![]() | struct |
Prev | Data File Format | Next |
Name
struct — A single angle structure
Synopsis
Content Model | |
struct ::= (#PCDATA,
| |
Attributes | |
Name | Type |
len | NUMBER (required) |
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
represents the angle assigned to the edge in tetrahedron
t
:ab
/cd
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 k
th of these angles, take
the k
th integer in the angle structure
vector, divide by the final element of the vector and multiply by π.
Flags
The child flags
element can be used to store properties of the
angle structure. The flags should be a bitwise combination of the
following values:
Value | Meaning |
1 | The angle structure is strict (all angles are strictly between 0 and π). This flag is only meaningful if the angle structure type has been calculated; see below. |
2 | The angle structure is taut (all angles are either 0 or π). This flag is only meaningful if the angle structure type has been calculated; see below. |
4 | The angle structure type (strict/taut) has been calculated. |
Attributes
len
The length of the angle structure vector. This will always be 3
T
+1, whereT
is the number of tetrahedra in the underlying 3-manifold triangulation.
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).
The flags indicate that the angle structure type has been calculated but the angle structure was found to be neither strict nor taut.
<struct len="7"> 2 2 3 1 4 1 6 2 <flags value="4"/></struct>
Prev | Contents | Next |
splitsfce | Up | surface |