Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
Convexity-preserving interpolatory subdivision
Computer Aided Geometric Design
A shape controlled fitting method for Be´zier curves
Computer Aided Geometric Design
Convexity preservation of the four-point interpolatory subdivision scheme
Computer Aided Geometric Design
Designing Bézier conic segments with monotone curvature
Computer Aided Geometric Design
An interpolating 4-point C 2 ternary stationary subdivision scheme
Computer Aided Geometric Design
Planar G2 transition with a fair Pythagorean hodograph quintic curve
Journal of Computational and Applied Mathematics
Non-linear subdivision using local spherical coordinates
Computer Aided Geometric Design
Interpolation with cubic spirals
Computer Aided Geometric Design
A generalisation of the Pythagorean hodograph quintic spiral
Journal of Computational and Applied Mathematics
On PH quintic spirals joining two circles with one circle inside the other
Computer-Aided Design
G2 Pythagorean hodograph quintic transition between two circles with shape control
Computer Aided Geometric Design
G2 curve design with a pair of Pythagorean Hodograph quintic spiral segments
Computer Aided Geometric Design
A family of subdivision schemes with cubic precision
Computer Aided Geometric Design
Computer-Aided Design
Normal based subdivision scheme for curve design
Computer Aided Geometric Design
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
Exponential splines and minimal-support bases for curve representation
Computer Aided Geometric Design
Curvature of approximating curve subdivision schemes
Proceedings of the 7th international conference on Curves and Surfaces
Geometric conditions for tangent continuity of interpolatory planar subdivision curves
Computer Aided Geometric Design
Matching admissible G2 Hermite data by a biarc-based subdivision scheme
Computer Aided Geometric Design
Generalization of the incenter subdivision scheme
Graphical Models
A new four-point shape-preserving C3 subdivision scheme
Computer Aided Geometric Design
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A new geometry driven subdivision scheme for curve interpolation is presented in this paper. Given a sequence of points and associated tangent vectors, we get a smooth curve interpolating the initial points by inserting new points iteratively. The new point corresponding to an edge is the incenter of a triangle, which is formed by the edge and the two tangent lines of the two end points, so we call such scheme incenter subdivision scheme. The limit curves are proved to be shape preserving and G^1 continuous, but many numerical examples show that they are G^2 continuous and fair. Generating spiral from two-vertices G^1 Hermite data by the incenter subdivision scheme is also introduced. If all the initial points and their initial tangent vectors are sampled from a circular arc segment, the circular arc segment is reproduced. Several examples are given to demonstrate the excellent properties of the scheme.