Alvar Vinacua

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.

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.

Technical Section: User-guided inverse reflector design

This paper proposes a technique for the design of luminaire reflector shapes from prescribed optical properties (far-field radiance distribution), geometrical constraints and users knowledge. This is an important problem in the field of Lighting Engineering, more specifically for Luminaire Design. The reflectors shape to be found is just a part of a set of pieces called in Lighting Engineering an optical set. This is composed of a light bulb (the source), the reflector and usually a glass that acts as a diffusor for the light, and protects the system from dust and other environmental phenomena. Thus, we aim at the design and development of a system capable of generating automatically a reflector shape in a way such that the optical set emits a given, user-defined, far-field radiance distribution for a known bulb. In order to do so, light propagation inside and outside the optical set must be simulated and the resulting radiance distribution compared to the desired one. Constraints on the shape imposed by industry needs and experts knowledge must be taken into account, bounding the set of possible shapes. The general approach taken is based on a minimization procedure on the space of possible reflector shapes, starting from a user-provided starting shape. The algorithm moves towards minimizing the distance, in the l^2 metric, between the resulting illumination from the reflector and the prescribed, ideal optical radiance distribution specified by the user. The initial shape and a provided confidence value are used during the whole process as a boundary for the space of spanned reflectors used during the simulation.

Computing Maximal Tiles and Application to Impostor‐Based Simplification

The computation of the largest planar region approximating a 3D object is an important problem with wide applications in modeling and rendering. Given a voxelization of the 3D object, we propose an efficient algorithm to solve a discrete version of this problem. The input of the algorithm is the set of grid edges connecting the interior and the exterior of the object (called sticks). Using a voting‐based approach, we compute the plane that slices the largest number of sticks and is orientation‐compatible with these sticks. The robustness and efficiency of our approach rests on the use of two different parameterizations of the planes with suitable properties. The first of these is exact and is used to retrieve precomputed local solutions of the problem. The second one is discrete and is used in a hierarchical voting scheme to compute the global maximum. This problem has diverse applications that range from finding object signatures to generating simplified models. Here we demonstrate the merits of the algorithm for efficiently computing an optimized set of textured impostors for a given polygonal model.

Steady affine motions and morphs

We propose to measure the quality of an affine motion by its steadiness, which we formulate as the inverse of its Average Relative Acceleration (ARA). Steady affine motions, for which ARA&equal;0, include translations, rotations, screws, and the golden spiral. To facilitate the design of pleasing in-betweening motions that interpolate between an initial and a final pose (affine transformation), <i>B</i> and <i>C</i>, we propose the Steady Affine Morph (SAM), defined as <i>A</i>^t∘ <i>B</i> with <i>A</i> &equal; <i>C</i> ∘ <i>B</i>⁻¹. A SAM is affine-invariant and reversible. It preserves isometries (i.e., rigidity), similarities, and volume. Its velocity field is stationary both in the global and the local (moving) frames. Given a copy count, <i>n</i>, the series of uniformly sampled poses, <i>A</i>^&fracin;∘ <i>B</i>, of a SAM form a regular pattern which may be easily controlled by changing <i>B</i>, <i>C</i>, or <i>n</i>, and where consecutive poses are related by the same affinity <i>A</i>^&frac1n. Although a real matrix <i>A</i><i>^t</i> does not always exist, we show that it does for a convex and large subset of orientation-preserving affinities <i>A</i>. Our fast and accurate Extraction of Affinity Roots (EAR) algorithm computes <i>A</i><i>^t</i>, when it exists, using closed-form expressions in two or in three dimensions. We discuss SAM applications to pattern design and animation and to key-frame interpolation.

Pressing: Smooth isosurfaces with flats from binary grids

We explore the automatic recovery of solids from their binary volumetric discretizations. In particular, we propose an approach, called Pressing, for smoothing isosurfaces extracted from binary volumes while recovering their large planar regions (flats). Pressing yields a surface that is guaranteed to contain the samples of the volume classified as interior and exclude those classified as exterior. It uses global optimization to identify flats and constrained bilaplacian smoothing to eliminate sharp features and high frequencies from the rest of the isosurface. It recovers sharp edges between flat regions and between flat and smooth regions. Hence, the resulting isosurface is usually a very accurate approximation of the original solid. Furthermore, the segmentation of the isosurface into flat and curved faces and the sharp/smooth labelling of their edges may be valuable for shape recognition, simplification, compression and various reverse engineering and manufacturing applications.

Piecewise algebraic surface computation and smoothing from a discrete model

This paper describes a constrained smoothing method for implicit surfaces defined on a voxelization. This method is suitable for computing a closed smooth surface that approximates an initial set of face connected voxels. The implicit surface is defined as the zero-set of a tensor-product uniform cubic Bspline. The smoothing process is based on increasing the Bspline continuity from C^2 to C^3 on the boundary faces of the voxels. The final surface is guaranteed to pierce a predefined subset of voxels.

REFLECTOR DESIGN FROM RADIANCE DISTRIBUTIONS

This paper proposes a technique for the design of reflector shapes from prescribed optical properties (far field radiance distribution) and geometrical constraints, which is of high importance in the field of Lighting Engineering, more specifically for Luminaire Design. The reflector shape to be found is just a part of a set of pieces of what is known in lighting engineering as an optical set, and is composed of a lamp (light source), a reflector, a holding case and a glass that protects the system from dust and other environmental phenomena. Thus, we aim at the design and development of a system capable of generating a reflector shape in a way such that the optical set emits a given, user defined, far field radiance distribution. This problem can be put in the mathematical context of inverse problems, which refer to all the problems where, contrary to what happens with traditional direct problems, several aspects of the scene are unknown. Then, the algorithm is allowed to work backwards to establish the missing parameters. In order to do so, light propagation inside and outside the optical set must be computed and the resulting radiance distribution compared to the desired one. Finally, constraints on the shape imposed by industry needs must be taken into account, bounding the set of possible shape definitions. The general approach taken is based on a minimization procedure on the space of possible reflector shapes. The algorithm moves towards minimizing the distance, in the l2 metric, between the resulting illumination far from the reflector and a prescribed, ideal optical radiance distribution specified at the far field by the user.

Multiresolution for algebraic curves and surfaces using wavelets

This paper describes a multiresolution method for implicit curves and surfaces. The method is based on wavelets, and is able to simplify the topology. The implicit curves and surfaces are defined as the zero‐valued piece‐wise algebraic isosurface of a tensor‐product uniform cubic B‐spline. A wavelet multiresolution method that deals with uniform cubic B‐splines on bounded domains is proposed. In order to handle arbitrary domains the proposed algorithm dynamically adds appropriate control points and deletes them in the synthesis phase.

High quality illustrative effects for molecular rendering

All-atom simulations are crucial in biotechnology. In Pharmacology, for example, molecular knowledge of protein-drug interactions is essential in the understanding of certain pathologies and in the development of improved drugs. To achieve this detailed information, fast and enhanced molecular visualization is critical. Moreover, hardware and software developments quickly deliver extensive data, providing intermediate results that can be analyzed by scientists in order to interact with the simulation process and direct it to a more promising configuration. In this paper we present a GPU-friendly data structure for real-time illustrative visualization of all-atom simulations. Our system generates both ambient occlusion and halos using an occupancy pyramid that needs no precalculation and that is updated on the fly during simulation, allowing the real time rendering of simulation results at sustained high framerates. Graphical abstractDisplay Omitted HighlightsAn algorithm for rendering complex, dynamic molecules at interactive frame rates.Renders high and low frequency ambient occlusion shading.Our algorithms can be applied to Space-filling and Ball and Stick models.