This work shows how differential geometry, with relaxed mathematical rigour, can be used to design curves and surfaces, and how it can be made more accessible, more appealing, and more understandable to engineers. It presents a unified approach to the synthesis of curves and surfaces using simple mathematics, restricted to vector and matrix algebra, familiar to all engineers. The authors introduce the cyclidal patch as a new element for surface synthesis. There is a substantial amount of new material hitherto unpublished, or found only in research papers.
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