Isosurfaces Over Simplicial Partitions of Multiresolution Grids

We provide a simple method that extracts an isosurface that is manifold and intersection‐free from a function over an arbitrary octree. Our method samples the function dual to minimal edges, faces, and cells, and we show how to position those samples to reconstruct sharp and thin features of the surface. Moreover, we describe an error metric designed to guide octree expansion such that flat regions of the function are tiled with fewer polygons than curved regions to create an adaptive polygonalization of the isosurface. We then show how to improve the quality of the triangulation by moving dual vertices to the isosurface and provide a topological test that guarantees we maintain the topology of the surface. While we describe our algorithm in terms of extracting surfaces from volumetric functions, we also show that our algorithm extends to generating manifold level sets of co‐dimension 1 of functions of arbitrary dimension.     

Global Structure Optimization of Quadrilateral Meshes

We introduce a fully automatic algorithm which optimizes the high‐level structure of a given quadrilateral mesh to achieve a coarser quadrangular base complex. Such a topological optimization is highly desirable, since state‐of‐the‐art quadrangulation techniques lead to meshes which have an appropriate singularity distribution and an anisotropic element alignment, but usually they are still far away from the high‐level structure which is typical for carefully designed meshes manually created by specialists and used e.g. in animation or simulation. In this paper we show that the quality of the high‐level structure is negatively affected by helical configurations within the quadrilateral mesh. Consequently we present an algorithm which detects helices and is able to remove most of them by applying a novel grid preserving simplification operator (GP‐operator) which is guaranteed to maintain an all‐quadrilateral mesh. Additionally it preserves the given singularity distribution and in particular does not introduce new singularities. For each helix we construct a directed graph in which cycles through the start vertex encode operations to remove the corresponding helix. Therefore a simple graph search algorithm can be performed iteratively to remove as many helices as possible and thus improve the high‐level structure in a greedy fashion. We demonstrate the usefulness of our automatic structure optimization technique by showing several examples with varying complexity.     

G2 Tensor Product Splines over Extraordinary Vertices

We present a second order smooth filling of an n‐valent Catmull‐Clark spline ring with n biseptic patches. While an underdetermined biseptic solution to this problem has appeared previously, we make several advances in this paper. Most notably, we cast the problem as a constrained minimization and introduce a novel quadratic energy functional whose absolute minimum of zero is achieved for bicubic polynomials. This means that for the regular 4‐valent case, we reproduce the bicubic B‐splines. In other cases, the resulting surfaces are aesthetically well behaved. We extend our constrained minimization framework to handle the case of input mesh with boundary.     

Dirichlet Harmonic Shape Compression with Feature Preservation for Parameterized Surfaces

With the rapid advancement of 3D scanning devices, large and complicated 3D shapes are becoming ubiquitous, and require large amount of resources to store and transmit them efficiently. This makes shape compression a demanding technique in order for the user to reduce the data transmission latency. Existing shape compression methods could achieve very low bit‐rates by sacrificing shape quality. But none of them guarantees the preservation of salient feature lines that users care. In addition, many 3D shapes come with parametric information for texture mapping purposes. In this paper we describe a spectral method to compress the geometric shapes equipped with arbitrary valid parametric information. It guarantees to preserve user‐specified feature lines while achieving a high compression ratio. By applying the spectral shape analysis – Dirichlet Manifold Harmonics, in the 2D parametric domain, this method provides a progressive compression mechanism to trade‐off between bit‐rate and shape quality. Experiments show that this method provides very low bit‐rate with high shape‐quality and still guarantees the preservation of user‐specified feature lines.     

Para-Graph: Graph-Based Parameterization of Triangle Meshes with Arbitrary Genus

This paper describes a novel approach to the parameterization of triangle meshes representing 2‐manifolds with an arbitrary genus. A topology‐based decomposition of the shape is computed and used to segment the shape into primitives, which define a chart decomposition of the mesh. Then, each chart is parameterized using an extension of the barycentric coordinates method. The charts are all 0‐genus and can be of three types only, depending on the number of boundary components. The chart decomposition and the parameterization are used to define a shape graph where each node represents one primitive and the arcs code the adjacency relationships between the primitives. Conical and cylindrical primitives are coded together with their skeletal lines that are computed from and aligned with their parameterization. The application of the parameterization approach to remeshing guarantees that extraordinary vertices are localized only where two patches share a boundary and they are not scattered on the whole surface.     

Smart Motion Synthesis

Creating long motion sequences is a time‐consuming task even when motion capture equipment or motion editing tools are used. In this paper, we propose a system for creating a long motion sequence by combining elementary motion clips. The user is asked to first input motions on a timeline. The system then automatically generates a continuous and natural motion. Our system employs four motion synthesis methods: motion transition, motion connection, motion adaptation, and motion composition. Based on the constraints between the feet of the animated character and the ground, and the timing of the input motions, the appropriate method is determined for each pair of overlapped or sequential motions. As the user changes the arrangement of the motion clips, the system interactively changes the output motion. Alternatively, the user can make the system execute an input motion as soon as possible so that it follows the previous motion smoothly. Using our system, users can make use of existing motion clips. Because the entire process is automatic, even novices can easily use our system. A prototype system demonstrates the effectiveness of our approach.     

Localized Quadrilateral Coarsening

In this paper we introduce a coarsening algorithm for quadrilateral meshes that generates quality, quad-only connectivity during level-of- coarsening creation. A novel aspect of this work is development and implementation of a localized adaptation of the polychord collapse operator to better control and preserve important surface components. We describe a novel weighting scheme for automatic deletion selection that considers surface attributes, as well as localized queue updates that allow for improved data structures and computational performance opportunities over previous techniques. Additionally, this work supports optional and intuitive user controls for tailored simplification results.     

Embedded Implicit Stand-Ins for Animated Meshes: A Case of Hybrid Modelling

In this paper, we address shape modelling problems, encountered in computer animation and computer games development that are difficult to solve just using polygonal meshes. Our approach is based on a hybrid-modelling concept that combines polygonal meshes with implicit surfaces. A hybrid model consists of an animated polygonal mesh and an approximation of this mesh by a convolution surface stand-in that is embedded within it or is attached to it. The motions of both objects are synchronised using a rigging skeleton. We model the interaction between an animated mesh object and a viscoelastic substance, which is normally represented in an implicit form. Our approach is aimed at achieving verisimilitude rather than physically based simulation. The adhesive behaviour of the viscous object is modelled using geometric blending operations on the corresponding implicit surfaces. Another application of this approach is the creation of metamorphosing implicit surface parts that are attached to an animated mesh. A prototype implementation of the proposed approach and several examples of modelling and animation with near real-time preview times are presented.     

Semi-regular Quadrilateral-only Remeshing from Simplified Base Domains

Semi-regular meshes describe surface models that exhibit a structural regularity that facilitates many geometric processing algorithms. We introduce a technique to construct semi-regular, quad-only meshes from input surface meshes of arbitrary polygonal type and genus. The algorithm generates a quad-only model through subdivision of the input polygons, then simplifies to a base domain that is homeomorphic to the original mesh. During the simplification, a novel hierarchical mapping method, keyframe mapping , stores specific levels-of-detail to guide the mapping of the original vertices to the base domain. The algorithm implements a scheme for refinement with adaptive resampling of the base domain and backward projects to the original surface. As a byproduct of the remeshing scheme, a surface parameterization is associated with the remesh vertices to facilitate subsequent geometric processing, i.e. texture mapping, subdivision surfaces and spline-based modeling.     

Soft Articulated Characters with Fast Contact Handling

Fast contact handling of soft articulated characters is a computationally challenging problem, in part due to complex interplay between skeletal and surface deformation. We present a fast, novel algorithm based on a layered representation for articulated bodies that enables physically-plausible simulation of animated characters with a high-resolution deformable skin in real time. Our algorithm gracefully captures the dynamic skeleton-skin interplay through a novel formulation of elastic deformation in the pose space of the skinned surface. The algorithm also overcomes the computational challenges by robustly decoupling skeleton and skin computations using careful approximations of Schur complements, and efficiently performing collision queries by exploiting the layered representation. With this approach, we can simultaneously handle large contact areas, produce rich surface deformations, and capture the collision response of a character/s skeleton.