Abstract
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 (H.G. Grassmann, 1894-1911). The author considers at length the theoretical advantages of the coordinate-free approach to understanding geometry. He focuses attention on the operations of addition, subtraction, and scalar multiplication because these are the operations best suited for the construction of freeform curves and surfaces. But there are also spaces with multiplicative structures: structures already coming into vogue in physics (D. Hestenes, 1992) and perhaps of use as well in the fields of computer graphics and computer aided design.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
