In
computer graphics
Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. ...
, free-form deformation (FFD) is a geometric technique used to model simple
deformations of rigid objects. It is based on the idea of enclosing an object within a
cube
A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It i ...
or another hull object, and transforming the object within the hull as the hull is deformed. Deformation of the hull is based on the concept of so-called ''hyper-patches'', which are three-dimensional analogs of
parametric curve
In mathematics, a parametric equation expresses several quantities, such as the coordinates of a point (mathematics), point, as Function (mathematics), functions of one or several variable (mathematics), variables called parameters.
In the case ...
s such as
Bézier curve
A Bézier curve ( , ) is a parametric equation, parametric curve used in computer graphics and related fields. A set of discrete "control points" defines a smooth, continuous curve by means of a formula. Usually the curve is intended to approxima ...
s,
B-spline
In numerical analysis, a B-spline (short for basis spline) is a type of Spline (mathematics), spline function designed to have minimal Support (mathematics), support (overlap) for a given Degree of a polynomial, degree, smoothness, and set of bre ...
s, or
NURBs. The technique was first described by Thomas W. Sederberg and Scott R. Parry in 1986, and is based on an earlier technique by Alan Barr. It was extended by Coquillart to a technique described as ''extended free-form deformation'', which refines the hull object by introducing additional geometry or by using different hull objects such as cylinders and prisms.
Applications
* Free-Form Deformation is used in
computer graphics
Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. ...
for solid geometric models. For example, the Lattice Modifier in
Blender (software)
Blender is a Free and open-source software, free and open-source 3D computer graphics software tool set that runs on Microsoft Windows, Windows, macOS, BSD, Haiku (operating system), Haiku, IRIX and Linux. It is used for creating animated films, ...
.
* It is used in the
image registration
Image registration is the process of transforming different sets of data into one coordinate system. Data may be multiple photographs, data from different sensors, times, depths, or viewpoints. It is used in computer vision, medical imaging, mil ...
in both rigid and non-rigid
transformation.
Nonrigid Registration Using Free-Form Deformations: Application to Breast MR Images
archived
"Nonrigid Registration using Free-Form Deformations: Application to Breast MR Images"
References
External links
C++ Library
Geometry in computer vision
Graphic design
Curves
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