More Curved Spirolaterals
Multi regional state space systems -- controller design and stability
Nested sequences of Chebyshev spaces and shape parameters
New algorithms and techniques for computing with geometrically continuous spline curves of arbitrary degree
New efficient numerical method for 3D point cloud surface reconstruction by using level set methods
In this article, we present a mathematical model and numerical method for surface reconstruction from 3D point cloud data, using the level-set method. The presented method solves surface reconstruction by the computation of the distance function to the shape, represented by the point cloud, using the so called Fast Sweeping Method, and the solution of advection equation with curvature term, which creates the evolution of an initial condition to the final state. A crucial point for efficiency is...
On computer aided shape optimization
On one approach to local surface smoothing
A bicubic model for local smoothing of surfaces is constructed on the base of pivot points. Such an approach allows reducing the dimension of matrix of normal equations more than twice. The model enables to increase essentially the speed and stability of calculations. The algorithms, constructed by the aid of the offered model, can be used both in applications and the development of global methods for smoothing and approximation of surfaces.
On the arc length of parametric cubic curves.
Parametric representation of quadric surfaces
Point ordering with natural distance based on Brownian motion.
Polynomial best constrained degree reduction in strain energy.
Problems with defining barycentric coordinates for the sphere
Properties of functions in an auxiliary spline space.
Quadratic spline quasi-interpolants on bounded domains of .
Rational Bézier curves with infinitely many integral points
In this paper we consider rational Bézier curves with control points having rational coordinates and rational weights, and we give necessary and sufficient conditions for such a curve to have infinitely many points with integer coefficients. Furthermore, we give algorithms for the construction of these curves and the computation of theirs points with integer coefficients.
Relation between algebraic and geometric view on NURBS tensor product surfaces
NURBS (Non-Uniform Rational B-Splines) belong to special approximation curves and surfaces which are described by control points with weights and B-spline basis functions. They are often used in modern areas of computer graphics as free-form modelling, modelling of processes. In literature, NURBS surfaces are often called tensor product surfaces. In this article we try to explain the relationship between the classic algebraic point of view and the practical geometrical application on NURBS.
Robot motion using Delaunay triangulation.
RTIN-based strategies for local mesh refinement
Longest-edge bisection algorithms are often used for local mesh refinements within the finite element method in 2D. In this paper, we discuss and describe their conforming variant. A particular attention is devoted to the so-called Right-Triangulated Irregular Network (RTIN) based on isosceles right triangles and its tranformation to more general domains. We suggest to combine RTIN with a balanced quadrant tree (QuadTree) decomposition. This combination does not produce hanging nodes within the...
Smooth local interpolation of surfaces using normal vectors.
Subdivision depth computation for tensor product -ary volumetric models.