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I am studying computer science and I am working on a project for my next semester. I am stuck with a problem and I am not that good in math. Imagine I have an "arm" shape line where it has 5 nodes A, B, C, D and E. 4 of these nodes have an angle b, c, d, e where A, the 5th node, is the end of this arm.

How can I calculate x for this graph:

enter image description here

And how could I prevent this or solve this case where x did not change:

enter image description here

So generally, What is the math behind calculating the distance x of my end node A whatever the shape of my arm and however it moves?

Rodrigo de Azevedo
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Kyle Khalaf
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  • Technically you will want to get the coordinates of $A$, then project it orthogonally to the surface somehow. To arrive at $A$, knowing the angles $b,c,d,e$ is not enough, we need to know the distances as well. How is the surface given? – Berci Jul 02 '16 at 20:27
  • @Berci Right and let's assume that distances are fixed, if you mean for the arm parts ED, DC, CB and BA and assume they are L1, L2, L3, L4 respectively. Do we still need the distance from the Surface oint to node E? – Kyle Khalaf Jul 02 '16 at 20:31
  • Well, it depends what we know about the surface. In this generality I doubt you would find a simple formula for the problem. – Berci Jul 02 '16 at 20:42
  • The shape of the surface most definitely affects the distance from $A$ to it. – Fimpellizzeri Jul 02 '16 at 21:14
  • @Fimpellizieri sure. And the main goal is to analyze the shape of the surface. Here I am assuming first that it is a flat surface – Kyle Khalaf Jul 02 '16 at 22:20
  • It would be good to specify what kind of surface it is. Are we to suppose it is a rectangle? How far from a corner is point $E$? There are far too many variables unspecified right now. As is, the problem is underdetermined. – Fimpellizzeri Jul 02 '16 at 22:24
  • @Fimpellizieri What are the needed variables? What are the information that I am missing? And why at this point the matter of the surface still matters? – Kyle Khalaf Jul 02 '16 at 22:26
  • I meant kind as in shape. The location of point $E$ is also needed. – Fimpellizzeri Jul 02 '16 at 22:31
  • @Fimpellizieri so my question is: if location of E is given, so the surface point location is known, what would be the equation to find x? – Kyle Khalaf Jul 03 '16 at 00:43
  • AS starter - assume E coordinates. Using angel b and distance DE, find coordinates of D. From D find C and than follow to B and finally get A coordinates. Than you need the surface information (line definition) to get distance from it. – Moti Jul 03 '16 at 17:34

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