Problem of Apollonius: Difference between revisions

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Line 216: R2: 2.000 0.833 1.167</pre> =={{header\|ALGOL 68}}== {{Trans\|Java\|Algol 68 doesn't actually do javadoc comments but they seemed useful...}} <syntaxhighlight lang="algol68"> BEGIN # solve the problem of Apollonius - find circles tangential to 3 others # # translation of the Java sample # OP FMT = ( REAL v )STRING: BEGIN STRING result := fixed( v, -12, 2 ); INT start := LWB result; WHILE IF start >= UPB result THEN FALSE ELSE result[ start ] = " " FI DO start +:= 1 OD; result[ start : ] END # FMT # ; MODE CIRCLE = STRUCT( REAL x, y, radius ); OP TOSTRING = ( CIRCLE c )STRING: "Circle[x=" + FMT x OF c + ",y=" + FMT y OF c + ",r=" + FMT radius OF c + "]"; ### Solves the Problem of Apollonius (finding a circle tangential to three other * circles in the plane). The method uses approximately 68 heavy operations * (multiplication, division, square-roots). * @param c1 One of the circles in the problem * @param c2 One of the circles in the problem * @param c3 One of the circles in the problem * @param s1 An indication if the solution should be externally or internally * tangent (+1/-1) to c1 * @param s2 An indication if the solution should be externally or internally * tangent (+1/-1) to c2 * @param s3 An indication if the solution should be externally or internally * tangent (+1/-1) to c3 * @return The circle that is tangent to c1, c2 and c3. # PROC solve apollonius = ( CIRCLE c1, c2, c3, INT s1, s2, s3 )CIRCLE: BEGIN REAL x1 = x OF c1; REAL y1 = y OF c1; REAL r1 = radius OF c1; REAL x2 = x OF c2; REAL y2 = y OF c2; REAL r2 = radius OF c2; REAL x3 = x OF c3; REAL y3 = y OF c3; REAL r3 = radius OF c3; REAL v11 = 2x2 - 2x1; REAL v12 = 2y2 - 2y1; REAL v13 = x1x1 - x2x2 + y1y1 - y2y2 - r1r1 + r2r2; REAL v14 = 2s2r2 - 2s1r1; REAL v21 = 2x3 - 2x2; REAL v22 = 2y3 - 2y2; REAL v23 = x2x2 - x3x3 + y2y2 - y3y3 - r2r2 + r3r3; REAL v24 = 2s3r3 - 2s2r2; REAL w12 = v12/v11; REAL w13 = v13/v11; REAL w14 = v14/v11; REAL w22 = v22/v21-w12; REAL w23 = v23/v21-w13; REAL w24 = v24/v21-w14; REAL p = -w23/w22; REAL q = w24/w22; REAL m = -w12p-w13; REAL n = w14 - w12q; REAL a = nn + qq - 1; REAL b = 2mn - 2nx1 + 2pq - 2qy1 + 2s1r1; REAL c = x1x1 + mm - 2mx1 + pp + y1y1 - 2py1 - r1r1; # Find a root of a quadratic equation. This requires the circle centers not # # to be e.g. colinear # REAL d = bb-4ac; REAL rs = (-b-sqrt(d))/(2a); REAL xs = m + n rs; REAL ys = p + q * rs; ( xs, ys, rs ) END # solve apollonius # ; CIRCLE c1 = ( 0, 0, 1 ); CIRCLE c2 = ( 4, 0, 1 ); CIRCLE c3 = ( 2, 4, 2 ); # should output "Circle[x=2.00,y=2.10,r=3.90]" (green circle in image) # print( ( TOSTRING solve apollonius( c1, c2, c3, 1, 1, 1 ), newline ) ); # should output "Circle[x=2.00,y=0.83,r=1.17]" (red circle in image) # print( ( TOSTRING solve apollonius( c1, c2, c3, -1, -1,-1 ), newline ) ) END </syntaxhighlight> {{out}} <pre> Circle[x=2.00,y=2.10,r=3.90] Circle[x=2.00,y=0.83,r=1.17] </pre> =={{header\|Arturo}}== Line 1,070 ⟶ 1,168: <pre>Circle[x=2,y=2.1,r=3.9] Circle[x=2,y=0.8333333333333333,r=1.1666666666666667]</pre> =={{header\|EasyLang}}== [https://easylang.online/show/#cod=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 Run it] {{trans\|Java}} <syntaxhighlight> proc solve c1[] c2[] c3[] s1 s2 s3 . r[] . len r[] 3 x1 = c1[1] ; y1 = c1[2] ; r1 = c1[3] x2 = c2[1] ; y2 = c2[2] ; r2 = c2[3] x3 = c3[1] ; y3 = c3[2] ; r3 = c3[3] # v11 = 2 * x2 - 2 * x1 v12 = 2 * y2 - 2 * y1 v13 = x1 * x1 - x2 * x2 + y1 * y1 - y2 * y2 - r1 * r1 + r2 * r2 v14 = 2 * s2 * r2 - 2 * s1 * r1 v21 = 2 * x3 - 2 * x2 v22 = 2 * y3 - 2 * y2 v23 = x2 * x2 - x3 * x3 + y2 * y2 - y3 * y3 - r2 * r2 + r3 * r3 v24 = 2 * s3 * r3 - 2 * s2 * r2 w12 = v12 / v11 w13 = v13 / v11 w14 = v14 / v11 w22 = v22 / v21 - w12 w23 = v23 / v21 - w13 w24 = v24 / v21 - w14 P = -w23 / w22 Q = w24 / w22 M = -w12 * P - w13 N = w14 - w12 * Q a = N * N + Q * Q - 1 b = 2 * M * N - 2 * N * x1 + 2 * P * Q - 2 * Q * y1 + 2 * s1 * r1 c = x1 * x1 + M * M - 2 * M * x1 + P * P + y1 * y1 - 2 * P * y1 - r1 * r1 # D = b * b - 4 * a * c rs = (-b - sqrt D) / (2 * a) r[1] = M + N * rs r[2] = P + Q * rs r[3] = rs . c1[] = [ 0 0 1 ] c2[] = [ 4 0 1 ] c3[] = [ 2 4 2 ] solve c1[] c2[] c3[] 1 1 1 r1[] print r1[] solve c1[] c2[] c3[] -1 -1 -1 r2[] print r2[] # proc circ x y r . . text "" for a = 0 to 360 line x + sin a * r y + cos a * r . . proc draw col c[] . . color col circ c[1] * 10 + 30 c[2] * 10 + 30 c[3] * 10 . background 888 clear linewidth 0.5 color 000 drawgrid move 30 0 line 30 100 move 0 30 line 100 30 draw 000 c1[] draw 000 c2[] draw 000 c3[] sleep 0.5 draw 070 r1[] sleep 0.5 draw 700 r2[] </syntaxhighlight> {{out}} <pre> [ 2 2.10 3.90 ] [ 2 0.83 1.17 ] </pre> =={{header\|Elixir}}== Line 2,135 ⟶ 2,313: 2.000, 2.100, 3.900 2.000, 0.833, 1.167 =={{header\|Lua}}== <syntaxhighlight lang="lua"> function solveApollonius(x1, y1, r1, x2, y2, r2, x3, y3, r3, s1, s2, s3) local v11 = 2x2 - 2x1 local v12 = 2y2 - 2y1 local v13 = x1x1 - x2x2 + y1y1 - y2y2 - r1r1 + r2r2 local v14 = 2s2r2 - 2s1r1 local v21 = 2x3 - 2x2 local v22 = 2y3 - 2y2 local v23 = x2x2 - x3x3 + y2y2 - y3y3 - r2r2 + r3r3 local v24 = 2s3r3 - 2s2r2 local w12 = v12 / v11 local w13 = v13 / v11 local w14 = v14 / v11 local w22 = v22 / v21 - w12 local w23 = v23 / v21 - w13 local w24 = v24 / v21 - w14 local p = -w23 / w22 local q = w24 / w22 local m = -w12p - w13 local n = w14 - w12q local a = nn + qq - 1 local b = 2mn - 2nx1 + 2pq - 2qy1 + 2s1r1 local c = x1x1 + mm - 2mx1 + pp + y1y1 - 2py1 - r1r1 local d = bb - 4ac local rs = (-b - math.sqrt(d)) / (2a) local xs = m + nrs local ys = p + q*rs return xs, ys, rs end </syntaxhighlight> <syntaxhighlight lang="lua"> -- Example usage local x1, y1, r1 = 0, 0, 1 local x2, y2, r2 = 4, 0, 1 local x3, y3, r3 = 2, 4, 2 print(solveApollonius( x1, y1, r1, x2, y2, r2, x3, y3, r3, 1, 1, 1 )) print(solveApollonius( x1, y1, r1, x2, y2, r2, x3, y3, r3, -1, -1, -1 )) --Output: --2.0 2.1 3.9 --2.0 0.83333333333333 1.1666666666667 </syntaxhighlight> =={{header\|Mathematica}}/{{header\|Wolfram Language}}== Line 3,621 ⟶ 3,863: {{trans\|Kotlin}} {{libheader\|Wren-dynamic}} <syntaxhighlight lang="~~ecmascript~~wren">import "./dynamic" for Tuple var Circle = Tuple.create("Circle", ["x", "y", "r"])