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Re: Fiting squares under a curve.

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Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:

> Maybe there's enough theoretical content here to justify a post to
> comp.theory, though it's largely a practical problem.
>
> I have an image made up of a frieze of square cells. I can add cells
> at will to the left or the rich (within reason). I want to fit it to a
> wall with a curved top, retaining the aspect ratio as much as
> possible. So small cells in low parts of the wall, large cells in high
> parts.
>
> The flat top case is easy. The cell width is given by the height of
> the wall to make a square.  It is then rounded to make a whole number
> of cells. As long as the wall is longer than it is high, the worst
> case is a 150% scaling in the x direction. Normally the wall is much
> longer than high, and distortion is negligible.
>
> However I want to allow a curved top. So the cells are no longer of
> the same height, in fact they are quads with two right angles at the
> bottom and a sloping top. The stright line function of the cell tops
> approximates the wall top curve.
>
> if we consider the solution to be a set of points in x along the wall
> representing cells, and the midpints the boundaries of cells, then we
> need to minimise the function
>
> sum over each cell : integral of wall function from cell x low to cell
> x high minus (cell x high - cell x low) squared.
>
> Is there a fast way of doing this? 

It might be useful to know why I didn't comment before in
comp.programming: I didn't understand what the constraints are.

You can add cells to some already given strip of cells but what is "with
reason"?  Can you add cells from some restricted set, or can you choose
everything about the cells you add?  Can you choose anything about the
initial frieze?

You can scale something.  It is the function to be fitted or the frieze
of cells?  Scaling implies an origin.  What is that origin and/or can
the scaling be accompanied by a translation making the origin
unimportant?

Do you have any extra information about the function?  For example, is
it everywhere continuous and maybe even smooth?

-- 
Ben.

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Thread

Fiting squares under a curve. Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2021-09-15 06:59 -0700
  Re: Fiting squares under a curve. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-09-15 15:17 +0100
    Re: Fiting squares under a curve. Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2021-09-15 08:06 -0700
      Re: Fiting squares under a curve. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-09-15 22:33 +0100
        Re: Fiting squares under a curve. Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2021-09-15 15:01 -0700
          Re: Fiting squares under a curve. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-09-16 00:33 +0100
            Re: Fiting squares under a curve. Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2021-09-17 03:25 -0700
              Re: Fiting squares under a curve. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-09-17 14:22 +0100
                Re: Fiting squares under a curve. Andy Walker <anw@cuboid.co.uk> - 2021-09-17 16:25 +0100
                Re: Fiting squares under a curve. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-09-17 20:59 +0100
                Re: Fiting squares under a curve. Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2021-09-23 02:14 -0700

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