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