> On 4 Jul 2003 09:59:39 GMT, Hans-Bernhard Broeker

> >I'm quite certain that won't help him, because he's not using a single

> >matrix to transform all vertices by, in the first place.

Right, each vertex is transformed using a different matrix.

Quote:> But assume the question means find a matrix that

> transforms the plane of a, b, c into the plane of a', b', c'; and all

> the mess about A, B, and C is just to indicate we're not given an

> explicit point-to-point transform.

I'm sorry for not being clear. Yes, I am looking for the matrix that

transforms the plane of a b c into the plane of a' b' c'.

Quote:> But before I spend time solving the wrong problem, I'd like OP to tell

> us what this is really about. What's the bigger problem this is a part

> of, because it's an unusual question.

Essentially, it is related to skinning of skeletally articulated

meshes. Each vertex is affected by a set of bone transforms, each

represented by a matrix, which are then added together to form a

transformation matrix for the vertex itself. These are the A B and C

matrices from my original post.

Now of course, for just skinning a mesh, you don't really care about

the plane itself, just transform the vertices and render the

corresponding triangles. The reason I am looking for an answer to

this more complicated question has to do with some ideas I have for

analyzing properties of deformable meshes. One thing that I would

like to be able to do is, given a point relative to the local

coordinate system of a deformed triangle/plane, transform it back into

the coordinate system of the plane in the reference model, which can

then be easily converted into world coordinates. For this, it would be

great to just have the matrix that transforms the reference plane into

the deformed plane, which I can then invert.

Thanks to everyone for taking a look at this.

Chris DeCoro