Apparent contours in Minkowski 3-space and first order ordinary differential equations

Abstract

We consider projections of a smooth and regular surface M in the Minkowski 3-space along lightlike directions to a fixed transverse plane. The lightlike directions in can be parametrized by a circle on the lightcone and the resulting 1-parameter family of projections can be considered as viewing M along a special ‘camera motion’. The associated 1-parameter families of contour generators and apparent contours reveal some aspects of the extrinsic and intrinsic geometry of M. We characterize geometrically the generic -codimension ⩽1 singularities of a given projection and consider their bifurcations in the family of projections. We show that the families of contour generators and apparent contours are solutions of certain first order ordinary differential equations and obtain their generic local configurations.