Bohumír Bastl

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The aim of this article is to focus on the investigation of such rationally parametrized hypersurfaces which admit rational convolution (RC) generally, or in some special cases. Examples of such hypersurfaces are presented and their properties are discussed. We also aim to examine links between well-known curves and surfaces (PH/PN or LN) and general(More)
The offset surfaces to non-developable quadratic triangular Bézier patches are rational surfaces. In this paper we give a direct proof of this result and formulate an algorithm for computing the parameterization of the offsets. Based on the observation that quadratic triangular patches are capable of producing C smooth surfaces, we use this algorithm to(More)
MOS surfaces are rational surfaces in R which provide rational envelopes of the associated two-parameter family of spheres. Moreover, all the offsets admit rational parameterizations as well. Recently, it has been proved that quadratic triangular Bézier patches in R are MOS surfaces. Following this result, we describe an algorithm for computing an exact(More)
We present a new method for constructing G blending surfaces between an arbitrary number of canal surfaces. The topological relation of the canal surfaces is specified via a convex polyhedron and the design technique is based on a generalization of the medial surface transform. The resulting blend surface consists of trimmed envelopes of oneand(More)
Ringed surfaces and canal surfaces are surfaces that contain a one-parameter family of circles. Ringed surfaces can be described by a radius function, a directrix curve and vector field along the directrix curve, which specifies the normals of the planes that contain the circles. In particular, the class of ringed surfaces includes canal surfaces, which can(More)
In this paper, we describe an algorithm for generating an exact rational envelope of a two-parameter family of spheres given by a quadratic patch in R<sup>3, 1</sup>, which is considered as a medial surface transform (MST) of a spatial domain. Recently, it has been proved that quadratic triangular B&#233;zier patches in R<sup>3, 1</sup> belong to the class(More)