Shape Modification for -Bézier Curves Based on Constrained Optimization of Position and Tangent Vector

Table 1

Performance comparisons of -Bézier curves, Bézier curves, and NURBS.

Property	λ-Bézier curves	Bézier curves	NURBS curves
Property of basis functions
Nonnegativity	✓	✓	✓
Partition of unity	✓	✓	✓
Symmetry	✓	✓	✓
Shape parameters	✓	✗
Linear independence	✓	✓	✓
Degeneracy	✓	✗	✓
Property of the Curves
Variation diminishing property	✓	✓	✓
Affine invariability	✓	✓	✓
Convex hull property		✓	✓
Symmetry	✓	✓	✓
End-point properties	✓	✓	✓
Extra degree of freedom	✓	✗	✓
Computational complexity	Low	Low	High

The weights in NURBS methods possess an effect for adjusting the shape of the curves.