struct

Description

A struct element stores a single angle structure on a 3-manifold triangulation.

An angle structure on a T-tetrahedron triangulation is represented by a vector of 3T+1 integers. This vector is stored as the character data of this XML element as follows.

Since an angle structure vector will generally contain many zeroes, only the non-zero elements are listed. The character data should thus consist of a whitespace-separated sequence of integer pairs. Each integer pair represents a non-zero coordinate in the vector; the first element of the pair identifies which coordinate is being described (coordinates are numbered 0, 1, 2, ...) and the second element of the pair is the actual value at this coordinate.

There are 3T actual angles stored in an angle structure; these are 0:01/23, 0:02/13, 0:03/12, 1:01/23, 1:02/13, 1:03/12, 2:01/23, etc, where t:ab/cd represents the angle assigned to the edge in tetrahedron t that joins tetrahedron vertices a and b, as well as the (opposite) edge that joins tetrahedron vertices c and d (a, b, c and d will always be 0, 1, 2 and 3 in some order).

To determine the kth of these angles, take the kth integer in the angle structure vector, divide by the final element of the vector and multiply by π.

Attributes

Example

The following XML snippet represents an angle structure on a 2-tetrahedron triangulation. The angle structure vector is (0, 0, 2, 1, 1, 0, 2). The corresponding six angles are (0, 0, π, π/2, π/2, 0).

<struct len="7"> 2 2 3 1 4 1 6 2 </struct>