How to resolve the algorithm Problem of Apollonius step by step in the CoffeeScript programming language

Published on 12 May 2024 09:40 PM
#Coffeescript

How to resolve the algorithm Problem of Apollonius step by step in the CoffeeScript programming language

Table of Contents

Problem Statement

Implement a solution to the Problem of Apollonius   (description on Wikipedia)   which is the problem of finding the circle that is tangent to three specified circles   (colored black in the diagram below to the right). There is an   algebraic solution   which is pretty straightforward.

The solutions to the example in the code are shown in the diagram   (below and to the right). The red circle is "internally tangent" to all three black circles,   and the green circle is "externally tangent" to all three black circles.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Problem of Apollonius step by step in the CoffeeScript programming language

Source code in the coffeescript programming language

class Circle
  constructor: (@x, @y, @r) ->
 
apollonius = (c1, c2, c3, s1=1, s2=1, s3=1) ->
  [x1, y1, r1] = [c1.x, c1.y, c1.r]
  [x2, y2, r2] = [c2.x, c2.y, c2.r]
  [x3, y3, r3] = [c3.x, c3.y, c3.r]
  
  sq = (n) -> n*n

  v11 = 2*x2 - 2*x1
  v12 = 2*y2 - 2*y1
  v13 = sq(x1) - sq(x2) + sq(y1) - sq(y2) - sq(r1) + sq(r2)
  v14 = 2*s2*r2 - 2*s1*r1

  v21 = 2*x3 - 2*x2
  v22 = 2*y3 - 2*y2
  v23 = sq(x2) - sq(x3) + sq(y2) - sq(y3) - sq(r2) + sq(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 = sq(n) + sq(q) - 1
  b = 2*m*n - 2*n*x1 + 2*p*q - 2*q*y1 + 2*s1*r1
  c = sq(x1) + sq(m) - 2*m*x1 + sq(p) + sq(y1) - 2*p*y1 - sq(r1)

  d = sq(b) - 4*a*c
  rs = (-b - Math.sqrt(d)) / (2*a)
  xs = m + n*rs
  ys = p + q*rs
  
  new Circle(xs, ys, rs)
  
 
console.log c1 = new Circle(0, 0, 1)
console.log c2 = new Circle(2, 4, 2)
console.log c3 = new Circle(4, 0, 1)
 
console.log apollonius(c1, c2, c3)
console.log apollonius(c1, c2, c3, -1, -1, -1)


> coffee foo.coffee 
{ x: 0, y: 0, r: 1 }
{ x: 2, y: 4, r: 2 }
{ x: 4, y: 0, r: 1 }
{ x: 2, y: 2.1, r: 3.9 }
{ x: 2, y: 0.8333333333333333, r: 1.1666666666666667 }

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