Planar Bisector CurvesBased on Developable

نویسنده

  • Jung-Ju Choi
چکیده

This paper presents an algorithm to compute the bisector curve of two planar paramet-ric curves. We reduce the problem of computing a bisector curve to that of intersecting two developable surfaces. Given an input curve C (t) = (x(t); y(t)), the corresponding developable surface D C(t) is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the paraboloid z = x 2 + y 2 along a lifted curve b C (t) = ? x(t); y(t); x(t) 2 + y(t) 2. Compared with general surface/surface intersection, de-velopable surface/surface intersection is considerably more robust and eecient.

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تاریخ انتشار 2007