Advanced Course on FAIRSHAPE

The content covers various aspects of curve and surface fairing and shape preservation. It begins with experiences in curve fairing, discussing co-convexity preserving curve interpolation and shape-preserving interpolation for both planar and three-dimensional curves, including a comparative study of two methods in Tribon Initial Design. The next section focuses on fairing B-spline curves and surfaces, introducing declarative modeling as an additional approach for computations. Shape preservation is further explored with variable degree polynomial splines, emphasizing the importance of maintaining shape integrity. The fairing of surfaces is addressed through functional aspects of fairness, including surface design based on brightness intensity and an overview of industrial challenges in fair surface blending. The text also delves into parametrizing wing surfaces using partial differential equations and algorithms for convexity-preserving interpolation of scattered data. It discusses abstract schemes for functional shape-preserving interpolation and tensor product spline interpolation under piecewise bilinear bounds. Additionally, it covers the construction of surfaces through shape-preserving approximation of contour data, B-spline approximation with energy constraints, curvature approximation for surface modeling, and scattered data approximation with triangular B-splines. Finally, benchmarks in planar shape-preserving