spirograph.c File Reference

Implementation of Spirograph More...

#include <math.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>

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Macros
#define	_USE_MATH_DEFINES
	required for MSVC compiler

Functions
void	spirograph (double *x, double *y, double l, double k, size_t N, double rot)
	Generate spirograph curve into arrays x and y such that the i^th point in 2D is represented by (x[i],y[i]).
void	test (void)
	Test function to save resulting points to a CSV file.
int	main (int argc, char **argv)
	Main function.

Detailed Description

Implementation of Spirograph

Author

Krishna Vedala

Implementation of the program is based on the geometry shown in the figure below:

Function Documentation

main()

int main	(	int	argc,
		char **	argv
	)

Main function.

{
    test();
 
#ifdef USE_GLUT
    glutInit(&argc, argv);
    glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE);
    glutCreateWindow("Spirograph");
    glutInitWindowSize(400, 400);
    // glutIdleFunc(glutPostRedisplay);
    glutTimerFunc(animation_speed, timer_cb, 0);
    glutKeyboardFunc(keyboard_cb);
    glutDisplayFunc(test2);
    glutMainLoop();
#endif
 
    return 0;
}

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spirograph()

void spirograph	(	double *	x,
		double *	y,
		double	l,
		double	k,
		size_t	N,
		double	rot
	)

Generate spirograph curve into arrays x and y such that the i^th point in 2D is represented by (x[i],y[i]).

The generating function is given by:

\begin{eqnarray*} x &=& R\left[ (1-k) \cos (t) + l\cdot k\cdot\cos \left(\frac{1-k}{k}t\right) \right]\\ y &=& R\left[ (1-k) \sin (t) - l\cdot k\cdot\sin \left(\frac{1-k}{k}t\right) \right] \end{eqnarray*}

where

• \(R\) is the scaling parameter that we will consider \(=1\)
• \(l=\frac{\rho}{r}\) is the relative distance of marker from the centre of inner circle and \(0\le l\le1\)
• \(\rho\) is physical distance of marker from centre of inner circle
• \(r\) is the radius of inner circle
• \(k=\frac{r}{R}\) is the ratio of radius of inner circle to outer circle and \(0<k<1\)
• \(R\) is the radius of outer circle
• \(t\) is the angle of rotation of the point i.e., represents the time parameter

Since we are considering ratios, the actual values of \(r\) and \(R\) are immaterial.

Parameters

[out]	x	output array containing absicca of points (must be pre-allocated)
[out]	y	output array containing ordinates of points (must be pre-allocated)
	l	the relative distance of marker from the centre of inner circle and \(0\le l\le1\)
	k	the ratio of radius of inner circle to outer circle and \(0<k<1\)
	N	number of sample points along the trajectory (higher = better resolution but consumes more time and memory)
	num_rot	the number of rotations to perform (can be fractional value)

{
    double dt = rot * 2.f * M_PI / N;
    double t = 0.f, R = 1.f;
    const double k1 = 1.f - k;
 
    for (size_t dk = 0; dk < N; dk++, t += dt)
    {
        x[dk] = R * (k1 * cos(t) + l * k * cos(k1 * t / k));
        y[dk] = R * (k1 * sin(t) - l * k * sin(k1 * t / k));
    }
}

test()

void test

(

void

)

Test function to save resulting points to a CSV file.

{
    size_t N = 500;
    double l = 0.3, k = 0.75, rot = 10.;
    char fname[50];
    snprintf(fname, 50, "spirograph_%.2f_%.2f_%.2f.csv", l, k, rot);
    FILE *fp = fopen(fname, "wt");
    if (!fp)
    {
        perror(fname);
        exit(EXIT_FAILURE);
    }
 
    double *x = (double *)malloc(N * sizeof(double));
    double *y = (double *)malloc(N * sizeof(double));
 
    spirograph(x, y, l, k, N, rot);
 
    for (size_t i = 0; i < N; i++)
    {
        fprintf(fp, "%.5g, %.5g", x[i], y[i]);
        if (i < N - 1)
        {
            fputc('\n', fp);
        }
    }
 
    fclose(fp);
 
    free(x);
    free(y);
}

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