C2 Hermite interpolation by Minkowski Pythagorean hodograph curves and medial axis transform approximation
نویسندگان
چکیده
Article history: Available online 29 April 2010
منابع مشابه
C 1 Hermite interpolation by Pythagorean hodograph quintics in Minkowski space
Curves in the Minkowski space R2,1 are very well suited to describe the medial axis transform (MAT) of planar domains. Among them, Minkowski Pythagorean hodograph (MPH) curves correspond to domains where both the boundaries and their offsets admit rational parameterizations [4,13]. We construct MPH quintics which interpolate two points with associated first derivative vectors and analyze the pr...
متن کاملG1 Hermite interpolation by Minkowski Pythagorean hodograph cubics
As observed by Choi et al. (1999), curves in Minkowski space R2,1 are very well suited to describe the medial axis transform (MAT) of a planar domain, and Minkowski Pythagorean hodograph (MPH) curves correspond to domains, where both the boundaries and their offsets are rational curves (Moon, 1999). Based on these earlier results, we give a thorough discussion of G1 Hermite interpolation by MPH...
متن کاملPii: S0010-4485(98)00080-3
We present a new approach to medial axis transform and offset curve computation. Our algorithm is based on the domain decomposition scheme which reduces a complicated domain into a union of simple subdomains each of which is very easy to handle. This domain decomposition approach gives rise to the decomposition of the corresponding medial axis transform which is regarded as a geometric graph in...
متن کاملA unified Pythagorean hodograph approach to the medial axis transform and offset approximation
Algorithms based on Pythagorean hodographs (PH) both in Euclidean plane and Minkowski space share common goals, the main one being rationality of offsets of planar domains. However, only separate interpolation techniques based on these curves can be found in the literature. It was recently revealed that rational PH curves in Euclidean plane and Minkowski space are very closely related. In this ...
متن کاملC Hermite Interpolation by Pythagorean Hodograph Space Curves
We solve the problem of C2 Hermite interpolation by Pythagorean Hodograph (PH) space curves. More precisely, for any set of C2 space boundary data (two points with associated first and second derivatives) we construct a four–dimensional family of PH interpolants of degree 9 and introduce a geometrically invariant parameterization of this family. This parameterization is used to identify a parti...
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عنوان ژورنال:
- Computer Aided Geometric Design
دوره 27 شماره
صفحات -
تاریخ انتشار 2010