Paulo Roma Cavalcanti

Point in Polyhedron Testing Using Spherical Polygons

This chapter presents a method based on spherical polygons to determine if a given point is inside or outside a three-dimensional polyhedron, given by its face list. This approach extends a well-known 2D technique to 3D. In two dimensions, one can decide whether a point p is inside a simple polygon P by computing the signed angle around p determined by each side of P . If p is not on the boundary of P , the sum S of all such signed angles is necessarily −2π, 0, or 2π. If S = 0, p is exterior to P , otherwise p is interior to P . Usually, this method is considered to be inferior to the one that is based on counting the number of intersections with P of a ray through p . However, it deserves attention for its elegance and simplicity. The chapter shows how to extend the signed angle method to the 3D problem. It is assumed that P is a simple polyhedron, given by its face list, in which the faces are consistently oriented.

Efficient Point-Based Rendering Using Image Reconstruction

Image-space reconstruction of continuous surfaces from scattered one-pixel projections of points is known to potentially offer an advantageous time complexity compared to surface splatting techniques. We propose a new algorithm for hardware-accelerated image-space reconstruction using pull-push interpolation and present an efficient GPU implementation. Compared to published image-space reconstruction approaches employing the pull-push interpolation, our method offers a significantly improved image quality because of the integration of elliptic boxfilters and support for deferred Phong shading. For large point-based models, our GPU implementation is capable of rendering more than 50M points per second—including image-space reconstruction and deferred shading.

A New Interface Paradigm for Motion Capture Based Animation Systems

This paper proposes a new user interface paradigm for motion capture based animation systems, providing intuitive and efficient ways to visualize the main motion capture concepts and operations. A prototype system was built, implementing the proposed interface model and supported by a flexible architecture that is suitable to work with the motion capture methodology.

A modeling methodology for finite element mesh generation of multi-region models with parametric surfaces☆

Abstract This paper presents a description of the reorganization of a geometric modeler, MG, designed to support new capabilities of a topological module (CGC) that allows the detection of closed-off solid regions described by surface patches in non-manifold geometric models defined by NURBS. These patches are interactively created by the user by means of the modelers graphics interface, and may result from parametric–surface intersection in which existing surface meshes are used as a support for a discrete definition of intersection curves. The geometry of realistic engineering objects is intrinsically complex, usually composed by several materials and regions. Therefore, automatic and adaptive meshing algorithms have become quite useful to increase the reliability of the procedures of a FEM numerical analysis. The present approach is concerned with two aspects of 3D FEM simulation: geometric modeling, with automatic multi-region detection, and support to automatic finite-element mesh generation.

An architecture for motion capture based animation

The paper proposes an architecture for motion capture based animation systems, which works with several data formats and uses the building block paradigm for motion processing operations. Also, a user interface is proposed to perform an intuitive visualization of the animation main elements. A prototype system has been implemented, based on the presented concepts, and its operation is discussed.

Special Section: Point-Based Graphics: Efficient image reconstruction for point-based and line-based rendering

We address the problem of an efficient image-space reconstruction of adaptively sampled scenes in the context of point-based and line-based graphics. The image-space reconstruction offers an advantageous time complexity compared to surface splatting techniques and, in fact, our improved GPU implementation performs significantly better than splatting implementations for large point-based models. We discuss the integration of elliptical Gaussian weights for enhanced image quality and generalize the image-space reconstruction to line segments. Furthermore, we present solutions for the efficient combination of points, lines, and polygons in a single image.

A Collision Detection and Response Scheme for Simplified Physically Based Animation

In this paper we describe a system for physical animation of rigid and deformable objects. These are represented as groups of particles linked by linear constraints, while a Verlet integrator is used for motion computation. Unlike traditional approaches, we accomplish physical simulation without explicitly computing orientation matrices, torques or inertia tensors. The main contribution of our work is related to the way collisions are handled by the system, which employs different approaches for deformable and rigid bodies. In particular, we show how collision detection using the GJK algorithm [9] and bounding sphere hierarchies can be combined with the projection based collision response technique described by Jakobsen [14].

A Generic Programming Approach to Multiresolution Spatial Decompositions

We present a generic programming approach to the implementation of multiresolution spatial decompositions. From a set of simple and necessary requirements, we arrive at the Binary Multitriangulation (BMT) concept. We also describe a data structure that models the BMT concept in its full generality. Finally, we discuss applications of the BMT to visualization of volumetric datasets.

Fast polygonization of variational implicit surfaces

This article presents a simple hierarchical adaptation of the marching cubes algorithm for polygonizing variational implicit surfaces used in modelling and reconstruction applications. The technique relies on placing the normal and boundary constraint points respecting pseudo-Euclidean distance metrics. This procedure makes it possible to quickly prune the space and minimize the number of costly function evaluations and thus converge rapidly to the surface. Timings show that this technique tends to perform faster than Bloomenthals (1994) continuation polygonizer.

Multi-resolution triangulations with adaptation to the domain based on physical compression

This paper presents a method for generating multi-resolution triangulations of non-manifold objects composed of several regions with arbitrary geometry. The process of adapting the triangulation to the boundary of the object is based on physical compression, more specifically, a mass-spring system. The final triangulation usually has no degenerated triangles and provides an approximation of the boundary based on a chosen resolution.