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Extrusion Effect For Bezier Curves In JS

is there a tool available for JS to perform a simple extrusion effect to composite cubic Bezier curves (which I will refer to as composite curves), like they are used in SVGs, similar to figure (5) in the picture below? I want the result as a composite curve, not just the rasterization.

The mathematical formulation for this would be dilation with a structural element in the form of a line segment (which can be w.l.o.g. be the unit interval [0, 1] embedded in R^2). So given a set A of points in the plane whose boundary can be described by a composite curve, I am looking for a composite curve describing the set A' := [p ∈ R^2 : ∃q ∈ A : p − q ∈ [0, 1]] of points which are to the right of a point from A, but not further than distance 1.

I imagine one must first find all points on a Bezier segment where the derivative of the curve is horizontal (unless the curve is a horizontal straight line) and divide the curve there. Then horizontal straight lines are inserted between certain (new or old) curve segments. If the shape has holes, the holes are just duplicated, moved to the right and intersected with the original hole. Possibly related to finding the points of inflection.

about 4 years ago · Juan Pablo Isaza
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