Perpendiculars

I often need to construct perpendiculars in my code and found a very elegant solution to this problem in CGAL source.

Given points A(x_a, y_a) and B(x_b, y_b), perpendiculars BB_ccw and BB_cw to the line AB can be constructed at B using either of the following points:

B_ccw(x_b – (y_b – y_a), y_b + (x_b – x_a)) // such that ABB_ccw is oriented counter-clockwise

B_cw(x_b + (y_b – y_a), y_b – (x_b – x_a)) // such that ABB_cw is clockwise.

This follows from the fact that the product of the slopes of perpendicular lines is -1.

Here is code to return either of these points.

#include <cstdio>

struct P2 {
  float x;
  float y;

  P2(float x, float y) : x(x), y(y) {
  }
};

P2 PerpendicularCW(const P2& a, const P2& b){
  return P2(b.x + (b.y - a.y), b.y - (b.x - a.x));
}

P2 PerpendicularCCW(const P2& a, const P2& b){
  return P2(b.x - (b.y - a.y), b.y + (b.x - a.x));
}

int main(){
  P2 a(20, 20), b(80, 60);
  P2 pccw = PerpendicularCCW(a, b);
  P2 pcw = PerpendicularCW(a, b);

  printf("a(%f,%f),b(%f,%f)\n";, a.x, a.y, b.x, b.y);
  printf("pccw(%f,%f)\n", pccw.x, pccw.y);
  printf("pcw(%f,%f)\n", pcw.x, pcw.y);

  return 0;
}

#include

struct P2 {

float x;

float y;

P2(float x, float y) : x(x), y(y) {

}

};

P2 PerpendicularCW(const P2& a, const P2& b){

return P2(b.x + (b.y - a.y), b.y - (b.x - a.x));

}

P2 PerpendicularCCW(const P2& a, const P2& b){

return P2(b.x - (b.y - a.y), b.y + (b.x - a.x));

}

int main(){

P2 a(20, 20), b(80, 60);

P2 pccw = PerpendicularCCW(a, b);

P2 pcw = PerpendicularCW(a, b);

printf("a(%f,%f),b(%f,%f)\n";, a.x, a.y, b.x, b.y);

printf("pccw(%f,%f)\n", pccw.x, pccw.y);

printf("pcw(%f,%f)\n", pcw.x, pcw.y);

return 0;

}

Output:

a(20.000000,20.000000),b(80.000000,60.000000)
pccw(120.000000,0.000000)
pcw(40.000000,120.000000)

a(20.000000,20.000000),b(80.000000,60.000000)

pccw(120.000000,0.000000)

pcw(40.000000,120.000000)