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revision 1.38 by tjl, Wed Nov 13 13:13:27 2002 UTC revision 1.39 by tjl, Wed Nov 13 13:20:12 2002 UTC
# Line 281  of the canvas. Line 281  of the canvas.
281  \subsection{Algorithm ``How?''}  \subsection{Algorithm ``How?''}
282    
283  In this subsection, we formulate the design criteria of the preceding section mathematically  In this subsection, we formulate the design criteria of the preceding section mathematically
284  to obtain a simple algorithm with the desired properties and an interesting graphical explanation  and discuss
285    a simple algorithm for a shape with the desired properties
286    and an interesting graphical explanation
287  for the algorithm.  for the algorithm.
288    
289  To start off, assume that we are drawing the torn edge around a given  To start off, assume that we are drawing the torn edge around a given
# Line 293  Locally, we can approximate the curve by Line 295  Locally, we can approximate the curve by
295  The resulting shape of the edge should be continuous w.r.t.~both the local  The resulting shape of the edge should be continuous w.r.t.~both the local
296  point and normal vector.  point and normal vector.
297    
298    For the attached edge, we can obtain the final curve by simply shifting the original
299    smooth curve to its normal direction by a function which only depends on the location $(x, y)$.
300    
301    The sprinkled case, on the other hand, can be obtained through a decision process:
302    again using a function of location $f(x,y)$, a given point is {\em inside} the curve,
303    iff $f(x,y) < d_C(x,y)$, where $d_C(x,y)$ is the distance of the point $(x,y)$ from
304    the contents of the curve $C$.
305    
306  - the torn shape of a point on an edge should be a continuous function of the point's location on the paper\\  - the torn shape of a point on an edge should be a continuous function of the point's location on the paper\\
307  - the function should change slowly enough so that the dot product of movement direction and edge normal  - the function should change slowly enough so that the dot product of movement direction and edge normal

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