Raymarching Distance Fields with CUDA

Raymarching is a technique for rendering implicit surfaces using signed distance fields. It has been known and used since the 1980s for rendering fractals and CSG (constructive solid geometry) surfaces, but has rarely been used for commercial rendering applications such as film and 3D games. Raymarching was first used for photorealistic rendering in the mid 2000s by demoscene developers and hobbyist graphics programmers, receiving little to no attention from the academic community and professional graphics engineers. In the present work, we explain why the use of Simple and Fast Multimedia Library (SFML) by nearly all existing approaches leads to a number of inefficiencies, and hence set out to develop a CUDA oriented approach instead. We next show that the usual data handling pipeline leads to further unnecessary data flow overheads and therefore propose a novel pipeline structure that eliminates much of redundancy in the manner in which data are processed and passed. We proceed to introduce a series of data structures which were designed with the specific aim of exploiting the pipeline’s strengths in terms of efficiency while achieving a high degree of photorealism, as well as the accompanying models and optimizations that ultimately result in an engine which is capable of photorealistic and real-time rendering on complex scenes and arbitrary objects. Lastly, the effectiveness of our framework is demonstrated in a series of experiments which compare our engine both in terms of visual fidelity and computational efficiency with the leading commercial and open source solutions, namely Unreal Engine and Blender.

HEXAGONAL PWR-CORE MODELING AND SIMULATION WITH APPLICATION OF NECP-BAMBOO

In this paper, the modeling and simulation of the PWRs loaded with hexagonal fuel assemblies has been implemented with the NECP-Bamboo code. NECP-Bamboo, consisting of a 2D lattice code named Bamboo-Lattice and a 3D steady-state core code named Bamboo-Core, was primitively designed for the PWRs loaded with the rectangular fuel assemblies. As the capability extension for PWRs with hexagonal fuel assemblies, four aspects of improvement have been implemented in NECP-Bamboo. Firstly, the Constructive Solid Geometry (CSG) has been implemented in Bamboo-Lattice for the lattice modeling. Secondly, the explicit modeling of the reflector assembly has been applied to provide more reliable few-group constants, compared with the conventional 1D model for the reflector assembly. Thirdly, the assembly-homogenization capability has been extended to the hexagonal assembly. Fourthly, the diffusion solver in Bamboo-Core based on the Variational Nodal Method (VNM) has been extended to handle hexagonal geometry. With application of the capability-extended NECP-Bamboo, the modeling and simulations for the VVER-1000 benchmark loaded with MOX fuel has been implemented. It can be observed that the numerical results provided by NECP-Bamboo can agree well with corresponding results by the Monte-Carlo code.

Geometric Constructions On a Plane with a Single Ruler

One section of a special course “Constructive Solid Geometry” is presented in this paper in short. The course is conducted to the students of Mari State University who are future Math's teachers. The material is arranged in such a way that it can be recommended to all Math's teachers as a part of their special course in their schools.

EQUATIONS AND INTERVAL COMPUTATIONS FOR SOME FRACTALS

Very few characteristic functions, or equations, are reported so far for fractals. Such functions, called Rvachev functions in function-based modeling, are zero on the boundary, negative for inside points and positive for outside points. This paper proposes Rvachev functions for some classical fractals. These functions are convergent series, which are bounded with interval arithmetic and interval analysis in finite time. This permits to extend the Recursive Space Subdivision (RSS) method, which is classical in Computer Graphics (CG) and Interval Analysis, to fractal geometric sets. The newly proposed fractal functions can also be composed with classical Rvachev functions today routinely used in Constructive Solid Geometry (CSG) trees of CG or function-based modeling.