diff --git a/app/lib/world/ellipse.coffee b/app/lib/world/ellipse.coffee index 92f76db88..e940ce8d4 100644 --- a/app/lib/world/ellipse.coffee +++ b/app/lib/world/ellipse.coffee @@ -50,50 +50,18 @@ class Ellipse if shape.isEllipse then @distanceSquaredToEllipse shape else @distanceSquaredToRectangle shape containsPoint: (p, withRotation=true) -> - [a, b] = [@width / 2, @height / 2] - [h, k] = [@x, @y] - [x, y] = [p.x, p.y] - x2 = Math.pow(x, 2) - a2 = Math.pow(a, 2) - a4 = Math.pow(a, 4) - b2 = Math.pow(b, 2) - b4 = Math.pow(b, 4) - h2 = Math.pow(h, 2) - k2 = Math.pow(k, 2) - if withRotation and @rotation - 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 + # "ellipse space" is the cartesian space + # where the ellipse becomes the unit + # circle centered at (0, 0) + [x, y] = [p.x - @x, p.y - @y] # translate point into ellipse space + if withRotation and @rotation # optionally rotate point into ellipse space + c = Math.cos(@rotation) + s = Math.sin(@rotation) + [x, y] = [x*c + y*s, y*c - x*s] + x = x / @width * 2 # scale point into ellipse space + y = y / @height * 2 + x*x + y*y <= 1 #if the resulting point falls on/in the unit circle at 0, 0 + intersectsLineSegment: (p1, p2) -> [px1, py1, px2, py2] = [p1.x, p1.y, p2.x, p2.y]