Spline Library 2.3 Release

Written for SplineLibrary by Lakshmi Krishnamurthy on 2014-01-23

SplineLibrary provides the functionality for building, calibrating, and evaluating different kinds of splines.

SplineLibrary implements the functionality behind spline design, spline constructions, customization, calibration, and evaluation of a wide variety of spline types and basis functions.

SplineLibrary achieves its design goal by implementing its functionality over several packages the perform the following:

Spline Calibration Framework: Schematic spline segment/span partitioning, elastic/inelastic entity-variate separation, mathematical calibration formulation framework with constraints/boundary incorporation, sensitivity Jacobian estimator setup, Hard/Soft (Truthness/Smoothness) partitioning.
Shape Preserving Spline Suite: B-splines, Polynomial Splines and Variants (Bernstein, Kaklis-Pandelis, Manni), Integrated Tension Splines (exponential/hyperbolic), partitioned tension splines (explicit shape control using rational splines).
Space Spline Curves: Hermitian, Catmull-Rom, Cardinal Cubic, Space Loops.
B Splines: Polynomial Koch/Loche/Kvasov Tension B Splines Monic/Multic Sequence Generation and Setup.
Spline Calibration: Explicit segment formulation frame work, Optimizing shape preserving splines, curvature/segment-length (or criterion-defined) penalty minimizing mu-splines, segment/span self-Jacobian, quote-Jacobian, and micro-Jacobian.
Spline Smoothing Schemes: Akima, Bessel, Harmonic, Hyman83, Hyman89, Kruger, Preuss, Hagan-West, and Preuss schemes.
Regression Splines: Curveture/Length Penalizing and Best-Fit Splines.
Spline Evaluation: Metric'ed evaluation of monotonicity, convexity, smoothness, locality, and approximation order.
Spline Extensions: Variational Smoothing, density smoothing technique, alternate smoothener customization extension, multi-dimensional (including thin plate) splines.
Documentation: Literature review, framework description, mathematical and formulation details of the different components, spline library synthetic knowledge unit (SKU) composition, and module and API usage guide.
Regression Tests: Statistical regression analysis and dispersion metric evaluation for the initialization and the iteration components of the different basis spline construction, usage, and span interpolation methodologies.