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: Ondra Cada <email@hidden>
- Date: Mon, 17 Sep 2001 23:36:56 +0200
Matthew,
>
>>>>> Matthew Cox (MC) wrote at Mon, 17 Sep 2001 16:29:38 -0400:
MC> So my question is: since these seem to operate on points individually,
MC> how can multiplying a point by the scaling matrix enlarge it?
Right. It does *never* enlarge a point (which would be, as you correctly
assumed, kinda impossible for a dimensionless doodad) -- it just moves it
elswhere.
It is important, though, to understand that you never seen a point either.
What you have seen were small rectangles, or circles, or similar things.
_They_ of course, being de facto filled areas whose _boundaries_ are
specified by points, can be enlarged (just as points which specify their
boundaries move: if they move farther, area is larger; if they go closer,
area gets smaller).
MC> simply spit out a new point, and the same sort of idea for Rotation, is
MC> it not just rotating a point, which is essentially a zero-dimensional
MC> object? Or am I missing a portion of the step?
Well, it again _moves_ a point (does not rotate it). The movement though is
based on rotation, eg. as the angle increases, the points would move by
circular routes.
MC> For instance, wouldn't
MC> the rotation matrix need to "know" what the center of rotation is?
Of course it would. The center is always (with the matrix you used) in the
origin, [0,0]. Any rotation round a different center is just a result of
superimposing translate and rotate matrixes (which of course make one result
matrix, which can be interpreted as "rotation round [X,Y]").
---
Ondra Cada
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