Casteljaufolyamatban

The Casteljau algorithm is a computationally efficient method for evaluating a polynomial curve, particularly Bezier curves. Invented by Paul de Casteljau in 1959, it offers a stable and numerically robust approach compared to direct evaluation using the Bernstein polynomial form. The algorithm works by iteratively applying a linear interpolation process. Given a set of control points and a parameter t, typically between 0 and 1, the algorithm constructs a sequence of new sets of points. Each subsequent set is derived from the previous one by linearly interpolating between adjacent points. This process is repeated until a single point is obtained, which represents the point on the curve corresponding to the parameter t. The geometric interpretation of the Casteljau algorithm is that it traces out a smaller and smaller simplex within the original control polygon. This iterative subdivision is the core of its computational power and stability. It is widely used in computer graphics, computer-aided design, and font rendering due to its efficiency and reliability.