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List of Figures
Figure 1.1 Deformation for implicit surfaces with a variational warp. Since
the warp is applied not only to the surface but also the en-
tire scalar field, the desirable scalar field property is preserved.
Therefore, implicit operators, such as blending and CSG, can be
applied even after deformation. In this figure, the iso-surface is
highlighted in red. . . . . . . . . . . . . . . . . . . . . . . . . . 4
Figure 2.1 Skeletons and skeletal primitives generated from the skeletons.
Deep color frames represent skeletons and light color areas are
skeletal primitives. . . . . . . . . . . . . . . . . . . . . . . . . . 8
Figure 2.2 4 distance functions. The Blobby Molecules function (a), the
Metaballs function (b), the Soft Objects function (c), and the
Wyvill function (d). These 4 functions are fall-off functions. . . 8
Figure 2.3 Variational interpolation procedure. A set of points are sam-
pled along the contour and work as constraints of interpolation
(a). Two additional points are assigned to each sampled point
as off-surface points (b). Off-surface points are placed inside
and outside the iso-surface and are along vectors normal to the
iso-surface. A scalar field is created by applying variational in-
terpolation to sampled points (c). . . . . . . . . . . . . . . . . 10
Figure 2.4 Two implicit spheres to which CSG operators are applied and
the result scalar fields. Union operator (a), Intersection operator
(b), and Difference operator (c). . . . . . . . . . . . . . . . . . 11
Figure 2.5 Two implicit spheres to which Ricci blend is applied and the
result scalar fields. Blending parameter n = 1 (a), n = 2 (b),
and n = 4 (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
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