Simple 2D collision algorithms

From GDWiki

This article is a stub. You can help out by expanding it.

Sometimes, it is necessary to have formulas for 2D collision detection, and sometimes we do not know how to do the checking. Here follows some basic algorithms for checking whether simple 2D primitives collide or not.

Contents 1 Point collisions 1.1 Point in triangle 1.2 Point in rectangle 1.3 Point in circle 2 Circle collisions 2.1 Circle in circle 2.2 Circle in rectangle 3 Rectangle collisions 3.1 Rectangle in rectangle

[edit] Point collisions

[edit] Point in triangle

// The names t1x, t3y, etc refer to the triangle corners' x and y values
// t1x being the first corner's x value and so on.
// px/py means the point'sx and y values
function PointInTriangle(t1x, t1y, t2x, t2y, t3x, t3y, px, py)
 
  // absolute means the positive version of a number. Ex:
  // absolute(-5) = 5
  // absolute(5)  = 5
  a1 = absolute((t2x-t1x) * (t3y-t1y)  - (t3x-t1x)  * (t2y-t1y))
  a2 = absolute((t1x-px)  * (t2y-py)   - (t2x-px)   * (t1y-py))
  a3 = absolute((t2x-px)  * (t3y-py)   - (t3x-px)   * (t2y-py))
  a4 = absolute((t3x-px)  * (t1y-py)   - (t1x-px)   * (t3y-py))
  result = absolute(a2+a3+a4-a1)
 
  if result <= 1/256
    return true
  else
    return false
end

[edit] Point in rectangle

// rx/ry defines the rectangle's x/y coordinates
// rw/rh defines the rectangle's width and height, respectively 
function PointInRectangle(rx, ry, rw, rh, px, py)
  if px < rx     return false
  if px > rx+rw  return false
  if py < ry     return false
  if py > ry+rh  return false
 
  return true
end

[edit] Point in circle

// cx/cy = the center of the circle, x and y coordinates
// r = radius of the circle
// px/py = the point's x and y coordinates
function PointInCircle(cx, cy, r, px, py)
  if(((px-cx)*(px-cx) + (py-cy)*(py-cy)) <= r*r)
    return true
  return false
end

Note: It is a lot faster without using sqrt. Instead we just use r*r and no sqrt on the other side.

[edit] Circle collisions

[edit] Circle in circle

// c1x/c1y is the first circle's x/y coordinates
// c1r is the first circle's radius
// The same applies to the other parameters, only that it's the second circle
function CircleInCircle(c1x, c1y, c1r, c2x, c2y, c2r)
  if(sqr((c2x-c1x)*(c2x-c1x) + (c2y-c1y)*(c2y-c1y)) <= c1r+c2r)
    return true
  return false
end

[edit] Circle in rectangle

[edit] Rectangle collisions

[edit] Rectangle in rectangle

// r1x/r1y is the first rectangle's x and y position
// r1w/r1h is the first rectangle's width and height
// r2x/r2y/r2w/r2h follow the same principle, but apply to the second rectangle
function RectangleInRectangle(r1x, r1y, r1w, r1h, r2x, r2y, r2w, r2h)
  if r1x+r1w < r2x return false
  if r1x > r2x+r2w return false
  if r1y+r1h < r2y return false
  if r1y > r2y+r2h return false
 
  return true
end