Graphics Reference
In-Depth Information
Figure 4.2.
A shape coordinate system.
x 2 2
49 1
+=.
The equation of that ellipse with respect to the standard world coordinate system
would be much more complicated.
The Camera Coordinate System. A view of the world obtained from a central pro-
jection onto a plane is called a perspective view . To specify such view we shall borrow
some ideas from the usual concept of a camera (more precisely, a pinhole camera
where the lens is just a point). When taking a picture, a camera is at a particular posi-
tion and pointing in some direction. Being a physical object with positive height and
width, one can also rotate the camera, or what we shall consider as its “up” direction,
to the right or left. This determines whether or not the picture will be “right-side up”
or “upside down.” Another aspect of a camera is the film where the image is projected.
We associate the plane of this film with the view plane. (In a real camera the film is
behind the lens, whose position we are treating as the location of the camera, so that
an inverted picture is cast onto it. We differ from a real camera here in that for us
the film will be in front of the lens.) Therefore, in analogy with such a “real” camera,
let us define a camera (often referred to as a synthetic camera ) as something specified
by the following data:
a location p
a “ view direction v (the direction in which the camera is looking)
an “ up direction w (specifies the two-dimensional orientation for the camera)
a real number d (the distance that the view plane is in front of the camera)
Clearly, perspective views are defined by such camera data and are easily manipulated
by means of it. We can view the world from any point p , look in any direction v , and
specify what should be the top of the picture. We shall see later that the parameter d,
in addition to specifying the view plane, will also allow us to zoom in or out of views
easily.
A camera and its data define a camera coordinate system specifed by a camera
frame ( u 1 , u 2 , u 3 , p ). See Figure 4.3(a). This is a coordinate system where the camera
sits at the origin looking along the positive z-axis and the view plane is a plane
parallel to the x-y plane a distance d above it. See Figure 4.3(b). We define this
coordinate system from the camera data as follows:
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