[enhancement] New Graphics implementation with algorithm for spirograph (#936)

* added spirograph program

* add graphics forlder to cmake

* updating DIRECTORY.md

* enable VNC for GUI programs on gitpod

* fix cpplint error

* fix macro definitions for correct documentation

* fix filename in docs

* move include from namespace to global

* download and build freeglut if not available

* install opengl libraries for build check

* fix syntax error

* fix quotes

* install mesa-utils instead

* use markepplace tool instead of installing

* fix syntax

* undo changes to github actions

* OpenGL not mandatory

* add private option to compile definition

* fix: corrected to compile definitions instead of options

* use the macro USE_GLUT

* compile FREEGLUT as a subdirectory. this maintains a consistency

* build freeglut_static when GLUT library not available

* provide keyboard control

* clang-tidy fixes for cb284bddb2a361370d08fe6926036947236bd4c5
Co-authored-by: Ngithub-actions <${GITHUB_ACTOR}@users.noreply.github.com>

.gitpod.dockerfile

-FROM gitpod/workspace-full
+FROM gitpod/workspace-full-vnc
 
 RUN sudo apt-get update \
- && sudo apt-get install -y \
-    doxygen \
-    graphviz \
-    ninja-build \
- && pip install cpplint \
- && sudo rm -rf /var/lib/apt/lists/*
+   && sudo apt-get install -y \
+   doxygen \
+   graphviz \
+   ninja-build \
+   && pip install cpplint \
+   && sudo rm -rf /var/lib/apt/lists/*

CMakeLists.txt

@@ -17,7 +17,28 @@ if(MSVC)
 endif(MSVC)
 
 option(USE_OPENMP "flag to use OpenMP for multithreading" ON)
-
+if(USE_OPENMP)
+    find_package(OpenMP)
+    if (OpenMP_CXX_FOUND)
+        message(STATUS "Building with OpenMP Multithreading.")
+    else()
+        message(STATUS "No OpenMP found, no multithreading.")
+    endif()
+endif()
+    
+add_subdirectory(math)
+add_subdirectory(others)
+add_subdirectory(search)
+add_subdirectory(ciphers)
+add_subdirectory(strings)
+add_subdirectory(sorting)
+add_subdirectory(geometry)
+add_subdirectory(graphics)
+add_subdirectory(probability)
+add_subdirectory(data_structures)
+add_subdirectory(machine_learning)
+add_subdirectory(numerical_methods)
+    
 cmake_policy(SET CMP0054 NEW)
 cmake_policy(SET CMP0057 NEW)
 find_package(Doxygen OPTIONAL_COMPONENTS dot dia)
@@ -34,6 +55,7 @@ if(DOXYGEN_FOUND)
     set(DOXYGEN_STRIP_CODE_COMMENTS NO)
     set(DOXYGEN_EXT_LINKS_IN_WINDOW YES)
     set(DOXYGEN_BUILTIN_STL_SUPPORT YES)
+    set(DOXYGEN_ENABLE_PREPROCESSING YES)
     set(DOXYGEN_CLANG_ASSISTED_PARSING YES)
     set(DOXYGEN_FILE_PATTERNS *.cpp *.h *.hpp *.md)
     set(DOXYGEN_MATHJAX_EXTENSIONS  TeX/AMSmath TeX/AMSsymbols)
@@ -48,6 +70,12 @@ if(DOXYGEN_FOUND)
         set(DOXYGEN_INTERACTIVE_SVG YES)
         set(DOXYGEN_DOT_IMAGE_FORMAT "svg")
     endif()
+    if(OPENMP_FOUND)
+        set(DOXYGEN_PREDEFINED "_OPENMP=1")
+    endif()
+    if(GLUT_FOUND)
+        set(DOXYGEN_PREDEFINED ${DOXYGEN_PREDEFINED} "GLUT_FOUND=1")
+    endif()
 
     doxygen_add_docs(
         doc
@@ -56,27 +84,6 @@ if(DOXYGEN_FOUND)
     )
 endif()
 
-if(USE_OPENMP)
-    find_package(OpenMP)
-    if (OpenMP_CXX_FOUND)
-        message(STATUS "Building with OpenMP Multithreading.")
-    else()
-        message(STATUS "No OpenMP found, no multithreading.")
-    endif()
-endif()
-
-add_subdirectory(math)
-add_subdirectory(others)
-add_subdirectory(search)
-add_subdirectory(ciphers)
-add_subdirectory(strings)
-add_subdirectory(sorting)
-add_subdirectory(geometry)
-add_subdirectory(probability)
-add_subdirectory(data_structures)
-add_subdirectory(machine_learning)
-add_subdirectory(numerical_methods)
-
 set(CPACK_PROJECT_NAME ${PROJECT_NAME})
 set(CPACK_PROJECT_VERSION ${PROJECT_VERSION})
 include(CPack)

DIRECTORY.md

@@ -84,6 +84,9 @@
   * [Topological Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/topological_sort.cpp)
   * [Topological Sort By Kahns Algo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/topological_sort_by_kahns_algo.cpp)
 
+## Graphics
+  * [Spirograph](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graphics/spirograph.cpp)
+
 ## Greedy Algorithms
   * [Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/dijkstra.cpp)
   * [Huffman](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/huffman.cpp)

graphics/CMakeLists.txt

+find_package(OpenGL)
+if(OpenGL_FOUND)
+    find_package(GLUT)
+    if(NOT GLUT_FOUND)
+        message("FreeGLUT library will be downloaded and built.")
+        include(ExternalProject)
+        ExternalProject_Add (
+            FREEGLUT-PRJ
+            URL https://sourceforge.net/projects/freeglut/files/freeglut/3.2.1/freeglut-3.2.1.tar.gz
+            URL_MD5 cd5c670c1086358598a6d4a9d166949d
+            CMAKE_GENERATOR ${CMAKE_GENERATOR}
+            CMAKE_GENERATOR_TOOLSET ${CMAKE_GENERATOR_TOOLSET}
+            CMAKE_GENERATOR_PLATFORM ${CMAKE_GENERATOR_PLATFORM}
+            CMAKE_ARGS  -DCMAKE_BUILD_TYPE=Release
+                        -DFREEGLUT_BUILD_SHARED_LIBS=OFF
+                        -DFREEGLUT_BUILD_STATIC_LIBS=ON
+                        -DFREEGLUT_BUILD_DEMOS=OFF
+            PREFIX ${CMAKE_CURRENT_BINARY_DIR}/freeglut
+            # BINARY_DIR ${CMAKE_CURRENT_BINARY_DIR}/freeglut-build
+            # BUILD_IN_SOURCE ON
+            # UPDATE_COMMAND ""
+            INSTALL_COMMAND ""
+            # CONFIGURE_COMMAND ""
+            # BUILD_COMMAND ""
+        )
+        ExternalProject_Get_Property(FREEGLUT-PRJ SOURCE_DIR)
+        ExternalProject_Get_Property(FREEGLUT-PRJ BINARY_DIR)
+        set(FREEGLUT_BIN_DIR ${BINARY_DIR})
+        set(FREEGLUT_SRC_DIR ${SOURCE_DIR})
+        # add_library(libfreeglut STATIC IMPORTED)
+        # set_target_properties(libfreeglut PROPERTIES IMPORTED_LOCATION ${FREEGLUT_BIN_DIR})
+
+        # set(FREEGLUT_BUILD_DEMOS OFF CACHE BOOL "")
+        # set(FREEGLUT_BUILD_SHARED_LIBS OFF CACHE BOOL "")
+        # set(FREEGLUT_BUILD_STATIC_LIBS ON CACHE BOOL "")
+        # add_subdirectory(${FREEGLUT_SRC_DIR} ${FREEGLUT_BIN_DIR} EXCLUDE_FROM_ALL)
+        # add_subdirectory(${BINARY_DIR})
+        # find_package(FreeGLUT)
+    endif(NOT GLUT_FOUND)
+else(OpenGL_FOUND)
+    message(WARNING "OPENGL not found. Will not build graphical outputs.")
+endif(OpenGL_FOUND)
+
+# If necessary, use the RELATIVE flag, otherwise each source file may be listed
+# with full pathname. RELATIVE may makes it easier to extract an executable name
+# automatically.
+file( GLOB APP_SOURCES RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} *.cpp )
+# file( GLOB APP_SOURCES ${CMAKE_SOURCE_DIR}/*.c )
+# AUX_SOURCE_DIRECTORY(${CMAKE_CURRENT_SOURCE_DIR} APP_SOURCES)
+foreach( testsourcefile ${APP_SOURCES} )
+    # I used a simple string replace, to cut off .cpp.
+    string( REPLACE ".cpp" "" testname ${testsourcefile} )
+    add_executable( ${testname} ${testsourcefile} )
+
+    set_target_properties(${testname} PROPERTIES LINKER_LANGUAGE CXX)
+    if(OpenMP_CXX_FOUND)
+        target_link_libraries(${testname} PRIVATE OpenMP::OpenMP_CXX)
+    endif()
+    
+    if(OpenGL_FOUND)
+        if(NOT GLUT_FOUND)
+            add_dependencies(${testname} FREEGLUT-PRJ)
+            target_compile_definitions(${testname} PRIVATE FREEGLUT_STATIC)
+            target_include_directories(${testname} PRIVATE ${FREEGLUT_SRC_DIR}/include)
+            target_link_directories(${testname} PRIVATE ${FREEGLUT_BIN_DIR}/lib)
+            target_link_libraries(${testname} PRIVATE OpenGL::GL)
+            target_link_libraries(${testname} INTERFACE FREEGLUT-PRJ)
+            # target_include_directories(${testname} PRIVATE ${FREEGLUT_INCLUDE_DIRS})
+            # target_link_libraries(${testname} INTERFACE freeglut_static)
+        else()
+            target_include_directories(${testname} PRIVATE ${GLUT_INCLUDE_DIRS})
+            target_link_libraries(${testname} PRIVATE OpenGL::GL ${GLUT_LIBRARIES})
+        endif()
+        target_compile_definitions(${testname} PRIVATE USE_GLUT)
+    endif(OpenGL_FOUND)
+    
+    if(APPLE)
+        target_compile_options(${testname} PRIVATE -Wno-deprecated)
+    endif(APPLE)
+    
+    install(TARGETS ${testname} DESTINATION "bin/graphics")
+
+endforeach( testsourcefile ${APP_SOURCES} )

graphics/spirograph.cpp

+/**
+ * @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;
+}