Deriving an angle from three points

gmccarthy gmccarthy at people.net.au
Wed Dec 16 05:07:46 EST 2009


By the way again, Mark's method is also correct if you fix the variable names
as shown below.
Normally a triangle with points ABC have their sides named with side b
between A and C so it is opposite angle B...etc.

on mouseUp
   put cd fld "A" into pointA
   put cd fld "B" into pointB -- assumed center of angle
   put cd fld "C" into pointC
   -- 
   -- get the lengths of the three sides of the triangle
   put SideLength(pointA, pointB) into lengthC
   put SideLength(pointB, pointC) into lengthA
   put SideLength(pointA, pointC) into lengthB
   
   --calculate the angle as arccos( (b2+c2-a2) / 2bc)
   --the other two angles are arccos( (a2+c2-b2) / 2ac)
   -- and arccos( (a2+b2-c2) / 2ab)
   put (lengthA * lengthA) + (lengthC * lengthC) - (lengthB * lengthB) into
tSub
   put acos(tSub / (2 * lengthA * lengthC))  into tRadians
   put (tRadians * 180 / pi) into cd fld "AngleABC"-- convert from radians
to degrees
end mouseUp

-- calculate (x2-x1)^2 + (y2-y1)^2
-- return the square root of that
function SideLength pPointA, pPointB
    local lengthX, lengthY
   
    set the itemdelimiter to comma
    put item 1 of pPointB - item 1 of pPointA into lengthX
    put lengthX * lengthX into lengthX -- x squared
    put item 2 of pPointB - item 2 of pPointA into lengthY
    put lengthY * lengthY into lengthY -- y squared
    return sqrt(lengthX + lengthY) -- length of hypotenuse
end SideLength 
-- 
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