Geometric Construction of a Rational Quadratic Bezier Curve

This example demonstrates how to construct a rational quadratic Bezier curve from three control points and how introducing weights changes the curve shape (a “rational” pull compared to the non-rational quadratic Bezier). Key concepts include rational Bezier parameterization, quadratic interpolation, the role of weight parameters (w0, w1, w2), and representing the curve as a parametric Cartesian curve (CurveCartesian). In GeoGebra, construction is carried out using core commands such as Point and Segment to define control points and auxiliary elements (e.g., P_0, P_1, P_2 and intermediate points/segments), then computing parameter-dependent objects like P_t and weighted combinations (via intermediate variables such as h, a, and the weights w0,w1,w2) to generate the final curve object (e.g., q). It is well-suited for advanced high-school geometry, pre-university calculus/analytic geometry enrichment, and introductory computer graphics or geometric modeling lessons.