A gradient descent algorithm for computing circle patterns

2025/12/11 by Te Ba, Ze Zhou, Ba, Te +1
Computer Science · Engineering · #52C26 #65D18 #68U05 #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Image and Object Detection Techniques #Medical Image Segmentation Techniques #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2512.10387

openalex publication_date 2025/12/11 · openalex created_date 2025/12/13 · openalex updated_date 2026/07/28

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.

Citations

• Generalizing Andreev's Theorem via circle patterns
• Producing circle patterns via configurations
• Combinatorics encoding geometry: the legacy of Bill Thurston in the story of one theorem
• Circle patterns on surfaces of finite topological type
• Circle patterns with obtuse exterior intersection angles
• Combinatorial Ricci Flows on Surfaces
• Random walks of circle packings

Related

• Producing circle patterns via configurations
• String Art: Circle Drawing Using Straight Lines
• Circle patterns with obtuse exterior intersection angles
• Algorithms for laying points optimally on a plane and a circle
• Tame the flexibility of circle patterns