Take-Home Final Exam

Think of a interesting 3D surface patch (e.g. an S-shaped surface patch) Mathematically construct it as a composite 3D surface patch using Cubic Bezier Curves. A set of 4x4 control points should be employed for this purpose. Show all the steps of the construction in detail. Illustrate the construction on a milimetric grid, as a drawing (or set of drawings) with control points clearly marked. You can use orthogonal projections in illustrations. Analyse and illustrate the behaviour of the construction under modification of control points. Your paper should clearly show all the required calculations for the construction and modifications. Evaluate the method used in terms of its suitability for the construction and modifications and flexibility. Your paper should reflect a true engineering effort to construct something from scratch using pen paper and knowledge. You can not use any data from any external source. Construction must be original and truly your own.