Some thoughts on mass producing solutions
]P
5 1 2 1 6 2 6 6
2 4 2 5 6 1 5 4
]NAMES=:'ABCDEFGH'
ABCDEFGH
]SEGS=:2{\"1 NAMES
---T--T--T--T--T--T--┐
│AB│BC│CD│DE│EF│FG│GH│
L--+--+--+--+--+--+---
]PAIRS=:2+\"1 P
5 1
1 2
2 1
1 6
6 2
2 6
6 6
2 4
4 2
2 5
5 6
6 1
1 5
5 4
]SLOPES=:%%/"2 -/"1 PAIRS
_0.5 _2 _3 0.2 1.25 1 _
]MP=:-%/"2 -/"1 PAIRS
2 0.5 0.333333 _5 _0.8 _1 0
]MIDS=:|:-: +/"1 PAIRS
3 3
1.5 3
1.5 3.5
3.5 5.5
4 3.5
4 3
6 4.5
]BS=:(1{"1 MIDS)-MP*0{"1 MIDS
_3 2.25 3 23 6.7 7 4.5
]YS=:BS+MP*0{"1 MIDS
3 3 3.5 5.5 3.5 3 4.5
Next, I thought I could find the intersections of pairs of perpendicular
bisectors so here are the x and y's for equations in the form Ax +By = C.
I can find A, B and C and then find the intersections solving the
simultaneous equations with matrices.
EQXY=:>|:2{\"1 P
0{"3 EQXY
5 1
2 4
1{"3 EQXY
1 2
4 2
Have a good day. Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Linda Alvord
Sent: Monday, July 23, 2012 8:36 PM
To: [email protected]
Subject: Re: [Jprogramming] Challenge 13 Plot Alot
Thanks for your reorganization of the code. You need:
load'plot'
To see the results use:
dolindaplots ''
All the different cases will appear sooner or later.
I was trying to avoid using explicit definitions which means that you must
not use control structures. This was my own restriction which I seemed
unable to achieve very successfully
Each of the plots has a third point, and the next problem is to divide the
square in three parts which show the areas that are closest to each of the
three points.
If possible, eventually extend to 8 points, as I did in the viewmat example,
or even beyond. The code for the viewmat solution is based on a finite
lattice of points. This approach involves an infinite collection of points.
I think an area approach conveys the concept better than the lattice
approach. The many examples of the voronoi problem found on wiki or the web
are based upon lattices.
My solution is similar to many of my strategies. I tend to think of how to
start to develop a concept with high school students. Thus, especially in
this case, it is simplistic. I really am using J as a tool for teaching
mathematics. This problem would be probably more interesting to consider
than some of the Euclidean proofs that are so much of the focus of geometry.
However, I do think the problem is worth pushing forward as the real
applications seem to apply to area rather than to lattices.
I look forward to images which divide the region into three parts and
beyond.
Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Mike Day
Sent: Monday, July 23, 2012 10:28 AM
To: [email protected]
Subject: Re: [Jprogramming] Challenge 13 Plot Alot
Is this the sort of thing you wanted? It's pretty simple- minded and hardly
worth bothering you or the Forum with.... code follows my sign-off.
usage:
dolindaplot ''
output: the plot you want and an smoutput line showing which mask won.
Please note that I'm censoring earlier messages below.
Mike
dolindadata =: 3 : 0 NB. Globals still global
P=:1+?(2,8)$6
Q=:0 1{"1 P
MID=:-:+/"1 Q
MP=:-%/-/"1 Q
X1=:0
Y1=:(MP*( X1- 0{MID)) + 1{MID
Y2=:7
X2=:(Y2+(MP*0{MID)-1{MID)%MP
X3=:7
Y3=:(MP*( X3- 0{MID)) + 1{MID
Y4=:0
X4=:(Y4+(MP*0{MID)-1{MID)%MP
V=:Y1,X2,Y3,X4
POS=:(2=+/"1#:i.16)##:i.16
R=:|:(0,0,0, X2,7,7, 7,X4),.0,Y1,7,7, 7 , Y3,0,0
S=:(*./"2 (0<:R)*. R<:7)#"1 R
Y1=:(0>.Y1)
Y1=:(Y1<.7)
X2=:(0>.X2)
T1=:6($"1)3 5 4 {"1 S
T2=:6($"1)3 5 0 1 2 {"1 S
T3=:6($"1)5 2 3 4 {"1 S
T4=:6($"1)5 2 1 0 {"1 S
T5=:6($"1)2 4 3 {"1 S
T6=:6($"1)2 4 5 0 1 {"1 S
T7=:6($"1)1 5 0 {"1 S
T8=:6($"1)1 5 4 3 2 {"1 S
T9=:6($"1)1 4 3 2{"1 S
T10=:6($"1)1 4 5 0 {"1 S
T11=:6($"1)3 1 2 {"1 S
T12=:6($"1)3 1 0 5 4 {"1 S
T=:(T1,T2);(T3,T4);(T5,T6);(T7,T8);(T9,T10);(T11,T12)
TESTVP =: *./"1((0<:V)*.V<:7)="1 POS
)
dolindaplots=: 3 : 0
# dolindadata 1
for_i. i.#T do.
dat =.(<"2)>2 2$0 2 1 3 { >i{T
mask =. 1 i} 0#~#T
if. *./ mask = TESTVP do.
lindaplot dat;P
smoutput mask
end.
end.
''
)
lindaplot =: 3 : 0
'dat P'=. y
pd 'reset'
pd 'aspect 1'
pd 'type poly'
pd 'itemcolor blue, yellow, green, red'
pd dat
pd 'type marker'
pd 'markersize 1.2'
pd 'itemcolor black'
pd (<"1) 0 1 2{"1 P
pd 'show'
)
On 23/07/2012 11:39 AM, Linda Alvord wrote:
> Can you help me show only the correct solution for this code. It is
> the one image that is preceded by a 1. Any simplifications would be
> fun
too.
>
> load 'plot'
> pd 'reset'
> P=:1+?(2,8)$6
> Q=:0 1{"1 P
> MID=:-:+/"1 Q
> MP=:-%/-/"1 Q
> X1=:0
> Y1=:(MP*( X1- 0{MID)) + 1{MID
> Y2=:7
> X2=:(Y2+(MP*0{MID)-1{MID)%MP
> X3=:7
> Y3=:(MP*( X3- 0{MID)) + 1{MID
> Y4=:0
> X4=:(Y4+(MP*0{MID)-1{MID)%MP
> V=:Y1,X2,Y3,X4
> POS=:(2=+/"1#:i.16)##:i.16
> R=:|:(0,0,0, X2,7,7, 7,X4),.0,Y1,7,7, 7 , Y3,0,0
> S=:(*./"2 (0<:R)*. R<:7)#"1 R
> Y1=:(0>.Y1)
> Y1=:(Y1<.7)
> X2=:(0>.X2)
> T1=:6($"1)3 5 4 {"1 S
> T2=:6($"1)3 5 0 1 2 {"1 S
> T3=:6($"1)5 2 3 4 {"1 S
> T4=:6($"1)5 2 1 0 {"1 S
> T5=:6($"1)2 4 3 {"1 S
> T6=:6($"1)2 4 5 0 1 {"1 S
> T7=:6($"1)1 5 0 {"1 S
> T8=:6($"1)1 5 4 3 2 {"1 S
> T9=:6($"1)1 4 3 2{"1 S
> T10=:6($"1)1 4 5 0 {"1 S
> T11=:6($"1)3 1 2 {"1 S
> T12=:6($"1)3 1 0 5 4 {"1 S
> dat=:(<"2)>2 2$0 2 1 3 { T1,T2
> 'aspect 1'plot dat
> P
> V
> ]*./ 1 0 0 0 0 0=*./"1((0<:V)*.V<:7)="1 POS pd 'type poly'
> pd 'itemcolor blue, yellow, green, red'
> pd dat
> pd 'type marker'
> pd 'markersize 1.2'
> pd 'itemcolor black'
> pd (<"1) 0 1 2{"1 P
> pd 'show'
> ]*./ 0 1 0 0 0 0=*./"1((0<:V)*.V<:7)="1 POS
> dat=:(<"2)>2 2$0 2 1 3 { T3,T4
> pd 'type poly'
> pd 'itemcolor blue, yellow, green, red'
> pd dat
> pd 'type marker'
> pd 'markersize 1.2'
> pd 'itemcolor black'
> pd (<"1) 0 1 2{"1 P
> pd 'show'
> ]*./ 0 0 1 0 0 0=*./"1((0<:V)*.V<:7)="1 POS
> dat=:(<"2)>2 2$0 2 1 3 { T5,T6
> pd 'type poly'
> pd 'itemcolor blue, yellow, green, red'
> pd dat
> pd 'type marker'
> pd 'markersize 1.2'
> pd 'itemcolor black'
> pd (<"1) 0 1 2{"1 P
> pd 'show'
> ]*./ 0 0 0 1 0 0=*./"1((0<:V)*.V<:7)="1 POS
> dat=:(<"2)>2 2$0 2 1 3 { T7,T8
> pd 'type poly'
> pd 'itemcolor blue, yellow, green, red'
> pd dat
> pd 'type marker'
> pd 'markersize 1.2'
> pd 'itemcolor black'
> pd (<"1) 0 1 2{"1 P
> pd 'show'
> ]*./ 0 0 0 0 1 0=*./"1((0<:V)*.V<:7)="1 POS
> ]dat=:(<"2)>2 2$0 2 1 3 { T9,T10
> pd 'type poly'
> pd 'itemcolor blue, yellow, green, red'
> pd dat
> pd 'type marker'
> pd 'markersize 1.2'
> pd 'itemcolor black'
> pd (<"1) 0 1 2{"1 P
> pd 'show'
> ]*./ 0 0 0 0 0 1=*./"1((0<:V)*.V<:7)="1 POS
> dat=:(<"2)>2 2$0 2 1 3 { T11,T12
> pd 'type poly'
> pd 'itemcolor blue, yellow, green, red'
> pd dat
> pd 'type marker'
> pd 'markersize 1.2'
> pd 'itemcolor black'
> pd (<"1) 0 1 2{"1 P
> pd 'show'
>
> Linda
>
>
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