Re: Design problem


Robert C. Martin wrote:
On 1 Feb 2006 02:29:31 -0800, "Mark Nicholls"
<Nicholls.Mark@xxxxxxxxx> wrote:


Robert C. Martin wrote:
On 6 Jan 2006 13:38:11 -0800, roberts.noah@xxxxxxxxx wrote:

I'm having trouble with what seems like it should be a relatively
simple problem and am wondering what ideas people here might have.

I have a shape class and inside this shape are "elements" (vector drawn
based system). Certain things can be done to shapes, namely you can
rotate, skew, flip, zoom..ummm...that's about it but you never know
what could be added. Elements at this point can comprise of one of the
following three constructs: A line; a polygon/polyline; or a circle.
Lines are two point elements that contain a line from one to the other.
Polygons are point coordinate arrays with a start and an end; empty
polygons are actually lines from point to point otherwise it is a
filled element. A circle is a center and a radius.

Now the problem. Sometimes these operations are done one after the
other and I can increase speed (and yes we want it to be fast) if I can
do them all at once. I want a raw "perform" function on either the
element or the operation so that I can pass in individual operations or
constructs of operations. The easy way to do this is to build matrices
and pass them in, but how to apply these to a circle?? I can of course
have enums representing types of operations and have some ifs in the
circle construct but this fails the LSP (and I happen to agree with
that principle). I do have a couple of ideas but there are failings in
all of them (including rethinking how a circle is represented).

What ideas do you guys have?

Think of a circle as being defined by the radius line. It's not a
point and a length, it's two points.


Thats fine and dandy, but the space of circles is not closed under the
operations described...

i.e. compressing the Y axis makes a circle into a ellipse, not a little
circle.

Compressing the Y axis wasn't on the list above.

True, I assumed the etc...meant all the linear transformations on a
vector space, but it doesn't matter,skew was mentioned....a skewed
circle is not a circle, so the same logic applies.

I presume, then,
that you can compress or expand either axis. Can you define the
behavior of the system when you expand or compress an axis?

yes, 'linear vector spaces'.....though you need to throw in something
about ellipses or more generally conic sections.

For
example, does the aspect ratio of a square change if you expand or
compress the Y axis?

yes....so it's not a closed space.

If not, then how does the square behave?

it would have to change into a rectangle else exception.

What
about a rectangle, does the aspect ratio change?

yes....but it's still a rectangle...it is closed...thus we do not need
to know it's concrete shape in order to define what it becomes....it's
always a rectangle.

but it doesn't work for skew....so you'd need quadrilateral....though
the OP has solved this by using line segments.

Why would it change
for a rectangle and not for a square?

because squares cannot change aspect ratio, so you would have to map a
square to a rectangle....in which case you need to know both operation
and concrete class...i.e. double dispatch.

What about equilateral
triangles, or any regular polyhedron?

same as above, not closed.

Do they become irregular?

yes

Or
do they maintain their regularity?

no

What should the behavior of a
circle be if the Y axis is compressed?


it should 'become' an ellipse.

Some spaces are closed and some not....so if we want a single model
(and not have to dispatch on shape and operation), we need a
representation that is closed.

using points are the general representation is fantasic in theory
because points are closed under all transformation, and points on a
locus=>points on a locus.

but you have to pick a finite set of points that uniquely identify the
'shape' of a given shape....or end up with unbounded sets of
points.....or a representation that does not identify the resultant
shape.

.

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