How to find points on circle when center, radius, and angle is given in C?

Question

I have a triangle that i am trying to rotate(on 2D plain). I calculated it's centroid so, now i have an imaginary circle with center(centroid),points at 0 degree angle (1st vertex of the trangle). My idea is to rotate each vertex by increasing it's angle(on a loop) and finding new coordinates for the vertex at that angle.


#include <stdio.h>
#include <math.h>

//"the function"

int calculate_new_vertex_for_trangle(int center_x, int center_y,int x_at_0,int y_at_0,int angle)
{
    double radius = sqrt(pow(x_at_0-center_x,2)+pow(y_at_0-center_y,2));

    float angle_to_radian = ((22.0/7.0)/180)*angle;

    // googled formula 
    float new_x = center_x + radius*cos(angle_to_radian);
    float new_y = center_y + radius*sin(angle_to_radian);

    printf("x : %f, y : %f \nradius : %f\n",  new_x, new_y,radius);

    return 0;
}

Expected Output

But the result I got was :Image

Numbers at the end of the lines are coordinate's position at respective angle i got using "the function".

You're not taking into account your starting vertex's angle, so your essentially rotating the point at (radius, 0). 22/7 is a poor approximation for Pi, see https://stackoverflow.com/questions/1727881/how-to-use-the-pi-constant-in-c — Mat, Sep 01 '22 at 15:53
Related question: [2D Euclidean vector rotations](https://stackoverflow.com/questions/4780119/2d-euclidean-vector-rotations) — Weather Vane, Sep 01 '22 at 16:13

score 1 · Answer 1 · answered Sep 01 '22 at 16:41

I think, a good way to rotate a point around another one, is to use the rotation matrix. You can find more details about this on Wikipedia: https://en.wikipedia.org/wiki/Rotation_matrix

I hope this sample code will help you:

#include <stdio.h>
#include <math.h>

int main()
{

    // Center on circle
    float center_x = 0.0;
    float center_y = 0.0;
    
    // Point on circle
    float point_x = 1.0;
    float point_y = 1.0;
    
    // Rotation angle
    float rotation_deg = 180;
    float rotation_rad = rotation_deg * M_PI / 180.0;
    
    // Rotation matrix
    float a = cos(rotation_rad);
    float b = -sin(rotation_rad);
    float c = sin(rotation_rad);
    float d = cos(rotation_rad);
    
    // Matrix multiplication
    float dx = point_x - center_x;
    float dy = point_y - center_y;
    float new_x = a * dx + b * dy;
    float new_y = c * dx + d * dy;
    
    // Add center point
    new_x += center_x;
    new_y += center_y;
    
    printf("old_point = %.2f|%.2f\n", point_x, point_y);
    printf("new_point = %.2f|%.2f\n", new_x, new_y);
    
}

Regards.

thanks, i was searching for this before but i got lost in the google's mess. — Nabin Paudel, Sep 03 '22 at 12:05

Ripi2 · Accepted Answer · 2022-09-01T17:12:29.410

This formula:

float new_x = center_x + radius*cos(angle_to_radian);
float new_y = center_y + radius*sin(angle_to_radian);

gives the new position of the vertex at angle=0 after a counter-clockwise rotation around (center_x, center_y). But you want the new position for any vertex.

You can calculate the initial angle (counter-clockwise) for a point at (px,py):

float angle_ini = atan2(px-center_x, py-center_y);

And then use it for the rotated position:

float new_x = center_x + radius*cos(angle_to_radian + angle_ini);
float new_y = center_y + radius*sin(angle_to_radian + angle_ini);

There's a second formula wich achieves the same result, called "rotation transform"

float angle_to_radian = (3.14159265358979/180)*angle;
float sinA = sin(angle_to_radian);
float cosA = cos(angle_to_radian);
float new_x = center_x + (px-center_x)*cosA - (py-center_y)*sinA;
float new_y = center_y + (px-center_x)*sinA + (py-center_y)*cosA;

Notice that with this second way you avoid calculating the radius.

Shouldn't `px*cosA` be `(px-center_x)*cosA`, etc.? – Ian Abbott Sep 01 '22 at 17:07 — Ian Abbott, Sep 01 '22 at 17:07

How to find points on circle when center, radius, and angle is given in C?

2 Answers2