Metric-Induced Rotations with Gielis-Based Geometry
Mathematics, cilt.14, sa.15, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 14 Sayı: 15
- Basım Tarihi: 2026
- Doi Numarası: 10.3390/math14152828
- Dergi Adı: Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: kinematics of a rigid body, quaternion algebra, rotation matrix, screw motion
- Ankara Üniversitesi Adresli: Evet
Özet
In this work, we present a generalized geometric framework that extends quaternion-based rotation and translation operators within a generalized inner product and vector product setting defined on Gielis-type superquadrics. By incorporating the multiplicative shape factor (Formula presented.), we formulate rotation matrices and quaternion mappings adapted to the elastic and non-Euclidean behavior of biological growth surfaces. The proposed framework extends classical Euclidean constructions to the generalized metric setting, enabling smooth, direction-dependent deformations and providing a unified description of curvature-induced growth, differential thickening, and torsional motions observed in plants. The resulting formulation offers a mathematically consistent and biologically interpretable tool with potential applications in computational botany, growth-based animation, and the design of biologically inspired structures.