Icon - Department of Computer Science - University of Victoria

outside the deformation field is evaluated. In order to keep continuity of a scalar
field, however, the point where the scalar field reaches 0 must have a zero first deriva-
tive. Therefore, a field discontinuity is generated on the boundary of the deformation
field. This discontinuity can be seen in Figure 5.14b. Due to this discontinuity, a
scalar field created in the interactive deformation approximation pass cannot guaran-
tee continuity. When a blending operator is applied to the scalar field, it also creates
undesirable visual artifacts (Figure 5.14c). This resulting transition is not smooth,
so the blending property is also not satisfied.
Variational warping is used to compute a deformation field in the scalar field re-
construction pass. Since variational warping globally interpolates the vertices of the
deformation grid, the entire scalar field can be contained in the deformation field.
Variational warping has C 2 continuity, so the continuity of the deformed scalar field
is also guaranteed. Blending and CSG operators are applied to a scalar field after
variational warping in Figure 5.15c. Since constraints (the vertices of the deformation
grid) are not placed outside the iso-surface, the resulting scalar field is a little distorted
compared to a scalar field created based on a distance field. Nevertheless, this small
distortion is acceptable because the resulting model still has a smooth transition and
sharp edges.
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