Calculate coordinate in 3D triangle.

In summary, the conversation discusses finding the y value for a point D in a three-dimensional triangle with vertices A, B, and C. The suggested solution is to set up a plane equation and insert the known x and z coordinates of point D to solve for y.
  • #1
pjhphysics
16
0
Hi,
I'm looking for an efficient way of achieving the following, but having trouble thinking it through:

Let's say I have a triangle in three dimensions with vertices A, B and C.
Let's say I also have a three dimensional coordinate D. I know the x and z component values for D and I am trying to find the y value such that the point resides on the plane of triangle ABC.

What would be a good way of doing that?

Thanks!
 
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  • #2
You could set up the plane equation

[tex]ax + by +cz + d = 0[/tex]

of the plane containing the triangle ABC, insert the known (x, z) coordinates of your point D and solve for y
 
  • #3
That does it. Thanks a ton
 

1. How do I calculate the coordinates of a point in a 3D triangle?

In order to calculate the coordinates of a point in a 3D triangle, you will need to know the coordinates of the three vertices of the triangle and the coordinates of the point in question. You can then use the formula for barycentric coordinates to determine the coordinates of the point. This formula involves taking the dot products of vectors and solving a system of equations.

2. What is the importance of calculating coordinates in a 3D triangle?

Calculating coordinates in a 3D triangle is important in various fields such as engineering, computer graphics, and physics. It allows us to determine the position of a point in a 3D space and can be used in various calculations and simulations.

3. Can I use the Pythagorean theorem to calculate coordinates in a 3D triangle?

No, the Pythagorean theorem only applies to right triangles in a 2D plane. To calculate coordinates in a 3D triangle, you will need to use the barycentric coordinate formula or other methods such as vector cross products.

4. What are the limitations of calculating coordinates in a 3D triangle?

One limitation of calculating coordinates in a 3D triangle is that it requires the known coordinates of the three vertices of the triangle. If these coordinates are not accurate or known, the calculation will not be accurate. Additionally, the barycentric coordinate formula can become more complex in higher dimensions, making it more difficult to calculate coordinates in higher-dimensional triangles.

5. Are there any tools or software that can help with calculating coordinates in a 3D triangle?

Yes, there are various mathematical software such as MATLAB, Mathematica, and GeoGebra that have built-in functions for calculating coordinates in a 3D triangle. Additionally, there are online calculators and tutorials available that can assist with these calculations.

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