MaplePrimes - answers and comments on Question, United Colors of Benetton

uniting

Robert Israel — Mon, 10 Oct 2011 10:16:00 Z

Do you mean you want to unite them visually (i.e. erase the boundaries between them)? That's probably simpler than actually uniting the polygons, especially since the joined polygon might not be simply connected. All you have to do is plot the polygons using style=patchnogrid.
Now perhaps you want to put back in the boundaries between different colours.

For example:

Data:= [[[[0,4],[1,3.2],[2,4]],[[1,3.2],[2,4],[2,2]]],
[[[0,4],[1,3.2],[0,2]],[[0,2],[1,3.2],[2,2],[1,1.4]],[[0,2],[1,1.4],[0,0]]],
[[[0,0],[1,1.4],[2,2],[2,0]]]];
Colours:= [red,green,yellow];
# original plot:
display(map(op,zip((d,c) -> map(polygonplot,d,colour=c), Data, Colours)),axes=none);

getedges:= L -> (seq({L[i],L[i+1]},i=1..nops(L)-1),{L[1],L[-1]});
Cedges:= [seq([seq](getedges(P),P=d),d=Data)];
outedges:= `union`(seq(convert(map(convert,select(t -> numboccur(t,C)=1, C),list),set),C=Cedges));
display(plot(outedges,colour=black),
map(op,zip((d,c) -> map(polygonplot,d,colour=c), Data, Colours)),
style=patchnogrid,axes=none);

Solving the problem without patchnogrid option

Kitonum — Mon, 09 Jan 2012 12:57:51 Z

DelBar.mw

Download DelBar.mw

The Code for Mr. Markiyan Hirnyk

Kitonum — Wed, 11 Jan 2012 12:22:17 Z

DelBar2.mw

Here is the code, where only one joint edge of adjacent polygons of the same color is deleted!

Something to adjust

Markiyan Hirnyk — Mon, 10 Oct 2011 20:58:57 Z

I am grateful to you for your answer to my question. Your code is really good.
However, you do not take into account the case when numboccur(t, C) > 1. If two polygons of the same color have several joint edges, then one of these should be deleted. That is a difficulty. This place is to adjust.
Take a look at
Data := [[[[0, 0], [0, 4], [1, 4], [1, 0]], [[1, 3], [1, 4], [4, 4], [4, 0], [1, 0], [1, 1], [3, 1], [3, 3]]],
[[[1, 1], [1, 3], [3, 3], [3, 1]]]];
Colours := [red, green];
display(map(op, zip( (d, c) -> map(polygonplot, d, colour = c) , Data, Colours)), axes = none)#before uniting

getedges := proc (L) options operator, arrow; seq({L[i], L[i+1]}, i = 1 .. nops(L)-1), {L[-1], L[1]} end proc;
Cedges := [seq(([seq])(getedges(P), P = d), d = Data)];
outedges := `union`(seq(convert(map(convert, select((t) -> numboccur(t, C) = 1, C), list), set), C = Cedges));
display(plot(outedges, colour = black), map(op, zip( (d, c) -> map(polygonplot, d, colour = c), Data, Colours)),
style = patchnogrid, axes = none)#the same after uniting

The style=patchnogrid option does not help here.

Incomplete answer

Markiyan Hirnyk — Mon, 09 Jan 2012 21:12:12 Z

The code, where only one joint edge of adjacent polygons of the same color is deleted, should be presented to complete your good answer.

This is not that

Markiyan Hirnyk — Wed, 11 Jan 2012 23:43:47 Z

Thank you. Unfortunately, this is not the required result. Firstly, polygons as in the polygon command should be produced. It is not difficult to draw those. Secondly, in your example 4 the final result should consist of a red octagon with two coincident edges and a blue pentagon with two coincident edges.