Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Visualizing n-dimensional virtual worlds with n-vision
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions
Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions
Robot Vision
Visualizing the fourth dimension using geometry and light
VIS '91 Proceedings of the 2nd conference on Visualization '91
Hypervolume visualization: a challenge in simplicity
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Space-time points: 4d splatting on efficient grids
VVS '02 Proceedings of the 2002 IEEE symposium on Volume visualization and graphics
Quaternion Frame Approach to Streamline Visualization
IEEE Transactions on Visualization and Computer Graphics
Chronovolumes: a direct rendering technique for visualizing time-varying data
VG '03 Proceedings of the 2003 Eurographics/IEEE TVCG Workshop on Volume graphics
VIS '95 Proceedings of the 6th conference on Visualization '95
Four-dimensional views of 3D scalar fields
VIS '92 Proceedings of the 3rd conference on Visualization '92
Interactive visualization methods for four dimensions
VIS '93 Proceedings of the 4th conference on Visualization '93
The Quantum Coulomb Three-Body Problem: visualization of simulation results and numerical methods
VIS '93 Proceedings of the 4th conference on Visualization '93
Visualizing flow with quaternion frames
VIS '94 Proceedings of the conference on Visualization '94
Virtual reality performance for virtual geometry
VIS '94 Proceedings of the conference on Visualization '94
High Dimensional Direct Rendering of Time-Varying Volumetric Data
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Virtual Environments with Four or More Spatial Dimensions
Presence: Teleoperators and Virtual Environments
Visualizing quaternions: course notes for Siggraph 2007
ACM SIGGRAPH 2007 courses
Shadow-Driven 4D Haptic Visualization
IEEE Transactions on Visualization and Computer Graphics
Physically interacting with four dimensions
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part I
VG'05 Proceedings of the Fourth Eurographics / IEEE VGTC conference on Volume Graphics
Visualization of data on unfolded hypercubes
Journal of Visualization
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A family of techniques for creating intuitively informative shaded images of 4-D mathematical objects is proposed. The rendering of an object in a 4-D world is described by considering step-by-step how objects might be rendered into images in simpler worlds. The mathematical principles needed to compute projected images of objects and their shadows in D dimensions are outlined. The issues involved in producing shaded images of objects in four dimensions, including extending rendering from 3-D to 4-D, smooth shading, and specularity, are discussed. Results of rendering a Steiner surface, torus, and knotted sphere in four dimensions are presented.