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 f(x; y; z) 0. 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 crosssections is discussed too. Potential applications of this algorithm are in tomography, image processing, animation and CAD for bodies with complex surfaces. 1. Introduction There are a number of applied problems that require interpolation or smoothing of large arrays of randomly measured points of a surface. The main sources of such data are physical measurements taken by scanning an object from different viewing directions. Scattered points arise also in mathematical simulation, for examp...

We present an approach to real-time animation of deformable objects. Optimization of algorithms using compactly supported radial basis functions (CSRBF) allows us to generate deformations performed fast enough for such real-time applications as computer games. The algorithm described in detail in this paper uses space mapping technique. Smooth local deformations of animation objects can be defined by only a moderate number of control vectors and locality of deformations can be defined by radius of support. We also present examples of animations and speed benchmarks.

A set of software tools that use compactly supported radial basis functions (CSRBFs) to process scattered data is proposed in this paper. To solve problems concerning the processing of scattered data in such applications as reconstruction of functionaly defined geometric objects, surface retouching, and shape modifications, we employ a specially designed C++ software library. Thanks to the efficient octree algorithm used in this study, the resulting matrix is a band-diagonal matrix that permits handling of large data sets in a reasonable time.

In this paper, we present an application of a space mapping technique for surface reconstruction (more precisely: reconstruction of missing parts of a real geometric object represented by volume data). Using a space mapping technique, the surface of a given model, in particular tooth shape is fitted by a shape transformation to extrapolate the remaining surface of a patient's tooth with occurring damage such as a “drill hole. ” The genetic algorithm minimizes the error of the approximation by optimizing a set of control points that determine the coefficients for spline functions, which in turn define a space transformation. The fitness function to be minimized consists of two components. First one is the error between the blended surface of an object and the surface of the object to be blended in some predefined points. The second is a component that is responsible for the bending energy being minimized.

In this paper the use of compactly-supported radial basis functions for surface reconstruction is described. To solve the problem of reconstruction or volume data generation specially designed software is employed. Time performance of the algorithm and numerical error estimation of the reconstruction are also investigated. Thanks to the efficient octree algorithm used in this study, the resulting matrix is a band diagonal matrix that reduces computational cost and permits handling large data sets.

In this chapter the use of compactly-supported radial basis functions for surface reconstruction is described. To solve the problem of reconstruction or volume data generation specially designed software is employed. Time performance of the algorithm is investigated. Thanks to the efficient octree algorithm used in this study, the resulting matrix is a band diagonal matrix that reduces computational costs. 1

This paper would not have been completed without the help of many generous, caring people. In an effort to give credit to those who deserve so much more, the author would like to thank the following people in not particular order, for their generous help

In this paper, we present a novel fast algorithm for image retouching. A space-mapping technique is used to transform a missing (or damaged) part of a surface into a different shape in a continuous manner. Experimental results are included to demonstrate the feasibility of our approach. The proposed approach shows the obvious relationship between the surface retouching problem and image inpainting. We consider shape transformation as a general type of operation for restoring missing data, and attempt to approach the well-known problem of "fulfillment" of damaged or missing areas from a single point of view, namely, that of the space mapping technique.

This paper presents work in progress and continues a project devoted to developing shape modeling system based on implementation of radial based function (RBF) technology. In this paper, we study the opportunities offered by this technology to computer-aided design and computer graphics communities by looking at the problems of surface generation and enhancement. Experimental results are included to demonstrate the functionality of our mesh-modeling tool.

A spherical spline is the smooth volume swept out by moving sphere whose centre follows a 3-D spline curve, surface or the volume of a volumetric spline. Spherical splines can be rendered rapidly, in composition they can form branched and highly concave objects. The spline in our method provides an underlying skeleton of the modelled object, making it easier to edit in an animation environment. Key Words: blending, three-dimensional modelling, skeletal design 1