Geometric modeling using continuous real functions of several variables is discussed. Modeling concepts include sets of objects, operations and relations. An object is a closed point set of n-dimensional Euclidean space with a defining inequality f x x x n ( , ,..., ) 1 2 0 ≥ . Transformations of a defining function are described for the set-theoretic operations, blending, offsetting, bijective mapping, projection, Cartesian product and metamorphosis. Inclusion, point membership and intersection relations are described. In the implemented interactive modeling system, we use highlevel geometric language that provides extendibility of the modeling system by input symbolic descriptions of primitives, operations and predicates. This approach supports combinations of representational styles, including constructive geometry, sweeping, soft objects, voxel-based objects, deformable and other animated objects. Application examples of aesthetic design, collisions simulation, NC machining, range data processing, and 3D texture generation are given.

This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality The volume spline is based on use of the Green's function for interpolation of scalar function values of a chosen "carrier" solid. Our algorithm is capable of generating highly concave and branching objects automatically. The particular case where the surface is reconstructed from cross-sections is discussed too. Potential applications of this algorithm are in tomography, image processing, animation and CAD f o r bodies with complex surfaces.

No abstract

No abstract

No abstract