This is an unofficial implementation of the following publication:

Seamless surface mappings
Noam Aigerman, Roi Poranne, and Yaron Lipman
ACM Transactions on Graphics 34(4), Article No. 72 (August 2015)
https://doi.org/10.1145/2766921

See build.yml for the steps to build the application.

As in the original paper, the code depends on the Second-Order Cone Programming (SOCP) solver provided by MOSEK. To run the main executable seamlesssurfmap, you need to have the license file mosek.lic installed on your system. You can get a Personal Academic License at https://www.mosek.com/products/academic-licenses/ for free.

The build process generates a few executable files, among which landmarker and seamlesssurfmap are mainly useful.

Common to these two executables, the two surface models, A and B, should be placed in a common directory (called data directory) as A-orig.obj and B-orig.obj. Through the various computational steps in the pipeline, the executables generate some intermediate files named as A-xxx.obj (e.g., A-disk.obj, B-gmap.obj).

A list of pairs of corresponding landmark vertices should be given in a file landmarks.txt in the data directory. landmarker is a small interactive OpenGL utility for easily creating these landmark pairs (as well as cutting high-genus surfaces into genus zero). landmarks.txt is created by landmarker (or by any other means) and is read by seamlesssurfmap as an input.

seamlesssurfmap computes a G-mapping between the two models (written as A-gmap.obj and B-gmap.obj), and computes images of A's vertices onto B as barycentric coordinates (written as AtoB.txt) and vice versa (BtoA.txt). The two files AtoB.txt and BtoA.txt are in the so-called IJV-triplet sparse matrix format which is assumed as input to the Compatible Intrinsic Triangulations code. seamlesssurfmap also generates AonB.obj as a quick vizualization of AtoB.txt by mapping the vertices in A-orig.obj onto B using the vertex image (and vice versa).

Synopsis:

  landmarker {OPTIONS}

  OPTIONS:

      --data-dir=[path]                 Path to the data directory to read from
                                        / write to (default: current directory)
      --white-background                Use white background instead of vertical
                                        color gradient
      --write-normalized                Write area-normalized mesh as
                                        *-normalized.obj

• ALT + drag: Rotate
• SHIFT + ALT + drag: Zoom
• CTRL + ALT + drag: Pan
• C key: Change camera center to cursor position

(This step is skipped for genus zero models.)

For high genus models with one or more handles, those handles need to be cut open so that the surface genus becomes zero (with boundary loops regarded as virtual faces). To cut along a handle, SHIFT + click on each model to specify a landmark to be cut, and press ENTER to perform handle cutting.

To choose a tunnel loop rather than a handle loop for the cutting, use CTRL + ENTER.

These landmarks specified on handles are called handle landmarks and treated differently than other (normal) landmarks.

After cutting all the handles, the executable generates A-genus0.obj and B-genus0.obj which are read by seamlesssurfmap. The vertex indices in landmarks.txt refer to the mesh topology in the genus zero surfaces (where vertices along the cut loops are duplicated).

• SHIFT + click: Specify a landmark on each model, and ENTER to confirm the landmark pair.

• SHIFT + CTRL + click: Delete the landmark pair.

• Drag: Shift a landmark to a nearby vertex.

• CTRL + click: (for high genus models only) Switch between the two possible pair assignments for a handle landmark.

Synopsis:

  seamlesssurfmap {OPTIONS}

  OPTIONS:

      --data-dir=[path]                 Path to the data directory to read from
                                        / write to (default: current directory)
      --num-iter=[integer]              Number of iterations for G-mapping
                                        optimization. Negative value means to
                                        iterate indefinitely (default: -1).
      --debug-output                    Enable outputting debug files
      --dont-refine                     Do not perform triangle refinement
                                        around landmarks and between close-by
                                        seams (increases chance of failure)

By default (without this flag), the program refines the mesh locally around each landmark vertex so that more triangles are available. This is to lower the possibility of the algorithm failing due to too few triangles available around landmark vertices which may make it impossible to have the final G-mapping completely free of flipped triangles. The refinement process generates a few additional meshes (X-orig-refined.obj and X-disk-refined.obj, and X-genus0-refined.obj for high genus cases), and the resulting barycentric coordinate files (AtoB.txt and BtoA.txt) are with respect to the refined meshes (A-orig-refined.obj and B-orig-refined.obj).