ProjectiveAnimation.cpp

/*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/

#include <GL/gl.h>
#include <GL/glu.h>
#include <GL/glut.h>

#include <cmath>
#include <utility>
#include <vector>
#include <complex>

#define PRECISION 0.0001

using namespace std;

vector<pair<pair<float, float> , float> > circles;
complex<float> polarCenter(0.0f, 0.0f);
float polarRadius = 10.0f;

void driveCircle(int x, int y)
{
	polarCenter.real((x - 300) / 3);
	polarCenter.imag((300 - y) / 3);

	return;
}

void circle(pair<pair<float, float> , float> c)
{
	glBegin(GL_LINE_LOOP);
	for (float i = 0; i < 2 * M_PI; i += PRECISION)
		glVertex2f(c.second * cos(i) + c.first.first, c.second * sin(i) + c.first.second);
	glEnd();
}

void display()
{
	glClear(GL_COLOR_BUFFER_BIT);
	glMatrixMode(GL_MODELVIEW);
	glLoadIdentity();

	glColor3f(1.0f, 1.0f, 1.0f);

	complex<float> i(0.0f, 1.0f);

	//circle(make_pair(make_pair(polarCenter.real(), polarCenter.imag()), polarRadius));

	for (vector<pair<pair<float, float> , float> >::iterator k = circles.begin(); k < circles.end(); k++)
	{
		complex<float> newCircle(k->first.first, k->first.second);
		float newRadius = k->second;

		glColor3f(1.0f, 1.0f, 0.0f);
		//circle(*k);

		glColor3f(1.0f, 0.0f, 0.0f);
		glBegin(GL_POINTS);
		for (float k = 0.0f; k < 2 * M_PI; k += PRECISION)
		{
			complex<float> point(newRadius * cos(k), newRadius * sin(k));

			float projLength = ((polarCenter - point - newCircle) * abs(point) / (i * point)).real();
			complex<float> projection = point + newCircle + i * projLength * point / abs(point);
			complex<float> pole = pow(30.0f, 2) / conj(projection - polarCenter) + polarCenter;

			glVertex2f(pole.real(), pole.imag());
		}
		glEnd();
	}

	glutSwapBuffers();
}

void init()
{
	glClearColor(0.0f, 0.0f, 0.0f, 1.0f);
	glMatrixMode(GL_PROJECTION);
	glLoadIdentity();
	gluOrtho2D(-100.0f, 100.0f, -100.0f, 100.0f);
	glMatrixMode(GL_MODELVIEW);

	return;
}

int main(int argc, char** argv)
{
	glutInit(&argc, argv);
	glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB);
	glutInitWindowSize(600, 600);
	glutCreateWindow("Projective Animation");
	glutIdleFunc(display);
	glutPassiveMotionFunc(driveCircle);

	circles.push_back(make_pair(make_pair(0.0f, 0.0f), 10.0f));
	circles.push_back(make_pair(make_pair(0.0f, 0.0f), 20.0f));
	circles.push_back(make_pair(make_pair(0.0f, 0.0f), 30.0f));
	circles.push_back(make_pair(make_pair(0.0f, 0.0f), 40.0f));
	circles.push_back(make_pair(make_pair(0.0f, 0.0f), 50.0f));
	circles.push_back(make_pair(make_pair(0.0f, 0.0f), 60.0f));
	circles.push_back(make_pair(make_pair(0.0f, 0.0f), 70.0f));
	circles.push_back(make_pair(make_pair(0.0f, 0.0f), 80.0f));
	circles.push_back(make_pair(make_pair(0.0f, 0.0f), 90.0f));
	circles.push_back(make_pair(make_pair(0.0f, 0.0f), 100.0f));

	init();

	glutMainLoop();

	return 0;
}