### Converting Between 2D UV and 3D XYZ Coordinates

I have been busy the last couple of days preparing for the upcoming Revit API training in Saudi Arabia. First it was the challenging issue of obtaining a visa on short notice. That happily worked out fine. The last couple of days I spent getting training material ready. It will be interesting to see how it goes, both the training itself and also the visit to this inaccessible country, which according to Wikipedia has some of the most restrictive travel policies in the world.

Meanwhile, here is an interesting little question on converting between the two-dimensional UV coordinates of a face and the three dimensional XYZ coordinates in space:

Question: How can I get the UV coordinates corresponding to the X,Y,Z coordinates of a vertex on a plane? For example, I have the XYZ coordinates of a vertex on a cylindrical plane and want to get the UV coordinates of the point. I want to get the normal to the plane using the UV coordinates.

Answer: I thought it would give me a welcome chance to implement some sample code for you, but unfortunately it seems easy enough to answer just looking at the documentation, with no need for any code or testing.

You ask how to obtain the UV coordinates of the parameterisation of a point on a face, given the XYZ coordinates of the point in 3D space.

Before getting into that, let me mention that some background information on Revit geometry faces and their parameterisations is presented in the discussion of faces and their methods and parameterisation.

Also, for completeness sake, the inverse of what you are asking for, obtaining the XYZ 3D space coordinates from a given UV parameterisation point on the face, is quite trivial and provided by both the Face Evaluate and ComputeDerivatives methods. The former takes the UV point and returns the XYZ, whereas the second returns an entire transform whose origin represents the same XYZ point on the face, the X and Y basis vectors are the tangents in the U and V directions, and the BasisZ vector the face normal at the given point.

Now to address your question: one way that I see to solve it is to use the Face.Project method. It takes an XYZ point in 3D space, which could presumably also be a point on the face itself, and projects it onto the face. If it already lies on the face, I would expect the resulting intersection will be identical to the input point.

The point of this, though (please excuse the pun) is that the method returns an IntersectionResult instance. That in turn provides a UVPoint property, which gives you the 2D UV parameters on the face of the point of intersection. The IntersectionResult may also be used to return intersection results for curves, in which case the UVPoint property information may even just be one-dimensional instead of two-dimensional.