This node computes UV maps that measure distance and direction along a surface. This can be useful for applying masking, decaling, and surface traversal operations that are based on these attributes. These UV coordinates can also be reliably generated without much user input, making them suitable for procedural UV map generation. This node assigns to each vertex a UV coordinate describing the tangent vector from the point in the source group that is closest to it. It uses a distance measured along the surface, not through 3D space. From the source point, if you follow the shortest path along the surface pointing in the direction of a vector, it will terminate at the vertex. This results in the lines of constant angle through the origin describe the geodesics from the source point (pink/purple lines) and the circles of constant radius describe the geodesic disks centered at the source point (red/yellow lines).

When multiple source points are specified, the UV coordinates describe the distance and direction from the closest source point. This means it computes Voronoi diagrams on surfaces along with UV coordinates to the generating points. Vertices that are not reachable from any of the points in the source group will not be assigned any UV coordinates and their existing UV coordinates will not be modified).

These UV maps are known in mathematics as geodesic normal coordinates or surface logarithmic maps (closely related to the exponential map). They can be thought of as surface polar coordinates. Two methods are available that provide a tradeoff between computational cost and accuracy.

• The direction to the nearest source point can be computed as an angle f@theta = atan2(v@uv[1], v@uv[0]) and the distance can be computed as f@dist = length(v@uv). For this to hold, the source points need to be placed at the origin in UV space using the None layout option. The node enforces this property and will produce overlapping UV islands. Further separation of the islands can be achieved using UV Layout.

• This method only works for flattening portions of manifold surfaces, meaning distances and directions cannot be tracked across non-manifold edges or points. Non-manifold edges and points are interpreted as though being cut away from the surface, leaving narrow slits or tiny holes in their places.

• The Fast method is useful if the source points are modified frequently, e.g. in a loop network. Once you modify the source group, it maintains a cache to recompute the UV flattening quickly and with the same accuracy.

• Surface Voronoi diagrams and their boundary seams are byproducts of the computation. They can be computed (without any UV coordinates) by using the Only Seams method.

• Unlike UV Flatten, this node does not produce an angle-preserving (conformal) flattening. As a result, there may be high distortion far away from the source points. Options for pruning the high distortion regions from the parameterization are provided through the post-processing tab. The maximal amount of distortion will be found near the cut locus, the set of points that have more than one shortest path back to the source point.