您好我在C ++中创建了一个小型的运动模拟。当我想向学生展示Euler，Runge-Kutta和MidPoint方法的差异时，有些材料点可以移动和反弹。
但是当我切换到Rungy-Kutta模式时，我在某个地方犯了一个错误，所有的材料点都消失了。我犯的错误是在solveRK4方法中。 MinGW Developer Studio项目中的附件，也有库文件夹放入mingw编译目录： http://speedy.sh/CvDHj/LABO3.zip
按下“R”按钮时，当“M”到MidPoint时，当“E”到欧拉时，它会切换到RK4。
问题是我在solveRK4函数中出错了什么？
结果（发布）看起来像这样：http://speedy.sh/h28VP/zad3.exe按R键，点数将从屏幕上消失。
Punkt - Point Wektor - 矢量
主要：
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <GL\glut.h>
#include <math.h>
#include <time.h>
#include "struktury.h"
#define YS 1.0f
#define PI 3.1415
double rot=0.0f;
int solver=0;
//--------------------------------------------------------------
//
// to solve
// {dr/dt=v
// {d2r/dt2=F/m
//
// Solvery:
// solveEuler
// solveMidpoint
// solveRK4
//
//
//--------------------------------------------------------------
void derivatives(Wektor *in, Wektor *out, Punkt *p){
// dr/dt =v
// d2r/dt2=F/m
out[0]=in[1];
out[1]=p->f*(1.0/p->m);
}
void calcForce(Punkt *p, Wektor v){
// p->f = p->m * 9.72 - (1 * v) ;
}
void solveEuler(Punkt *p, float dt){
Wektor in[2] , out [2];
in[0] = p->r ;
in[1] = p->v ;
derivatives(in, out ,p);
p->v = p->v + out [1] * dt;
p->r = p->r + out [0] * dt;
}
void solveMidPoint(Punkt *p, float dt){
//r,v,f ->Wektor
Wektor k1[2],k2[2];
Wektor y_k[2];
Wektor y_h[2];
Wektor yout[2];
y_h[0]=p->r;
y_h[1]=p->v;
derivatives(y_h,yout,p);
k1[1]=yout[1];
k1[0]=yout[0];
y_k[0]=y_h[0]+k1[0]*0.5*dt;
y_k[1]=y_h[1]+k1[1]*0.5*dt;
derivatives(y_k,yout,p);
k2[1]=yout[1];
k2[0]=yout[0];
p->r=p->r+k2[0]*dt;
p->v=p->v+k2[1]*dt;
}
//MISTAKE HERE mistake here
void solveRK4(Punkt *p, float dt){
//r,v,f ->Wektor
Wektor k1[2],k2[2],k3[2],k4[2];
Wektor y_k[2];
Wektor y_h[2];
Wektor y_a[2];
Wektor y_b[2];
Wektor yout[2];
y_h[0]=p->r;
y_h[1]=p->v;
derivatives(y_h,yout,p);
k1[0]=yout[0];
k1[1]=yout[1];
y_k[0]=y_h[0]+k1[0]*0.5*dt;
y_k[1]=y_h[1]+k1[1]*0.5*dt;
derivatives(y_k,yout,p);
k2[1]=yout[1];
k2[0]=yout[0];
y_a[0]=y_k[0]+k2[0]*0.5*dt;
y_a[1]=y_k[1]+k2[1]*0.5*dt;
derivatives(y_a,yout,p);
k3[0]=yout[0];
k3[1]=yout[1];
y_b[0]=y_a[0]+k3[0]*dt;
y_b[1]=y_a[1]+k3[1]*dt;
derivatives(y_b,yout,p);
p->r=p->r+y_b[0]+yout[0]*dt;
p->v=p->v+y_b[1]+yout[1]*dt;
}
//--------------------------------------------------------------
// RESZTA KODU
//--------------------------------------------------------------
struct SferaN{
Wektor r1;
float r;
float t;
float color[3];
SferaN *right;
};
Wektor g(0,-1.0,0);
Punkt *root=NULL;
SferaN *sroot=NULL;
int loop=0;
SferaN *SphereAlloc(float R, Wektor r1, float t, float c[3])
{
SferaN *tmp;
if (!(tmp=(SferaN*)malloc(sizeof(SferaN))))
return NULL;
tmp->right=NULL;
tmp->r=R;
tmp->r1=r1;
tmp->t=t;
tmp->color[0]=c[0];
tmp->color[1]=c[1];
tmp->color[2]=c[2];
return tmp;
}
void SphereTest(SferaN *s, Punkt *p)
{
float d;
Wektor n;
float z;
d=(s->r1-p->r).len();
if (d-s->r<0)
{
n=(s->r1-p->r);
n.norm();
z=d-s->r;
p->r=p->r+n*z;
Wektor vs,vn;
vn=n*(n*p->v);
vs=p->v-vn;
p->v=(vs-vn*s->t);
}
}
void AddSphere(SferaN *ro, float R, Wektor r1, float t, float c[3])
{
SferaN *tmp;
for (tmp=ro; tmp->right!=NULL; tmp=tmp->right);
tmp->right=SphereAlloc(R,r1,t,c);
}
Punkt *PointAlloc(float m, int flaga, Wektor r, Wektor v)
{
Punkt *tmp;
if (!(tmp=(Punkt*)malloc(sizeof(Punkt))))
return NULL;
tmp->m=m;
tmp->flag=flaga;
tmp->r=r;
tmp->v=v;
tmp->right=NULL;
return tmp;
}
void AddPoint(Punkt *ro, float m, int flag, Wektor r, Wektor v)
{
Punkt *tmp;
for (tmp=ro; tmp->right!=NULL; tmp=tmp->right);
tmp->right=PointAlloc(m,flag,r,v);
}
Wektor W_Euler(Wektor f, float h)
{
return (f*h);
}
void calcDeriv(Punkt *p){
}
void Solver(Punkt *ro, float dt)
{
//0 euler, 1 midpoint, 2 RK4
Punkt *tmp;
for (tmp=ro;tmp!=NULL;tmp=tmp->right)
{
switch (solver){
case 0:
solveEuler(tmp,dt);
break;
case 1:
solveMidPoint(tmp,dt);
break;
case 2:
solveRK4(tmp,dt);
break;
default:
solveEuler(tmp,dt);
}
/*
tmp->dv=W_Euler(tmp->f*(1/tmp->m),dt);
tmp->v=tmp->v+tmp->dv;
tmp->dr=tmp->v*dt;
tmp->r=tmp->r+tmp->dr;
*/
/*
Wektor a=tmp->f*(1.0/tmp->m);
//--------------
Wektor k1=W_Euler(a,dt);
Wektor k2=W_Euler(a+0.5*k1,dt);
Wektor k3=W_Euler(a+0.5*k2,dt);
Wektor k4=W_Euler(a+k3,dt);
Wektor kk=(1.0/6.0)*(k1+2.0*k2+2.0*k3+k4);
tmp->v=tmp->v+kk;
tmp->r=tmp->r+tmp->v*dt;
*/
}
}
void Sily(Punkt *ro)
{
Punkt *tmp;
for (tmp=ro;tmp!=NULL; tmp=tmp->right)
{
tmp->f=g*tmp->m;
}
}
void AnimateScene(void)
{
glClearColor(0.0f,0.0f,0.0f,0.0f);
//if (loop==0)
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
Punkt *tmp;
//Sily(root);
Solver(root,0.008);
Sily(root);
// glRotatef(0.1,0.0f,1.0f,0.0f);
rot+=0.01;
//if (rot>36) rot=0.0f;
glPointSize(5);
glDisable(GL_LIGHTING);
glDisable(GL_LIGHT0);
for(tmp=root;tmp!=NULL;tmp=tmp->right)
{
//glBegin(GL_POINTS);
//glColor3f(rand()/(float)RAND_MAX,rand()/(float)RAND_MAX,rand()/(float)RAND_MAX);
glColor3f(1,1,1);
// glVertex3f(tmp->r.x/1.0,tmp->r.y/1.0,tmp->r.z/1.0);
glPushMatrix();
glTranslatef(tmp->r.x/1.0,tmp->r.y/1.0,tmp->r.z/1.0);
glutSolidSphere(0.011,5,5);
glPopMatrix();
SferaN *stmp;
for(stmp=sroot;stmp!=NULL;stmp=stmp->right)
{
SphereTest(stmp,tmp);
}
//glVertex2f(0,0);
//printf("%f %f\n",tmp->r.x, tmp->r.y);
// glEnd();
glBegin(GL_LINES);
glColor3f(1,0,0);
double x1,x2,y1,y2,z1,z2;
x1=tmp->r.x;
y1=tmp->r.y;
x2=tmp->v.x;
y2=tmp->v.y;
z1=tmp->r.z;
z2=tmp->v.z;
glVertex3f(x1,y1,z1);
glVertex3f(x1+(x2)*0.05,y1+(y2)*0.05,z1+(z2)*0.05);
glEnd();
}
glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0);
SferaN *stmp;
for(stmp=sroot;stmp!=NULL;stmp=stmp->right)
{
glPushMatrix();
glTranslatef(stmp->r1.x,stmp->r1.y,stmp->r1.z);
glColor3fv(stmp->color);
glutSolidSphere(stmp->r,50,50);
glPopMatrix();
}
// printf("****\n");
glFlush();
glutSwapBuffers();
loop++;
if (loop>2000)
{
double vx,vy,vz;
double zz=0.01;
for(tmp=root;tmp!=NULL;tmp=tmp->right)
{
vx=0.5-rand()/(float)RAND_MAX;
vy=1.0-rand()/(float)RAND_MAX;
vz=0.5-rand()/(float)RAND_MAX;
vz=0.0f;
vy*=YS;
vy+=zz;
zz+=0.001;
tmp->r.x=0;
tmp->r.y=0;
tmp->v=Wektor(vx,vy,vz);
}
loop=0;
}
}
void InitGraphics()
{
GLfloat mat_specular[] = { 1.0, 1.0, 1.0, 1.0 };
GLfloat mat_shininess[] = { 90.0 };
GLfloat light_position[] = {1.0, 1.0, 1.0, 0.0};
glMaterialfv(GL_FRONT, GL_SPECULAR, mat_specular);
glMaterialfv(GL_FRONT, GL_SHININESS, mat_shininess);
glLightfv(GL_LIGHT0, GL_POSITION, light_position);
glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0);
glDepthFunc(GL_LEQUAL);
glEnable(GL_DEPTH_TEST);
glShadeModel(GL_SMOOTH);
glEnable(GL_COLOR_MATERIAL);
}
void myReshape(GLsizei w, GLsizei h)
{
glViewport(0, 0, w, h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
double p1=1.0f;
if(w <= h)
glOrtho(-p1,p1,-p1*(GLfloat)h/(GLfloat)w,p1*(GLfloat)h/(GLfloat)w,-10.0,10.0);
else
glOrtho(-p1*(GLfloat)w/(GLfloat)h,p1*(GLfloat)w/(GLfloat)h,-p1,p1,-10.0,10.0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
}
void keyboard(unsigned char key, int x, int y){
switch (key){
case 'e':
solver=0;
printf("Solver --> Euler\n");
break;
case 'm':
solver=1;
printf("Solver --> MidPoint\n");
break;
case 'r':
solver=2;
printf("Solver --> RK4\n");
break;
}
}
void idle(void)
{
glutPostRedisplay();
}
int main(int argc, char *argv[])
{
double vx,vy,vz;
int i;
srand(time(NULL));
double zz=0.01;
for (i=1; i<620; i++)
{
vx=0.5-rand()/(float)RAND_MAX;
vy=1.0-rand()/(float)RAND_MAX;
vz=0.5-rand()/(float)RAND_MAX;
vz=0.0f;
vy*=YS;
vy+=zz;
zz+=0.001;
if (!root)
root=PointAlloc(1,0,Wektor(0,0,0),Wektor(vx,vy,vz));
else
AddPoint(root,1,0,Wektor(0,0,0),Wektor(vx,vy,vz));
}
zz=-0.2;
for (i=1; i<140; i++)
{
AddPoint(root,10,0,Wektor(zz,1,0),Wektor(0,0,0));
zz+=0.01;
}
float c1[] = {0,0,1};
float c2[] = {0,1,0};
float c3[] = {1,1,0};
float c4[] = {1,0,1};
float c5[] = {0.6,0.5,1};
float c6[] = {0.6,0.5,0.3};
sroot=SphereAlloc(0.5,Wektor(0,-0.5,0),0.9,c1);
AddSphere(sroot,0.1,Wektor(-0.5,0.5,0),0.8,c2);
AddSphere(sroot,0.1,Wektor(0.5,0.5,0),0.3,c3);
AddSphere(sroot,0.1,Wektor(1,0.0),0.3,c4);
AddSphere(sroot,0.15,Wektor(0,0.7,0),0.9,c5);
AddSphere(sroot,0.2,Wektor(-1,-0.2,0),1.0,c6);
Sily(root);
glutInit(&argc, argv);
glutInitWindowSize(600,600);
glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH);
glutCreateWindow("GLUT example");
InitGraphics();
glutDisplayFunc(AnimateScene);
glutIdleFunc(idle);
glutKeyboardFunc(keyboard);
glutReshapeFunc(myReshape);
glutMainLoop();
return 0;
}
结构：
#ifndef __STRUKTURY_H
#define __STRUKTURY_H
class Wektor{
public:
Wektor(double _x=0, double _y=0, double _z=0):
x(_x),y(_y),z(_z){}
Wektor operator+(Wektor const &);
Wektor operator-(Wektor const &);
double operator*(Wektor const &);
Wektor operator*(double);
double len();
void norm();
double x,y,z;
};
Wektor operator*(double, Wektor const &);
Wektor Wektor::operator-(Wektor const &w)
{
return Wektor(x-w.x,y-w.y,z-w.z);
}
double Wektor::operator*(Wektor const &w)
{
return (x*w.x + y*w.y + z*w.z);
}
double Wektor::len()
{
return sqrt((*this)*(*this));
}
Wektor Wektor::operator+(Wektor const &w)
{
return Wektor(x+w.x,y+w.y,z+w.z);
}
Wektor Wektor::operator*(double l)
{
return Wektor(x*l, y*l, z*l);
}
Wektor operator*(double s, Wektor const &w)
{
return Wektor(s*w.x, s*w.y, s*w.z);
}
void Wektor::norm()
{
double d = len();
if (d)
(*this)=(*this)*(1/d);
}
struct Punkt{
int flag;
float m;
Wektor f;
Wektor r;
Wektor v;
Wektor dr;
Wektor dv;
Punkt *right;
};
#endif
答案 0 :(得分：1)
这些行中的一些指数似乎是错误的：
y_b[1]=y_a[0]+k3[0]*dt;
p->v=p->v+y_b[0]+yout[1]*dt;
请仔细阅读您的RK4并检查所有指数。甚至可能存在更多的复制/粘贴错误。
答案 1 :(得分：0)
我修好了，现在工作得很好！ ： - ）
<强> 0 在开始之前 - 请仔细阅读WIKI段落！
1。你在实际的整合部分做错了，你写了
p->r = p->r + y_b[0] + yout[0] * dt;
与经典的4阶runge-kutta mtehod的维基百科版本无关。这是一个核心线：
p->r = p->r + (yout[0][0] + 2* yout[1][0] + 2* yout[2][0] + yout[3][0] )* dt * (1.0/6);
所以，再看一遍wiki并进行比较。
2. 后来我发现了一系列行
y_a[...] = y_k[...] + k2[...] * 0.5*dt;
y_b[...] = y_a[...] + k3[...] * dt;
你应该写：
y_a[0] = y_h[0] + k2[0] * 0.5*dt;
y_b[0] = y_h[0] + k2[0] * 0.5*dt;
使用INPUT但不是新计算的代理（临时）值。 你只是弄乱了y_h，y_k，y_a y_b ... y_qwertyuiop !!!! 不要这样命名）））
3。你也有太多的变数...我让它变得更容易和可读，也使用更少的内存。
无论如何，更少的单词更多交易：这里是工作方法代码，复制粘贴和享受：
void solveRK4(Punkt *p, float dt) {
Wektor y_in[2];
Wektor y_temp[2];
Wektor k[4][2];
y_in[0] = p->r;
y_in[1] = p->v;
derivatives(y_in, k[0], p);
y_temp[0] = y_in[0] + k[0][0] * 0.5*dt;
y_temp[1] = y_in[1] + k[0][1] * 0.5*dt;
derivatives(y_temp, k[1], p);
y_temp[0] = y_in[0] + k[1][0] * 0.5*dt;
y_temp[1] = y_in[1] + k[1][1] * 0.5*dt;
derivatives(y_temp, k[2], p);
y_temp[0] = y_in[0] + k[2][0] * dt;
y_temp[1] = y_in[1] + k[2][1] * dt;
derivatives(y_temp, k[3], p);
p->r = p->r + (k[0][0] + 2* k[1][0] + 2* k[2][0] + k[3][0] )* dt * (1.0/6);
p->v = p->v + (k[0][1] + 2 * k[1][1] + 2 * k[2][1] + k[3][1]) * dt * (1.0/6);
}
4. 不要使用GLUT;使用GLFW！ ; - ）