Intersection of a ruled surface with a free-form surface

Free Form Surface Design with A-Patches·

We present a sufficient criterion for the Bernstein-Bezier (BB) form of a trivariate polynomial within a tetrahedron, such that the real zero contour of the polynomial defines a smooth and single sheeted algebraic surface patch. We call this an A-patch. We present algorithms to build a mesh of cubic A-patches to interpolate a given set of scattered point data in three dimensions, respecting the...

Free-Form Surface Matching for Surface Inspection

Free-Form Surface Registration using Surface Signatures

This paper introduces a new free-form surface representation scheme for the purpose of fast and accurate registration and matching. Accurate registration of surfaces is a common task in computer vision. The proposed representation scheme captures the surface curvature information, seen from certain points and produces images, called surface signatures, at these points. Matching signatures of di...

Effective Divisor Classes on a Ruled Surface

The Neron-Severi group of divisor classes modulo algebraic equivalence on a smooth algebraic surface is often not difficult to calculate, and has classically been studied as one of the fundamental invariants of the surface. A more difficult problem is the determination of those divisor classes which can be represented by effective divisors; these divisor classes form a monoid contained in the N...

Free-Form Modeling with Implicit Surface Patches

While it is possible to model a general closed surface of arbitrary genus as a single implicit surface patch, the geometry of such a global surface is di cult to specify, interactively control, and polygonize. The main di culties stem from the fact that implicit representations are iso-contours which generally have multiple real sheets, self{intersections and several other undesirable singulari...