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Generating the density function

The first step to defining the density function f=f(x,y,z) is prescribing the base or primary shape. The primary shape determines the initial values of all points in the voxel volume. A typical primary shape is the plane, where for a plane normal to the y-axis the density function f = -y. The selection of the iso-value determines where the unmodified primary mesh would be generated. Density values less than this iso-value designate above a solid surface whereas values greater than this iso-value imply inside a solid.

Other primary shapes include:

 

Volumetric modifiers

Volumetric modifiers are functions that are applied by the user to alter density field values. Modifiers can affect the entire volume or just user-defined regions. A region is itself a volumetric modifier that nests modifiers specific to a user constrained volume. Modifiers are classed into three categories:

 

Surface generation

Once the values of the density volume are known an iso-surface is extracted using Marching Cubes. Marching Cubes is an algorithm for extracting a polynomial of an iso-surface from a three-dimensional scalar field. Essentially taking the values from the eight corners of a cube (the voxel) the algorithm determines the polygons necessary to represent the iso-surface passing through the cube.

References

http://en.wikipedia.org/wiki/Marching_cubes

 
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