Analysis of Elliptical Tubes Under the Relative Curvature Condition
Check the Legality of an Elliptical Tube (ETRep)
Create a Discrete Elliptical Tube (ETRep)
Convert an ETRep to a Matrix in the Convex Transformed Space.
Calculating the intrinsic distance between two ETReps
Calculate Intrinsic Mean of ETReps
Intrinsic Transformation Between Two ETReps
Calculating the non-intrinsic distance between two ETReps
Compute Non-Intrinsic Mean of ETReps
Non-Intrinsic Transformation Between Two ETReps
Plot an Elliptical Tube (ETRep)
Simulate Random Elliptical Tubes (ETReps)
Analysis of elliptical tubes with applications in biological modeling. The package is based on the references: Taheri, M., Pizer, S. M., & Schulz, J. (2024) "The Mean Shape under the Relative Curvature Condition." arXiv <doi:10.48550/arXiv.2404.01043>. Mohsen Taheri Shalmani (2024) "Shape Statistics via Skeletal Structures", PhD Thesis, University of Stavanger, Norway <doi:10.13140/RG.2.2.34500.23685>. Key features include constructing discrete elliptical tubes, calculating transformations, validating structures under the Relative Curvature Condition (RCC), computing means, and generating simulations. Supports intrinsic and non-intrinsic mean calculations and transformations, size estimation, plotting, and random sample generation based on a reference tube. The intrinsic approach relies on the interior path of the original non-convex space, incorporating the RCC, while the non-intrinsic approach uses a basic robotic arm transformation that disregards the RCC.