Last time updated 23 April, 2010
Functionbased shape modeling is becoming increasingly popular in
computer graphics. The idea of this approach is that complex geometric shapes
can be
produced from a "small formula". In
this research, a general method of functionbased shape modeling is studied. This method
assumes that geometric shapes are represented with the inequality
f(x,y,z)=>0,
where the real function f is positive for the points inside the shape, equal to
zero on its border and negative outside the shape. The function can be defined
analytically, or with a function evaluation algorithm, or with
tabulated values (e.g., CT or MRI volume data) and an appropriate interpolation procedure. To transform the shape thus defined or to create another shape as Boolean combination of the previously defined ones, different operations can be applied. They are, for example, affine, perspective and projective transformations, settheoretic operations (union, intersection, subtraction), blending and morphing operations. They all are defined in function form as function superpositions and the result of any operation is a functiondefined shapes as well and it can be used as an argument for other operations. For example, the exact analytical definition of the settheoretic operations is obtained with socalled Rfunctions. Function representation (Frep) lets us unify in one single model such representation as CSG, sweeps, blobby objects and even volume data. The same set of operations and relations can be applied to any object that often lets us find interesting and unusual solutions to some longstanding problems. 
Refer to [1], [2] and [4] for the details.
Refer to [1], [2] and [4] for the details.
Refer to [2] and [3] for the details. Click here for more hair.
Refer to [2] and [5] for the details.
In this scene, the head with a drawer filled with CSG primitives, is created by trilinear interpolation of the CT volume data and settheoretic operations applied to the head and functionally defined CSG primitives. The hair is modeled with function defined generalized cylinders. The hairstyle has been made with the settheoretic operations and nonlinear transformations. The candle holder is modeled as a patterned lattice. It results from the set difference between a hemispherical shell and a swept pattern. The candle is modeled as a cylinder with the top part sculpted by applying a splitting operation to remove the undesirable parts. The candle is then unified with the droplets of wax which are defined by the onedimensional medial axis model. The table and the tray are created using functionally defined CSG primitives. The lizards sitting on the leg of the table are created with the relief carving model using offsetting along the normal. The background with the clouds and the stylized comet are created with scattered data approximation and onedimensional skeletons respectively. Refer to [3] and [7] for the details. Rendering has been done with POVRay 
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