Curves and Surfaces in Computer Aided Geometric Design

CAD geometry is a branch of computer-aided design (CAD) that originally referred to software tools enabling a computer to replace the drawing board. Software generally incorporates business rules, effectively captures user intent and enables complex operations to be carried out. CAD software generally consists of a geometric modeler, a visualization tool and calculation tools. The vocabulary of the geometric modeler is that of geometry: points, lines, planes, Bézier curves, spline curves, Bézier surfaces, spline surfaces, NURBS surfaces... and also that of topology: vertices, edges, faces, interior/exterior, union, intersection... We are interested here in the modeling of complex 2D or 3D geometric shapes, which are used in a wide variety of fields: mechanical design, digital design, fashion design, animation and video games... The idea behind this modeling is the creation of mathematical tools motivated by the intuitive and easy use of these models by stylists, designers, graphic artists... Thus, 2D and 3D modeling involves a set of curves and surfaces to represent the boundaries of modeled objects. The representation model that naturally emerged was the polynomial model.