Draw an Ellipse rotating over a Circle in C++ graphics

graphics.h library is used to include and facilitate graphical operations in the program. graphics.h functions can be used to draw different shapes, display text in different fonts, change colours and many more. Using functions of graphics.h you can make graphics programs, animations, projects and games. You can draw circles, lines, rectangles, bars and many other geometrical figures. You can change their colours using the available functions and fill them.

Approach:
The idea is to decrease the angle(through which ellipse is going to slide) by an integral value and calculating the corresponding angle swiped by the circle’s radius using the ratio of their perimeters.

How to show the sliding on screen:



  1. Draw the Ellipse at calculated point using white color.
  2. Introduce some delay in function(in ms).
  3. Erase the previous Ellipse by drawing the Ellipse at same point using black color.
  4. Repeat from Step 1.

Below is the C++ representation of the above problem

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// C++ program to draw an Ellipse
// rotating over a Circle using graphics
  
#include <conio.h>
#include <graphics.h>
#include <iostream>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
  
using namespace std;
  
// Ellipse drawing function
void drawEllipse(int xc, int yc, int a, int b,
                 float alpha, int color)
{
    float t = 3.14 / 180;
    alpha = 360 - alpha;
    setcolor(color);
    int theta;
  
    // Filling each pixel corresponding
    // to every angle from 0 to 360
    for (int i = 0; i < 360; i += 1) {
        theta = i;
        int x = a * cos(t * theta) * cos(t * alpha)
                + b * sin(t * theta) * sin(t * alpha);
  
        int y = b * sin(t * theta) * cos(t * alpha)
                - a * cos(t * theta) * sin(t * alpha);
  
        putpixel(xc + x, yc - y, color);
    }
}
  
// Function to calculate the position
// of ellipse after each rotation
void slidePattern(int xc, int yc, int r, int a, int b,
                  int alpha, float p, int color)
{
    setcolor(color);
    float t = 3.14 / 180;
    float t1, t2, d;
    float angle = (p * alpha);
  
    // Calculation for center of Ellipse
    t1 = cos(t * fmod(angle, 360));
    t2 = sin(t * fmod(angle, 360));
    t1 *= t1;
    t2 *= t2;
    t1 = t1 / (a * a);
    t2 = t2 / (b * b);
    d = sqrt(t1 + t2);
    d = 1 / d;
  
    int draw_x = xc + (r + d) * cos(t * alpha);
    int draw_y = yc - (r + d) * sin(t * alpha);
    int draw_ang = angle + alpha;
  
    drawEllipse(draw_x, draw_y, a,
                b, draw_ang, color);
}
  
// Function to increment the angle
// of rotation
void ellipseovercircle(int xc, int yc,
                       int r, int a, int b)
{
    float theta = 0;
    double h, p1;
  
    // Calculating the ratio of
    // perimeters of Ellipse and Circle
    h = (a * a) + (b * b);
    h /= 2;
    p1 = sqrt(h);
    p1 /= r;
    p1 = 1 / (p1);
  
    // by decreasing theta we can
    // move Ellipse clockwise
    for (;; theta -= 1) {
  
        // Draw Ellipse at new location
        // using White color
        slidePattern(xc, yc, r, a, b,
                     theta, p1, WHITE);
  
        circle(xc, yc, r); // Drawing Circle
        delay(25); // Introducing delay
  
        // Erase the existing Ellipse
        slidePattern(xc, yc, r, a, b,
                     theta, p1, BLACK);
    }
}
  
// Driver code
int main()
{
    // Initialize graphics function
    int gd = DETECT, gm;
    initgraph(&gd, &gm, "");
  
    // maximum X-coordinate for the window
    int maxx = getmaxx();
  
    // maximum Y-coordinate for the window
    int maxy = getmaxy();
  
    // Start drawing from the mid of the screen
    ellipseovercircle(maxx / 2, maxy / 2,
                      100, 40, 28);
  
  
    closegraph();
    return 0;
}

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