In all the following pictures, surfaces are displayed as meshes with hidden-line-removal turned off. The thick red curves are the intersection curves. Two views are shown for each case.
The following two pictures show the intersections between a surface and a set of parallel planes:
The following two pictures show surface-surface intersection that consists of a single curve:
The following two pictures show a surface-surface intersection that consists of serveral curves:
The following two pictures show a surface-surface intersection that contains one closed curve:
The following two pictures show a more general case: several curves and a closed curve. Note that the almost flat yellow surface is indeed a a Bezier surface of degree 10 x 10, with control points on a 2-dimensional parabolic surface.
The intersection curve may look dashed, because of the occlusion of the mesh. They are indeed very smooth curves. For example, the curve of the last case is shown as following:
Thank you very much.
Comments: yzhuang@cs.berkeley.edu