Equivolumetric tubular solids for volume-preserving bend of cylinders
We present the equivolumetric tubular solid which is a model of volume-preserving bend of right cylinders. The equivolumetric tubular solid is a special class of tubular solids which are the generalization of pipe solids or normal ringed solid. For a ...
Two C1-methods to generate Bézier surfaces from the boundary
Two methods to generate tensor-product Bezier surface patches from their boundary curves and with tangent conditions along them are presented. The first one is based on the tetraharmonic equation: we show the existence and uniqueness of the solution of @...
Quasi-hierarchical Powell--Sabin B-splines
Hierarchical Powell-Sabin splines are C^1-continuous piecewise quadratic polynomials defined on a hierarchical triangulation. The mesh is obtained by partitioning an initial conforming triangulation locally with a triadic split, so that it is no longer ...
Fitting curves and surfaces to point clouds in the presence of obstacles
We consider the problem of fitting B-spline curves and surfaces to point clouds in the presence of obstacles constraining this approximation at the same time. Therefore, we describe the fitting problem as optimization problem and employ an iterative ...
Stable, linear spline wavelets on nonuniform knots with vanishing moments
In wavelet analysis on nonuniform grids it is desirable that the wavelet scheme is stable in some norm independently of the grid spacing (grid stability). It is known that this kind of stability is difficult to achieve for spline wavelets based on ...
μ-bases for polynomial systems in one variable
The notion of a @m-basis for an arbitrary number of polynomials in one variable is defined. The basic properties of these @m-bases are derived, and an algorithm is presented based on Gaussian Elimination to calculate a @m-basis for any collection of ...
On the smoothness of real-valued functions generated by subdivision schemes using nonlinear binary averaging
Our main result is that two point interpolatory subdivision schemes using C^k nonlinear averaging rules on pairs of real numbers generate real-valued functions that are also C^k. The significance of this result is the following consequence: Suppose that ...
Classification and resolution of critical cases in Grandine and Klein's topology determination using a perturbation method
We classify and resolve all critical cases in the topology determination method proposed in [Grandine, T.A., Klein IV, F.W., 1997. A new approach to the surface intersection problem. Computer Aided Geometric Design 14 (2), 111-134]. Their algorithm for ...
