Geometric Tools for Computer Graphics

P

parabolas

curve of intersection as, 378

defining, 573

equation, 255

focus, 574

geometric definitions, 570

intersection with ellipse, 256

plane/cone intersection, 565, 572–575

vertex, 574

parabolic cylinder

defined, 353

illustrated, 355

See also cylinders

paraboloids

elliptic, 352, 354

hyperbolic, 352, 354

parallel projection, 159

parallel segments distance (3D), 429

defined, 429

implementation, 432–433

See also segment to segment distance (3D)

parallel vectors, 15

parallelism

affine map preservation of, 100

vector product, 93–94

parallelograms

area, 154

formula, 954

parameter plane

defined, 98

partitioning, 199

See also interior-to-edge search

parameterization surface, 597

parameterized standard cylinder ...