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TAPESTRY: The Art of Representation and Abstraction

# Simple Transformations

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.

We'll explore three additional techniques this week: revolution, sweeps and boolean operations.

### Transformations?

Your geometry data is like an object in the real world, but the mouse is not like a hand and arm, flexibly able to move the object around and place it where we want, oriented how we want.

So, the question becomes, "In what ways can we manipulate the coordinates of the object, and do these manipulations change the fundamental shape of the object or not." There are actually a great many possible transformations, some of which are useful, some of which are not.

The simple transformations (also called, shape preserving transformations) change the shape without changing its proportions or the angles at which the parts come together. Simple transformations include

• Translation (what you might call "moving" the object)
• Rotation ("turning" the object)
• Scaling ("enlarging" or "shrinking" the shape)
• Mirroring (sometimes called "handing" or "flipping")

Last updated: April, 2014