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to ensure that they are embedded in the currently-visible surface. When one of the
curves is manipulated, the warp is re-computed using this new curve and all the
previous curves. All other curves are then projected onto the new surface (Figure
4.3).
Figure 4.3: The user can pull the model from several positions with multiple curves.
The user can also turn on or off the visualization of the deformation grid (see Sec-
tion 5.2 for details of the deformation grid) and the deformation curves. The default
status is that the visualization of the deformation grid is off and the visualization of
the deformation curves is on. The deformation grid is invisible in the default status
because the user does not need to directly interact with it. For the user who wants to
see the internal deformation grid, however, the system can present the visualization
of it (Figure 4.4b). The deformation curves are visualized as handles to manipulate
deformations, however the switch to turn off the deformation curves is provided so
that the user can see the deformation results without the curves (Figure 4.4c).
4.2.2 Variational Warping
Once deformation is achieved, the user can apply variational warping to the model
in order to re-construct the scalar field. This pass must be executed after interactive
deformation because the resulting scalar field generated in the interactive deformation
approximation pass is not usable for further modeling. If the user applies another
operator such as blending and CSG without variational warping, undesirable visual
artifacts are produced.
Variational warping can be applied at any time by crossing the button with a
stroke. The button for variational warping is displayed in the parameter toolbar
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