Lupa ş q-Bernstein operator is the first proposed qinteger based qanalogue Bernstein operator in rational form. By using the
recurrence formulas in reverse as a pyramid algorithm, the nth degree Lupaş q-Bernstein basis function sequence is generated via discrete convolution.
Owing to the commutativity of discrete convolution, for each Lupaş q-Bézier curve of degree n, the hodograph and the collection of n!
recursive evaluation algorithms are derived. Unlike the tangent point obtained
by de Casteljau algorithm of Bézier curve, de Casteljau
algorithm of Lupa ş q-Bézier curve obtains a point on the curve being one of the two cut
points where the line intersects the curve. For quadratic Lupa ş q-Bézier curve,
sufficient and necessary conditions for computing left and right cut points are
obtained. In addition, the left and right cut points can be computed
simultaneously by proposing a dual cut point algorithm.