Re: Barycentric to cartesian?


"Kaba" <none@xxxxxxxx> wrote in message
news:MPG.22eeba963e34b3f19896d5@xxxxxxxxxxxxxxxxx
Ron Francis wrote:
When finding an intersection of a line and a triangle I find the point on
the plane and then determine if it is in the triangle.
I have been reading some stuff which id supposed to do it more
efficiently,
but it leaves me with barycentric coordinates (t,u,v).
I haven't used these before and couldn't find any information on
converting
back to cartesian.
Sorry if this is a stupid question, but is it possible?
If so, how can I do it?

Your choice of names for the ordinates suggests you are actually using
the Moller-Trumbore ray-triangle intersection algorithm. In that case,
(t, u, v) are not barycentric coordinates. The barycentric coordinates
are (u, v, 1 - (u + v)), while t is the parameter of the ray. You can
use either to get the point of intersection (t is along the ray, the
barycentric coordinates are along the triangle). Barycentric coordinates
are useful to interpolate values along the triangle, position being just
one example.

Kaba,
Thanks for responding.
My apologies, you are right, I was looking at the Moller-Trumbore algorithm
and with a little further study I found that 't' wasn't one of the
coordinates.
In the case of intersecting a triangle with a ray, it is simple for me to
use 't' to find the Cartesian point because I already have the origin and
vector, however I'm also thinking ahead to textures on triangles that change
shape, interpolating normals when looking at a pixel in a triangle for
reflections etc., so this has created some interest for me in the
barycentric system.
So, even though my original question is no longer urgent, I am still
interested in knowing how to convert from barycentric to cartesian if, for
example, I have a triangle vertices A,B,C, and barycentric coordinates (u,
v, 1 - (u + v))?

I must warn you though that maths is not one of my strong points, especially
converting from notation to algorithm, but I try.

Regards,
Ron Francis
www.RonaldFrancis.com





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