2016 Update

Task/Problem-of-Apollonius/00DESCRIPTION

@@ -1,3 +1,7 @@
-Implement a solution to the Problem of Apollonius ([[wp:Problem_of_Apollonius|description on wikipedia]]) which is the problem of finding the circle that is tangent to three specified circles. There is an [[wp:Problem_of_Apollonius#Algebraic_solutions|algebraic solution]] which is pretty straightforward. The solutions to the example in the code are shown in the image (the red circle is "internally tangent" to all three black circles and the green circle is "externally tangent" to all three black circles).
+[[File:Apollonius.png|400px|Two solutions to the problem of Apollonius|right]]
 
-[[File:Apollonius.png|200px|Two solutions to the problem of apollonius]]
+;Task:
+Implement a solution to the Problem of Apollonius   ([[wp:Problem_of_Apollonius|description on Wikipedia]])   which is the problem of finding the circle that is tangent to three specified circles.   There is an [[wp:Problem_of_Apollonius#Algebraic_solutions|algebraic solution]] which is pretty straightforward.
+
+The solutions to the example in the code are shown in the image (below and right).   The red circle is "internally tangent" to all three black circles, and the green circle is "externally tangent" to all three black circles.
+<br><br>

Task/Problem-of-Apollonius/PowerShell/problem-of-apollonius-1.psh

@@ -0,0 +1,69 @@
+function Measure-Apollonius
+{
+    [CmdletBinding()]
+    [OutputType([PSCustomObject])]
+    Param
+    (
+        [int]$Counter,
+        [double]$x1,
+        [double]$y1,
+        [double]$r1,
+        [double]$x2,
+        [double]$y2,
+        [double]$r2,
+        [double]$x3,
+        [double]$y3,
+        [double]$r3
+    )
+
+    switch ($Counter)
+    {
+        {$_ -eq 2} {$s1 = -1; $s2 = -1; $s3 = -1; break}
+        {$_ -eq 3} {$s1 =  1; $s2 = -1; $s3 = -1; break}
+        {$_ -eq 4} {$s1 = -1; $s2 =  1; $s3 = -1; break}
+        {$_ -eq 5} {$s1 = -1; $s2 = -1; $s3 =  1; break}
+        {$_ -eq 6} {$s1 =  1; $s2 =  1; $s3 = -1; break}
+        {$_ -eq 7} {$s1 = -1; $s2 =  1; $s3 =  1; break}
+        {$_ -eq 8} {$s1 =  1; $s2 = -1; $s3 =  1; break}
+        Default    {$s1 =  1; $s2 =  1; $s3 =  1; break}
+    }
+
+    [double]$v11 = 2 * $x2 - 2 * $x1
+    [double]$v12 = 2 * $y2 - 2 * $y1
+    [double]$v13 = $x1 * $x1 - $x2 * $x2 + $y1 * $y1 - $y2 * $y2 - $r1 * $r1 + $r2 * $r2
+    [double]$v14 = 2 * $s2 * $r2 - 2 * $s1 * $r1
+
+    [double]$v21 = 2 * $x3 - 2 * $x2
+    [double]$v22 = 2 * $y3 - 2 * $y2
+    [double]$v23 = $x2 * $x2 - $x3 * $x3 + $y2 * $y2 - $y3 * $y3 - $r2 * $r2 + $r3 * $r3
+    [double]$v24 = 2 * $s3 * $r3 - 2 * $s2 * $r2
+
+    [double]$w12 = $v12 / $v11
+    [double]$w13 = $v13 / $v11
+    [double]$w14 = $v14 / $v11
+
+    [double]$w22 = $v22 / $v21 - $w12
+    [double]$w23 = $v23 / $v21 - $w13
+    [double]$w24 = $v24 / $v21 - $w14
+
+    [double]$P = -$w23 / $w22
+    [double]$Q = $w24 / $w22
+    [double]$M = -$w12 * $P - $w13
+    [double]$N = $w14 - $w12 * $Q
+
+    [double]$a = $N * $N + $Q * $Q - 1
+    [double]$b = 2 * $M * $N - 2 * $N * $x1 + 2 * $P * $Q - 2 * $Q * $y1 + 2 * $s1 * $r1
+    [double]$c = $x1 * $x1 + $M * $M - 2 * $M * $x1 + $P * $P + $y1 * $y1 - 2 * $P * $y1 - $r1 * $r1
+
+    [double]$D = $b * $b - 4 * $a * $c
+
+    [double]$rs = (-$b - [Double]::Parse([Math]::Sqrt($D).ToString())) / (2 * [Double]::Parse($a.ToString()))
+    [double]$xs = $M + $N * $rs
+    [double]$ys = $P + $Q * $rs
+
+    [PSCustomObject]@{
+        X      = $xs
+        Y      = $ys
+        Radius = $rs
+    }
+}

Task/Problem-of-Apollonius/PowerShell/problem-of-apollonius-2.psh

@@ -0,0 +1,4 @@
+for ($i = 1; $i -le 8; $i++)
+{
+    Measure-Apollonius -Counter $i -x1 0 -y1 0 -r1 1 -x2 4 -y2 0 -r2 1 -x3 2 -y3 4 -r3 2
+}