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- W1428878580 abstract "This chapter describes the fundamental geometric setting for 3D modeling and addresses Euclidean, affine, and projective geometry. It defines conic sections and quadrics as the simplest figures in affine space besides lines and planes. The chapter introduces Pascal's and Brianchon's theorems. Pascal's theorem states that the three pairs of opposite sides of a hexagon inscribed in a conic section meet in three points of a line, whereas Brianchon's theorem states that the three connections of opposite points of a hexilateral circumscribed to a conic section intersects in one point. The chapter further deals with differential fundamentals. Arc length, curvature, and torsion describe the local properties of a curve, the curvature of principal normal sections describe the local properties of surfaces. The main tool for such investigations is a local frame." @default.
- W1428878580 created "2016-06-24" @default.
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- W1428878580 date "2002-01-01" @default.
- W1428878580 modified "2023-09-27" @default.
- W1428878580 title "Geometric Fundamentals" @default.
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- W1428878580 doi "https://doi.org/10.1016/b978-044451104-1/50003-4" @default.
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