Programming
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Double-Pendulum Writen in Cpp Porgramming

Djie sam soe Djie sam soe  As Yab@jieyab 
 
  admin
 Freelance | Student




  19-Apr-2021 00:50:41



Main.cpp 

#include <iostream>
#include "draw.h"
#include <cmath>
#include <conio.h>
#include <cstdlib>
#include <chrono>
#define M_PI 3.14159265358979323846
using namespace std;


class Timer
{
public:
    Timer() : beg_(clock_::now()) {}
    void reset() { beg_ = clock_::now(); }
    float elapsed() const { 
        return std::chrono::duration_cast<second_>
            (clock_::now() - beg_).count(); }


private:
    typedef std::chrono::high_resolution_clock clock_;
    typedef std::chrono::duration<float, std::ratio<1> > second_;
    std::chrono::time_point<clock_> beg_;
};


int main()
{
	constexpr int n=10000;
	float 
	l1[n],l2[n],	//lengths
	m1[n],m2[n],	//masses
	O1[n],O2[n],	//angles
	w1[n],w2[n],	//angular velocities
	g=9.81f;
	
	for(int i=0;i<n;i++)
	{
		float epsilon=0.000001f;
		l1[i]=150.0f;
		l2[i]=150.0f;
		m1[i]=10.0f;
		m2[i]=10.0f;
		O1[i]=2.0f*M_PI/2.0f+epsilon*(float)(2*i-n+1);
		O2[i]=2.0f*M_PI/2.0f;
		w1[i]=0.0f;
		w2[i]=0.0f;
	}
	
	//time
	const float fps=300.0f;
	const float dt=1.0f/fps;
	float accumulator = 0.0f;
	Timer tmr;
	float frameStart=tmr.elapsed();
	
	char platno[HEIGHT/dH][WIDTH/dW+1];
	for(int i=0;i<HEIGHT/dH-1;i++)	platno[i][WIDTH/dW]='\n';
	platno[HEIGHT/dH-1][WIDTH/dW]='\0';
	for(int i=0;i<HEIGHT/dH;i++)
	{
		for(int j=0;j<WIDTH/dW;j++)
		{
			platno[i][j]=' ';
		}
	}
	//main loop
	while(true)
	{
		gotoxy(0,0);
		//time
		float currentTime=tmr.elapsed();
		accumulator+=currentTime-frameStart;
		
		frameStart=currentTime;
		
		
		if(accumulator>=1.0f/30.0f)	accumulator=1.0f/30.0f;
		
		while(accumulator > dt)
		{
			//calculation
			for(int i=0;i<n;i++)
			{
				//just trust the formulas
				float
				alfa1=(  -g*(2*m1[i]+m2[i])*sin(O1[i])-g*m2[i]*sin(O1[i]-2*O2[i])-2*m2[i]*sin(O1[i]-O2[i])*(w2[i]*w2[i]*l2[i]+w1[i]*w1[i]*l1[i]*cos(O1[i]-O2[i]))  )/(  l1[i]*(2*m1[i]+m2[i]-m2[i]*cos(2*O1[i]-2*O2[i]))  ),
				alfa2=(  2*sin(O1[i]-O2[i])  )*(  w1[i]*w1[i]*l1[i]*(m1[i]+m2[i]) + g*(m1[i]+m2[i])*cos(O1[i]) + w2[i]*w2[i]*l2[i]*m2[i]*cos(O1[i]-O2[i])  )/l2[i]/(  2*m1[i]+m2[i]-m2[i]*cos(2*O1[i]-2*O2[i])  );
				
				//time is sped up 10 times for better effect
				w1[i]+=10*dt*alfa1;
				w2[i]+=10*dt*alfa2;
				O1[i]+=10*w1[i]*dt;
				O2[i]+=10*w2[i]*dt;
			}
			
			accumulator-=dt;
		}
		
		//drawing
		for(int i=0;i<HEIGHT/dH;i++)
		{
			for(int j=0;j<WIDTH/dW;j++)
			{
				platno[i][j]=' ';
			}
		}
		
		for(int i=0;i<n;i++)
		{
			int x1=(WIDTH/2+sin(O1[i])*l1[i]+dW*0.5f)/dW;
			int y1=(cos(O1[i])*l1[i]+dH*0.5f)/dH+HEIGHT/dH/2;
			int x2=x1+(sin(O2[i])*l2[i]+dW*0.5f)/dW;
			int y2=y1+(cos(O2[i])*l2[i]+dH*0.5f)/dH;
			
			if(i%2==0)
			{
				drawLine(platno,WIDTH/2/dW,HEIGHT/dH/2,x1,y1,'*');
				drawLine(platno,x1,y1,x2,y2,'*');
				drawPoint(platno,WIDTH/2/dW,HEIGHT/dH/2,'O');
				drawPoint(platno,x1,y1,'@');
				drawPoint(platno,x2,y2,'@');
			}
			else
			{
				drawLine(platno,WIDTH/2/dW,HEIGHT/dH/2,x1,y1,'.');
				drawLine(platno,x1,y1,x2,y2,'.');
				drawPoint(platno,WIDTH/2/dW,HEIGHT/dH/2,'O');
				drawPoint(platno,x1,y1,'@');
				drawPoint(platno,x2,y2,'@');
			}
		}
		puts(platno[0]);
	}
	return 0;
	
}


Draw.h 

#include <iostream>
#include <windows.h>


constexpr int WIDTH = 1000,HEIGHT = 600;
constexpr int dW=8,dH=16;


void gotoxy ( short x, short y )
{
COORD coord = {x, y};
SetConsoleCursorPosition ( GetStdHandle ( STD_OUTPUT_HANDLE ), coord );
}


void plotLineLow(char platno[HEIGHT/dH][WIDTH/dW+1],int x0,int y0,int x1,int y1,char c);
void plotLineHigh(char platno[HEIGHT/dH][WIDTH/dW+1],int x0,int y0,int x1,int y1,char c);
void drawPoint(char platno[HEIGHT/dH][WIDTH/dW+1],int A,int B,char c);
void drawLine(char platno[HEIGHT/dH][WIDTH/dW+1],int A,int B,int C,int D,char c);


void drawPoint(char platno[HEIGHT/dH][WIDTH/dW+1],int A,int B,char c)
{
	if(A<0||B<0||A>=WIDTH/dW||B>=HEIGHT/dH)	return;
	platno[B][A]=c;
}


void drawLine(char platno[HEIGHT/dH][WIDTH/dW+1],int A,int B,int C,int D,char c)
{
	//sorting
	if(A>C)
	{
		int t;
		t=A;
		A=C;
		C=t;
		t=B;
		B=D;
		D=t;
	}
	//algorithm
	if(B==D)
	{
		for(int i=A;i<=C;i++)
			drawPoint(platno,i,B,c);//platno[B][i]=c;
		return;
	}
	if(A==C)
	{
		int min=B,max=D;
		if(D<B)
		{
			min=D;
			max=B;
		}
		for(int i=min;i<=max;i++)
			drawPoint(platno,A,i,c);//platno[i][A]=c;
		return;
	}
	if(abs(D-B)<abs(C-A))
		plotLineLow(platno,A,B,C,D,c);
	else
	{
		if(B>D)	plotLineHigh(platno,C,D,A,B,c);
		else	plotLineHigh(platno,A,B,C,D,c);
	}
}


void plotLineLow(char platno[HEIGHT/dH][WIDTH/dW+1],int x0,int y0,int x1,int y1,char c)
{
    int dx = x1 - x0, dy = y1 - y0, yi = 1;
    if (dy < 0)
    {
        yi = -1;
        dy = -dy;
	}
    int D = 2*dy - dx;
    int y = y0;


    for (int x=x0;x<=x1;x++)
    {
        drawPoint(platno,x,y,c);
        if( D > 0)
        {
            y += yi;
            D -= 2*dx;
		}
        D += 2*dy;
	}
}


void plotLineHigh(char platno[HEIGHT/dH][WIDTH/dW+1],int x0,int y0,int x1,int y1,char c)
{
    int dx = x1 - x0, dy = y1 - y0, xi = 1;
    if (dx < 0)
    {
        xi = -1;
        dx = -dx;
	}
    int D = 2*dx - dy;
    int x = x0;


    for (int y=y0;y<=y1;y++)
    {
        drawPoint(platno,x,y,c);
		if( D > 0)
        {
            x += xi;
            D -= 2*dy;
		}
        D += 2*dx;
	}
}

Pendulum trace.cpp

#include <iostream>
#include "draw.h"
#include <cmath>
#include <conio.h>
#include <cstdlib>
#include <chrono>
#define M_PI 3.14159265358979323846
using namespace std;


class Timer
{
public:
    Timer() : beg_(clock_::now()) {}
    void reset() { beg_ = clock_::now(); }
    float elapsed() const { 
        return std::chrono::duration_cast<second_>
            (clock_::now() - beg_).count(); }


private:
    typedef std::chrono::high_resolution_clock clock_;
    typedef std::chrono::duration<float, std::ratio<1> > second_;
    std::chrono::time_point<clock_> beg_;
};


int main()
{
	float 
	l1,l2,	//lengths
	m1,m2,	//masses
	O1,O2,	//angles
	w1,w2,	//angular velocities
	g=9.81f;
	
	l1=150.0f;
	l2=150.0f;
	m1=10.0f;
	m2=10.0f;
	O1=2.0f*M_PI/2.0f;
	O2=2.0f*M_PI/3.0f;
	w1=0.0f;
	w2=0.0f;
	
	//time
	const float fps=300.0f;
	const float dt=1.0f/fps;
	float accumulator = 0.0f;
	Timer tmr;
	float frameStart=tmr.elapsed();
	
	char platno[HEIGHT/dH][WIDTH/dW+1];
	for(int i=0;i<HEIGHT/dH-1;i++)	platno[i][WIDTH/dW]='\n';
	platno[HEIGHT/dH-1][WIDTH/dW]='\0';
	for(int i=0;i<HEIGHT/dH;i++)
	{
		for(int j=0;j<WIDTH/dW;j++)
		{
			platno[i][j]=' ';
		}
	}
	
	int trace[HEIGHT/dH][WIDTH/dW];
	for(int i=0;i<HEIGHT/dH;i++)
	{
		for(int j=0;j<WIDTH/dW;j++)
		{
			trace[i][j]=0;
		}
	}
	
	//main loop
	while(true)
	{
		gotoxy(0,0);
		//time
		float currentTime=tmr.elapsed();
		accumulator+=currentTime-frameStart;
		
		frameStart=currentTime;
		
		
		if(accumulator>=1.0f/30.0f)	accumulator=1.0f/30.0f;
		
		while(accumulator > dt)
		{
			//just trust the formulas
			float
			alfa1=(  -g*(2*m1 +m2 )*sin(O1 )-g*m2 *sin(O1 -2*O2 )-2*m2 *sin(O1 -O2 )*(w2 *w2 *l2 +w1 *w1 *l1 *cos(O1 -O2 ))  )/(  l1 *(2*m1 +m2 -m2 *cos(2*O1 -2*O2 ))  ),
			alfa2=(  2*sin(O1 -O2 )  )*(  w1 *w1 *l1 *(m1 +m2 ) + g*(m1 +m2 )*cos(O1 ) + w2 *w2 *l2 *m2 *cos(O1 -O2 )  )/l2 /(  2*m1 +m2 -m2 *cos(2*O1 -2*O2 )  );
			
			//time is sped up 10 times for better effect
			w1 +=10*dt*alfa1;
			w2 +=10*dt*alfa2;
			O1 +=10*dt*w1;
			O2 +=10*dt*w2;
				
			
			accumulator-=dt;
			
			for(int i=0;i<HEIGHT/dH;i++)
			{
				for(int j=0;j<WIDTH/dW;j++)
				{
					if(trace[i][j]>0)	trace[i][j]--;	
				}
			}	
		}
		
		//drawing
		for(int i=0;i<HEIGHT/dH;i++)
		{
			for(int j=0;j<WIDTH/dW;j++)
			{
				
				if(platno[i][j]=='@')	trace[i][j]=fps;
				
				if(trace[i][j]>=3*(int)fps/4)	platno[i][j]=':';
				else if(trace[i][j]>=2*(int)fps/4)	platno[i][j]='.';
				else if(trace[i][j]>=(int)fps/4)	(i+j)%2?platno[i][j]='.':platno[i][j]=' ';
				else	platno[i][j]=' ';
			}
		}
		
		int x1=(WIDTH/2+sin(O1)*l1+dW*0.5f)/dW;
		int y1=(cos(O1)*l1+dH*0.5f)/dH+HEIGHT/dH/2;
		
		int x2=x1+(sin(O2)*l2+dW*0.5f)/dW;
		int y2=y1+(cos(O2)*l2+dH*0.5f)/dH;
		
		drawLine(platno,WIDTH/2/dW,HEIGHT/dH/2,x1,y1,'#');
		drawLine(platno,x1,y1,x2,y2,'#');
		
		drawPoint(platno,WIDTH/2/dW,HEIGHT/dH/2,'O');
		drawPoint(platno,x1,y1,'@');
		drawPoint(platno,x2,y2,'@');
		
		puts(platno[0]);
	}
	return 0;
	
}

Detail code here 👇🏻

📌 Github : https://github.com/DinoZ1729/Double-Pendulum

*Beware click the link!

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