Fast, robust, and faithful methods for detecting crest lines on meshes
The crest lines, salient subsets of the extrema of the principal curvatures over their corresponding curvature lines, are powerful shape descriptors which are widely used for shape matching, interrogation, and visualization purposes. In this paper, we ...
Toward an efficient triangle-based spherical harmonics representation of 3D objects
In classical frequency-based surface decomposition, there is always a restriction about the genus number of the object to obtain the spherical harmonics decomposition of spherical functions representing these objects. Such spherical functions are ...
Paper-craft from 3D polygonal models using generalized cylinders
We introduce an algorithm for approximating a 2-manifold 3D mesh by a set of developable surfaces. Each developable surface is a generalized cylinder represented as a strip of triangles not necessarily taken from the original mesh. Our algorithm is ...
A genus oblivious approach to cross parameterization
In this paper we present a robust approach to construct a map between two triangulated meshes, M and M^' of arbitrary and possibly unequal genus. We introduce a novel initial alignment scheme that allows the user to identify ''landmark tunnels'' and/or ...
Exact evaluation of limits and tangents for non-polynomial subdivision schemes
In this paper, we describe a method for exact evaluation of a limit mesh defined via subdivision and its associated tangent vectors on a uniform grid of any size. Other exact evaluation technique either restrict the grids to have subdivision sampling ...
Pairs of bi-cubic surface constructions supporting polar connectivity
Surface constructions of polynomial degree (3,3) come in four flavours that complement each other: one pair extends the subdivision paradigm, the other the NURBS patch approach to free-form modeling. The first pair, Catmull-Clark subdivision and Polar ...
Topology and arrangement computation of semi-algebraic planar curves
We describe a new subdivision method to efficiently compute the topology and the arrangement of implicit planar curves. We emphasize that the output topology and arrangement are guaranteed to be correct. Although we focus on the implicit case, the ...
Covering Minkowski sum boundary using points with applications
Minkowski sum is a fundamental operation in many geometric applications, including robotic motion planning, penetration depth estimation, solid modeling, and virtual prototyping. However, due to its high computational complexity and several non-trivial ...
Blossoming and curvatures of surface patches
The ratio of curvatures of a polynomial curve p of degree n and its blossom curve of degree k at a given point u is a constant depending only on n and k. In this paper analogous properties of polynomial and rational patches (in triangular and tensor ...
Detail preserving deformation of B-spline surfaces with volume constraint
Geometric constraints have proved to be helpful for shape modeling. Moreover, they are efficient aids in controlling deformations and enhancing animation realism. The present paper addresses the deformation of B-spline surfaces while constraining the ...
A simple method for approximating rational Bézier curve using Bézier curves
This paper presents a simple method for approximating a rational Bezier curve with Bezier curve sequence, whose control points are those of degree-elevated rational Bezier curves. It is proved that the derivatives with any given degree of the Bezier ...
A note on the paper “Normal based subdivision scheme for curve design” by Xunnian Yang
In a recent paper (Computer Aided Geometric Design 23 (3), 243-260), Yang presented a novel kind of nonlinear and geometry driven subdivision scheme for curve interpolation. The author declared that this scheme was shape preserving when all free ...
