This course covers some of the mathematical methods for describing physical or virtual objects needed in computer aided geometric design (CAGD) and computer graphics. We will emphaize methods for curve and surface modelling. We will discuss both the underlying geometric ideas and concepts, and the practical aspects of constructing geometric models of objects. Topics covered will include Bezier curves, Hermite curves, B-splines, Bezier patches, subdivision surfaces. In discussing these methods for creating curves and surfaces, we will need to use some basic analytic geometry, differential geometry, and introduce some affine geometry, combinatorial geometry, and projective geometry.