Re: Math/Theory Questions about PostScript-style drawing
Re: Math/Theory Questions about PostScript-style drawing
- Subject: Re: Math/Theory Questions about PostScript-style drawing
- From: Rob Rix <email@hidden>
- Date: Mon, 17 Sep 2001 17:12:27 -0400
So my question is: since these seem to operate on points individually,
how can multiplying a point by the scaling matrix enlarge it? It would
simply spit out a new point, and the same sort of idea for Rotation, is
it not just rotating a point, which is essentially a zero-dimensional
object? Or am I missing a portion of the step? For instance, wouldn't
the rotation matrix need to "know" what the center of rotation is? Or
would the scale need to know where to find the center of the construct,
so it could "stretch" points accordingly? I'm interested more in the
mathematics of it than the actual implementation and use, but still
real-world usage would be appreciated.
Well, points are not just locations in space. Points (or vectors) are
actually locations in space relative to another location in space. So
basically, a point is really a distance.
You measure the length of a point (or vector) with simple pythagorean
theorem: a^2 + b^2 = c^2 (where c is the length/hypoteneuse).
I've been doing a _lot_ of work with vectors and affine transforms
recently (just not in Cocoa: I've been learning everything about them
instead), so if you have any further questions, I'd be pleased to answer.
-- Rob
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