Laplacian surface editing

Sorkine, Olga; Cohen–Or, Daniel; Lipman, Yaron; Alexa, Marc; Rössl, Christian; Seidel, Hans‐Peter

doi:10.1145/1057432.1057456

Cited by 1,026 publications

(957 citation statements)

References 45 publications

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“…A very popular source of spd systems is the discrete Laplace-Beltrami operator ∆ S [30], which is closely related to frequencies of scalar fields defined on a two-manifold surface S [41]. This operator has various applications in surface smoothing [13,41], surface parameterization [32,12], variational surface modeling [25,7,38,44], mesh morphing [3,4,43], and shape analysis [31]. Besides from surfaces, the standard Laplace operator is for instance also used in image editing [40] and fluid simulation [39].…”

Section: Introductionmentioning

confidence: 99%

Efficient Linear System Solvers for Mesh Processing

Botsch

Bommes

Kobbelt

2005

Mathematics of Surfaces XI

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Abstract. The use of polygonal mesh representations for freeform geometry enables the formulation of many important geometry processing tasks as the solution of one or several linear systems. As a consequence, the key ingredient for efficient algorithms is a fast procedure to solve linear systems. A large class of standard problems can further be shown to lead more specifically to sparse, symmetric, and positive definite systems, that allow for a numerically robust and efficient solution. In this paper we discuss and evaluate the use of sparse direct solvers for such kind of systems in geometry processing applications, since in our experiments they turned out to be superior even to highly optimized multigrid methods, but at the same time were considerably easier to use and implement. Although the methods we present are well known in the field of high performance computing, we observed that they are in practice surprisingly rarely applied to geometry processing problems.

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Section: Introductionmentioning

confidence: 99%

Efficient Linear System Solvers for Mesh Processing

Botsch

Bommes

Kobbelt

2005

Mathematics of Surfaces XI

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“…In this method, the anisotropy vectors in nodes of an FE model were interpolated using the Laplacian smoothing method [4] based on user-defined sketches. These strokes were drawn according to the main characteristic of the Langer's lines distribution.…”

Section: Sketch-based Laplacian Smoothing Methods (Methods Ii)mentioning

confidence: 99%

Numerical Simulation of Anisotropy Directions in Soft Tissues and in Particular in Skin

Raith

Itskov

2013

Proc Appl Math and Mech

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Orientation of collagen fibers and their spatial distribution predefine macroscopic mechanical properties of the soft tissue and in particular its anisotropy directions. In this contribution, we apply two different procedures to automatically generate these directions for a 3D FE-model. The first procedure is based on an analogy with a heat conduction problem. Accordingly, a thermal flux under certain temperature boundary conditions is calculated by the same FE model and is further utilized for the definition of the anisotropy directions. The numerical result shows good agreement with Langer's lines data in human skin. Within the second procedure, the fiber vector field is calculated by the Laplacian smoothing method based on the user defined fiber direction sketches.

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“…A vast literature exists on mesh optimization, processing and discretizing continuousdomain operators (e.g., see Refs. [18,19]). Polygon models are usually interpolating the control points coinciding with the mesh vertices; this property implies that the shape is modified by points which directly lie on the boundary of the object.…”

Section: Discrete Closed Surfacesmentioning

confidence: 99%

Smooth shapes with spherical topology: Beyond traditional modeling, efficient deformation, and interaction

2017

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Existing shape models with spherical topology are typically designed either in the discrete domain using interpolating polygon meshes or in the continuous domain using smooth but non-interpolating schemes such as subdivision or NURBS. Both polygon models and subdivision methods require a large number of parameters to model smooth surfaces. NURBS need fewer parameters but have a complicated rational expression and non-uniform shifts in their formulation. We present a new method to construct deformable closed surfaces, which includes exact spheres, by combining the best of two worlds: a smooth, interpolating model with a continuously varying tangent plane and well-defined curvature at every point on the surface.Our formulation is considerably simpler than NURBS and requires fewer parameters than polygon meshes. We demonstrate the generality of our method with applications including intuitive user-interactive shape modeling, continuous surface deformation, shape morphing, reconstruction of shapes from parameterized point clouds, and fast iterative shape optimization for image segmentation. Comparisons with discrete methods and non-interpolating approaches highlight the advantages of our framework.

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Laplacian surface editing

Cited by 1,026 publications

References 45 publications

Efficient Linear System Solvers for Mesh Processing

Efficient Linear System Solvers for Mesh Processing

Numerical Simulation of Anisotropy Directions in Soft Tissues and in Particular in Skin

Smooth shapes with spherical topology: Beyond traditional modeling, efficient deformation, and interaction

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