We consider the problem of reconstructing a curve or a surface from discrete noisy samples by approximating the point set with non-uniform rational B-splines. We show how to set up the free knot problem such that constrained nonlinear optimization can be applied efficiently. An approach for realizing the optimization in parallel will be described in detail. Our foremost objective in our paralle...

Automatic labeling of the gyri and sulci on the cortical surface is important for studying cortical morphology and brain functions within populations. A method to simultaneously label gyral regions and extract sulcal curves is proposed. Assuming that the gyral regions parcellate the whole cortical surface into contiguous regions with certain fixed topology, the proposed method labels the subjec...

Article history: Received 6 February 2008 Received in revised form 5 February 2009 Accepted 6 February 2009 Available online 11 February 2009

The main motivation of this work is the problem of compute intersection curve between two surface. The surface/surface intersection, is a fundamental problem in computational geometry and geometric modelling of complex shapes. In general surface intersections, the most commonly used methods include subdivision and marching. Marching-based algorithms begin by finding a starting point on the inte...

This paper presents a new interpretation of the binary blending operator of implicit modeling. Instead of considering the operator as a composition of potential functions, we propose to consider it as an implicit curve extruded in an implicit extrusion field. An implicit extrusion field is a 2D space for which each coordinate is a potential field. The study of general concepts around implicit e...

This paper presents the relationship between the Recursive Arbitrary Topology Splines (RATS) method, derived by the authors, and the Catmull and Clark recursive B-Spline method. Both methods are capable of defining surfaces of any arbitrary topology of control points. They "fill-in" n-sided regions with foursided patches. The Catmull & Clark method is derived from the midpoint subdivision of B-...

Definitions. A parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J). The image C=f(S)C V is called a (non-parametrized) J-curve in V. A curve C C V is called closed if it can be (holomorphically !) parametrized by a closed surface S. We call C regular if there is a parametrization f : S ~ V whic...

During last few years the use of Terrestrial Laser Scanner has increased notably in different application fields, like architecture, geology and geodesy. The paper focuses in the use of TLS data for deformation measurement and monitoring purposes which concerns both engineering geology and geodesy. The paper presents a new approach for deformation measurement which fully takes advantage of the ...

We present an algorithm that, starting from the surface skeleton of a 3D solid object, computes the curve skeleton. The algorithm is based on the detection of curves and junctions in the surface skeleton. It can be applied to any surface skeleton, including the case in which the surface skeleton is two-voxel thick.

This article presents a new method to nd the best spatial registration between a rigid curve and a rigid surface. We show how to locally exploit the knowledge of diierential properties computed on both the curve and the surface to constrain the rigid matching problem. It is in fact possible to write a compatibility equation between a curve point and a surface point, which constrains completely ...