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Examples of these operators are shown in Figure 2.4. One of advantages to use CSG
is that topological changes can be handled easily. For example, a hole can be created
on an implicit volume using the difference operator with another implicit volume.
Nevertheless, CSG creates discontinuity between two scalar fields, which results in
undesirable artifacts when blending (Section 2.1.3) is applied. There are several
approaches for applying CSG operators while preserving continuity. For example,
R-Functions in FRep construct C n continuous CSG operators [40]. Barthe proposed
CSG operators which can preserve G 1 continuous scalar fields [5].
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).
2.1.3 Blending
Blending is another modeling advantage of implicit surfaces in addition to CSG op-
erators. This operator can create smooth transitions between two objects. It is quite
difficult to apply blending to other shape representations such as point based repre-
sentations and parametric representations while blending can be trivially computed
in implicit surface representations. A blending operator fA+B(p) between two scalar
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