Game Development Reference

In-Depth Information

These vertices are arranged in a counterclockwise winding order so that the front

of the quad faces the camera. The corresponding two-dimensional texture map-

ping coordinates are given by

s

,

t

=

1,1

s

,

t

=

0,1

11

2 2

st

,

=

0, 0

st

,

=

1, 0

.

(9.21)

33

44

Billboarded quads whose vertices derive from the vectors
X
and
Y
given by

Equation (9.18) are always aligned to the plane of the camera. As Figure 9.5

demonstrates, this alignment can differ significantly from the plane perpendicular

to the true direction from the quad's center to the camera position. When hun-

dreds or thousands of small particles are being rendered, one may wish to use

Equation (9.18) for efficiency, but large quads may look better if oriented to face

the actual camera position instead of the plane of the camera.

We align a quad so that it faces the camera position by presenting a more

computationally expensive formulation of the vectors
X
and
Y
. Let the vector
C

denote the world space camera position. Assuming that the center
P
of the quad

does not lie on the line containing
C
and running in the direction
U
, we can

calculate

CP

Z
CP

UZ

A
UZ

BZA

=
−

=
×

=×

.

(9.22)

Figure 9.5.
A billboarded quad that is aligned to the plane of the camera may differ sig-

nificantly from a quad that directly faces the camera position.

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