Game Development Reference
In-Depth Information
// Calculate the clip-space corner point opposite the clipping plane
// using Equation (5.64) and transform it into camera space by
// multiplying it by the inverse of the projection matrix.
q.x = (sgn(clipPlane.x) + matrix[8]) / matrix[0];
q.y = (sgn(clipPlane.y) + matrix[9]) / matrix[5];
q.z = -1.0F;
q.w = (1.0F + matrix[10]) / matrix[14];
// Calculate the scaled plane vector using Equation (5.68)
// and replace the third row of the projection matrix.
Vector4D c = clipPlane * (2.0F / Dot(clipPlane, q));
matrix[2] = c.x;
matrix[6] = c.y;
matrix[10] = c.z + 1.0F;
matrix[14] = c.w;
// Load it back into OpenGL.
glMatrixMode(GL_PROJECTION);
glLoadMatrix(matrix);
}
Chapter 5 Summary
Lines
A line passing through the point P and running parallel to the direction V is ex-
pressed as
()
PP
t
=+
t
.
0
()
The distance from a point Q to the line
P
t
is given by
[
(
)
]
QP V
V −⋅
2
2
0
(
)
d
=
QP
.
0
2
Planes
A plane having normal direction N and containing the point P is expressed as
N P
⋅+ =
0
,
D
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