Graphics Reference
In-Depth Information
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if (Din != Cin):
// Crossed the line
result.append(intersection(C, D, P, n))
if (Din): result.append(D)
return result
The algorithm produces some degenerate edges, which don't matter for poly-
gon rasterization but can cause problems when we apply the same ideas in other
contexts.
36.5.2.2 Near-Plane Clipping
The 2D Sutherland-Hodgman algorithm generalizes to higher dimensions. To clip
a polygon to a plane, we walk the edges finding intersections with the plane. We
can do this for the whole view frustum, processing one plane at a time. Consider
just the step of clipping to the near plane for now, however.
In camera space, the intersections between polygon edges and the near plane
are easy to find because the near plane has a simple equation:
z
=
n
. In fact,
this is exactly the same problem as clipping a polygon by a line, since we can
project the problem orthogonally into either the
xz
-or
yz
-plane. We interpolate
vertex attributes that vary linearly across the polygon linearly to the new vertices
introduced by clipping, as if they were additional spatial dimensions. Listing 36.4
gives the details in pseudocode for clipping a polygon specified by its vertex list
against the plane
z=zn
, where
zn<0
.
−
Listing 36.4: Clipping of the polygon represented by the
vertex
array
against the near plane
z=zn
.
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function clipPolygon(inVertices, zn):
outVertices = []
Let start = inputVertices.last();
for end in inputVertices:
if end.z <= zn:
if start.z > zn:
// We crossed into the frustum
outVertices.append( clipLine(start, end, zn) )
// the endpoint of this edge is in the frustum
outVertices.append( end )
elif start.z <= zn:
// We crossed out of the frustum
outVertices.append( clipLine(start, end, zn) )
start = end
return outVertices
function clipLine(start, end, zn):
a = (zn - start.z) / (end.z - start.z)
// This holds for any vertex properties that we
// wish to linearly interpolate, not just position
return start
*
a + end
*
(1-a)
