Quasi-Bézier Curves with Shape Parameters

Table 1

Properties of the basis functions and the curves with shape parameters.

Property	[7]	[8]	[9]	[10]	[11]	[12]	This paper
Basis functions with multiple shape parameters
Nonnegativity	✓	✓	✓	✓	✓	✓	✓
Partition of unity	✓	✓	✓	✓	✓	✓	✓
Symmetry	✓	*	*	*	×	✓	✓
Multiple shape parameters	×	✓	✓	✓	✓	×	✓
Linear independence	✓	×	×	✓	✓	✓	✓
Degeneracy	✓	✓	✓	×	×	✓	✓
Curve with multiple shape parameters
Geometric and affine invariability	✓	✓	✓	✓	✓	✓	✓
Convex hull property	✓	✓	✓	✓	✓	✓	✓
Symmetry	✓	*	*	*	×	✓	✓
Interpolation at the endpoints	✓	✓	✓	✓	✓	✓	✓
Tangent at the end edge	✓	✓	✓	✓	×	✓	✓

*The property of symmetry in [8–10] is based on the shape parameters.