Skip to content
Go to file

Latest commit


Git stats


Failed to load latest commit information.
Latest commit message
Commit time



A tetrahedral mesh generator based on Jonathon Shewchuk's isosurface stuffing 
algorithm in combination with the A15 acute tetrahedral tile.

written by:
Robert Bridson (
Crawford Doran (


Quartet converts a watertight triangle mesh into a high-quality uniform 
tetrahedral mesh that closely approximates the geometry, up to the curvature 
implied by the specified grid sampling (dx). Optionally, the tetrahedral mesh 
can be warped to match sharp features on the input, and also improved by a 
quality optimization pass.

Building Quartet

1) It may be necessary to edit Makefile.defs in order to ensure that 
   platform-specific variables are set correctly. These include the compiler,
   linker, and all flags associated with them, including libraries.
2) Run 'make depend'
3) Run 'make' and/or 'make release' ('make' is equivalent to 'make debug')

Running Quartet

Quartet is run from the command line with the following syntax:

quartet <input.obj> <dx> <output.tet> [-f <feature.feat>] [-a <angle_threshold>]
[-s <surface.obj>] [-i] [-o]

- <input.obj> is the OBJ file containing the surface to be converted to a 
  tetrahedral mesh.
- <dx> is the grid spacing used in the isosurface stuffing algorithm. The 
  generated tetrahedra will be approximately this size.
- <output.tet> is a path to the file where the resulting tetrahedral mesh will 
  be saved.

The optional flags have the following effects:
-f <features.feat>   -- The given file <features.feat> contains lists of 
                        points and edges indicating sharp corners and ridges 
                        in the input. The output mesh will resolve these 
                        features as well as possible.
-a <angle_threshold> -- Auto-detects sharp features in the input.  Edges with
                        a dihedral angle smaller than <angle_threshold> degrees
                        will be resolved in the output as well as possible.
                        In addition, these features will be written to a file
                        called 'auto.feat' (which can then be fed to the -f 
                        option in future executions).
-s <surface.obj>     -- The boundary of the resulting tetrahedral mesh is
                        written to <surface.obj>.  This is largely for 
                        convenience of visualizing the result.
-i                   -- Intermediate stages of the mesh generation process are
                        saved to disk in files named 'N_*_.tet' where N is the 
                        numbering of the steps.
-o                   -- Perform quality optimization on the resulting 
                        tetrahedral mesh.

Example inputs can be found in the 'meshes' directory.  For the inputs with
sharp features, corresponding .feat files are provided.

Example usages:
quartet dragon.obj 0.01 dragon_01.tet -o -s dragon.obj
quartet fandisk.obj 0.1 fandisk_1.tet -f fandisk.feat
quartet block.obj 0.5 block_5.tet -a 110.0 -o

Running view_tet

We have included an OpenGL viewer application for visualizing resulting tet 
meshes.  The viewer is called view_tet, and can be called with the following 

view_tet <input.tet> [-s] [-f <features.feat>] [-p (x|y|z)<cutting-plane-pos>]*
[-w <num_tets>]

Here, <input.tet> is the TET file produced by quartet containing the tet mesh.

The optional flags have the following effects:
-s                            -- Assume that <input.tet> is actually
                                 <input.obj> and read it in as a surface
                                 mesh from an OBJ file.
-f <features.feat>            -- Displays the sharp features in the file
                                 <features.feat> alongside the mesh.
-p (x|y|z)<cutting-plane-pos> -- Specifies a plane to cut the mesh so the
                                 viewer can see "inside" of it.  The plane is
                                 specified by which coordinate axis is its 
                                 normal and its position along that axis.
                                 Multiple planes can be specified with multiple
                                 occurrences of this flag.
-w num_tets                   -- Draw the mesh so that the <num_tets>
                                 worst-quality tetrahedra are highlighted.

Example usages:
view_tet block.tet -p x0.0
view_tet dragon.obj -s
view_tet fandisk.tet -f fandisk.feat -w 10

Once view_tet is running, the viewer can be controlled with the following 

Shift+LeftMouseButton   -- Rotate camera
Shift+RightMouseButton  -- Zoom camera
Shift+MiddleMouseButton -- Pan camera

Source Code overview

The following files make up the quartet source:

Utilities / Data Structures:

 - a bunch of small useful functions

 - a convenience wrapper around fixed-length arrays (for vectors in 3D etc.)

 - a convenience wrapper around STL vectors to get 3D arrays

 - a signed-distance-field data structure for working with level sets

 - code to read in a Wavefront .OBJ file

 - a simple half-edge triangle mesh data structure

 - an index-based tetrahedral mesh data structure.  Maintains incidence 
   relationships as necessary for fast adjacency queries.

 - Data structures representing sharp features of a triangle mesh and 
   aggregations of those features (called FeatureSets)

Meshing Functions:

 - some simple and not-so-simple geometric operations needed for creating
   signed distance functions from triangle meshes.
   Uses Jonathan Shewchuk's robust geometric predicates code, found in 
   predicates.cpp (

 - code for robustly creating a fairly accurate signed distance function
   of a watertight triangle mesh, sampled on a regular 3D grid.

 - code to create a quality tetrahedral mesh of the interior of a level set

 - functions for measuring quality of tetrahedra based on various metrics

 - code to restore desired sharp features onto a tetrahedral mesh

 - code to improve the overall quality of a given tetrahedral mesh.  Uses as 
   much data from the meshing step (ie: sdf, sharp features, etc.) as possible.

 - quartet command-line program 

Viewer Application:

 - code for creating a simple generic OpenGL viewer application

 - view_tet main code file for viewing tet meshes


A tetrahedral mesh generator that does isosurface stuffing with an acute tetrahedral tile.




No releases published
You can’t perform that action at this time.