The generalised balanced power diagram: flat sections, affine transformations and an improved rendering algorithm

TL;DR

This paper explores properties of the generalized balanced power diagram (GBPD), focusing on affine transformations and flat sections, and introduces an improved, more efficient algorithm for generating digital images of GBPDs compared to traditional methods.

Contribution

It extends an existing power diagram algorithm to GBPDs, enhancing efficiency in digital image generation and analyzing geometric properties relevant to microstructure modeling.

Findings

GBPDs exhibit specific properties under affine transformations.

The new algorithm outperforms brute force methods in efficiency.

Enhanced rendering techniques for GBPDs improve microstructure visualization.

Abstract

The generalised balanced power diagram (GBPD) is regarded in the literature as a suitable geometric model for describing polycrystalline microstructures with curved grain boundaries. This article compiles properties of GBPDs with regard to affine transformations and flat sections. Furthermore, it extends an algorithm known for power diagrams for generating digital images, which is more efficient than the usual brute force approach, on GBPDs.