tasks a-s

Task/Problem-of-Apollonius/J/problem-of-apollonius-1.j

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+require 'math/misc/amoeba'
+
+NB.*apollonius v solves Apollonius problems
+NB. y is Cx0 Cy0 R0,  Cx1 Cy1 R1,:  Cx2 Cy2 R2
+NB. x are radius scale factors to control which circles are included
+NB.   in the common tangent circle.  1 to surround, _1 to exclude.
+NB. returns Cxs Cys Rs
+apollonius =: verb define"1 _
+ 1 apollonius y
+:
+ centers=. 2{."1 y
+ radii=. x * {:"1 y
+ goal=. 1e_20                               NB. goal simplex volume
+ dist=. radii + [: +/"1&.:*: centers -"1 ]  NB. distances to tangents
+ 'soln err'=. ([: +/@:*:@, -/~@dist) f. amoeba goal centers
+ if. err > 10 * goal do. '' return. end.    NB. no solution found
+ avg=. +/ % #
+ (, avg@dist) soln
+)

Task/Problem-of-Apollonius/J/problem-of-apollonius-2.j

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+   ]rctst=: 0 0 1,4 0 1,:2 4 2           NB. Task circles
+0 0 1
+4 0 1
+2 4 2
+   (_1 _1 _1 ,: 1 1 1) apollonius rctst  NB. internally & externally tangent solutions
+2 0.83333333 1.1666667
+2        2.1       3.9