On the Q-Bernstein Bézier curves

This survey focus on Bernstein polynomials, q-Bernstein polynomials from the geometric point of view and Bézier curves tecniques. First we give the approximation properties of Bernstein polynomials as well as generalized Bernstein polynomials and then show that these operators are shape-preserving operators. This lead us to the Bézier curves representations. The tecniques such as subdivision and degree elevation are demonstrated. Keywords: Bernstein polynomial approximation, q-Bernstein polynomial, Bézier curve, q-Bernstein Bézier curve