Subdivision Algorithms for Ruled Surfaces
نویسنده
چکیده
Recent research has produced results on subdivision in arbitrary manifolds. These results can be applied to the manifold of lines and thus we can create subdivision schemes especially for ruled surfaces. We present different methods for refining discrete models of ruled surfaces: An algorithm combining subdivision and projection to the manifold of lines in Euclidean three-space. A further algorithm combines subdivision for the striction curve with geodesic subdivision in the Euclidean unit sphere. The third method is based on the Denavit-HartenbergMethod for serial robots. We refine the sequence of motions of the Sannia frame by means of geodesic subdivision in the group of Euclidean motions.
منابع مشابه
Approximation of ruled and canal surfaces by means of subdivision
Subdivision schemes were originally defined for data in affine spaces and their applications were thus restricted to polygons and polyhedra. Nowadays subdivision schemes for data in arbitrary manifolds are available and the convergence and smoothness behaviour is studied. This opens a wide field of applications and makes it posible to apply suitably modified known refinement schemes to sets of ...
متن کاملCharacterizations of Slant Ruled Surfaces in the Euclidean 3-space
In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...
متن کاملREVERSE LOOP SUBDIVISION FOR GEOMETRY AND TEXTURES
Reverse subdivision aims at constructing a coarser representation of an object given by a fine polygon mesh. In this paper, we first derive a mask for reverse Loop subdivision that can be applied to both regular and extraordinary vertices. The mask is parameterized, and thus can also be used in reversing variants of Loop subdivision, such as those proposed by Warren and Litke. We apply this mas...
متن کاملA G 2 {subdivision Algorithm 1
In this paper we present a method to optimize the smoothness order of subdivision algorithms generating surfaces of arbitrary topology. In particular we construct a subdivision algorithm with some negative weights producing G 2 {surfaces. These surfaces are piecewise bicubic and are at at their extraordinary points. The underlying ideas can also be used to improve the smoothness order of subdiv...
متن کاملA Degree Estimate for PolynomialSubdivision Surfaces of Higher RegularitybyUlrich
Subdivision algorithms can be used to construct smooth surfaces from control meshes of arbitrary topological structure. However, in contrast to tangent plane continuity, which is well understood, very little is known about the generation of subdivision surfaces of higher regularity. This work presents an estimate for piecewise polynomial subdivision surfaces by pointing out that curvature conti...
متن کامل