Math4StainedGlass

Math4StainedGlass Dr. Marco Reidelbach 15.10.2025 Stained Glass in Literature (I) - Arts and Humanities (42.9%) - Social Sciences (36.2%) - Engineering (8.5%) - historical and geographical dimensions - technical and compositional aspects 1 1 2 Stained Glass in Literature (II) - growing interest in physical / technical aspects - digital technologies in analysis, visualization and restoration - highly interdisciplinary - expansion of the field in terms of methodologies and thematic focus 1 1 3 Making Art with Mathematics Non-photorealistic Rendering of Images K23 - A007678 23 MathAlgoDB Databases 4 Mathematical Databases zbMath Open – mathematical publications swMath – mathematical software DLMF – mathematical functions OEIS – integer sequences LMFDB – L-functions and modular forms ATLAS of Finite Groups GAP Small Groups Library … 5 San Vitale Challenge “Find the best algorithm able to automatically detect connections between the glass fragments, which originally formed circular colored glass windows of various diameters” 4 4 MathAlgoDB MathExDB 6 ●Measurement & Modeling ●Analysis of... –Individual Window –Window Corpora ●Contextual Analysis Mathematical Perspectives 7 Measurement & Modeling Hyperspectral Imaging5 to identify hidden details, study pigments and materials, detect damages/degradation, and guide appropriate conservation measures. time-consuming acquisition process temporal illumination variations spectral vector reflectance (or transmittance) illumination spectrum observation matrix coefficient matrix weight matrix basis vector matrix Task: Determine Weight Matrix Algorithmic Task: Factorize c SVD algorithms Algorithmic-Task: Linear Regression (Y = AW) Least Square algorithms MathModDB MathAlgoDB 8 Analysis: Individual Window Symmetry: “...the French Cistercians used four of the seven recognized one-dimensional symmetries, and seven of the seventeen known two-dimensional types. Window designs of the latter type included rotation, translation, reflection, and glide symmetries.”6 “...Münder und die Korkenzieherlöckchen zu beiden Seiten der Gesichter, die sich in den Bartpartien in zwei spiegelsymmetrische Wellen teilen.”7 Analyze Symmetries and Annotate Stained Glass Windows? Data with mix of ideal symmetry and real-world imperfection to study algorithms. 9