[Cyan]<CedarChest6.1>Geometry3d>Geometry3dDoc.Tioga!1

Geometry3dDoc.tioga

Bloomenthal, December 23, 1986 1:17:23 pm PST

CEDAR 6.1 — FOR INTERNAL XEROX USE ONLY

Geometry3d

Jules Bloomenthal

Abstract: This package comprises several interfaces of geometric functions: vector arithmetic for operating on vectors and points, planar arithmetic for operating on planes, matrix arithmetic for representing simple geometric transformations, and an interface for three dimensional splines. The interfaces are exported by Geometry3dPackage.bcd.

Created by: Jules Bloomenthal

Maintained by: Jules Bloomenthal <Bloomenthal.pa>

Keywords: geometry, three-dimensional, 3d, vectors, points, planes, lines, matrices, clipping, curves, splines

DF File: [Cedar]<CedarChest6.0>Top>Geometry3d.df

XEROX Xerox Corporation
Palo Alto Research Center
3333 Coyote Hill Road
Palo Alto, California 94304

For Internal Xerox Use Only

Basic Notes

In ThreeDWorld, polygons are rendered according to the normal of the polygon or its constituent vertices. In general, the normal should face towards the outside of a surface; for a convex solid, for example, all visible polygons will have normals which face towards the viewer.

The proper order of vertices such that the normal will face the viewer is clockwise.

Interfaces

Vector3d

Operations on three-dimensional points and vectors. This collection of procedures allows fundamental vector arithmetic to be performed on simple geometric primitives such as vectors and points.

Plane3d

Operations on three-dimensional planes. This collection of procedures allows fundamental planar arithmetic to be performed on simple geometric primitives such as lines and points.

Matrix3d

Operations on four by four matrices, useful for homogeneous transformations. This collection of procedures allows the creation and concatenation of transformation matrices which represent fundamental three-dimensional geometric transformations such as scale, translation, rotation, and perspective.

Spline3d

Interpolation, conversion, evaluation, size, search, subdivision, and miscellaneous functions of three-dimensional curves.

Clip3d

Three dimensional clipping functions when displaying via a perspective transformation.