Rectangle Face

A rectangular face is an optimized face representation that is rectangular and lies parallel on a coordinate plane (either xy-, xz-, or yz-plane), and may have an affine matrix applied.

The face specifies its position by using a first corner point and a second corner point in local coordinates. Because the face must lie parallel to a coordinate plane, the corner points share a common coordinate value. For example, if the rectangular face lies on the xy-plane, the corner points share a common z-value. As well, the other two coordinates must both be either larger or smaller than the values of the other corner (that is, one must be a "min point' and the other a "max point").

The surface normal of this rectangular face depends on the numeric comparison of the corner points, as described in the following table.

Plane to Which Rectangle is Parallel	Comparison of (Coordinates of) the Corners	Direction of the Surface Normal
XY	first corner < second corner	Positive Z-axis
YZ	first corner < second corner	Positive X-axis
XZ	first corner < second corner	Positive Y-axis
XY	first corner > second corner	Negative Z-axis
YZ	first corner > second corner	Negative X-axis
XZ	first corner > second corner	Negative Y-axis

The surface normal determines the orientation of the rectangular face; that is, the direction in which the surface normal points indicates which side is the front.

Rectangle faces may also store and apply a 4 X 4 transformation matrix. In this way, a rectangle face can be used for a representation that is not parallel to the coordinate plane. This matrix can store affine transformations, which may also result in non-rectangular surfaces.

Rectangle faces do not have measures on their boundary.

Optionally, rectangle faces may possess front or back appearances, and may be single- or double-sided.