Triangle Interpolation: Find Exact Value

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Riccardo Mari
Riccardo Mari 2022-11-4
评论： Riccardo Mari 2022-11-7
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.

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采纳的回答

Daniel Neubauer
Daniel Neubauer 2022-11-4
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.
  2 个评论
John D'Errico
John D'Errico 2022-11-4
... and the intersection of that line with the edges of the triangle will produce the desired interpolated points along the edges.
Riccardo Mari
Riccardo Mari 2022-11-7
Thank you both for the idea! That worked perfectly.

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