Data update

Task/Problem-of-Apollonius/ALGOL-68/problem-of-apollonius.alg

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+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 = 2*x2 - 2*x1;
+            REAL v12 = 2*y2 - 2*y1;
+            REAL v13 = x1*x1 - x2*x2 + y1*y1 - y2*y2 - r1*r1 + r2*r2;
+            REAL v14 = 2*s2*r2 - 2*s1*r1;
+
+            REAL v21 = 2*x3 - 2*x2;
+            REAL v22 = 2*y3 - 2*y2;
+            REAL v23 = x2*x2 - x3*x3 + y2*y2 - y3*y3 - r2*r2 + r3*r3;
+            REAL v24 = 2*s3*r3 - 2*s2*r2;
+
+            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 = -w12*p-w13;
+            REAL n = w14 - w12*q;
+
+            REAL a = n*n + q*q - 1;
+            REAL b = 2*m*n - 2*n*x1 + 2*p*q - 2*q*y1 + 2*s1*r1;
+            REAL c = x1*x1 + m*m - 2*m*x1 + p*p + y1*y1 - 2*p*y1 - r1*r1;
+
+            # Find a root of a quadratic equation. This requires the circle centers not #
+            # to be e.g. colinear                                                       #
+            REAL d  = b*b-4*a*c;
+            REAL rs = (-b-sqrt(d))/(2*a);
+            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

Task/Problem-of-Apollonius/Lua/problem-of-apollonius-1.lua

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+function solveApollonius(x1, y1, r1, x2, y2, r2, x3, y3, r3, s1, s2, s3)
+	local v11 = 2*x2 - 2*x1
+	local v12 = 2*y2 - 2*y1
+	local v13 = x1*x1 - x2*x2 + y1*y1 - y2*y2 - r1*r1 + r2*r2
+	local v14 = 2*s2*r2 - 2*s1*r1
+
+	local v21 = 2*x3 - 2*x2
+	local v22 = 2*y3 - 2*y2
+	local v23 = x2*x2 - x3*x3 + y2*y2 - y3*y3 - r2*r2 + r3*r3
+	local v24 = 2*s3*r3 - 2*s2*r2
+
+	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 = -w12*p - w13
+	local n = w14 - w12*q
+
+	local a = n*n + q*q - 1
+	local b = 2*m*n - 2*n*x1 + 2*p*q - 2*q*y1 + 2*s1*r1
+	local c = x1*x1 + m*m - 2*m*x1 + p*p + y1*y1 - 2*p*y1 - r1*r1
+
+	local d = b*b - 4*a*c
+	local rs = (-b - math.sqrt(d)) / (2*a)
+	local xs = m + n*rs
+	local ys = p + q*rs
+
+	return xs, ys, rs
+end

Task/Problem-of-Apollonius/Lua/problem-of-apollonius-2.lua

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+-- 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