// Formulae for simple plane geometry.

// Find the length of the hypotenuse of a right triangle given sides a and b.
hypotenuseLength[a, b] := sqrt[a^2 + b^2]

// Calculate area of arbitrary triangle given 3 sides of known length.
// Calculate using Heron's formula.
triangleArea[a, b, c] :=
{
   // Semiperimeter s
   s = 1/2 (a + b + c)

   area = sqrt[s (s-a) (s-b) (s-c)]

   return area
}


// Find the distance between a point (x0,y0) and a line specified by
// two points (x1, y1), (x2, y2)
pointToLineDistance[x0, y0, x1, y1, x2, y2] :=
{
   abs[ (x2-x1)(y1-y0) - (x1-x0)(y2-y1)] / sqrt[(x2-x1)^2+(y2-y1)^2 ]
}


// Returns true if a point is inside a polygon.
// Adapted from
// http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html
//
// points is an array of two-dimensional arrays of points.
// x,y is the point to test.
//
// Returns:
//   true if [x,y] is inside the polygon, false otherwise.
pointInPolygon[points, x, y] :=
{
   c = false
   i = 0
   npol = length[points]
   j = npol-1
   while i < npol
   {
      xi = points@i@0
      xj = points@j@0
      yi = points@i@1
      yj = points@j@1
      if ((((yi<=y) and (y<yj)) or ((yj<=y) and (y<yi))) and (x < (xj - xi) * (y - yi) / (yj - yi) + xi))
         c = !c
      j = i
      i = i + 1
   }

   return c;
}


"Geometry.frink included OK"