Back-face Culling
[Hill: 406.407. Foley & van Dam: p. 663-664]
Back-face culling directly eliminates polygons not facing the viewer.
Back-Face Culling in VCS
Back-face culling can be performed in either
VCS or NDCS. We'll first discuss face-culling in VCS.
A first attempt at performing back-face culling might directly use the
z-component of the surface normal, as expressed in VCS. This does not always
work, however.
A better strategy is to construct the plane equation for the polygon and to
test whether the eye-point falls above or below this
plane.
Plane(Peye)<0 implies the eyepoint is below the plane
containing the polygon and that the polygon should thus be culled.
Summary for VCS culling
- Calculate a surface normal, N = (A,B,C).
This need not be normalized.
- Compute D in plane equation by substituting any polygon vertex into the
plane equation.
Plane(P) = Ax + By + Cz + D = 0
- Calculate Plane(eyept) to determine if eye is above or
below.
This corresponds to checking the sign of D.
Face Culling in NDCS
In NDCS, the z-component of the surface normal does
reflect the true visibility, as desired. If the z-component is positive, the
normal points away from the eye and the polygon should thus be culled.
Computing Surface Normals
[Hill: 347-350]
In order to do the
face culling, we need a surface normal.
Method 1
Use the cross-product of two polygon edges. The order in which
vertices are stored should be consistent. For example, if polygon vertices are
stored in CCW order when viewed from above the `front face', then we could use
N = ( P2 - P1 ) x ( P3 - P2 )
Method 2
A more robust method is to use the projected area onto the yz,
xz, and yz planes. To see that areas can be used to calculate a normal, first
consider the 2D case.
The areas for the required 3D projections (and thus the components of the
normal) can be calculated as follows:
