Convexity-preserving interpolatory subdivision
Computer Aided Geometric Design
A variational approach to subdivision
Computer Aided Geometric Design
Convexity preservation of the four-point interpolatory subdivision scheme
Computer Aided Geometric Design
An interpolating 4-point C 2 ternary stationary subdivision scheme
Computer Aided Geometric Design
Non-linear subdivision using local spherical coordinates
Computer Aided Geometric Design
Surface interpolation of meshes by geometric subdivision
Computer-Aided Design
A note on the paper “Normal based subdivision scheme for curve design” by Xunnian Yang
Computer Aided Geometric Design
A local fitting algorithm for converting planar curves to B-splines
Computer Aided Geometric Design
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In this paper we propose a new kind of nonlinear and geometry driven subdivision scheme for curve interpolation. Instead of using linear combination of old vertexes, displacement vector for every new vertex is given by normal vectors at old vertexes. The normal vectors are computed adaptively for each time of subdivision, and the limit curve is G1 smooth with wide ranges of free parameters. With this new scheme, normal vectors at selected vertexes can be interpolated efficiently. A shape preserving subdivision scheme with explicit choices of all free parameters is also presented.