In 1971 due to industry contacts, Wolfgang Boehm became interested in what had then been called Geometrische Datenverarbeitung (Geometric Data Processing), a field he had been well prepared for by his study of mathematics in Berlin where he specialized in constructive synthetic geometry and numerical analysis.
Wolfgang Boehm pioneered the field in several ways: In 1975 he discovered de Casteljau`s algorithm which had been kept secret by Citroen. Together with Bob Barnhill, he founded the journal Computer Aided Geometric Design (CAGD) launching with his widely cited survey on CAGD in its first issue in 1984. This survey was the first comprehensive text on CAGD and remains to be valuable even until today. Wolfgang Boehm started and co-organized the series of international CAGD conferences in Oberwolfach as well as further workshops in Israel, Italy and Germany.
Boehm’s knot insertion algorithm is one of the most popular spline algorithms used in practice. Besides inserting knots, this simple algorithm made obsolete and greatly simplified earlier constructions by him and others to generate a spline’s Bézier points. He found a recursion for box splines analogous to the recursion by Mansfield and de Boor for univariate B-splines and used it to develop a de Boor-like algorithm for box spline surfaces. He was the first to describe triangular and quadrilateral patches on quadrics and published several techniques, conditions, surfaces and constructions, in geometric terms amenable for simple direct constructions, e. g., gamma splines, G3 contact, cyclides, and knot insertion for rational splines.
He contributed two chapters to Farin’s renowned book on curves and surfaces. Furthermore, he gave Eurographics and SIGGRAPH tutorials and wrote books on numerical methods, geometric concepts and CAGD techniques, which have been translated into Chinese, Spanish and German. He supervised nearly 70 diploma theses and 15 PhD students – among them Gerald Farin, Bernd Fröhlich, and Hartmut Prautzsch – with whom he established the “Braunschweig School” of succinct geometric reasoning and aesthetics.