Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification

We present an efficient method for classifying the morphology of the intersection curve of two quadrics (QSIC) in PR3, 3D real projective space; here, the term morphology is used in a broad sense to mean the shape, topological, and algebraic properties of a QSIC, including singularity, reducibility, the number of connected components, and the degree of each irreducible component, etc. There are in total 35 different QSIC morphologies with non-degenerate quadric pencils. For each of these 35 QSIC morphologies, through a detailed study of the eigenvalue curve and the index function jump we establish a characterizing algebraic condition expressed in terms of the Segre characteristics and the signature sequence of a quadric pencil. We show how to compute a signature sequence with rational arithmetic so as to determine the morphology of the intersection curve of any two given quadrics. Two immediate applications of our results are the robust topological classification of QSIC in computing B-rep surface representation in solid modeling and the derivation of algebraic conditions for collision detection of quadric primitives

Efficient Point based Global Illumination on Intel MIC Architecture

International audiencePoint-Based Global Illumination (PBGI) is a popular rendering method in special effects and motion picture productions. The tree-cut computation is in general the most time consuming part of this algorithm, but it can be formulated for efficient parallel execution, in particular regarding wide-SIMD hardware. In this context, we propose several vectorization schemes, namely single, packet and hybrid, to maximize the utilization of modern CPU architectures. While for the single scheme, 16 nodes from the hierarchy are processed for a single receiver in parallel, the packet scheme handles one node for 16 receivers. These two schemes work well for scenes having smooth geometry and diffuse material. When the scene contains high frequency bumps maps and glossy reflections, we use a hybrid vectorization method. We conduct experiments on an Intel Many Integrated Corearchitecture and report preliminary results on several scenes, showing that up to a 3x speedup can be achieved when compared with non-vectorized execution