Elucidation of Fundamental Properties and Evaluation of Aesthetic Aspects for Free-form Surfaces

Surface Analysis by Equi-principal-curvature Curves and Extremum Curvature Curves

Abstract

To elucidate inherent properties of free-form surfaces independent from the viewing conditions and to apply them to styling design, equi-principal-curvature curves and extremum curvature curves are introduced. These curves visualize surface characteristics as a contour map of curvature values which conventional lines of curvature cannot display, and represent the third degree differentials of the surfaces. Furthermore, characteristic curves on sketches or renderings such as equi-highlight curves, a shilhouette pattern and a grid reflection pattern are analyzed by relating them with the fundamental properties of the surfaces. Examples of the curves are shown and analyzed along with equations of the third degree approximation of the surfaces.