Polygonization Of Implicit Surfaces Research Articles

GPU-based polygonization and optimization for implicit surfaces

Despite the popularity of polygonization of implicit surfaces in graphics applications, an efficient solution to both polygonize and optimize meshes from implicit surfaces on modern GPUs has not be...

Polygonization of implicit surfaces with sharp features by edge-spinning

This paper presents an adaptive approach for polygonization of implicit surfaces. The algorithm generates a well-shaped triangular mesh with respect to a given approximation error. The error is proportional to a local surface curvature estimation. Polygonization of surfaces of high curvature, as well as surfaces with sharp features, is possible using a simple technique combined with a particle system approach. The algorithm is based on a surface tracking scheme, and it is compared with other algorithms based on a similar principle, such as the marching cube and the marching triangle algorithms.

Trimming implicit surfaces

Algorithms for trimming implicit surfaces yielding surface sheets and stripes are presented. These two-dimensional manifolds with boundaries result from set-theoretic operations on an implicit surface and a solid or another implicit surface. The algorithms generate adaptive polygonal approximation of the trimmed surfaces by extending our original implicit surface polygonization algorithm. The presented applications include modeling several spiral shaped surface sheets and stripes (based on M. Escher’s artworks) and extraction of ridges on implicit surfaces. Another promising application of the presented algorithms is modeling heterogeneous objects as implicit complexes.

Modeling and rendering viscous liquids

AbstractWe present a particle‐based algorithm for modeling highly viscous liquids. Using a numerical time‐integration of particle acceleration and velocity, we apply external forces to particles and use a convenient organization, the adhesion matrix, to represent forces between different types of liquids and objects. Viscosity is handled by performing a momentum exchange between particle pairs such that momentum is conserved. Volume is maintained by iteratively adjusting particle positions after each time step. We use a two‐tiered approach to time stepping that allows particle positions to be updated many times per frame while expensive operations, such as calculating viscosity and adhesion, are done only a few times per frame. The liquid is rendered using an implicit surface polygonization algorithm, and we present an implicit function that convolves the liquid surface with a Gaussian function, yielding a smooth liquid skin. Copyright © 2004 John Wiley & Sons, Ltd.

Edge spinning algorithm for implicit surfaces

This paper presents a new fast method for polygonization of implicit surfaces. Our method put emphasis on the shape of triangles generated and on the polygonization speed. The main advantages of the triangulation presented are simplicity and the stable features that can be used for future expansion. The implementation is not complicated and only the standard data structures are used. This algorithm is based on the surface tracking scheme and it is compared with the well-known marching cubes algorithm that is based on the similar principle. The presented algorithm is accelerated by the space subdivision which is an effective technique to speed-up any geometric of this type.

Dynamic mesh optimization for polygonized implicit surfaces with sharp features

The paper presents a novel approach for accurate polygonization of implicit surfaces with sharp features. The approach is based on mesh evolution towards a given implicit surface with simultaneous control of the mesh vertex positions and mesh normals. Given an initial polygonization of an implicit surface, a mesh evolution process initialized by the polygonization is used. The evolving mesh converges to a limit mesh which delivers a high quality approximation of the implicit surface. For analyzing how close the evolving mesh approachesthe implicit surface we use two error metrics. The metrics measure deviations of the mesh vertices from the implicit surface and deviations of mesh normals from the normals of the implicit surface.

Implicit Surface-Based Geometric Fusion

This paper introduces a general purpose algorithm for reliable integration of sets of surface measurements into a single 3D model. The new algorithm constructs a single continuous implicit surface representation which is the zero-set of a scalar field function. An explicit object model is obtained using any implicit surface polygonization algorithm. Object models are reconstructed from both multiple view conventional 2.5D range images and hand-held sensor range data. To our knowledge this is the first geometric fusion algorithm capable of reconstructing 3D object models from noisy hand-held sensor range data.This approach has several important advantages over existing techniques. The implicit surface representation allows reconstruction of unknown objects of arbitrary topology and geometry. A continuous implicit surface representation enables reliable reconstruction of complex geometry. Correct integration of overlapping surface measurements in the presence of noise is achieved using geometric constraints based on measurement uncertainty. The use of measurement uncertainty ensures that the algorithm is robust to significant levels of measurement noise. Previous implicit surface-based approaches use discrete representations resulting in unreliable reconstruction for regions of high curvature or thin surface sections. Direct representation of the implicit surface boundary ensures correct reconstruction of arbitrary topology object surfaces. Fusion of overlapping measurements is performed using operations in 3D space only. This avoids the local 2D projection required for many previous methods which results in limitations on the object surface geometry that is reliably reconstructed. All previous geometric fusion algorithms developed for conventional range sensor data are based on the 2.5D image structure preventing their use for hand-held sensor data. Performance evaluation of the new integration algorithm against existing techniques demonstrates improved reconstruction of complex geometry.

An evaluation of implicit surface tilers

The authors review the principal algorithms for the polygonization of implicit surfaces and provide a framework for identifying their conceptual similarities and practical differences. The algorithms' merits are evaluated according to topological disambiguation, implementation complexity, and triangle count. Special attention is devoted to the ambiguity problem, and proposed solutions are analyzed in the context of consistency and correctness. It is argued that consistency suffices for many purposes and is achievable with single-entry tetrahedral or cubical tables. >