Article Free Access Share on Implicit fairing of irregular meshes using diffusion and curvature flow Authors: Mathieu Desbrun Caltech CaltechView Profile , Mark Meyer Peter Schröder Alan H. Barr Authors Info & Claims SIGGRAPH '99: Proceedings the 26th annual conference Computer graphics interactive techniquesJuly 1999 Pages 317–324https://doi.org/10.1145/311535.311576Online:01 July 1999Publication History 895citation4,558DownloadsMetricsTotal Citations895Total Downloads4,558Last 12...

A method for concise, faithful approximation of complex 3D datasets is key to reducing the computational cost graphics applications. Despite numerous applications ranging from geometry compression reverse engineering, efficiently capturing a surface remains tedious task. In this paper, we present both theoretical and practical contributions that result in novel versatile framework geometric surfaces. We depart usual strategy by casting shape as variational partitioning problem. Using concept...

Parameterization of discrete surfaces is a fundamental and widely-used operation in graphics, required, for instance, texture mapping or remeshing. As 3D data becomes more detailed, there an increased need fast robust techniques to automatically compute least-distorted parameterizations large meshes. In this paper, we present new theoretical practical results on the parameterization triangulated surface patches. Given few desirable properties such as rotation translation invariance, show...

In this paper, we propose a novel polygonal remeshing technique that exploits key aspect of surfaces: the intrinsic anisotropy natural or man-made geometry. particular, use curvature directions to drive process, mimicking lines artists themselves would when creating 3D models from scratch. After extracting and smoothing tensor field an input genus-0 surface patch, minimum maximum curvatures are used determine appropriate edges for remeshed version in anisotropic regions, while spherical...

This paper presents a robust, adaptive method for animating dynamic visco-elastic deformable objects that provides guaranteed frame rate. Our approach uses novel automatic space and time level of detail technique, in combination with large-displacement (Green) strain tensor formulation. The body is partitioned non-nested multiresolution hierarchy tetrahedral meshes. local resolution determined by quality condition indicates where when the too coarse. As object moves deforms, sampling refined...

With the increasing use of geometry scanners to create 3D models, there is a rising need for fast and robust mesh smoothing remove inevitable noise in measurements. While most previous work has favored diffusion-based iterative techniques feature-preserving smoothing, we propose radically different approach, based on statistics local first-order predictors surface. The robustness our estimates allows us derive non-iterative filtering technique applicable arbitrary "triangle soups". We...

In this paper, we propose a novel polygonal remeshing technique that exploits key aspect of surfaces: the intrinsic anisotropy natural or man-made geometry. particular, use curvature directions to drive process, mimicking lines artists themselves would when creating 3D models from scratch. After extracting and smoothing tensor field an input genus-0 surface patch, minimum maximum curvatures are used determine appropriate edges for remeshed version in anisotropic regions, while spherical...

In this paper, a novel Delaunay-based variational approach to isotropic tetrahedral meshing is presented. To achieve both robustness and efficiency, we minimize simple mesh-dependent energy through global updates of vertex positions connectivity. As known be the ∠ 1 distance between an quadratic function its linear interpolation on mesh, our minimization procedure generates well-shaped tetrahedra. Mesh design controlled gradation smoothness parameter selection desired number vertices. We...

We present a fast, scalable algorithm to generate high-quality blue noise point distributions of arbitrary density functions. At its core is novel formulation the recently-introduced concept capacity-constrained Voronoi tessellation as an optimal transport problem. This insight leads continuous able enforce capacity constraints exactly, unlike previous work. exploit variational nature this design efficient optimization technique via constrained minimization in space power diagrams. Our...

With the increasing use of geometry scanners to create 3D models, there is a rising need for fast and robust mesh smoothing remove inevitable noise in measurements. While most previous work has favored diffusion-based iterative techniques feature-preserving smoothing, we propose radically different approach, based on statistics local first-order predictors surface. The robustness our estimates allows us derive non-iterative filtering technique applicable arbitrary "triangle soups". We...

In this paper we introduce a discrete shell model describing the behavior of thin flexible structures, such as hats, leaves, and aluminum cans, which are characterized by curved undeformed configuration. Previously models required complex continuum mechanics formulations correspondingly algorithms. We show that simple can be derived geometrically for triangle meshes implemented quickly modifying standard cloth simulator. Our technique convincingly simulates variety objects with materials...

Abstract In this paper we present an easy computation of a generalized form barycentric coordinates for irregular, convex n-sided polygons. Triangular have had many classical applications in computer graphics, from texture mapping to ray tracing. Our new equations preserve the familiar properties triangular with equally simple calculation, contrary previous formulations. We illustrate propert ies and behavior these through several example applications.

Lossless transmission of 3D meshes is a very challenging and timely problem for many applications, ranging from collaborative design to engineering. Additionally, frequent delays in transmissions call progressive order the end user receive useful successive refinements final mesh. In this paper, we present novel, fully encoding approach lossless triangle with fine granularity. A new valence-driven decimating conquest, combined patch tiling an original strategic retriangulation used maintain...

We present a novel technique, both flexible and efficient, for interactive remeshing of irregular geometry. First, the original (arbitrary genus) mesh is substituted by series 2D maps in parameter space. Using these maps, our algorithm then able to take advantage established signal processing halftoning tools that offer real-time interaction intricate control. The user can easily combine create control map --- which controls sampling density over surface patch. This sampled at rates allowing...

Many high-resolution surfaces are created through isosurface extraction from volumetric representations, obtained by 3D photography, CT, or MRI. Noise inherent in the acquisition process can lead to geometrical and topological errors. Reducing errors during reconstruction is well studied. However, isosurfaces often contain many form of tiny handles. These nearly invisible artifacts hinder subsequent operations like mesh simplification, remeshing, parametrization. In this article we present a...

Article Share on Discrete differential forms for computational modeling Authors: Mathieu Desbrun Caltech CaltechView Profile , Eva Kanso Yiying Tong Authors Info & Claims SIGGRAPH '06: ACM 2006 CoursesJuly Pages 39–54https://doi.org/10.1145/1185657.1185665Online:30 July 2006Publication History 64citation184DownloadsMetricsTotal Citations64Total Downloads184Last 12 Months47Last 6 weeks8 Get Citation AlertsNew Alert added!This alert has been successfully added and will be sent to:You notified...

In this paper, we propose a valence-driven, single-resolution encoding technique for lossless compression of triangle mesh connectivity. Building upon valence-based approach pioneered by Touma and Gotsman22 , design new valence-driven conquest arbitrary meshes that always guarantees smaller rates than the original method. Furthermore, provide novel theoretical entropy study our technique, hinting optimality approach. Finally, demonstrate practical efficiency (in agreement with prediction) on...

We introduce an algorithm for reconstructing watertight surfaces from unoriented point sets. Using the Voronoi diagram of input set, we deduce a tensor field whose principal axes and eccentricities locally represent respectively most likely direction normal to surface, confidence in this estimation. An implicit function is then computed by solving generalized eigenvalue problem such that its gradient aligned with field, providing best-fitting isosurface reconstruction. Our approach possesses...

While 2D and 3D vector fields are ubiquitous in computational sciences, their use graphics is often limited to regular grids, where computations easily handled through finite-difference methods. In this paper, we propose a set of simple accurate tools for the analysis discrete on arbitrary tetrahedral grids. We introduce variational, multiscale decomposition into three intuitive components: divergence-free part, curl-free harmonic part. show how our approach matches its well-known smooth...

Visual quality, low computational cost, and numerical stability are foremost goals in computer animation. An important ingredient achieving these is the conservation of fundamental motion invariants. For example, rigid deformable body simulation benefits greatly from linear angular momenta. In case fluids, however, none current techniques focuses on conserving invariants, consequently, often introduce a visually disturbing diffusion vorticity . Just as resolution complex domains. Doing so...