Education-Driven Research in CAD
We argue for a new research category, which we call Education-Driven Research (abbreviated EDR), which fills the gap between traditional Research in any specific field (such as CAD), which is concerned with educational objectives, and research in Education, which is focus on fundamental teaching and learning principles and possibly their customization to broad areas, such as mathematics or physics. The objective of EDR is to simplify the formulation of the underlying theoretical foundations and of specific tools and solutions, so as to make them easy to understand and internalize. As such, EDR is a difficult and genuine research activity, which requires a deep understanding of the specific field and usually cannot be carried out by generalists with primary expertise in broad education principles. We illustrate the value of EDR with three examples in CAD: (1) the Split&Tweak subdivisions of a polygon and its use for generating curves, surfaces, and animations; (2) the construction of a topological partition of a plane induced by an arbitrary arrangement of edges; and (3) a romantic definition of the minimal and Hausdorff distances. These examples demonstrate the value of using analogies, of introducing evocative terminology, and of synthesizing the simplest fundamental building blocks. The intuitive understanding provided by EDR enables the students (and even the instructor) to better appreciate the limitations of a particular solution and to explore alternatives. In particular, un these examples, EDR has allowed the author to: (1) reduce the cost of evaluating a cubic B-spline curve; (2) develop a new curve that approximates a control polygon better than either a cubic B-spline or an interpolating 4-point subdivision curve; (3) discover how a circuit inclusion tree may be used for identifying the faces in an arrangement; and (4) rectify a common misconception about the computation of the Hausdorff error between triangle meshes. We invite the scientific community to encourage the development of EDR by publishing its results as genuine Research contributions in peer-reviewed professional journals.