Calculate a vector from the center of a square to edge based on radius

Question

Given a square (described by x, y, width, height) and an angle (in radians) I need to calculate a vector that originates at the squares centre and terminates at the point th

Answer 1

EDIT: the correct solution for rectangles. It even does not crash if width or height are zeros! Language: C++.

tan(89.99999) thanks to James Fassett for testing my code.

#include                   
#include                   

// declare nonstandard signum function
double sign(double x);                

//define pi because I forgot where it's declared
double const pi = 3.14159;                      

//declare non-standard contangent function      
double cot(double x);                           

int main()                                      
{                                               
    for (double angle = 0.0 ; angle<2*pi; angle += 0.1){
            //angle should be within [0, 2*pi) range    
            //x and y point to the _middle_ of the rectangle
            double x = 0; double y = 0 ;                    
            double width = 1, height = 4;                   
            double base_angle = atan(height/width);         
              // the angle between rectangle diagonal and Ox axis
            double px,py;                                        
            // Which side we're on?                              
            bool left = (fabs(angle - pi) < base_angle);         
            bool right = (angle> 2*pi-base_angle || angle < base_angle);
            bool top = (fabs(angle - pi/2) <= fabs(pi/2 - base_angle)); 
            bool bottom = (fabs(angle - 3*pi/2) <= fabs(pi/2 - base_angle));
            // The helper values used to adjust sides                       
            int lr = (left?-1:0) + (right?1:0);                             
            int tb = (bottom?-1:0) + (top?1:0);                             
            if (lr) {                                                       
                            // we're on vertical edge of rectangle          
                            px = x+width/2*lr;                              
                            py = y+width/2*tan(angle)*lr;
            } else {
                            // we're on the horizontal edge or in the corner
                            px = x+height/2*cot(angle)*tb;
                            py = y+height/2*tb;
            }
            printf("  a = %d deg: x = %lf; y = %lf\n",(int)(angle/pi*180),px,py);
    }

    return 0;
}

// define nonstandard signum function
double sign(double x)
{
    if (x<0) return -1;
    if (x>0) return 1;
    return 0;
}

//define non-standard contangent function
double cot(double x)
{
    return tan(pi/2 - x);
}