CHAPTER 9
834
Multimedia Features
work. The relationship between camera and artwork can be thought of in two
ways:
•
The 3D artwork is in a fixed position and orientation, and the camera moves to
different positions and orientations.
•
The camera is in a fixed location, and the 3D artwork is translated and rotated.
Both approaches can achieve the same visual effects; in practice, 3D systems typi-
cally use a combination of both. Conceptually, there are three distinct coordinate
systems:
•
The
artwork coordinate system.
•
The
camera coordinate system,
in which the camera is positioned at (0, 0, 0) fac-
ing out along the positive
z
axis, with the positive
x
axis to the right and the
positive
y
axis going straight up.
•
An intermediate system called the
world coordinate system.
Two 3D transformation matrices are used in coordinate conversions:
•
The
artwork-to-world matrix
specifies the position and orientation of the art-
work in the world coordinate system. This matrix is contained in the 3D
stream.
•
The
camera-to-world matrix
specifies the position and orientation of the cam-
era in the world coordinate system. This matrix is specified by either the
C2W
or
U3DPath
entries of the 3D view dictionary.
When drawing 3D artwork in a 3D annotation’s target coordinate system, the fol-
lowing transformations take place:
1. Artwork coordinates are transformed to world coordinates:
x
w
y
w
z
w
1
=
x
a
y
a
z
a
1
×
aw
2. World coordinates are transformed to camera coordinates:
x
c
y
c
z
c
1
=
x
w
y
w
z
w
1
× (
cw
)
–
1