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TAPESTRY: The Art of Representation and Abstraction

# Derivative Geometry: 3D Models from 2D Data

Most 3D modeling consists of defining 2D "controls" for 3D information in various ways. We've already discussed and seen how form•Z performs the simple extrusion operation, in which a uniform cross-section is swept through space perpendicular to the plane of the cross-section. Once we have some data, modifiers such as copy can be combined with basic transformations (move, rotate, scale, mirror) to make new data.

In contrast, complex transformations, (what form•Z calls Derivative Objects operations) fundamentally alter the geometry on which they act, turning a square into a cube, or a circle into a donut. The majority of these are associated with combining partial two-dimensional representations into complete three-dimensional representations. The list is quite long, but includes

• Extrusion (the tooth-paste tube effect)
• Revolution (sometimes called "lathing")
• Sweeps (essentially, extrusion along an irregular line)
• Skinning (stretching a surface over 2D "ribs" or cross-sections)
• Boolean Operations
These different transformations are described in this section.
Last updated: April, 2014