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From: pettit@newport.COM (Teri Pettit)
Newsgroups: sci.math,sci.bio,comp.graphics,comp.sys.mac
Subject: Re: shape-transform graphic programs
Message-ID: <3920@adobe.COM>
Date: 13 May 88 21:53:10 GMT
References: <1815@ucdavis.ucdavis.edu> <1762@pixar.UUCP> <3058@saturn.ucsc.edu>
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Reply-To: pettit@newport.UUCP (Teri Pettit)
Organization: Adobe Systems Incorporated, Mountain View
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In article <3058@saturn.ucsc.edu> alibaba@ucscb.UCSC.EDU (Alexander M. Rosenberg) writes:
>Adobe's Illustrator 88 will do shape transforms like you
>described. I haven't seen them done, but it does require
>that both object have the same number of points. I am not
>sure how well the transoforms turn out, except for the
>demonstration one of an "S" turned into a swan.

CORRECTION: Illustrator 88 does NOT require that both objects have
the same number of points. It does require that either both objects
are closed paths, or both are open (though one can effectively
blend from between an open and a closed path by duplicating the
closed path exactly on top of itself and joining the overlaid
endpoints.)

Probably what you are thinking of is that the user interface
allows the user to select one or more points on each path
before starting the blend, and then the algorithm matches
the selected points into pairs (navigating the paths in the
order that each was created.) Any selected points on one
which are "left over" after this matching are treated just
like unselected points, and since it is hard to remember
whether one created a path in clockwise or counterclockwise
order, the best way to know which points you are matching
up to other points is to select the same number on each path.

In general, the more points you select, the more reasonable
the intermediate shapes look when you are blending between
two complex shapes.

Any points not matched up by this method are inserted into
the created paths according to the ratio of the perimeter
at which they are encountered, unless they come within a
threshhold distance of another point on the other path.
For example, if path A had 6 points and path B had 9 points,
and 3 points on each path were selected, and both paths
had an unselected point exactly halfway between two matched
selected points, then the intermediate created paths would have
11 control points (3 corresponding to the selected pairs,
1 corresponding to the unselected halfway points which just
happen to match each other in the perimeter trace, 2 corresponding
to the unmatched points from path A, and 5 corresponding
to the unmatched points from path B.)

[I should know because I am one of the implementors of Illustrator
88, and in fact did the S to Swan blending (I didn't draw either
the swan or the S, just played around with selecting control
points until I got the best sequence of intermediate shapes.)
The swan probably has close to a hundred control points, the
S has I believe 18. I think I selected 11 on each shape to get
the blend which is in the promotional illustration.]

Once the points are matched and interserted on the two
starting shapes, the intermediate shapes are created by
linearly spacing points along a straight line between
two matched points, and likewise interpolating slope
and curvature. This results in a sequence of shapes which
is seldom the most intuitive for animation-like effects
(since generally speaking, a point on one shape moves
through a path which is not necessarily a straight line
in getting to where it is on the final shape.) However,
for doing general shading effects, it gives much more
control than the user can get by choosing only between
radial and rectangular "fountains", and a straight line
is usually exactly what is wanted. The shape-transforming
feature was designed for exactly this purpose, to get
realistic "air brush" shading effects on shapes other
than circles and rectangles. That it can be used to
create illustrations where a V contorts itself into a
violin or an angel degrades into a devil is just frosting
on the cake. (If time permits, I would like to add more
flexible control over the sequence of blended shapes
to the next version of Illustrator (89?), but to tell
the truth this kind of flashy feature does not really 
rank in utility up to more important things like easier
text manipulation in an illustration.)

	-- Teri Pettit
	adobe!pettit@decwrl.dec.com