Graphics Reference
In-Depth Information
θ
r
θ
r
θ
i
θ
r
θ
i
θ
i
(c)
Figure 8.32
A simple deformation changes only the orientation of the surface normal (top parts). This
amounts to a simple rotation of the reflectance function (bottom parts). The gray square
shows the part of the reflectance function to which the deformed surface corresponds.
(a) The original surface is oriented toward a specular highlight. (b) Rotating the surface
moves away from the highlight. (c) In the coordinate system of the surface normal, the
light and camera directions are what change in a deformation. (After [Hawkins et al. 04].)
(a)
(b)
geometric model is needed to approximate the surface of the face only to the
precision needed for the reflectance field, and to represent arbitrary synthesized
facial expressions. (A conventional rendering of the triangular model would not
be at all realistic.) The true geometry is contained in the reflectance field in the
form of reflectance functions from captured images.
In the original reflectance-field method described in the previous subsection,
the geometry of an object surface depends only on the surface normal direction.
As the normal direction changes due to a deformation, the lighting and view di-
rections change with respect to the normal, even if the actual positions of the light
and viewpoint remain the same. The top parts of Figure 8.32(a) and (b) show
how these angles change as a surface element rotates. The reflection map can
be sampled at the incident angles
θ
r
measured from the sur-
face normal after the deformation. Alternatively, the coordinate system can be
rotated so that the surface normal matches the predeformation (original) surface
element (
Figure 8.32(c)
). The reflectance functions can be resampled directly, or
approximated by simply rotating the predeformation reflectance function to match
the deformed normal. The bottom parts of Figure 8.32(a) and (b) illustrate how
the angles with respect to the deformed normal correspond to a different part of
the predeformation reflectance map; part (c) shows the effect of the rotation. The
square in this figure corresponds to the postdeformation reflectance map. In this
particular case, the contents are dark because the deformation has moved the sur-
face element away from the specular highlight.
θ
i
and view angle
