Geometrical Construction for Refracted Ray

Optical fiber index profiles by the refracted-ray method (refracted near-field scanning).

This paper has two primary purposes. First, it provides an elementary description and tutorial overview of the refracted-ray method of measuring fiber index profiles. Second, it presents new results concerning the theoretical foundation, the linearity and precision, and other aspects of the method. In particular, we find that index differences may be measured to 5% or better and conclude by sho...

Kikuchi / Refracted

Incremental BVH construction for ray tracing

We propose a new method for incremental construction of Bounding Volume Hierarchies (BVH). Despite the wide belief that the incremental construction of BVH is inefficient we show that our method incrementally constructs a BVH with quality comparable to the best SAH builders. We illustrate the versatility of the proposed method using a flexible parallelization scheme that opens new possibilities...

Geometrical Construction of Heterogeneous Loop Amplitudes in 2D Gravity

We study a disk amplitude which has a complicated heterogeneous matter configuration on the boundary in a system of the (3, 4) conformal matter coupled to two-dimensional gravity. It is analyzed using the two-matrix chain model in the large N limit. We show that the disk amplitude calculated by Schwinger-Dyson equations can completely be reproduced through purely geometrical consideration. From...

An Embedded Geometrical Language in Haskell: Construction, Visualisation, Proof

Geometric constructions based on compass and straight-edge have been thoroughly studied and explored. In this paper, we present a language embedded in Haskell, to describe, manipulate and analyse such constructions. The use of embedded languages has been explored in various specialised domains, and have been shown to be an excellent frontend to describe such specialised programs, enabling, for ...