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Polar NURBS surface is a kind of periodic NURBS surface, one boundary of which shrinks to a degenerate polar point. The specific topology of its control‐point mesh offers the ability to represent a cap‐like surface, which is common in geometric modeling. However, there is a critical and challenging problem that hinders its application: curvature continuity at the extraordinary singular pole. We first...
We discuss the theory, discretization, and numerics of curves which are evolving such that part of their shape, or at least their curvature as a function of arc length, remains unchanged. The discretization of a curve as a smooth sequence of circular arcs is well suited for such purposes, and allows us to reduce evolution of curves to the evolution of a control point collection in a certain finite‐dimensional...
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