Pere Brunet

Solid representation and operation using extended octrees

Solid modelers must be based on reliable and fast algorithms for Boolean operations. The octree model, as well as several generalizations (polytrees, integrated polytrees, extended octrees), is specially well suited for these algorithms and can be used either as a primary or as a secondary model in solid modeling systems. This paper is concerned with a precise definition of the extended octree model that allows the representation of nonmanifold objects with planar faces and, consequently, is closed under Boolean operations on polyhedrons. Boolean nodes and nearly vertex nodes are introduced, and the model is discussed in comparison with related representations. A fast algorithm for the direct generation of the extended octree from the geometry of the base polygon in extrusion solids is presented, and its complexity is studied. Boolean operation algorithms are introduced.

Integrating occlusion culling and levels of detail through hardly-visible sets

Occlusion culling and level‐of‐detail rendering have become two powerful tools for accelerating the handling of very large models in real‐time visualization applications. We present a framework that combines both techniques to improve rendering times. Classical occlusion culling algorithms compute potentially visible sets (PVS), which are supersets of the sets of visible polygons. The novelty of our approach is to estimate the degree of visibility of each object of the PVS using synthesized coarse occluders. This allows to arrange the objects of each PVS into several Hardly‐Visible Sets (HVS) with similar occlusion degree. According to image accuracy and frame rate requirements, HVS provide a way to avoid sending to the graphics pipeline those objects whose pixel contribution is low due to partial occlusion. The image error can be bounded by the user at navigation time. On the other hand, as HVS offer a tighter estimation of the pixel contribution for each scene object, it can be used for a more convenient selection of the level‐of‐detail at which objects are rendered. In this paper, we describe the new framework technique, provide details of its implementation using a visibility octree as the chosen occlusion culling data structure and show some experimental results on the image quality.

The Visibility octree. A data structure for 3D navigation

Abstract This paper describes the visibility octree, a data structure to accelerate 3D navigation through very complex scenes. A conservative visibility algorithm that computes and hierarchically stores the structure at a preprocessing stage is presented. The Visibility Octree is used during navigation and its main contribution is its ability to provide an effective control over the coarseness of the visibility approximation. Tests with indoor ship scenes show that the visibility octree performs well on densely occluded environments.

Topology-reducing surface simplification using a discrete solid representation

This paper presents a new approach for generating coarse-level approximations of topologically complex models. Dramatic topology reduction is achieved by converting a 3D model to and from a volumetric representation. Our approach produces valid, error-bounded models and supports the creation of approximations that do not interpenetrate the original model, either being completely contained in the input solid or bounding it. Several simple to implement versions of our approach are presented and discussed. We show that these methods perform significantly better than other surface-based approaches when simplifying topologically-rich models such as scene parts and complex mechanical assemblies.

Constructive constraint-based model for parametric CAD systems

Abstract The paper discusses proposed solutions for constraint-based modelling, with special emphasis on constructive approaches. A new constructive scheme is proposed that is based on a nonevaluated, constructive solid model. The model definition language is presented and discussed, with the general architecture of the system and the structure of the internal model representation. The proposed approach supports the instantiation of predefined models, parametric geometric operations 1D, 2D and 3D, variable topologies, and operations with structural constraints.

A geometric modeller based on the exact octtree representation of polyhedra

Geometric Modellers based on a Boundary Representation scheme are well suited for display operations, but boolean operations require algorithms with quadratic complexity. Using a class of extended octtrees which is presented here, boolean operations become linear, while exact recomputation of the boundary model in the case of polyhedral objects is possible, and memory requirements are less than in classical octtree encodings. Some bounds on the memory savings are given and discussed. The DMI system, a Geometric Modeller based on a hybrid model Boundary ‐ Extended Octtrees, is presented, discussing the main operations and the interface between both models. Some modelling examples are shown. Finally, a generalization of the extended octtree encoding which allows the exact representation of objects limited by sculptured surfaces is presented.

Omni‐directional Relief Impostors

Relief impostors have been proposed as a compact and high‐quality representation for high‐frequency detail in 3D models. In this paper we propose an algorithm to represent a complex object through the combination of a reduced set of relief maps. These relief maps can be rendered with very few artifacts and no apparent deformation from any view direction. We present an efficient algorithm to optimize the set of viewing planes supporting the relief maps, and an image‐space metric to select a sufficient subset of relief maps for each view direction. Selected maps (typically three) are rendered based on the well‐known ray‐height‐field intersection algorithm implemented on the GPU. We discuss several strategies to merge overlapping relief maps while minimizing sampling artifacts and to reduce extra texture requirements. We show that our representation can maintain the geometry and the silhouette of a large class of complex shapes with no limit in the viewing direction. Since the rendering cost is output sensitive, our representation can be used to build a hierarchical model of a 3D scene.

Automatic Generation of Multiresolution Boundary Representations

The paper focuses on automatic simplification algorithms for the generation of a multiresolution family of solid models from an initial boundary representation of a polyhedral solid. An algorithm for general polyhedra based on an intermediate octree representation is proposed. Simplified elements of the multiresolution family approximate the initial solid within increasing tolerances. A discussion among different octree‐based simplification methods and the standard marching cubes algorithm is presented.

Approximation of a Variable Density Cloud of Points by Shrinking a Discrete Membrane

This paper describes a method to obtain a closed surface that approximates a general 3D data point set with nonuniform density. Aside from the positions of the initial data points, no other information is used. Particularly, neither the topological relations between the points nor the normal to the surface at the data points are needed. The reconstructed surface does not exactly interpolate the initial data points, but approximates them with a bounded maximum distance. The method allows one to reconstruct closed surfaces with arbitrary genus and closed surfaces with disconnected shells.

Increasing the smoothness of bicubic spline surfaces

The generation of smooth and shape-preserving surfaces from a mesh of three-dimensional data points is a very important problem in the field of Computer Aided Geometric Design. If a mesh of curves has been obtained in a first interpolation step and they fulfil the user requirements, the surface generation algorithm must avoid further oscillations within the patches. However, it is known that unwanted oscillations may appear using C^2 surfaces. In the present paper, a smoothing algorithm for bicubic spline surfaces is presented. Having the piecewise cubic boundaries of the patches fixed, the algorithm chooses adequate twists factors in order to increase the smoothness. At the end, although the surface is only C^1, unwanted oscillations have been reduced. Practical examples and test results are presented and discussed.