// balls and springs

dag:{[n;m]_dv'[_draw[n;m]_draw'-n;!n]}						/ graph: n balls, m connections
ngon:{[n]pi:2*_asin 1;i:!n;k:i*(2*pi)%n;(_cos k;_sin k)}			/ polygon
connect:{[g;d]stretch lines[g;d],balls g}					/ draw balls and lines
stretch:{[g]g,(2#,,:)'3 -1}							/ stretch
balls:{[g]-1!,/(7 2#,!0){x,,y}/:(+g)+\:ball[]}			                / red balls
ball:{1+Size+Size*{(1+#x)#x}'ngon Sides}					/ ball
lines:{[g;d],/(7 2#,!0){x,,y}/:+:',/1+Size+d{x[z]{(x;y)}/:x y}[+g]'!#d}		/ black lines
matrix:{[d]c*~n=\:/:n:!#c:{x|+x}(!#d)_lin/:(),/:d}				/ connection matrix

/ spring model

spring:{[c;h;x;y]
 a:1-%l:c*ln[x;y]
 X:x+h*gr[c;a;x]
 Y:y+h*gr[c;a;y]
 :[eq[c*ln[X;Y]]<eq l;(c;h;X;Y);(c;h%2;x;y)]}

ln:{[x;y]_sqrt _sqr[x-\:/:x]+_sqr y-\:/:y}
gr:{[c;a;x]+/@[a*x-\:x;_n;{@[x;&~y;:;0]};c]}
eq:{[l]+/+/_sqr l-1}

next:{M::connect[2_ S::spring . S;D];if[Auto&Zero>S 1;Balls::]}			/ next state

.t..t:"if[.k.Auto;.k.next[]]"							/ timer

/ GUI

Sides:10
Size:.01
Balls:20
Springs:5
Force:1
Force..u:Springs..u:Balls..u:Size..u:Sides..u:{:[y>0;y;x]}
Zero:1.e-9
Zero..f:$:
D..d:"dag[Balls;Springs]"
N..d:"ngon Balls"
S..d:"spring[matrix D;Force]. N"
Next:"next[]"
Next..c:`button
Auto:0
Auto..c:`check
M..d:"connect[N;D]"
M..c:`plot
M..l:`
.k..a:(`Sides`Size`Balls`Springs`Force;`M;`Zero`Auto`Next)
.k..l:"Balls and Springs"
`show$`.k;
\t .001