The Surface Octree (SO) is an extension of the Classical Octree used to maintain a decimated codification of a surface while preserving volume data information. Constrained by a region of maximal interest, we present an algorithm to extract a multiresolution surface from a SO data structure. This algorithm reconstructs the surface with maximal precision in the focus of interest and at progressi...

Given a set of data points as measurements from a developable surface, the present paper investigates the recognition and reconstruction of these objects. We investigate the set of estimated tangent planes of the data points and show that classical Laguerre geometry is a useful tool for recognition, classification and reconstruction of developable surfaces. These surfaces can be generated as en...

Wepresent a new variationalmethod formesh segmentation by fitting quadric surfaces. Each component of the resulting segmentation is represented by a general quadric surface (including plane as a special case). A novel energy function is defined to evaluate the quality of the segmentation, which combines both L2 and L2,1 metrics from a triangle to a quadric surface. The Lloyd iteration is used t...

Kinematic surfaces form a general class of surfaces, including surfaces of revolution, helices, spirals, and more. Standard methods for fitting such surfaces are either specialized to a small subset of these surface types (either focusing exclusively on cylinders or exclusively on surfaces of revolution) or otherwise are basis-dependent (leading to scale-dependent results). Previous work has su...

This paper describes a method to approximate point sets by Loop subdivision surfaces based on geometric algorithms. We assume that the data points are given in triangular mesh of arbitrary topological type. The initial control mesh of the Loop subdivision surface is obtained by simplifying the input triangular mesh using QEM algorithm. Our algorithm iteratively updates the control mesh in a glo...

Ruled surfaces play an important role in many manufacturing and construction applications. In this work, we explore a multidimensional dynamic programming based ruled surface fitting scheme to a given freeform rational surface, S. Considering two initial opposite boundaries of S, sampled into a discrete piecewise linear polyline representation, the ruled surface fitting problem is reduced to a ...

The aim of this paper is to introduce a method for the conceptual design of membrane structures. Actually, there is a lack of computer based tools for the people involved in these first stages of the design process, in which the shape of the membrane is being defined. Not many parameters are needed at this stage for the designer. An easy graphic interface is needed, in which the designer had th...

Closed surfaces provide a useful model for 3-d shapes, with the data typically consisting of a cloud of points in R. The existing literature on closed surface modeling focuses on frequentist point estimation methods that join surface patches along the edges, with surface patches created via Bézier surfaces or tensor products of B-splines. However, the resulting surfaces are not smooth along the...