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This paper addresses new methods to solve point inversion problem for parametric surface. As a by-product a new method for ray-surface intersection is also developed. After further analysis, we reduce finding the corresponding parameters of a given point on a surface to the following steps: (1) construct a line segment with the given point as its one end and an arbitrarily selected point on the surface...
This paper presents new methods for G1 and G2 continuous interpolation of an arbitrary sequence of points on an implicit or parametric surface with prescribed tangent direction and both tangent direction and curvature vector, respectively, at every point. We design a G1 or G2 continuous curve in three-dimensional space, construct a so-called directrix vector field using the space curve and then...
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