Rotation about an Arbitrary Point

In this program we will perform Rotation about an Arbitrary Point i.e. the shape which we will rotate won't move to different position instead it will be at a fixed position on a point.

Here, first we translate the shape to Origin.
Then rotate it about the given angle and translate it back to it's original position i.e. the fixed point.

Translation: Translation is defined as moving the object from one position to another position along straight line path.

Rotation: A rotation repositions all points in an object along a circular path in the plane centered at the pivot point. We rotate an object by an angle theta.
New coordinates after rotation depend on both x and y

• x’ = xcosθ -y sinθ
• y’ = xsinθ+ ycosθ



Code:

	/*
	Title: Rotation about an Arbitrary Point
	Description: C Program to draw any shape and Rotate it about an Arbitrary Point i.e. Fixed Location
	Author: Saideep Dicholkar
	*/
	#include<stdio.h>
	#include<conio.h>
	#include<graphics.h>
	#include<math.h>
	void rotate1(int xt,int yt,double d);
	void stat2(int xt1,int yt1,double d);
	int x=330,y=250;
	int a[4][2]={{50,50},{100,50},{100,100},{50,100}};
	void draw(int x,int y)
	{
	setcolor(WHITE);
	line(x,y-250,x,y+250);
	line(x-330,y,x+330,y);
	}
	void stat(int x,int y)
	{
	line(x+a[0][0],y-a[0][1],x+a[1][0],y-a[1][1]);
	line(x+a[1][0],y-a[1][1],x+a[2][0],y-a[2][1]);
	line(x+a[2][0],y-a[2][1],x+a[3][0],y-a[3][1]);
	line(x+a[3][0],y-a[3][1],x+a[0][0],y-a[0][1]);
	}
	void translate(int x,int y)
	{
	int tx=-50,ty=50,xt,yt,xt1,yt1;
	double d;
	printf("\nEnter Angle of Rotation: ");
	scanf("%lf",&d);
	cleardevice();
	draw(x,y);
	setcolor(WHITE);
	stat(x,y);
	xt=x+tx;
	yt=y+ty;
	getch();
	setcolor(GREEN);
	stat(xt,yt);
	rotate1(xt,yt,d);
	xt1=x-tx;
	yt1=y-ty;
	stat2(xt1,yt1,d);
	}
	void rotate1(int xt,int yt,double d)
	{
	double x2r,y2r,x3r,y3r,x4r,y4r;
	d=(d*3.14)/180;
	x2r=a[0][0]+(((a[1][0]-a[0][0])*cos(d))-((a[1][1]-a[0][1])*sin(d)));
	y2r=a[0][1]+(((a[1][0]-a[0][0])*sin(d))+((a[1][1]-a[0][1])*cos(d)));
	x3r=a[0][0]+(((a[2][0]-a[0][0])*cos(d))-((a[2][1]-a[0][1])*sin(d)));
	y3r=a[0][1]+(((a[2][0]-a[0][0])*sin(d))+((a[2][1]-a[0][1])*cos(d)));
	x4r=a[0][0]+(((a[3][0]-a[0][0])*cos(d))-((a[3][1]-a[0][1])*sin(d)));
	y4r=a[0][1]+(((a[3][0]-a[0][0])*sin(d))+((a[3][1]-a[0][1])*cos(d)));
	getch();
	setcolor(YELLOW);
	line(xt+a[0][0],yt-a[0][1],xt+x2r,yt-y2r);
	line(xt+x2r,yt-y2r,xt+x3r,yt-y3r);
	line(xt+x3r,yt-y3r,xt+x4r,yt-y4r);
	line(xt+x4r,yt-y4r,xt+a[0][0],yt-a[0][1]);
	}
	void stat2(int xt1,int yt1,double d)
	{
	double x2r,y2r,x3r,y3r,x4r,y4r;
	d=(d*3.14)/180;
	x2r=a[0][0]+(((a[1][0]-a[0][0])*cos(d))-((a[1][1]-a[0][1])*sin(d)));
	y2r=a[0][1]+(((a[1][0]-a[0][0])*sin(d))+((a[1][1]-a[0][1])*cos(d)));
	x3r=a[0][0]+(((a[2][0]-a[0][0])*cos(d))-((a[2][1]-a[0][1])*sin(d)));
	y3r=a[0][1]+(((a[2][0]-a[0][0])*sin(d))+((a[2][1]-a[0][1])*cos(d)));
	x4r=a[0][0]+(((a[3][0]-a[0][0])*cos(d))-((a[3][1]-a[0][1])*sin(d)));
	y4r=a[0][1]+(((a[3][0]-a[0][0])*sin(d))+((a[3][1]-a[0][1])*cos(d)));
	getch();
	setcolor(RED);
	line(xt1,yt1,xt1+x2r-a[0][0],yt1-y2r+a[0][1]);
	line(xt1+x2r-a[0][0],yt1-y2r+a[0][1],xt1+x3r-a[0][0],yt1-y3r+a[0][1]);
	line(xt1+x3r-a[0][0],yt1-y3r+a[0][1],xt1+x4r-a[0][0],yt1-y4r+a[0][1]);
	line(xt1+x4r-a[0][0],yt1-y4r+a[0][1],xt1,yt1);
	}
	void main()
	{
	int gd=DETECT,gm,d;
	initgraph(&gd,&gm,"C:\\tc\\bgi");
	cleardevice();
	translate(x,y);
	getch();
	closegraph();
	restorecrtmode();
	}

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Output:

Note: Just copy the files "CGA.bgi" & "EGAVGA.bgi" from bgi folder to bin. So, if you have copied these 2 files then you can skip writing "C:\\tc\\bgi" in initgraph with just ""(2 double quotes)