2 research outputs found
Geometric Information and Rational Parametrization of Nonsingular Cubic Blending Surfaces
The techniques for parametrizing nonsingular cubic surfaces have shown to
be of great interest in recent years. This paper is devoted to the rational parametrization of nonsingular cubic blending surfaces. We claim that these nonsingular cubic blending surfaces can be parametrized using the symbolic computation due to their excellent geometric properties. Especially for the specific forms of these surfaces, we conclude that they must be 3, 4, or
5 surfaces, and a criterion is given for deciding their surface types. Besides, using the algorithm proposed by Berry and Patterson in 2001, we obtain the uniform rational parametric representation of these specific forms. It should be emphasized that our results in this paper are invariant under any nonsingular real projective transform. Two explicit examples are presented at the end of this paper
Heterogeneous Parametric Trivariate Fillets
Blending and filleting are well established operations in solid modeling and computer-aided geometric design. The
creation of a transition surface which smoothly connects the boundary surfaces of two (or more) objects has been
extensively investigated. In this work, we introduce several algorithms for the construction of, possibly heterogeneous,
trivariate fillets, that support smooth filleting operations between pairs of, possibly heterogeneous, input trivariates.
Several construction methods are introduced that employ functional composition algorithms as well as introduce a half
Volumetric Boolean sum operation. A volumetric fillet, consisting of one or more tensor product trivariate(s), is fitted
to the boundary surfaces of the input. The result smoothly blends between the two inputs, both geometrically and
material-wise (properties of arbitrary dimension). The application of encoding heterogeneous material information
into the constructed fillet is discussed and examples of all proposed algorithms are presented