Could I reproduce this graphic? Circles and spirals are easy, but I'd never drawn arcs. Was it even a genuine computer picture- 1978 meant computer graphics available to amateurs were primitive. Perhaps a spirograph contraption? I put it on the LB Forum as a challenge and Rod, Anatoly and Bplus produced excellent efforts.

Given two points and a circle-centre there are four arc solutions in two mirror-image pairs.

The geometry is basically right-angle triangles and trig. It still took some time before I was happy with my own solutions. Then I realised there were already solutions on Rosetta Code...

I now concentrated on fun USING arcs, and hope to come up with further variations. I use HSV colouring to get results I find pleasing.

'[RC] Circles of given radius through two points nomainwin global col$, pi, state$ pi =atn( 1) *4 WindowWidth =1000 WindowHeight =1040 open "Demo arcs" for graphics_nsb as #wg #wg "trapclose quit" #wg "fill darkblue ; color 100 255 255" radius =2000 x1 = 200 y1 = 250 x2 = 800 y2 = 750 #wg "up ; goto "; x1; " "; y1 #wg "down ; circle 4" #wg "up ; goto "; x2; " "; y2 #wg "down ; circle 4 ; flush" [H] call twoCircles x1, y1, x2, y2, radius scan radius =radius *0.98 if radius >400 then [H] #wg "flush ; getbmp scr 0 0 1000 1040" bmpsave "scr", "arcs.bmp" notice "arcs2.bmp saved" wait sub quit h$ close #wg end end sub sub twoCircles x1, y1, x2, y2, r if ( ( x1 =x2) and ( y1 =y2)) or ( r =0) then wait ' single point or radius zero! r2 =( ( x1 -x2)^2 +( y1 -y2)^2)^0.5 /2 ' half distance between points if rone revolution x =c *( 1 -abs( ( ( h /60) mod 2) -1)) m =v -c ' matching adjustment select case case h < 60 r = c: g = x: b = 0 case h <120 r = x: g = c: b = 0 case h <180 r = 0: g = c: b = x case h <240 r = 0: g = x: b = c case h <300 r = x: g = 0: b = c case else r = c: g = 0: b = x end select rd = abs( int( 256 *( r + m))) gn = abs( int( 256 *( g + m))) bu = abs( int( 256 *( b + m))) ' NB csv version .. <<<<<<<<<<<<<<<<<<<<<<<<<< col$ =right$( " " +str$( rd), 3) +" " +right$( " " +str$( gn), 3) +" " +right$( " " +str$( bu), 3) end sub function ATAN2( y, x) Result$ = "Undetermined" If ( x =0) and ( y >0) then ATAN2 = pi /2: Result$ ="Determined" if ( x =0) and ( y <0) then ATAN2 =3 * pi /2: Result$ ="Determined" if ( x >0) and ( y =0) then ATAN2 =0: Result$ ="Determined" if ( x <0) and ( y =0) then ATAN2 =pi: Result$ ="Determined" If Result$ <>"Determined" then BaseAngle =ATN( abs( y) /abs( x)) If ( x >0) and ( y >0) then ATAN2 = BaseAngle If ( x <0) and ( y >0) then ATAN2 = pi -BaseAngle If ( x <0) and ( y <0) then ATAN2 = pi +BaseAngle If ( x >0) and ( y <0) then ATAN2 = 2 *pi -BaseAngle end if End Function function cosRad( t) cosRad =cos( t /57.29577951) end function function sinRad( t) sinRad =sin( t /57.29577951) end function

I can always be contacted at mr.john.f@gmail.com