Modeling

Coordinates: Fixing Positions in Space

Geometers have used Descarte's ("cartesian") coordinate systems for many years, and most computer hardware and software is framed in terms of the familiar cartesian "X, Y, and Z" axes. The software may, in addition, allow the use of spherical or cylindrical coordinates, but only for the location of points--the geometryt constructed from those points is almost inevitably cartesian (that is, a line connecting two polar coordinates will cut across the circle, not follow around it).

Global vs. Local Coordinate Systems

We usually establish the location of a point relative to some other point, saying that the chair is "four feet away from the south wall" while we live "10 miles north of town". These are relative measurements, since the number depends on the reference point from which they are measured. Clearly, the chair is roughly 10 miles north of town too, but this isn't a convenient or flexible way to locate objects within the house. Thus, it is common to use multiple reference frames, or "local coordinate systems", though we know they could all be forced into longitude and latitude measurements within the "global" (yup, that's what it's called) coordinate system if we had to.

In order to know where all points in a CAD model are located, they are stored using a global coordinate system for reference. However, local coordinate systems, possibly rotated and offset from the global one, make it much easier to think about the project (four feet from the south wall of the first floor is not the same as four feet from the south wall of the second floor).

Relative vs. Absolute Coordinates

A special case of local coordinate input occurs when each input point (mouse click) is measured relative to the previous one, providing a chain of "delta" coordinates, or lengths (if you've ever measured your house of apartment using a tape-measure, you've created just such a chain of relative coordinates). In fact, for much architectural input, we care less "where" something is and more "how big" it is. Most programs have mechanisms for viewing or entering coordinates using either relative or absolute coordinates (which can, of course, be measured in either a local or the global coordinate system).

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