An error reduced and uniform parameter approximation in fitting of B-spline curves to data points

TL;DR

This paper introduces a method for fitting cubic B-spline curves to data points in higher-dimensional spaces, emphasizing error reduction and uniform parameterization for shape preservation and visual quality.

Contribution

It extends planar curve approximation techniques to higher dimensions and incorporates error minimization and tangent-based shape preservation.

Findings

Effective fitting of B-spline curves in multi-dimensional spaces.

Improved shape preservation through tangent constraints.

Error minimization using least squares with partial data points.

Abstract

Approximating data points in three or higher dimension space based on cubic B-spline curve is presented. Representations for planar curves, are merged and extended to the higher dimension. The curve is fitted to the order of data points, or uniform parameter values are assumed for the points. Tangents are assumed at the data points, corresponding to the property used in cardinal splines, for shape preserving and visually pleasing fit. Control points of piecewise continuous cubic bezier curves, meeting the boundary conditions of cardinal spline segments, are used for b-spline curve in corresponding coordinate planes. Approximation using error computed in the least square sense, based on a fraction of data points, is also presented.