Vector math - find a location on a triangular face

[ThinkInvisible]

I have three points that are all the same distance from each other on the XY plane (grid of points).
Each one has a different height. The heights can be negative and can have extreme differences.
I also have an X position and a Y position on this plane. I need to find the height of this point, interpolated from the other three.
How do?

Cluttered diagram:

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[!Trinick]

Hm. I have no idea how to do this, so I'll think about it and get back to you with an answer that makes sense in an hour or so.

Code: [Select]

$one = "10 10 -2";
$two = "20 10 50";
$three = "10 20 -50";

function calculateHeight(%x, %y)
{
    %two = vectorSub($two, $one);
    %three = vectorSub($three, $one);
    %xp = %x / getWord(%two, 0);
    %yp = %y / getWord(%three, 1);
    %xp *= getWord(%two, 2);
    %yp *= getWord(%three, 2);
    %height = %xp + %yp;
    %height += getWord($one, 2);
    return %height;
}

That's my first attempt, not sure if it'll work but I can't test it because I can't access Blockland right now.

[Ipquarx]

Wait, is this supposed to represent a 3d triangle, and you're trying to find the height of a single point on the triangle?

[phflack]

3 points all the same distance from eachother -> equilateral triangle?
not quite sure what you're trying to figure out though

3 points making a triangle, and then a 4th you're trying to figure out the height of?

[Treynolds416]

MSPaint to the rescue!



The random point is on the same plane as the three triangle vertices

[ThinkInvisible]

Never mind, got it myself.
For every square defined by two triangles:
 gridone = 0, 0 (upper left corner)
 gridtwo = 1, 0 (x axis)
 gridthree = 0, 1 (y axis)
 gridfour = 1, 1 (lower right corner)

Code: [Select]

function getGridHeight(%x, %y, %gridone, %gridtwo, %gridthree, %gridfour) {
 %xp = lerp(%gridone, %gridtwo, %x);
 %xb = lerp(%gridthree, %gridfour, %x);
 return lerp(%xp, %xb, %y);
}

function lerp(%a, %b, %x) {
 return %a + %x * (%b - %a);
}