Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm
SIAM Journal on Computing
Computational geometry: an introduction
Computational geometry: an introduction
Topology and mechanics with computer graphics
Advances in Applied Mathematics
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Finite element mesh generation methods: a review and classification
Computer-Aided Design
Display of Surfaces from Volume Data
IEEE Computer Graphics and Applications
Representing geometric structures in d dimensions: topology and order
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
An efficient 3-D visualization technique for finite element models and other coarse volumes
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
A computer generated census of cusped hyperbolic 3-manifolds
Proceedings of the third conference on Computers and mathematics
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
A rendering algorithm for visualizing 3D scalar fields
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Fast Triangulation of Simple Polygons
Proceedings of the 1983 International FCT-Conference on Fundamentals of Computation Theory
Visibility-ordering meshed polyhedra
ACM Transactions on Graphics (TOG)
Visualizing and Modeling Scattered Multivariate Data
IEEE Computer Graphics and Applications
On the intersection curve of three parametric hypersurfaces
Computer Aided Geometric Design
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Computer graphics has long been concerned with representing and displaying surfaces in 3-dimensional space R3. We address the questions of representation and display in a higher dimensional setting, specifically, that of 3-manifolds immersed in R4. We describe 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 may be computed on a per tetrahedron basis. The triangulated manifold is stored in a data structure which efficiently supports calculation of curvature. We expect the techniques, which we have implemented on the Personal IRIS, will support a highly-interactive system when implemented on a fine-grain parallel computer such as the Connection Machine.