Direct least-squares fitting of algebraic surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
IEEE Transactions on Pattern Analysis and Machine Intelligence
A front-tracking method for viscous, incompressible, multi-fluid flows
Journal of Computational Physics
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Simulating free surface flows with SPH
Journal of Computational Physics
Modelling merging and fragmentation in multiphase flows with SURFER
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
The approximation power of moving least-squares
Mathematics of Computation
SIAM Journal on Scientific Computing
Journal of Computational Physics
The point-set method: front-tracking without connectivity
Journal of Computational Physics
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Journal of Computational Physics
Ray Tracing Point Set Surfaces
SMI '03 Proceedings of the Shape Modeling International 2003
ACM SIGGRAPH 2004 Papers
Journal of Computational Physics
A Lagrangian particle level set method
Journal of Computational Physics
A simple package for front tracking
Journal of Computational Physics
ACM SIGGRAPH 2007 papers
A fast and accurate semi-Lagrangian particle level set method
Computers and Structures
On normals and projection operators for surfaces defined by point sets
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Interactive ray tracing of point-based models
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
A PLIC-VOF method suited for adaptive moving grids
Journal of Computational Physics
Generalized Hermitian Radial Basis Functions Implicits from polygonal mesh constraints
The Visual Computer: International Journal of Computer Graphics
Hi-index | 31.46 |
The representation of interfaces by means of the algebraic moving-least-squares (AMLS) technique is addressed. This technique, in which the interface is represented by an unconnected set of points, is interesting for evolving fluid interfaces since there is no surface connectivity. The position of the surface points can thus be updated without concerns about the quality of any surface triangulation. We introduce a novel AMLS technique especially designed for evolving-interfaces applications that we denote RAMLS (for Robust AMLS). The main advantages with respect to previous AMLS techniques are: increased robustness, computational efficiency, and being free of user-tuned parameters. Further, we propose a new front-tracking method based on the Lagrangian advection of the unconnected point set that defines the RAMLS surface. We assume that a background Eulerian grid is defined with some grid spacing h. The advection of the point set makes the surface evolve in time. The point cloud can be regenerated at any time (in particular, we regenerate it each time step) by intersecting the gridlines with the evolved surface, which guarantees that the density of points on the surface is always well balanced. The intersection algorithm is essentially a ray-tracing algorithm, well-studied in computer graphics, in which a line (ray) is traced so as to detect all intersections with a surface. Also, the tracing of each gridline is independent and can thus be performed in parallel. Several tests are reported assessing first the accuracy of the proposed RAMLS technique, and then of the front-tracking method based on it. Comparison with previous Eulerian, Lagrangian and hybrid techniques encourage further development of the proposed method for fluid mechanics applications.