This separates the UV reverse sampling and the barycentric mixing of
the mesh attribute into separate multi-functions. This separates
concerns and allows for future de-duplication of the UV sampling
function if that is implemented as an optimization pass. That would
be helpful since it's the much more expensive operation.
This was simplified by returning the triangle index in the reverse
UV sampler rather than a pointer to the triangle, which required
passing a span of triangles separately in a few places.
The case when the query uv is almost on an edge but outside of any
triangle was handled before. Now the case where the query uv is
almost on an edge but inside more than one triangle is handled as well.
Allow for a small epsilon to improve handling of uvs that are on edges.
Generally, when using reverse uv sampling, we expect that the sampling
is supposed to succeed.
This implements the new way to attach curves to a mesh surface using
a uv map (based on the recent discussion in T95776).
The curves data block now not only stores a reference to the surface object
but also a name of a uv map on that object. Having a uv map is optional
for most operations, but it will be required later for animation (when the
curves are supposed to be deformed based on deformation of the surface).
The "Empty Hair" operator in the Add menu sets the uv map name automatically
if possible. It's possible to start working without a uv map and to attach the
curves to a uv map later on. It's also possible to reattach the curves to a new
uv map using the "Curves > Snap to Nearest Surface" operator in curves sculpt
mode.
Note, the implementation to do the reverse lookup from uv to a position on the
surface is trivial and inefficient now. A more efficient data structure will be
implemented separately soon.
Differential Revision: https://developer.blender.org/D15125
