Techniques for visualizing 3-dimensional manifolds

Computer graphics has long been concerned with representing and displaying surfaces in three-dimensional space. The author addresses the questions of representation and display in a higher dimensional setting, specifically, that of 3-manifolds immersed in four-dimensional space. The author describes techniques for visualizing the cross-section surfaces of a 3-manifold formed by a cutting hyperplane. The manifold is first triangulated, so that the cross-section many be computed on a per tetrahedron basis. The triangulated manifold is stored in a data structure which efficiently supports calculation of curvature. These techniques have been implemented on a Silicon Graphics Personal IRIS. These techniques readily parallelize.