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Illuminating the Fourth Dimension
July/August 1992 (vol. 12 no. 4)
pp. 54, 58, 61-62

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.

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Andrew J. Hanson, Pheng A. Heng, "Illuminating the Fourth Dimension," IEEE Computer Graphics and Applications, vol. 12, no. 4, pp. 54, 58, 61-62, July-Aug. 1992, doi:10.1109/38.144827
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