今天要实现的是利用OpenGL模拟三个物理学中常见的运动:自由落体,匀速之间,弹簧振子。
首先要实现一个空间三维向量类,看这篇文章:向量类的实现
然后主要要实现的是质点类,
/* Copyright: 2012, ustc All rights reserved. contact:k283228391@126.com File name: mass.h Description:Particle in Physical Author:Silang Quan Version: 1.0 Date: 2012.12.21 */ #ifndef MASS_H #define MASS_H #include "vector3d.h" class Mass { public: Mass(); Mass(float _m,float _size){m=_m;size=_size;}; void init(); void simulate(float dt); void checkBnd(float x1,float x2,float y1,float y2); void setForce(Vector3D _force){force=_force;}; void setVel(Vector3D _vel){vel=_vel;}; virtual ~Mass(); inline Vector3D getPos(){return pos;}; inline Vector3D getVel(){return vel;}; inline Vector3D getForce(){return force;}; inline float getSize(){return size;}; protected: private: float size; //大小 float m; // 质量 Vector3D pos; // 位置 Vector3D vel; // 速度 Vector3D force; // 力 }; #endif // MASS_H
简单解释一下:质点主要有大小,质量,速度,受力这四个属性。除了一些getset方法外,最关键的是simulate和checkBnd连个方法,分别是模拟运动和边界检测,实现起来也比较简单。
/* Copyright: 2012, ustc All rights reserved. contact:k283228391@126.com File name: mass.cpp Description:Particle in Physical Author:Silang Quan Version: 1.0 Date: 2012.12.21 */ #include "mass.h" Mass::Mass() { //ctor } void Mass::init() { force=Vector3D::zero(); vel=Vector3D::zero(); } void Mass::simulate(float dt) { Vector3D acl=force/m; vel=vel+acl*dt; pos=pos+vel*dt; } Mass::~Mass() { //dtor } void Mass::checkBnd(float x1,float x2,float y1,float y2) { if (pos.x - size < x1 || pos.x +size > x2) vel.x = -vel.x; if (pos.y - size < y1 || pos.y + size > y2) vel.y = -vel.y; }
在simulate函数中我们用到了运动学的公式:a=F/m,Vt=Vo+at.deltaS=at^2.
接下来我们就可以来进行模拟了!
首先在main.cpp中声明几个全局变量:
GLUquadricObj *mySphere; Mass constVelBall; Mass gravityBall; Mass springBall;
GLUquadricObj是二次曲面对象的声明类,后面三个是声明三个质点。
接下来是对三个质点的初始化:
void initMasses() { constVelBall=Mass(5.0,3); constVelBall.init(); constVelBall.setVel(Vector3D(3.0,5.0,0.0)); gravityBall=Mass(5.0,2); gravityBall.init(); gravityBall.setVel(Vector3D(-1.0,0.0,0.0)); gravityBall.setForce(Vector3D(0.0,-2.0,0.0)); springBall=Mass(5.0,4); springBall.init(); springBall.setVel(Vector3D(2.0,0.0,2.0)); }
然后是模拟检测:
void simulateCheck() { Vector3D connectionPos = Vector3D(0.0f, 0.0f, 0.0f); constVelBall.simulate(0.1); constVelBall.checkBnd(-20,20,-20,20); gravityBall.simulate(0.1); gravityBall.checkBnd(-20,20,-20,20); springBall.simulate(0.1); Vector3D springVector = springBall.getPos() - connectionPos; springBall.setForce(springVector*(-0.1)); }
这两个函数在main中进行调用。
还需要添加一个绘制质点的函数。我们用球体来代表质点,Mass中的size域就用来做半径。
void drawMass(Mass m) { Vector3D tmp=m.getPos(); glPushMatrix(); glTranslatef(tmp.x,tmp.y,tmp.z); gluSphere(mySphere,m.getSize(), 32, 16); glPopMatrix(); }
最后来看渲染函数:
void renderGL() { // Clear the color and depth buffers. glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT ); // We don't want to modify the projection matrix. */ glMatrixMode( GL_MODELVIEW ); glLoadIdentity( ); // Move down the z-axis. glTranslatef(0.0f,0.0f,-35.0f); glColor3ub(0, 0, 255); // Draw In Blue glBegin(GL_LINES); // Draw The Vertical Lines for (float x = -20; x <= 20; x += 2.0f) // x += 1.0f Stands For 1 Meter Of Space In This Example { glVertex3f(x, 20, 0); glVertex3f(x,-20, 0); } // Draw The Horizontal Lines for (float y = -20; y <= 20; y += 2.0f) // y += 1.0f Stands For 1 Meter Of Space In This Example { glVertex3f( 20, y, 0); glVertex3f(-20, y, 0); } glEnd(); glColor3ub(0,255, 255); drawMass(constVelBall); glColor3ub(255,0, 255); drawMass(gravityBall); glColor3ub(255,255,0); drawMass(springBall); SDL_GL_SwapBuffers( ); }
先渲染一些网格,然后对质点进行渲染。
最后的效果就像这样: