Triangle Interpolation: Find Exact Value

Hi everyone,

I have a triangle with vertices:

coordinates=[0.397500000000000,0.402500000000000,0.400000000000000;0.615285115251741,0.615285115251741,0.619615242270663];

and i know the temperature on each of them:

temperature=[1.228022937634222e+02;1.228022937634234e+02;6.798453477959490e+02];

I would like to find the coordinates of some points (equally spaced including the two on the sides) that have a fixed value of temperature. Let's suppose:

Tfixed=650;

Is there a way to do this?

The same thing must be done on an arbitraty traingle with vertices that could not be symmetric.

Thanks in advance for the reply.

Answer 1

[Daniel Neubauer]

your 2D-triangle with temperature can be treated as a 3d plane defined by the three points in [x y z] such as

vertex=[x y t]

then calculate the equation for the resulting 3d plane and set equal to z=Tfixed.

the resulting line is the equation of all points having the desired temperature.

[John D'Errico]

... and the intersection of that line with the edges of the triangle will produce the desired interpolated points along the edges.

[Riccardo Mari]

Thank you both for the idea! That worked perfectly.