spirograph.c File Reference

Implementation of Spirograph More...

#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.
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

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));
    }
}