Path: utzoo!attcan!uunet!bloom-beacon!think!ames!dlb!ardent!ez!sleat
From: sleat@ez.ardent.com (Michael Sleator)
Newsgroups: comp.graphics
Subject: Re: Cleaning up freehand drawings
Message-ID: <8387@ardent.UUCP>
Date: 23 Sep 89 02:39:34 GMT
References: <1580002@hp-ptp.HP.COM>
Sender: news@ardent.UUCP
Reply-To: sleat@ez.ardent.com (Michael Sleator)
Organization: Ardent Computer Corp., Sunnyvale, CA
Lines: 55

In article <1580002@hp-ptp.HP.COM> garye@hp-ptp.HP.COM (Gary_Ericson) writes:

>What I mean is this.  Suppose I want to draw a straight line.  When I move the
>digitizing pen (or mouse), I will undoubtedly not keep my hand steady and the
>line will be crooked.  If the computer follows faithfully, I will end up with a
>multi-segmented or curved line.  But what if the system decided that because
>all the points I've digitized lie within a certain tolerance of a straight line
>that I really wanted a straight line and it draws one for me.  I'm thinking of
>maybe giving the pen a certain "thickness" (tolerance) and any points that lie
>within that thickness of a straight line really represent a straight line.
>Kind of like drawing with a fat felt-tip pen versus a fine pencil point.

>It's a little harder for curves or splines, but I wonder if the same idea would
>hold: if all the points, within the tolerance, lie along an arc or elipse or
>spline of some kind, then the computer translates my sketch into that figure.

I think that the threshold approach might be a little awkward.  For example,
if you do happen to stray out of the fit zone, then you get an abrupt
deviation in your curve which you have to go back and correct somehow.
It's also not clear to me how you decide what curve to use as a reference.
Offhand, it seems that you might run into serious dynamic instabilities in
trying to adaptively fit a curve while simultaneously performing this threshold
function against it.  On the other hand, I don't see how you could choose the
curve a priori.  Of course, you could specify the curve in some way, such as
using spline control points, but that's not freehand drawing.

Perhaps you are trying to solve the problem in the wrong domain.  It seems
to me that what you really want is a low pass filter on the curvature.  In
general, the "jigglies" (to coin a term) will be significantly higher frequency
curvature components than the intended curves.  This suggests that there is
ample room for choosing a filter cutoff frequency that will kill the jigglies
and still allow the desired curves to be drawn.  It does imply that if you
actually want to create an inflection point, you probably need to do it with
two different strokes, but that seems intuitively sensible.

I haven't thought very hard about it, but it seems that an algorithm for doing
this could be quite simple.  As you get each point from the input device,
you recompute the local curvature at the growing end of the curve.  You then
bias the placement of the point according to the filter function.

I wonder what it would be like to draw with a high pass curvature filter
rather than a low pass.  One could also experiment with bandpass and notch
filters.  A broad notch filter might work to eliminate the jigglies when
drawing lines or large-radius curve, yet still allow inflections.

Enough speculation.  I'd like to hear about it if you try (or anyone else
tries or has already tried) this.


Michael Sleator
Ardent Computer
880 W. Maude
Sunnyvale, CA  94086
408-732-0400
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