December 2013
Intermediate to advanced
508 pages
16h 50m
English
Content preview from Practical Algorithms for 3D Computer Graphics, 2nd Edition
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2.13. Parametric curves 41
Curve suitable for specification
in the form: y = f(x) form
A curve better suited to
specification in parametric form
x x
y
y
x = f(t)
y = g(t)
Figure 2.19: Two-dimensio n a l curves.
the clipping plane. For examp le, the pr ojection matrix for a xz clipping plane
located at y = d would be:
1 0 0 0
0 1 0 0
0 0 1 0
0
1
d
0 0
(2.19)
This tran s for mation sends a homogeneous point (x, y, z, 1) to the homogeneous
point (x, y, z,
y
d
), which after projective division becomes (d
x
y
, d, d
z
y
, 1), equ iva-
lent to the 2D coordinate (d
x
y
, d
z
y
) on the viewing plane (located at y = d).
2.13 Parametric curves
In two dimensions a curve is generally ...
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