11/7/2023 0 Comments Librecad 3![]() ![]() Var uy:Number = Math.pow( 3 * controlPointA.y - 2 * pointA.y - pointB.y, 2 ) Var ux:Number = Math.pow( 3 * controlPointA.x - 2 * pointA.x - pointB.x, 2 ) Here is a cool method to find flatness of a line. ![]() This will help optimize your algorithm for offsetting, by breaking the curve into as few of lines as visually required. You can check the flatness level to determine if the curve needs to be sub divided again and again. When your flattening a curve some curves need more subdivision than others. Var rightCurve:CubicBezierCurve = new CubicBezierCurve() Var leftCurve:CubicBezierCurve = new CubicBezierCurve() Var newPoint:Point = new StraightLine( innerA.lerp( time ), innerB.lerp( time )).lerp( time ) Var innerB:StraightLine = new StraightLine( outerBridge.lerp( time ), outerB.lerp( time )) Var innerA:StraightLine = new StraightLine( outerA.lerp( time ), outerBridge.lerp( time )) Var outerB:StraightLine = new StraightLine( controlPointB, pointB ) Var outerBridge:StraightLine = new StraightLine( controlPointA, controlPointB ) Var outerA:StraightLine = new StraightLine( pointA, controlPointA ) ![]() Public function subDivide( time:Number ):Vector. To convert the curve to line segments we use De Casteljau’s algorithm. Step #1: Subdivide the Curve into Line Segments However, there are heuristic methods that usually give an adequate approximation for practical purposes. The curve at a fixed offset from a given Bézier curve, often called an offset curve (lying “parallel” to the original curve, like the offset between rails in a railroad track), cannot be exactly formed by a Bézier curve (except in some trivial cases). Short answer it’s impossible to create a perfect offset curve. ![]()
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