The paper proposes a reliable method for estimating quadric surfaces from 3D range data in the framework of object recognition and localization or object modelling. Instead of estimating a quadric surface individually the approach fits all the surfaces captured in the scene together taking into account the geometric relationships between them and their specific characteristics. The technique is...

The paper proposes a reliable method for estimating quadric surfaces from 3D range data in the framework of object recognition and localization or reverse engineering. Instead of estimating a quadric surface in isolation, the approach ts all the surfaces captured in the scene together taking into account the geometric relationships between them and their speciic characteristics. The technique i...

By Bezout’s theorem, three quadric surfaces may have infinitely intersections, but have at most eight isolated intersections. In this paper, we present an efficient and robust algorithm to obtain the isolated and the connected components of the real intersections of three quadric surfaces. Moreover, the conditions under which the intersections are finite and infinite are thoroughly investigated...

Dupin cyclides are algebraic surfaces introduced for the first time in 1822 by the French mathematician Pierre-Charles Dupin. They have a low algebraic degree and have been proposed as a solution to a variety of geometric modeling problems. The circular curvature line’s property facilitates the construction of the cyclide (or the portion of a cyclide) that blends two circular quadric primitives...

Introduction Efficient fitting of quadric surfaces to unstructured point clouds or triangle meshes is an important component of many reverse engineering systems [6]. Users may prefer a given surface be fit by a specific quadric type: for example, they may want to ensure the quadric is a cone, ellipsoid, or a rotationally-symmetric subtype (spheroid, circular cone, etc). Methods for type-specifi...

We introduce a general framework for sweeping a set of curves embedded on a two-dimensional parametric surface. We can handle planes, cylinders, spheres, tori, and surfaces homeomorphic to them. A major goal of our work is to maximize code reuse by generalizing the prevalent sweep-line paradigm and its implementation so that it can be employed on a large class of surfaces and curves embedded on...