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Further simplify getConvexHull() by inlining cross product calculations.

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Jürg Lehni 2013-05-26 17:32:44 -07:00
parent 9edab9c3aa
commit 487c4c4aef
1 changed files with 11 additions and 24 deletions
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35
src/path/Curve.js
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@ -1318,42 +1318,29 @@ new function() { // Scope for methods that require numerical integration
// dq1 and dq2 lie on the same sides on [0, q0, 1, q3]. The hull can be // dq1 and dq2 lie on the same sides on [0, q0, 1, q3]. The hull can be
// a triangle or a quadrilateral and line [0, q0, 1, q3] is part of the // a triangle or a quadrilateral and line [0, q0, 1, q3] is part of the
// hull. Check if the hull is a triangle or a quadrilateral. // hull. Check if the hull is a triangle or a quadrilateral.
var dqMaxX, dqMaxY, vqa1a2X, vqa1a2Y, vqa1MaxX, vqa1MaxY, vqa1MinX, vqa1MinY; var dqmax, cross;
if (Math.abs(distq1) > Math.abs(distq2)) { if (Math.abs(distq1) > Math.abs(distq2)) {
dqMaxX = 1 / 3; dqmax = [ 1 / 3, dq1 ];
dqMaxY = dq1;
// apex is dq3 and the other apex point is dq0 vector // apex is dq3 and the other apex point is dq0 vector
// dqapex->dqapex2 or base vector which is already part of the hull. // dqapex->dqapex2 or base vector which is already part of the hull.
vqa1a2X = 1; // cross = (vqa1a2X * vqa1MinY - vqa1a2Y * vqa1MinX)
vqa1a2Y = dq3 - dq0; // * (vqa1MaxX * vqa1MinY - vqa1MaxY * vqa1MinX)
// vector dqapex->dqMax cross = (dq3 - dq2 - (dq3 - dq0) / 3)
vqa1MaxX = 2 / 3; * (2 * (dq3 - dq2) - dq3 + dq1) / 3;
vqa1MaxY = dq3 - dq1;
// vector dqapex->dqmin
vqa1MinX = 1 / 3;
vqa1MinY = dq3 - dq2;
} else { } else {
dqMaxX = 2 / 3; dqmax = [ 2 / 3, dq2 ];
dqMaxY = dq2;
// apex is dq0 in this case, and the other apex point is dq3 vector // apex is dq0 in this case, and the other apex point is dq3 vector
// dqapex->dqapex2 or base vector which is already part of the hull. // dqapex->dqapex2 or base vector which is already part of the hull.
vqa1a2X = -1; cross = (dq1 - dq0 + (dq0 - dq3) / 3)
vqa1a2Y = dq0 - dq3; * (-2 * (dq0 - dq1) + dq0 - dq2) / 3;
// vector dqapex->dqMax
vqa1MaxX = -2 / 3;
vqa1MaxY = dq0 - dq2;
// vector dqapex->dqmin
vqa1MinX = -1 / 3;
vqa1MinY = dq0 - dq1;
} }
// Compare cross products of these vectors to determine, if // Compare cross products of these vectors to determine, if
// point is in triangles [ dq3, dqMax, dq0 ] or [ dq0, dqMax, dq3 ] // point is in triangles [ dq3, dqMax, dq0 ] or [ dq0, dqMax, dq3 ]
return (vqa1a2X * vqa1MinY - vqa1a2Y * vqa1MinX) return cross < 0
* (vqa1MaxX * vqa1MinY - vqa1MaxY * vqa1MinX) < 0
// Point [2/3, dq2] is inside the triangle, hull is a triangle. // Point [2/3, dq2] is inside the triangle, hull is a triangle.
? [ ? [
[ 0, dq0 ], [ 0, dq0 ],
[ dqMaxX, dqMaxY ], dqmax,
[ 1, dq3 ] [ 1, dq3 ]
] ]
// Convexhull is a quadrilateral and we need all lines in the // Convexhull is a quadrilateral and we need all lines in the