  This study aims on proposing a new structure for constructing Bernstein-like
bases. The structure uses an auxiliary function and a shape parameter to
construct a new family of bases from any family of blending functions. The new
family of bases inherit almost all algebraic and geometric properties of the
initial blending functions. The corresponding curves have the freedom to travel
from the curve constructed from the initial blending functions to the line
segment joining the first and last control points. The new bases have the
monotonicity preservation property and the shape of the curve could be adjusted
by changing the parameter.
