Faculty of Science

Objectives

To introduce the differential geometry of curves and surfaces which precede the presentation of two widely used techniques for surface description.

Contents

Review of Differential Geometry: Tangent to a curve and tangent line; Normal and binormal; Torsion and French-serret Formulae; Metrical properties of surfaces; curvature of a surface; Interpolation: use of vector-valued parametric cubes; coons and Tensor product patches; correcting incompatibilities of twist vectors. Approximation: Bézier and B-spline curves and patches; Equivalence between Bézier and tensor product patches; continuity between adjacent curve segments and patches; Bézier-type curves; Applications: Ruled patches; ducts; patterns for prismatic dusts; curve fitting of profiles; Computer graphics.