File

Load Points
Shows a "Open file" dialog. A readable file is supposed to consist of a list of points that are separated by white spaces. A point has to be represented as a list of three coordinates that again are separated by white spaces.

Initialization

Empty scene
Deletes the current triangulation and initializes it with the empty triangulation.
Single point
Deletes the current triangulation and computes a new triangulation of one random point.
Random point set
Deletes the current triangulation and computes a new triangulation of 30 random points that are uniformly distributed inside the random cube.
Random planar point set
Deletes the current triangulation and computes a new triangulation of 10 random points that are uniformly distributed inside the side of the fundamental cube of z=0.
Point grid
Deletes the current triangulation and computes a new triangulation of a grid of 36 points. This is exactly the grid for which we know that it has a triangulation in 1-sheeted covering space. So this triangulation is the only one amongst the five initial triangulations that is represented in 1-sheeted covering.

Actions

Flying ball
Shows a ball that flies along a constant vector through the fundamental cube to show the periodicity.
Pause
Stops the ball.
Insert point
Inserts a point at the current position of the ball. It does not matter whether the ball is shown or not.
Insert random point
Inserts a point at a random position inside the fundamental cube.
Grab image
Stores a screenshot of what is currently displayed.

Features

Point location
Shows the tetrahedron that currently contains the flying ball. If several periodic copies of this tetrahedron are shown then all of them will be marked.
Conflict region
Shows the tetrahedra whose circumscribing balls currently contain the flying ball. If several periodic copies of a marked tetrahedron are shown then all of them will be marked.

Options

Wireframe
Draws lines and points instead of the GLU spheres and cylinders. This can accelerate the drawing of large scenes considerably.
Planar triangulation
Shows only the simplices that are completely contained in the plane z=0. In this mode the flying ball will always be inside the plane z=0 as well as all randomly inserted points.
Draw 1-sheeted covering
Draw each simplex exactly once, i.e. without periodic copies of itself. Note that the result of this does not necessarily show a triangulation and followingly does not necessarily correspond to the internal representation of the triangulation. This option is activated by default.
Draw bordering cells multiply
Draw all simplices that have a non-empty intersection with the fundamental cube. This option is activated by default.
Draw segments
Decide per segment whether or not to draw a simplex. This uses the Periodic_segment_iterator.
Draw triangles
Decide per triangle whether or not to draw a simplex. This uses the Periodic_triangle_iterator.
Draw tetrahedra
Decide per tetrahedron whether or not to draw a simplex. This uses the Periodic_tetrahedron_iterator. This is the default.
Draw domain (cube/square)
Toggle the drawing of the fundamental cube or square in case of a planar triangulation.
Clip along the cube/square
Toggle clipping of simplices that are outside of the fundamental cube or square in case of a planar triangulation.
2-color clipping
Show the clipped part of edges in a different color. This option is only active if clipping takes place.