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The Ambient Spaces of Computer Graphics and Geometric Modeling
March/April 2000 (vol. 20 no. 2)
pp. 76-84
Four types of ambient mathematical spaces underlie the algebra and geometry of computer graphics and geometric modeling: vector spaces, affine spaces, projective spaces, and Grassmann spaces. This article clarifies the relationships between these different ambient spaces and explains as well how they support the construction of the standard polynomial and rational freeform curves and surfaces of geometric design.

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Ron Goldman, "The Ambient Spaces of Computer Graphics and Geometric Modeling," IEEE Computer Graphics and Applications, vol. 20, no. 2, pp. 76-84, March-April 2000, doi:10.1109/38.824547
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