
		double objX=0, objY=0, objZ=0;
		gluUnProject(window_x,window_y, winZ,  MV,  P, viewport, &objX, &objY, &objZ);
		glm::vec3 pt(objX,objY, objZ);
		size_t i=0;
		for(i=0;i<total_points;i++) {
			if( glm::distance(Pos[i],pt)<0.1) {
				selected_index = i;
				printf("Intersected at %d\n",i);
				break;
			}
		}
	}

	if(button == GLUT_MIDDLE_BUTTON)
		state = 0;
	else
		state = 1;

	if(s==GLUT_UP) {
		selected_index= -1;
		glutSetCursor(GLUT_CURSOR_INHERIT);
	}
}

void OnMouseMove(int x, int y)
{
	if(selected_index == -1) {
		if (state == 0)
			dist *= (1 + (y - oldY)/60.0f);
		else
		{
			rY += (x - oldX)/5.0f;
			rX += (y - oldY)/5.0f;
		}
	} else {
		float delta = 1500/abs(dist);
		float valX = (x - oldX)/delta;
		float valY = (oldY - y)/delta;
		if(abs(valX)>abs(valY))
			glutSetCursor(GLUT_CURSOR_LEFT_RIGHT);
		else
			glutSetCursor(GLUT_CURSOR_UP_DOWN);

		Veloc[selected_index] = glm::vec3(0);
		Pos[selected_index].x += Right[0]*valX ;
		float newValue = Pos[selected_index].y+Up[1]*valY;
		if(newValue>0)
			Pos[selected_index].y = newValue;
		Pos[selected_index].z += Right[2]*valX + Up[2]*valY;
	}
	oldX = x;
	oldY = y;

	glutPostRedisplay();
}
int main(int argc, char * argv[])
{
	glutInit(&argc, argv);
	glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGBA | GLUT_DEPTH);
    glutInitWindowSize(1024, 1024);
    glutCreateWindow("Mass-Spring Model");

    initGL();
    glutDisplayFunc(OnRender);
    //指定窗口形状变化时的回调函数
	glutReshapeFunc(OnReshape);
	//指定程序空闲时调用函数
    glutIdleFunc(StepPhysics);
    glEnable(GL_DEPTH_TEST);
	glutMouseFunc(OnMouseDown);
	glutMotionFunc(OnMouseMove);
    glutMainLoop();
    return 0;
}

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[opengl]弹簧质点法模拟柔性布料以及椭球碰撞的opengl实现

原文：http://bbezxcy.iteye.com/blog/2214558