Open AccessPosted Content
Optimally cutting a surface into a disk
Jeff Erickson,Sariel Har-Peled +1 more
TLDR
In this article, the authors consider the problem of cutting a set of edges on a polyhedral manifold surface, possibly with boundary, to obtain a single topological disk, minimizing either the total number of cut edges or their total length.Abstract:
We consider the problem of cutting a set of edges on a polyhedral manifold surface, possibly with boundary, to obtain a single topological disk, minimizing either the total number of cut edges or their total length. We show that this problem is NP-hard, even for manifolds without boundary and for punctured spheres. We also describe an algorithm with running time n^{O(g+k)}, where n is the combinatorial complexity, g is the genus, and k is the number of boundary components of the input surface. Finally, we describe a greedy algorithm that outputs a O(log^2 g)-approximation of the minimum cut graph in O(g^2 n log n) time.read more
Citations
More filters
Proceedings ArticleDOI
Geometry images
TL;DR: This paper proposes to remesh an arbitrary surface onto a completely regular structure the authors call a geometry image, which captures geometry as a simple 2D array of quantized points.
Proceedings ArticleDOI
Global conformal surface parameterization
Xianfeng Gu,Shing-Tung Yau +1 more
TL;DR: This work analyzes the structure of the space of all global conformal parameterizations of a given surface and finds all possible solutions by constructing a basis of the underlying linear solution space.
Proceedings ArticleDOI
Mesh parameterization: theory and practice
TL;DR: This course outlines its mathematical foundations, describes recent methods for parameterizing meshes over various domains, discusses emerging tools like global parameterization and inter-surface mapping, and demonstrates a variety of parameterization applications.
Journal ArticleDOI
Feature-based surface parameterization and texture mapping
TL;DR: An automatic parameterization method for segmenting a surface into patches that are then flattened with little stretch, and an image-based error measure that takes into account stretch, seams, smoothness, packing efficiency, and surface visibility is described.
Proceedings ArticleDOI
Interactive geometry remeshing
TL;DR: This work presents a novel technique, both flexible and efficient, for interactive remeshing of irregular geometry that is able to produce arbitrarily complex meshes with a variety of properties including: uniformity, regularity, semi-regularity, curvature sensitive resampling, and feature preservation.
References
More filters
Journal ArticleDOI
A note on two problems in connexion with graphs
TL;DR: A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.
Journal ArticleDOI
On the shortest spanning subtree of a graph and the traveling salesman problem
TL;DR: Kurosh and Levitzki as discussed by the authors, on the radical of a general ring and three problems concerning nil rings, Bull Amer Math Soc vol 49 (1943) pp 913-919 10 -, On the structure of algebraic algebras and related rings.
Book
Parameterized Complexity
TL;DR: An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability, and introduces readers to new classes of algorithms which may be analysed more precisely than was the case until now.
Proceedings ArticleDOI
Topology matching for fully automatic similarity estimation of 3D shapes
TL;DR: A novel technique is proposed, called Topology Matching, in which similarity between polyhedral models is quickly, accurately, and automatically calculated by comparing Multiresolutional Reeb Graphs (MRGs), which operates well as a search key for 3D shape data sets.