Spirograph
S
/**
* @file
* @author [Krishna Vedala](https://github.com/kvedala)
* @brief Implementation of
* [Spirograph](https://en.wikipedia.org/wiki/Spirograph)
*
* @details
* Implementation of the program is based on the geometry shown in the figure
* below:
*
* <a
* href="https://commons.wikimedia.org/wiki/File:Resonance_Cascade.svg"><img
* src="https://upload.wikimedia.org/wikipedia/commons/3/39/Resonance_Cascade.svg"
* alt="Spirograph geometry from Wikipedia" style="width: 250px"/></a>
*/
#ifdef USE_GLUT
#ifdef __APPLE__
#include <GLUT/glut.h> // include path on Macs is different
#else
#include <GL/glut.h>
#endif // __APPLE__
#endif
#define _USE_MATH_DEFINES /**< required for MSVC compiler */
#include <array>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <sstream>
#ifdef _OPENMP
#include <omp.h>
#endif
/**
* @namespace spirograph Functions related to spirograph.cpp
*/
namespace spirograph {
/** 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:
* \f{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] \f}
* where
* * \f$R\f$ is the scaling parameter that we will consider \f$=1\f$
* * \f$l=\frac{\rho}{r}\f$ is the relative distance of marker from the centre
* of inner circle and \f$0\le l\le1\f$
* * \f$\rho\f$ is physical distance of marker from centre of inner circle
* * \f$r\f$ is the radius of inner circle
* * \f$k=\frac{r}{R}\f$ is the ratio of radius of inner circle to outer circle
* and \f$0<k<1\f$
* * \f$R\f$ is the radius of outer circle
* * \f$t\f$ is the angle of rotation of the point i.e., represents the time
* parameter
*
* Since we are considering ratios, the actual values of \f$r\f$ and
* \f$R\f$ are immaterial.
*
* @tparam N number of points = size of array
* @param [out] points Array of 2D points represented as std::pair
* @param l the relative distance of marker from the centre of
* inner circle and \f$0\le l\le1\f$
* @param k the ratio of radius of inner circle to outer circle and \f$0<k<1\f$
* @param rot the number of rotations to perform (can be fractional value)
*/
template <std::size_t N>
void spirograph(std::array<std::pair<double, double>, N> *points, double l,
double k, double rot) {
double dt = rot * 2.f * M_PI / N;
double R = 1.f;
const double k1 = 1.f - k;
int32_t step = 0;
#ifdef _OPENMP
#pragma omp for
#endif
for (step = 0; step < N; step++) {
double t = dt * step;
double first = R * (k1 * std::cos(t) + l * k * std::cos(k1 * t / k));
double second = R * (k1 * std::sin(t) - l * k * std::sin(k1 * t / k));
points[0][step].first = first;
points[0][step].second = second;
}
}
/**
* @brief Test function to save resulting points to a CSV file.
*
*/
void test() {
const size_t N = 500;
double l = 0.3, k = 0.75, rot = 10.;
std::stringstream fname;
fname << std::setw(3) << "spirograph_" << l << "_" << k << "_" << rot
<< ".csv";
std::ofstream fp(fname.str());
if (!fp.is_open()) {
perror(fname.str().c_str());
exit(EXIT_FAILURE);
}
std::array<std::pair<double, double>, N> points;
spirograph(&points, l, k, rot);
for (size_t i = 0; i < N; i++) {
fp << points[i].first << "," << points[i].first;
if (i < N - 1) {
fp << '\n';
}
}
fp.close();
}
#ifdef USE_GLUT
static bool paused = 0; /**< flag to set pause/unpause animation */
static const int animation_speed = 25; /**< animation delate in ms */
static const double step = 0.01; /**< animation step size */
static double l_ratio = step * 10; /**< the l-ratio defined in docs */
static double k_ratio = step; /**< the k-ratio defined in docs */
static const double num_rot = 20.; /**< number of rotations to simulate */
/** A wrapper that is not available in all GLUT implementations.
*/
static inline void glutBitmapString(void *font, char *message) {
for (char *ch = message; *ch != '\0'; ch++) glutBitmapCharacter(font, *ch);
}
/**
* @brief Function to graph (x,y) points on the OpenGL graphics window.
*
* @tparam N number of points = size of array
* @param [in] points Array of 2D points represented as std::pair
* @param l the relative distance of marker from the centre of
* inner circle and \f$0\le l\le1\f$ to display info
* @param k the ratio of radius of inner circle to outer circle and \f$0<k<1\f$
* to display info
*/
template <size_t N>
void display_graph(const std::array<std::pair<double, double>, N> &points,
double l, double k) {
glClearColor(1.0f, 1.0f, 1.0f,
0.0f); // Set background color to white and opaque
glClear(GL_COLOR_BUFFER_BIT); // Clear the color buffer (background)
glBegin(GL_LINES); // draw line segments
glColor3f(0.f, 0.f, 1.f); // blue
glPointSize(2.f); // point size in pixels
for (size_t i = 1; i < N; i++) {
glVertex2f(points[i - 1].first, points[i - 1].second); // line from
glVertex2f(points[i].first, points[i].second); // line to
}
glEnd();
glColor3f(0.f, 0.f, 0.f);
std::stringstream buffer;
buffer << std::setw(3) << "l = " << l;
glRasterPos2f(-.85, .85);
glutBitmapString(GLUT_BITMAP_TIMES_ROMAN_24,
const_cast<char *>(buffer.str().c_str()));
buffer.str("");
buffer.clear();
buffer << std::setw(3) << "k = " << k;
glRasterPos2f(-.85, .70);
glutBitmapString(GLUT_BITMAP_TIMES_ROMAN_24,
const_cast<char *>(buffer.str().c_str()));
glutSwapBuffers();
}
/**
* @brief Test function with animation
*
*/
void test2() {
const size_t N = 5000; // number of samples
static bool direction1 = true; // increment if true, otherwise decrement
static bool direction2 = true; // increment if true, otherwise decrement
std::array<std::pair<double, double>, N> points;
spirograph(&points, l_ratio, k_ratio, num_rot);
display_graph(points, l_ratio, k_ratio);
if (paused)
// if paused, do not update l_ratio and k_ratio
return;
if (direction1) { // increment k_ratio
if (k_ratio >= (1.f - step)) // maximum limit
direction1 = false; // reverse direction of k_ratio
else
k_ratio += step;
} else { // decrement k_ratio
if (k_ratio <= step) { // minimum limit
direction1 = true; // reverse direction of k_ratio
if (direction2) { // increment l_ratio
if (l_ratio >= (1.f - step)) // max limit of l_ratio
direction2 = false; // reverse direction of l_ratio
else
l_ratio += step;
} else { // decrement l_ratio
if (l_ratio <= step) // minimum limit of l_ratio
direction2 = true; // reverse direction of l_ratio
else
l_ratio -= step;
}
} else { // no min limit of k_ratio
k_ratio -= step;
}
}
}
/**
* @brief GLUT timer callback function to add animation delay.
*/
void timer_cb(int t) {
glutTimerFunc(animation_speed, timer_cb, 0);
glutPostRedisplay();
}
/**
* @brief Keypress event call back function.
*
* @param key ID of the key pressed
* @param x mouse pointer position at event
* @param y mouse pointer position at event
*/
void keyboard_cb(unsigned char key, int x, int y) {
switch (key) {
case ' ': // spacebar toggles pause
paused = !paused; // toggle
break;
case GLUT_KEY_UP:
case '+': // up arrow key
k_ratio += step;
break;
case GLUT_KEY_DOWN:
case '_': // down arrow key
k_ratio -= step;
break;
case GLUT_KEY_RIGHT:
case '=': // left arrow key
l_ratio += step;
break;
case GLUT_KEY_LEFT:
case '-': // right arrow key
l_ratio -= step;
break;
case 0x1B: // escape key exits
exit(EXIT_SUCCESS);
default:
return;
}
}
#endif
} // namespace spirograph
/** Main function */
int main(int argc, char **argv) {
spirograph::test();
#ifdef USE_GLUT
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE);
glutCreateWindow("Spirograph");
glutInitWindowSize(400, 400);
// glutIdleFunc(glutPostRedisplay);
glutTimerFunc(spirograph::animation_speed, spirograph::timer_cb, 0);
glutKeyboardFunc(spirograph::keyboard_cb);
glutDisplayFunc(spirograph::test2);
glutMainLoop();
#endif
return 0;
}
