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Chapter 3
Background and Previous Work
This chapter introduces the background and previous work related to this research:
free-form deformation (FFD) (Section 3.1), deformation for implicit surfaces (Sec-
tion 3.2) and sketch-based modeling systems (Section 3.3). The goals of this research
are to propose an FFD technique for implicit surfaces and also to develop a more
efficient interface to manipulate FFD than 3D lattices. Since the fundamentals of im-
plicit surfaces are described in the previous chapter (Chapter 2), this chapter rather
focuses on deformation techniques. Section 3.1 gives previous FFD techniques which
fall into lattice-based FFD (Section 3.1.1) and FFD without lattices (Section 3.1.2).
Several deformation techniques for implicit surfaces are described in Section 3.2. Note
that these deformation techniques are not FFD. This chapter also surveys interface
designs and techniques for the second goal. Section 3.1 mentions interfaces for FFD
as well. Because the solution for an FFD interface in this research is to develop
a sketch-based interface, an overview of existing sketch-based modeling systems is
provided in Section 3.3.
3.1 Free-Form Deformation
Free-Form Deformation (FFD) is a popular and well researched deformation tech-
nique in computer graphics and generally utilizes spatial deformation. Spatial defor-
mation for computer graphics was first introduced by Barr [4]. A conceptual process
of spatial deformation is to embed the object in a 3D volume called a deformation
field which defines a space mapping d : R 3 → R 3 , and deform the deformation field.
Accordingly, the embedded object is deformed. A survey of spatial deformation was
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