Results 1  10
of
214
Laplacian Surface Editing
, 2004
"... Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We p ..."
Abstract

Cited by 235 (27 self)
 Add to MetaCart
Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We provide such a representation of a surface, based on the Laplacian of the mesh, by encoding each vertex relative to its neighborhood. The Laplacian of the mesh is enhanced to be invariant to locally linearized rigid transformations and scaling. Based on this Laplacian representation, we develop useful editing operations: interactive freeform deformation in a region of interest based on the transformation of a handle, transfer and mixing of geometric details between two surfaces, and transplanting of a partial surface mesh onto another surface. The main computation involved in all operations is the solution of a sparse linear system, which can be done at interactive rates. We demonstrate the effectiveness of our approach in several examples, showing that the editing operations change the shape while respecting the structural geometric detail.
Shape modeling with pointsampled geometry
 ACM Transactions on Graphics
, 2003
"... Figure 1: Objects created with our system. (a) boolean operations with scanned geometry, (b) an Octopus modeled by deforming and extruding a sphere, (c) a design study for a Siggraph coffee mug created by boolean operations, freeform deformation and displacement mapping. We present a versatile and ..."
Abstract

Cited by 201 (30 self)
 Add to MetaCart
Figure 1: Objects created with our system. (a) boolean operations with scanned geometry, (b) an Octopus modeled by deforming and extruding a sphere, (c) a design study for a Siggraph coffee mug created by boolean operations, freeform deformation and displacement mapping. We present a versatile and complete freeform shape modeling framework for pointsampled geometry. By combining unstructured point clouds with the implicit surface definition of the moving least squares approximation, we obtain a hybrid geometry representation that allows us to exploit the advantages of implicit and parametric surface models. Based on this representation we introduce a shape modeling system that enables the designer to perform large constrained deformations as well as boolean operations on arbitrarily shaped objects. Due to minimum consistency requirements, pointsampled surfaces can easily be restructured on the fly to support extreme geometric deformations during interactive editing. In addition, we show that strict topology control is possible and sharp features can be generated and preserved on pointsampled objects. We demonstrate the effectiveness of our system on a large set of input models, including noisy range scans, irregular point clouds, and sparsely as well as densely sampled models.
CHARMS: A Simple Framework for Adaptive Simulation
 ACM Transactions on Graphics
, 2002
"... Finite element solvers are a basic component of simulation applications; they are common in computer graphics, engineering, and medical simulations. Although adaptive solvers can be of great value in reducing the often high computational cost of simulations they are not employed broadly. Indeed, bui ..."
Abstract

Cited by 146 (11 self)
 Add to MetaCart
Finite element solvers are a basic component of simulation applications; they are common in computer graphics, engineering, and medical simulations. Although adaptive solvers can be of great value in reducing the often high computational cost of simulations they are not employed broadly. Indeed, building adaptive solvers can be a daunting task especially for 3D finite elements. In this paper we are introducing a new approach to produce conforming, hierarchical, adaptive refinement methods (CHARMS). The basic principle of our approach is to refine basis functions, not elements. This removes a number of implementation headaches associated with other approaches and is a general technique independent of domain dimension (here 2D and 3D), element type (e.g., triangle, quad, tetrahedron, hexahedron), and basis function order (piecewise linear, higher order Bsplines, Loop subdivision, etc.). The (un)refinement algorithms are simple and require little in terms of data structure support. We demonstrate the versatility of our new approach through 2D and 3D examples, including medical applications and thinshell animations.
Normal Meshes
, 2000
"... Normal meshes are new fundamental surface descriptions inspired by differential geometry. A normal mesh is a multiresolution mesh where each level can be written as a normal offset from a coarser version. Hence the mesh can be stored with a single float per vertex. We present an algorithm to approxi ..."
Abstract

Cited by 144 (8 self)
 Add to MetaCart
Normal meshes are new fundamental surface descriptions inspired by differential geometry. A normal mesh is a multiresolution mesh where each level can be written as a normal offset from a coarser version. Hence the mesh can be stored with a single float per vertex. We present an algorithm to approximate any surface arbitrarily closely with a normal semiregular mesh. Normal meshes can be useful in numerous applications such as compression, filtering, rendering, texturing, and modeling.
Subdivision Surfaces: A New Paradigm For ThinShell FiniteElement Analysis
 INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
, 2000
"... We develop a new paradigm for thinshell finiteelement analysis based on the use of subdivision surfaces for: i) describing the geometry of the shell in its undeformed configuration, and ii) generating smooth interpolated displacement fields possessing bounded energy within the strict framework ..."
Abstract

Cited by 133 (30 self)
 Add to MetaCart
(Show Context)
We develop a new paradigm for thinshell finiteelement analysis based on the use of subdivision surfaces for: i) describing the geometry of the shell in its undeformed configuration, and ii) generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the KirchhoffLove theory of thin shells. The particular subdivision strategy adopted here is Loop's scheme, with extensions such as required to account for creases and displacement boundary conditions. The displacement fields obtained by subdivision are H 2 and, consequently, have a finite KirchhoffLove energy. The resulting finite elements contain three nodes and element integrals are computed by a onepoint quadrature. The displacement field of the shell is interpolated from nodal displacements only. In particular, no nodal rotations are used in the interpolation. The interpolation scheme induced by subdivision is nonlocal, i. e., the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighboring elements. However, the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface.
SemiRegular Mesh Extraction from Volumes
, 2000
"... We present a novel method to extract isosurfaces from distance volumes. It generates high quality semiregular multiresolution meshes of arbitrary topology. Our technique proceeds in two stages. First, a very coarse mesh with guaranteed topology is extracted. Subsequently an iterative multiscale f ..."
Abstract

Cited by 104 (13 self)
 Add to MetaCart
We present a novel method to extract isosurfaces from distance volumes. It generates high quality semiregular multiresolution meshes of arbitrary topology. Our technique proceeds in two stages. First, a very coarse mesh with guaranteed topology is extracted. Subsequently an iterative multiscale forcebased solver refines the initial mesh into a semiregular mesh with geometrically adaptive sampling rate and good aspect ratio triangles. The coarse mesh extraction is performed using a new approach we call surface wavefront propagation. A set of discrete isodistance ribbons are rapidly built and connected while respecting the topology of the isosurface implied by the data. Subsequent multiscale refinement is driven by a simple forcebased solver designed to combine good isosurface fit and high quality sampling through reparameterization. In contrast to the Marching Cubes technique our output meshes adapt gracefully to the isosurface geometry, have a natural multiresolution structure and good aspect ratio triangles, as demonstrated with a number of examples.
Flows on Surfaces of Arbitrary Topology
, 2003
"... In this paper we introduce a method to simulate fluid flows on smooth surfaces of arbitrary topology: an effect never seen before. We achieve this by combining a twodimensional stable fluid solver with an atlas of parametrizations of a CatmullClark surface. The contributions of this paper are: (i) ..."
Abstract

Cited by 92 (0 self)
 Add to MetaCart
In this paper we introduce a method to simulate fluid flows on smooth surfaces of arbitrary topology: an effect never seen before. We achieve this by combining a twodimensional stable fluid solver with an atlas of parametrizations of a CatmullClark surface. The contributions of this paper are: (i) an extension of the Stable Fluids solver to arbitrary curvilinear coordinates, (ii) an elegant method to handle crosspatch boundary conditions and (iii) a set of new external forces custom tailored for surface flows. Our techniques can also be generalized to handle other types of processes on surfaces modeled by partial differential equations, such as reactiondiffusion. Some of our simulations allow a user to interactively place densities and apply forces to the surface, then watch their effects in realtime. We have also computed higher resolution animations of surface flows offline.
Differential coordinates for interactive mesh editing
 In Proceedings of Shape Modeling International
, 2004
"... One of the main challenges in editing a mesh is to retain the visual appearance of the surface after applying various modifications. In this paper we advocate the use of linear differential coordinates as means to preserve the highfrequency detail of the surface. The differential coordinates represe ..."
Abstract

Cited by 91 (16 self)
 Add to MetaCart
(Show Context)
One of the main challenges in editing a mesh is to retain the visual appearance of the surface after applying various modifications. In this paper we advocate the use of linear differential coordinates as means to preserve the highfrequency detail of the surface. The differential coordinates represent the details and are defined by a linear transformation of the mesh vertices. This allows the reconstruction of the edited surface by solving a linear system that satisfies the reconstruction of the local details in least squares sense. Since the differential coordinates are defined in a global coordinate system they are not rotationinvariant. To compensate for that, we rotate them to agree with the rotation of an approximated local frame. We show that the linear least squares system can be solved fast enough to guarantee interactive response time thanks to a precomputed factorization of the coefficient matrix. We demonstrate that our approach enables to edit complex detailed meshes while keeping the shape of the details in their natural orientation. 1
4–8 Subdivision
, 2000
"... In this paper we introduce 4–8 subdivision, a new scheme that generalizes the fourdirectional box spline of class � � to surfaces of arbitrary topological type. The crucial advantage of the proposed scheme is that it uses bisection refinement as an elementary refinement operation, rather than more c ..."
Abstract

Cited by 66 (6 self)
 Add to MetaCart
In this paper we introduce 4–8 subdivision, a new scheme that generalizes the fourdirectional box spline of class � � to surfaces of arbitrary topological type. The crucial advantage of the proposed scheme is that it uses bisection refinement as an elementary refinement operation, rather than more commonly used face or vertex splits. In the uniform case, bisection refinement results in doubling, rather than quadrupling of the number of faces in a mesh. Adaptive bisection refinement, automatically generates conforming variableresolution meshes in contrast to face and vertex split methods which require an postprocessing step to make an adaptively refined mesh conforming. The fact that the size of faces decreases more gradually with refinement allows one to have greater control over the resolution of a refined mesh. It also makes it possible to achieve higher smoothness while using small stencils (the size of the stencils used by our scheme is similar to Loop subdivision). We show that the subdivision surfaces produced by the 4–8 scheme are � � continuous almost everywhere, except at extraordinary vertices where they are is �continuous.