Smooth Blending of Basic Surfaces Using Trivariate Box Splines
نویسنده
چکیده
To blend between basic implicitly deened CSG surfaces we propose to use the zero set of a spline in three variables. The resulting blend surface is generically curvature continuous, of algebraic degree four independent of the number of surfaces joined, and supports both point classiication and eecient rendering. A detailed exposition of the 2D analogue blend construction is given.
منابع مشابه
Blending Basic Implicit Shapes Using Trivariate Box Splines
To blend be~ween simple implicit surfaces, such as the sphere, the cone, the cylinder and the torus, we propose La locally employ the zero set of a serendipitous trivariate box spline. This box spline is defined by seven directions that form a regular partition of space into tetrahedra. The resulting blend surface is curvature continuous. An approxlmateparametrization of the piecewise implicit ...
متن کاملOptimal Sampling Lattices and Trivariate Box Splines
The Body Centered Cubic (BCe) and Face Centered Cubic (FCC) lattices along with a set of box splines for sampling and reconstruction of trivariate functions are proposed. The BCC lattice is demonstrated to be the optimal choice of a pattern for generic sampling purposes. While the FCC lattice is the second best choice for this purpose, both FCC and BCC lattices significantly outperform the accu...
متن کاملSmooth multi-sided blending of biquadratic splines
Biquadratic (bi-2) splines are the simplest choice for converting a regular quad meshes into smooth tensor-product spline surfaces. Existing methods for blending three, five or more such bi-2 spline surfaces using surface caps consisting of pieces of low polynomial degree suffer from artifacts ranging from flatness to oscillations. The new construction, based on reparameterization of the bi-2 s...
متن کاملHierarchical multiresolution reconstruction of shell surfaces
We present an adaptive, hierarchical Hh-multiresolution reconstruction algorithm to model shell surface objects from a matched pair of triangulated surfaces. Shell surfaces are an interval of contours of trivariate functions with prismatic support. In the H-direction, a hierarchical representation of the scaffold is constructed. For any adaptively extracted scaffold from the hierarchy, a sequen...
متن کاملComponent-aware tensor-product trivariate splines of arbitrary topology
The fundamental goal of this paper aims to bridge the large gap between the shape versatility of arbitrary topology and the geometric modeling limitation of conventional tensor-product splines for solid representations. Its contribution lies at a novel shape modeling methodology based on tensorproduct trivariate splines for solids with arbitrary topology. Our framework advocates a divide-andcon...
متن کامل