Narcís Coll

*Cages:: A multilevel, multi-cage-based system for mesh deformation

Cage-based deformation has been one of the main approaches for mesh deformation in recent years, with a lot of interesting and active research. The main advantages of cage-based deformation techniques are their simplicity, relative flexibility, and speed. However, to date there has been no widely accepted solution that provides both user control at different levels of detail and high-quality deformations. We present *Cages (star-cages), a significant step forward with respect to traditional single-cage coordinate systems, and which allows the usage of multiple cages enclosing the model for easier manipulation while still preserving the smoothness of the mesh in the transitions between them. The proposed deformation scheme is extremely flexible and versatile, allowing the usage of heterogeneous sets of coordinates and different levels of deformation, ranging from a whole-model deformation to a very localized one. This locality allows faster evaluation and a reduced memory footprint, and as a result outperforms single-cage approaches in flexibility, speed, and memory requirements for complex editing operations.

Multi-visibility maps of triangulated terrains

Visibility computation on terrain models is an important research topic with many applications in Geographical Information Systems. A multi‐visibility map is the subdivision of the domain of a terrain into regions that, according to different criteria, encodes the visibility with respect to a set of view elements. We present an approach for visualising approximated multi‐visibility maps of a triangulated terrain corresponding to a set of view elements by using graphics hardware. Our method supports heterogeneous sets of view elements containing points, segments, polygonal chains and polygons and works for weak and strong visibility. Moreover, we are also able to efficiently solve approximated point and polygonal region multi‐visibility queries. To illustrate the usefulness of our approach we present results obtained with an implementation of the proposed algorithms.

Approximations of 2D and 3D generalized Voronoi diagrams

We propose a new approach for computing in an efficient way polygonal approximations of generalized 2D/3D Voronoi diagrams. The method supports distinct site shapes (points, line-segments, curved-arc segments, polygons, spheres, lines, polyhedra, etc.), different distance functions (Euclidean distance, convex distance functions, etc.) and is restricted to diagrams with connected Voronoi regions. The presented approach constructs a tree (a quadtree in 2D/an octree in 3D) which encodes in its nodes and in a compact way all the information required for generating an explicit representation of the boundaries of the Voronoi diagram approximation. Then, by using this hierarchical data structure a reconstruction strategy creates the diagram approximation. We also present the algorithms required for dynamically maintaining under the insertion or deletion of sites the Voronoi diagram approximation. The main features of our approach are its generality, efficiency, robustness and easy implementation.

Mesh Modification Under Local Domain Changes

We propose algorithms to incrementally modify a mesh of a planar domain by interactively inserting and removing elements (points, segments, polygonal lines, etc.) into or from the planar domain, keeping the quality of the mesh during the process. Our algorithms, that combine mesh improvement techniques, achieve quality by deleting, moving or inserting Steiner points from or into the mesh. The changes applied to the mesh are local and the number of Steiner points added during the process remains low. Moreover, our approach can also be applied to the directly generation of refined Delaunay quality meshes.

Accurate Simplification of Multi-Chart Textured Models

Scanning and acquisition methods produce highly detailed surface meshes that need multi‐chart parameterizations to reduce stretching and distortion. From these complex shape surfaces, high‐quality approximations are automatically generated by using surface simplification techniques. Multi‐chart textures hinder the quality of the simplification of these techniques for two reasons: either the chart boundaries cannot be simplified leading to a lack of geometric fidelity; or texture distortions and artefacts appear near the simplified boundaries. In this paper, we present an edge‐collapse based simplification method that provides an accurate, low‐resolution approximation from a multi‐chart textured model. For each collapse, the model is reparameterized by local bijective mappings to avoid texture distortions and chart boundary artefacts on the simplified mesh due to the geometry changes. To better apply the appearance attributes and to guarantee geometric fidelity, we drive the simplification process with the quadric error metrics weighted by a local area distortion measure.

Combining improvement and refinement techniques: 2D Delaunay mesh adaptation under domain changes

We propose a framework that combines improvement and Delaunay refinement techniques for incrementally adapting a refined mesh by interactively inserting and removing domain elements. Our algorithms achieve quality mesh by deleting, moving or inserting Steiner points from or into the mesh. The modifications applied to the mesh are local and the number of Steiner points added during the mesh adaptation process remains low. Moreover, since a mesh generation process can be viewed as an adaptation mesh process when domain elements are inserted one by one, our approach can also be applied to the generation of refined Delaunay quality meshes by incorporating our framework in the main body of Delaunay refinement mesh generation algorithms.

Multiresolution Approximations of Generalized Voronoi Diagrams

A framework to support multiresolution approximations of planar generalized Voronoi diagrams is presented. Our proposal is: (1) A multiresolution model based on a quadtree data structure which encodes approximations of a generalized Voronoi diagram at different levels of detail. (2) A user driven refinement strategy which generates from the quadtree a continuous polygonal approximation of the Voronoi diagram.

Dynamically maintaining a hierarchical planar Voronoi diagram approximation

An approach for computing a hierarchical approximation of planar Voronoi diagrams for different site shapes (points, line-segments, curve-arc segments, ...) and different distance functions (Euclidean metrics, convex distance functions, ...) was presented in [3]. The approach is based on the Voronoi-Quadtree, a quadtree data structure from which a polygonal approximation, represented by a DCEL structure, of the associated Voronoi region boundaries can be computed at different levels of detail. In this paper we describe efficient algorithms for dynamically maintaining, under the insertion or deletion of sites, the Voronoi-Quadtree and the corresponding DCEL structure representing an approximation of a Generalized Voronoi diagram.

Computing terrain multi-visibility maps for a set of view segments using graphics hardware

A multi-visibility map is the subdivision of the domain of a terrain into different regions that, according to different criteria, encodes the visibility concerning a set of view elements. In this paper we present an approach for computing a discrete approximation of a multi-visibility map of a triangulated terrain corresponding to a set of view segments, for weak and strong visibility, by using graphics hardware.

Parallel constrained Delaunay triangulation on the GPU

ABSTRACT In this paper, we propose a new graphics processing unit (GPU) method able to compute the 2D constrained Delaunay triangulation (CDT) of a planar straight-line graph consisting of points and segments. All existing methods compute the Delaunay triangulation of the given point set, insert all the segments, and then finally transform the resulting triangulation into the CDT. To the contrary, our novel approach simultaneously inserts points and segments into the triangulation, taking special care to avoid conflicts during retriangulations due to concurrent insertion of points or concurrent edge flips. Our implementation using the Compute Unified Device Architecture programming model on NVIDIA GPUs improves, in terms of running time, the best known GPU-based approach to the CDT problem.