A Haptic-Rendering Technique Based on Hybrid Surface Representation
IEEE Computer Graphics and Applications
Signed Distance Computation Using the Angle Weighted Pseudonormal
IEEE Transactions on Visualization and Computer Graphics
Signed Distance Transform Using Graphics Hardware
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Short Note: A multi-phase flow method with a fast, geometry-based fluid indicator
Journal of Computational Physics
Interactive 3D distance field computation using linear factorization
I3D '06 Proceedings of the 2006 symposium on Interactive 3D graphics and games
GI '07 Proceedings of Graphics Interface 2007
Out-of-core and compressed level set methods
ACM Transactions on Graphics (TOG)
A simple embedding method for solving partial differential equations on surfaces
Journal of Computational Physics
Exploration of a cluttered environment using Voronoi Transform and Fast Marching
Robotics and Autonomous Systems
Exploration of 2D and 3D Environments using Voronoi Transform and Fast Marching Method
Journal of Intelligent and Robotic Systems
An Implicit Method for Interpolating Two Digital Closed Curves on Parallel Planes
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
A spatial warping method for freeform modeling based on a level-set method
Computer-Aided Design
SARDF: signed approximate real distance functions in heterogeneous objects modeling
Heterogeneous objects modelling and applications
STACOM'10/CESC'10 Proceedings of the First international conference on Statistical atlases and computational models of the heart, and international conference on Cardiac electrophysiological simulation challenge
Distance to objects built with set operations in constructive solid modeling
Proceedings of the 13th International Conference on Humans and Computers
A virtual test facility for simulating detonation-induced fracture of thin flexible shells
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Generalized distance transforms and skeletons in graphics hardware
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
Robust generation of signed distance fields from triangle meshes
VG'05 Proceedings of the Fourth Eurographics / IEEE VGTC conference on Volume Graphics
Hemodynamic assessment of pre- and post-operative aortic coarctation from MRI
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Computing local signed distance fields for large polygonal models
EuroVis'08 Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization
Closest point turbulence for liquid surfaces
ACM Transactions on Graphics (TOG)
An Eulerian-Lagrangian moving immersed interface method for simulating burning solids
Journal of Computational Physics
Hi-index | 0.01 |
We present an algorithm for computing the closest point, transform to an explicitly described manifold on a rectilinear grid in low dimensional spaces. The closest point transform finds the closest point on a manifold and the Euclidean distance to a manifold for the points in a grid. We consider manifolds composed of simple geometric shapes, such as, a set of points, piecewise linear curves or triangle meshes. The algorithm solves the eikonal equation |∇u| = 1 with the method of characteristics. For many problems, the computational complexity of the algorithm is linear in both the number of grid points and the complexity of the manifold. Many query problems can be aided by using orthogonal range queries (ORQ). There are several standard data structures for performing ORQ's in 3-D, including kd-trees, octrees, and cell arrays. We develop additional data structures based on cell arrays. We study the characteristics of each data structure and compare their performance. We present a new algorithm for solving the single-source, non-negative weight, shortest-paths problem. Dijkstra's algorithm solves this problem with computational complexity O ((E + V)log V) where E is the number of edges and V is the number of vertices. The new algorithm, called Marching with a Correctness Criterion (MCC), has computational complexity O (E + RV), where R is the ratio of the largest to smallest edge weight. Sethian's Fast Marching Method (FMM) may be used to solve static Hamilton-Jacobi equations. It has computational complexity O (N log N), where N is the number of grid points. The FMM has been regarded as an optimal algorithm because it is closely related to Dijkstra's algorithm. The new shortest-paths algorithm discussed above can be used to develop an ordered, upwind, finite difference algorithm for solving static Hamilton-Jacobi equations. This algorithm requires difference schemes that difference not only in coordinate directions, but in diagonal directions as well. It has computational complexity O(RN), where R is the ratio of the largest to smallest propagation speed and N is the number of grid points.