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

Include dependency graph for spirograph.c:

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])`. More...

void	test (void)
	Test function to save resulting points to a CSV file. More...

int	main (int argc, char **argv)
	Main function. More...

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;
}

Here is the call graph for this function:

◆ 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);
}