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Update ellipse.coffee

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An improved (and untested) implementation for containsPoint
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coder0xff 2015-02-23 01:09:39 -05:00
parent 63b24b9bf1
commit 9a85db4a91
1 changed files with 11 additions and 44 deletions
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55
app/lib/world/ellipse.coffee
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@ -50,50 +50,17 @@ class Ellipse
if shape.isEllipse then @distanceSquaredToEllipse shape else @distanceSquaredToRectangle shape if shape.isEllipse then @distanceSquaredToEllipse shape else @distanceSquaredToRectangle shape
containsPoint: (p, withRotation=true) -> containsPoint: (p, withRotation=true) ->
[a, b] = [@width / 2, @height / 2] # "ellipse space" is the cartesian space
[h, k] = [@x, @y] # where the ellipse becomes the unit
[x, y] = [p.x, p.y] # circle centered at (0, 0)
x2 = Math.pow(x, 2) [x, y] = [p.x - @x, p.y - @y] # translate point into ellipse space
a2 = Math.pow(a, 2) if withRotation and @rotation # optionally rotate point into ellipse space
a4 = Math.pow(a, 4) c = Math.cos(@rotation)
b2 = Math.pow(b, 2) s = Math.sin(@rotation)
b4 = Math.pow(b, 4) [x, y] = [x*c + y*s, y*c + x*s]
h2 = Math.pow(h, 2) x = x / @width # scale point into ellipse space
k2 = Math.pow(k, 2) y = y / @height
if withRotation and @rotation x*x + y*y <= 1 #if the resulting point falls on/in the unit circle at 0, 0
sint = Math.sin(@rotation)
sin2t = Math.sin(2 * @rotation)
cost = Math.cos(@rotation)
cos2t = Math.cos(2 * @rotation)
numeratorLeft = (-a2 * h * sin2t) + (a2 * k * cos2t) + (a2 * k) + (a2 * x * sin2t)
numeratorMiddle = Math.SQRT2 * Math.sqrt((a4 * b2 * cos2t) + (a4 * b2) - (a2 * b4 * cos2t) + (a2 * b4) - (2 * a2 * b2 * h2) + (4 * a2 * b2 * h * x) - (2 * a2 * b2 * x2))
numeratorRight = (b2 * h * sin2t) - (b2 * k * cos2t) + (b2 * k) - (b2 * x * sin2t)
denominator = (a2 * cos2t) + a2 - (b2 * cos2t) + b2
solution1 = (numeratorLeft - numeratorMiddle + numeratorRight) / denominator
solution2 = (numeratorLeft + numeratorMiddle + numeratorRight) / denominator
if (not isNaN solution1) and (not isNaN solution2)
[bigSolution, littleSolution] = if solution1 > solution2 then [solution1, solution2] else [solution2, solution1]
if y > littleSolution and y < bigSolution
return true
else
return false
else
return false
else
numeratorLeft = a2 * k
numeratorRight = Math.sqrt((a4 * b2) - (a2 * b2 * h2) + (2 * a2 * b2 * h * x) - (a2 * b2 * x2))
denominator = a2
solution1 = (numeratorLeft + numeratorRight) / denominator
solution2 = (numeratorLeft - numeratorRight) / denominator
if (not isNaN solution1) and (not isNaN solution2)
[bigSolution, littleSolution] = if solution1 > solution2 then [solution1, solution2] else [solution2, solution1]
if y > littleSolution and y < bigSolution
return true
else
return false
else
return false
false
intersectsLineSegment: (p1, p2) -> intersectsLineSegment: (p1, p2) ->
[px1, py1, px2, py2] = [p1.x, p1.y, p2.x, p2.y] [px1, py1, px2, py2] = [p1.x, p1.y, p2.x, p2.y]