On Mon, Mar 1, 2010 at 8:04 AM, James Fisher <
jameshfisher@gmail.com> wrote:
> I should say that the vertices of the superellipse are calculated
> correctly. The problem, it seems, is that for the vertices at right, top,
> left, and bottom, the angles of entry and exit need to be explicitly
> defined, rather than just relying on the '...' which coincidentally works
> for s>=0.5.
>
> I should say at this point that I am no maths whiz. But, sticking with the
> 'right ... topright ... top' line, the angle calculation needs to satisfy,
> for the exit angle of the first vertex:
>
> For s=0, angle = 180 degrees (vector to the left)
> For s = 0.5, angle = 135 degrees (45 degrees to the top left, producing a
> straight line to create the diamond shape)
> For s>0.5, angle = 90 degrees (vector vertically upwards)
>
> Suffice to say that I don't know how to produce that elegantly.
>
>
>
> James
>
>
> On Mon, Mar 1, 2010 at 3:54 PM, James Fisher <
jameshfisher@gmail.com> wrote:
>>
>> Hi again,
>>
>>
>> Another METAPOST problem. For the sake of curiosity, I've been looking at
>> and playing with the superellipse() function in plain METAPOST. This is all
>> fine and dandy until I try values of 'superness' less than 0.5, in which
>> case it generates shapes that are seemingly not superellipses. At s=0.5,
>> the function generates a diamond shape -- which, AFAIK, is correct.
>> However, s<0.5, the points of the diamond immediately turn to curves. (My
>> knowledge of superellipses here is just from
>>
http://en.wikipedia.org/wiki/Superellipse -- try the image at
>>
http://en.wikipedia.org/wiki/File:Lame_anima.gif to see how I expect the
>> shape to change with varying values of superness).
>>
>> Some code follows -- perhaps someone could run it and tell me if, for
>> starters, they get the same as me. (See
http://i49.tinypic.com/2ijqatl.jpg
>> for superellipse() with s=0.3).
>>
>>
>> Best,
>>
>>
>> James
>>
>>
>>
>> % The following is a superellipse function at
>> <
http://lists.foundry.supelec.fr/pipermail/metapost-commits/2008-June/000340.html>;
>> % I think it's the superellipse function in my copy of METAPOST; it at
>> least has the same behaviour.
>> % It seems to calculate the vertices correctly, but not the way they join
>> (try changing all ... to --).
>> %
>> %def superellipse(expr r,t,l,b,s)=
>> % r ... (s[xpart t,xpart r],s[ypart r,ypart t]){t-r} ...
>> % t ... (s[xpart t,xpart l],s[ypart l,ypart t]){l-t} ...
>> % l ... (s[xpart b,xpart l],s[ypart l,ypart b]){b-l} ...
>> % b ... (s[xpart b,xpart r],s[ypart r,ypart b]){r-b} ... cycle
>> %enddef;
>>
>> def supertest expr s =
>> superellipse(
>> ( 100, 50 ),
>> ( 50, 100 ),
>> ( 0, 50 ),
>> ( 50, 0 ),
>> s
>> );
>> enddef;
>>
>> % These >0 supernesses are fine, I think ...
>>
>> beginfig(0);
>> draw supertest 2;
>> endfig;
>>
>> beginfig(1);
>> draw supertest 1.01;
>> endfig;
>>
>> % The following, 0.5>=superness<=1,
>> % are from visual reference definitely right
>>
>> beginfig(2);
>> draw supertest 1;
>> endfig;
>>
>> beginfig(3);
>> draw supertest 0.99;
>> endfig;
>>
>> beginfig(4);
>> draw supertest 0.7;
>> endfig;
>>
>> beginfig(5);
>> draw supertest 0.51;
>> endfig;
>>
>> beginfig(6);
>> draw supertest 0.5;
>> endfig;
>>
>> % Now, for <0.5,
>> % things get problematic --
>> % the points in the shape generated by s=0.5
>> % should stay 'pointy'
>>
>> beginfig(7);
>> draw supertest 0.49;
>> endfig;
>>
>> beginfig(8);
>> draw supertest 0.3;
>> endfig;
>>
>> beginfig(9);
>> draw supertest 0.01;
>> endfig;
>>
>> beginfig(10);
>> draw supertest 0;
>> endfig;
>>
>> end;
>>
>
>