affine
basis (or frame), 9, 10, 19, 31, 34, 71, 239, 324, 326, 362, 580, 640
base point (origin), 9, 10, 19, 31, 34, 71, 239, 324, 326, 362, 580, 640
coordinate vector, 10, 34, 326, 640
orthonormal affine basis, 613, 625
natural affine basis for ? 2, 239
natural affine basis for ? 3, 581
coordinate system, 19, 34, 38, 324, 326, 328, 362, 640
affine coordinate, 19, 72, 239, 363, 641
barycentric coordinate, 19, 72, 363, 642
barycenter, 19, 72, 363
dependence of points, 32, 71, 239, 325, 362, 580, 640
geometry, 292, 640
invariant, 19, 90, 286, 374, 636, 638, 679
group, 238, 240, 580, 581, 656
independence of points, 33, 71, 239, 325, 362, 580, 640
invariant, 19, 90, 286, 310, 374, 636
space, 9, 12, 31, 34, 235, 324, 326, 640
one-dimensional, 8, 12
two-dimensional, 31, 36
three-dimensional, 324, 326
n-dimensional, 235
difference space, 235
zero vector, 235, 236
base point, 235
position vector (with initial point and terminal point), 235
free vector, 235
difference vector, 236
affine subspace, 236
affine transformation or mapping, 237
affine motion, 237, 240
subspace, 67, 236, 359, 425, 640, 724
dimension, 235
k-dimensional plane, 640
hyperplane, 641
dimension (or intersection) theorem, 644
operation of affine subspaces, 643
intersection, 644
sum, 644
relative positions of affine subspaces, 645
coincident, 645
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