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I have met problem where I need to calculate coordinates of x and y of graph or shape given only length between points I could find solutions like to calculate it for triangle shape Given that we know the lengths of the sides etc. but I could not find a solution that can calculate x and y of any possible graph or shape so Is it possible to convert shape or graph from all length sides to x and y coordinates like triangle

Chris Godsil
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Mohamed Abo AL Kear
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  • What do you mean by "length between points"? How are the points given? – saulspatz Jun 11 '21 at 16:04
  • I mean like sides of the shape – Mohamed Abo AL Kear Jun 11 '21 at 16:09
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    It isn't enough. Knowing the lengths of the sides of a quadrilateral doesn't determine the quadrilateral. Think of a square and a non-square rhombus with the same side length. – saulspatz Jun 11 '21 at 16:10
  • I know that it is not enough , this why I am asking if it is possible ....as with triangle we used the shape information it self but when the shape become unknown ...is it possible that we supposed something that can help this what I want to know – Mohamed Abo AL Kear Jun 11 '21 at 16:13
  • The sides and the angles between the sides given in order, would be enough, obviously. – saulspatz Jun 11 '21 at 16:18
  • Oh I figured this unfortunately i have only length between any two points combination in the shape this why I mentioned graph ... thanks you – Mohamed Abo AL Kear Jun 11 '21 at 16:21

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There is no unique solution. For example, say you have a polygon with four sides, all of length $a$. You would think that it's a square, but it does not have to be. Any rhombus with a side $a$ will work. So even if you fix two adjacent points, the other two are unknown.

Andrei
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  • If we supposed that we have fully graph connections of this shape where we have the length of all two points combination is it still impossible to calculate the coordinates – Mohamed Abo AL Kear Jun 11 '21 at 16:17
  • If you have all the lengths, there are only two ways to construct the polygon. Same as for a triangle. If you have two points and the distance to the third, you can construct the triangle on any side of the line. – Andrei Jun 11 '21 at 16:42
  • sorry for late response ,Yes I have just figured this out ...you are right the only way by suppose that one point is (0,0) then the nearest one is on same Axis x by length then we calculate each next point using those two or new ones created .... Thanks for the answer – Mohamed Abo AL Kear Jun 11 '21 at 18:57