Least Squares Subdivision Surfaces

Least Squares Subdivision Surfaces

The usual approach to design subdivision schemes for curves and surfaces basically consists in combining proper rules for regular configurations, with some specific heuristics to handle extraordinary vertices. In this paper, we introduce an alternative approach, called Least Squares Subdivision Surfaces (LS3), where the key idea is to iteratively project each vertex onto a local approximation o...

Surfaces Generated by Moving Least Squares Methods

An analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented. In particular, theorems are proved concerning the smoothness of interpolants and the description of m.l.s. processes as projection methods. Some properties of compositions of the m.l.s. projector, with projectors associated with finiteelement schemes, are also considered. The analys...

Least Squares Matching of 3d Surfaces

An algorithm for the least squares matching of overlapping 3D surfaces is presented. It estimates the transformation parameters of one or more fully 3D surfaces with respect to a template one, using the Generalized Gauss-Markoff model, minimizing the sum of squares of the Euclidean distances between the surfaces. This formulation gives the opportunity of matching arbitrarily oriented 3D surface...

Direct Least-Squares Fitting of Algebraic Surfaces

Least-Squares Fitting of Algebraic Spline Surfaces

We present an algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data. By simultaneously approximating points and associated normal vectors, we obtain a method which is computationally simple, as the result is obtained by solving a system of linear equations. In addition, the result is geometrically invariant, as no artificial normalization is introduced. The ...