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I need to find the y coordinate of a given point on a triangle in 3D space. If I'm not mistaken the equation for a plane is: $$ \left|\begin{matrix}x-A_x & y -A_y & z-A_ z \\ B_x-A_x & B_y -A_y & B_z-A_ z\\ C_x-A_x & C_y -A_y & C_z-A_ z\end{matrix}\right|=0. $$

So if I have the x and the z coordinate of a point on the plane and three points A, B and C which is on the plane how do I calculate the y of my coordinate? Basically as far as I can tell, what I'm trying to achieve is to isolate the y coordinate. (Resulting in a an equation of the form: y = ...) Can somebody help me out here? Thanks

I have found an answer where someone achieves basically what I want but for the z coordinate: https://math.stackexchange.com/a/851752/684967

Also extra points for pointing me in the direction of how to calculate this would be much appreciated. I would love to understand it! :)

(Here I'm talking an explanation of how to calulate the above. I'ts all greek to me)

CoolMcGrrr
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  • See how to compute a matrix. What is a point on a triangle? – Moti Jul 04 '19 at 16:22
  • I've updated my question with a (hopefully) better description of what I'm trying to achieve. – CoolMcGrrr Jul 06 '19 at 09:02
  • It is still not well defined - for every triple pair there are infinite y's that will allow you make a triangle. – Moti Jul 07 '19 at 00:57
  • Alright. I think I've done a poor job of explaining. I've included a link to a question that achieves some of the same i want here. And I've added an extra explanation to what I'm trying to achieve. But just to clarify. I know what A,B and C are when calculating the result. :) – CoolMcGrrr Jul 08 '19 at 07:58
  • Plug the x and z into the equation for the plan and solve for y. – Moti Jul 08 '19 at 15:32

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