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Surface Patches from Unorganized Space Curves
(The Eurographics Association and Blackwell Publishing Ltd., 2011)
Recent 3D sketch tools produce networks of three-space curves that suggest the contours of shapes. The shapes may be non-manifold, closed three-dimensional, open two-dimensional, or mixed. We describe a system that ...
Consistent Shape Maps via Semidefinite Programming
(The Eurographics Association and Blackwell Publishing Ltd., 2013)
Recent advances in shape matching have shown that jointly optimizing the maps among the shapes in a collection can lead to significant improvements when compared to estimating maps between pairs of shapes in isolation. ...
Curve Reconstruction with Many Fewer Samples
(The Eurographics Association and John Wiley & Sons Ltd., 2016)
We consider the problem of sampling points from a collection of smooth curves in the plane, such that the CRUST family of proximity-based reconstruction algorithms can rebuild the curves. Reconstruction requires a dense ...
Crawl through Neighbors: A Simple Curve Reconstruction Algorithm
(The Eurographics Association and John Wiley & Sons Ltd., 2016)
Given a planar point set sampled from an object boundary, the process of approximating the original shape is called curve reconstruction. In this paper, a novel non-parametric curve reconstruction algorithm based on Delaunay ...
Bijective Composite Mean Value Mappings
(The Eurographics Association and Blackwell Publishing Ltd., 2013)
We introduce the novel concept of composite barycentric mappings and give theoretical conditions under which they are guaranteed to be bijective. We then focus on mean value mappings and derive a simple procedure for ...
Splines in the Space of Shells
(The Eurographics Association and John Wiley & Sons Ltd., 2016)
Cubic splines in Euclidean space minimize the mean squared acceleration among all curves interpolating a given set of data points. We extend this observation to the Riemannian manifold of discrete shells in which the ...
A Complex View of Barycentric Mappings
(The Eurographics Association and Blackwell Publishing Ltd., 2011)
Barycentric coordinates are very popular for interpolating data values on polyhedral domains. It has been recently shown that expressing them as complex functions has various advantages when interpolating two-dimensional ...
Feature-Preserving Reconstruction of Singular Surfaces
(The Eurographics Association and Blackwell Publishing Ltd., 2012)
Reconstructing a surface mesh from a set of discrete point samples is a fundamental problem in geometric modeling. It becomes challenging in presence of 'singularities' such as boundaries, sharp features, and non-manifolds. ...
Parallel Blue-noise Sampling by Constrained Farthest Point Optimization
(The Eurographics Association and Blackwell Publishing Ltd., 2012)
We describe a fast sampling algorithm for generating uniformly-distributed point patterns with good blue noise characteristics. The method, based on constrained farthest point optimization, is provably optimal and may be ...
Nonrigid Matching of Undersampled Shapes via Medial Diffusion
(The Eurographics Association and Blackwell Publishing Ltd., 2012)
We introduce medial diffusion for the matching of undersampled shapes undergoing a nonrigid deformation. We construct a diffusion process with respect to the medial axis of a shape, and use the quantity of heat diffusion ...