C-essential surfaces in (3-manifold, graph) pairs

Let $T$ be a graph in a compact, orientable 3--manifold $M$ and let $\Gamma$ be a subgraph. $T$ can be placed in bridge position with respect to a Heegaard surface $H$. We show that if $H$ is what we call $(T,\Gamma)$-c-weakly reducible in the complement of $T$ then either a "degenerate" situation occurs or $H$ can be untelescoped and consolidated into a collection of "thick surfaces" and "thin surfaces". The thin surfaces are c-essential (c-incompressible and essential) in the graph exterior and each thick surface is a strongly irreducible bridge surface in the complement of the thin surfaces. This strengthens and extends previous results of Hayashi-Shimokawa and Tomova to graphs in 3-manifolds that may have non-empty boundary.Comment: 33 pages, 9 figures. Accepted for publication in Communications in Analysis and Geometr

Massively Parallel Ray Tracing Algorithm Using GPU

Ray tracing is a technique for generating an image by tracing the path of light through pixels in an image plane and simulating the effects of high-quality global illumination at a heavy computational cost. Because of the high computation complexity, it can't reach the requirement of real-time rendering. The emergence of many-core architectures, makes it possible to reduce significantly the running time of ray tracing algorithm by employing the powerful ability of floating point computation. In this paper, a new GPU implementation and optimization of the ray tracing to accelerate the rendering process is presented

Kinematic calibration of Orthoglide-type mechanisms from observation of parallel leg motions

The paper proposes a new calibration method for parallel manipulators that allows efficient identification of the joint offsets using observations of the manipulator leg parallelism with respect to the base surface. The method employs a simple and low-cost measuring system, which evaluates deviation of the leg location during motions that are assumed to preserve the leg parallelism for the nominal values of the manipulator parameters. Using the measured deviations, the developed algorithm estimates the joint offsets that are treated as the most essential parameters to be identified. The validity of the proposed calibration method and efficiency of the developed numerical algorithms are confirmed by experimental results. The sensitivity of the measurement methods and the calibration accuracy are also studied