Hermite type Spline spaces over rectangular meshes with complex topological structures

International audienceMotivated by the magneto hydrodynamic (MHD) simulation for Tokamaks with Isogeometric analysis, we present a new type of splines defined over a rectangular mesh with arbitrary topology, which are piecewise polynomial functions of bidegree (d,d) and C^r parameter continuity. In particular, We compute their dimension and exhibit basis functions called Hermite bases for bicubic spline spaces. We investigate their potential applications for solving partial differential equations (PDEs) over a complex physical domain in the framework of Isogeometric analysis. In particular, weanalyze the property of approximation of these spline spaces for the L2-norm. Despite the fact that the basis functions are singular at extraordinary vertices, we show that the optimal approximation order and numerical convergence rates are reached by setting a proper parameterization

Ray Tracing Gems

This book is a must-have for anyone serious about rendering in real time. With the announcement of new ray tracing APIs and hardware to support them, developers can easily create real-time applications with ray tracing as a core component. As ray tracing on the GPU becomes faster, it will play a more central role in real-time rendering. Ray Tracing Gems provides key building blocks for developers of games, architectural applications, visualizations, and more. Experts in rendering share their knowledge by explaining everything from nitty-gritty techniques that will improve any ray tracer to mastery of the new capabilities of current and future hardware. What you'll learn: The latest ray tracing techniques for developing real-time applications in multiple domains Guidance, advice, and best practices for rendering applications with Microsoft DirectX Raytracing (DXR) How to implement high-performance graphics for interactive visualizations, games, simulations, and more Who this book is for: Developers who are looking to leverage the latest APIs and GPU technology for real-time rendering and ray tracing Students looking to learn about best practices in these areas Enthusiasts who want to understand and experiment with their new GPU