A gradient descent algorithm for computing circle patterns

TL;DR

This paper introduces a gradient descent-based algorithm for efficiently generating planar circle patterns, capable of handling obtuse overlap angles and improving computational efficiency over existing methods.

Contribution

The paper proposes a novel gradient descent algorithm that separately computes circle radii and centers, enhancing efficiency and applicability for complex circle patterns.

Findings

More efficient than existing algorithms for circle center computation

Capable of realizing circle patterns with obtuse overlap angles

Demonstrates improved computational performance

Abstract

This paper presents a new algorithm for generating planar circle patterns. The algorithm employs gradient descent and conjugate gradient method to compute circle radii and centers separately. Compared with existing algorithms, the proposed method is more efficient in computing centers of circles and is applicable for realizing circle patterns with possible obtuse overlap angles.