# Signpost Intrinsic Triangulation

The signpost data structure encodes an intrinsic triangulation by storing “signposts” at mesh vertices. Explicitly, for each intrinsic edge it stores the edge’s length and direction at the two incident vertices. This information fully specifies how the intrinsic triangulation sits above the input mesh. For more details, see Navigating Intrinsic Triangulations.

The SignpostIntrinsicTriangulation is one concrete implementation (subclass) of intrinsic triangulations. Most of its functionality is documented there. Here, we document additional routines which are specific to signposts.

The signpost intrinsic triangulation is one of the two main intrinsic triangulation representations currently available in geometry-central, the other being integer coordinates. For many tasks, either reprentation will be highly effective, but there are some tradeoffs.

Pros:

• Performance. Signposts are moderately faster in terms of runtime than integer coordinates (although both are often on the order of milliseconds).

• Tangent vector data. Signposts naturally offer tangent space coordinate systems which are consistent with the input mesh, making it easy to work with tangent-valued data at vertices of the intrinsic triangulation.

Cons:

• Robustness. The representation relies heavily on tracing intrinsic edge paths across the input surface, which can be error-prone in floating-point arithmetic. In particular, reconstructing the common subdivision may fail if the input contains degenerate triangles.

### Constructors

SignpostIntrinsicTriangulation::SignpostIntrinsicTriangulation(ManifoldSurfaceMesh& mesh, IntrinsicGeometryInterface& inputGeom)

Initialize an intrinsic triangulation sitting on top of mesh. Recall that IntrinsicGeometryInterface can be almost any geometry object, including a VertexPositionGeometry.

Initially, the intrinsic triangulation will be identical to the input mesh; it can be modified with the routines below.

### Methods

std::vector<SurfacePoint> SignpostIntrinsicTriangulation::traceIntrinsicHalfedgeAlongInput(Halfedge intrinsicHe, bool trimEnd)

This function is generally the same as traceIntrinsicHalfedgeAlongInput().

When edges paths from signposts, the path often does not exactly hit the destination vertex, but rather ends somewhere very close in the adjacent 1-ring. If trimEnd=true, a simple heuristic is used to clean up the path so it exactly hits the target vertex; with trimEnd=false the result of tracing is directly reported.

By default traceIntrinsicHalfedgeAlongInput(he) is equivalent to traceIntrinsicHalfedgeAlongInput(he, true).

## Citation

@article{sharp2019navigating,
title={Navigating intrinsic triangulations},
author={Sharp, Nicholas and Soliman, Yousuf and Crane, Keenan},
journal={ACM Transactions on Graphics (TOG)},
volume={38},
number={4},
pages={55},
year={2019},
publisher={ACM}
}