Graphics Reference
In-Depth Information
Chapter 13
and Transformations
In this chapter, we briefly discuss camera specifications, which you already
encountered in Chapter 6. Recall that we specified a camera in WPF in code like
that shown below:
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<PerspectiveCamera
Position=
"57, 247, 41"
LookDirection=
"-0.2, 0, -0.9"
UpDirection=
"0, 1, 0"
NearPlaneDistance=
"0.02"
FarPlaneDistance=
"1000"
FieldOfView=
"45"
/>
From such a specification, we will create a sequence of transformations that
will transform the world coordinates of a point on some model to so-called “cam-
era coordinates,” and from there to image coordinates. We'll do so by repeatedly
using the Transformation Uniqueness principle.
Since an affine coordinate frame in three dimensions consists of four
noncoplanar points, this says that if we know where we want to send each of
four noncoplanar points, we know that there's exactly one affine transformation
that will do it for us. The corresponding theorem for the plane says that if we know
where we want to send some
three
noncollinear points, then there's a unique affine
transformation that will do it.
We start with an example of this kind of transformation in the plane. Next
we discuss basic perspective camera specifications and how we can convert such
specifications to a set of affine transformations, plus one projective transformation.
We briefly treat the case of “parallel” cameras, and discuss the details of that case
and of skewed projections, in this chapter's web materials.
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