PrevCurrent Data File Format  Next

Name

surface — A single normal surface in a 3-manifold triangulation

Synopsis

Content Model 
surface ::= (#PCDATA,
             compact?,
             connected?, euler?,
             orbl?, realbdry?,
             twosided?)
Attributes
NameTypeVersion
encNUMBER (required)Added in Regina 7.0
lenNUMBER (required) 
nameCDATA 

Description

A surface element stores a single normal surface in a 3-manifold triangulation.

A normal surface in a T-tetrahedron triangulation is traditionally represented by a vector of integers, whose length depends upon the specific vector encoding being used (which in turn depends upon the underlying coordinate system). For instance, a vector encoded in standard tri-quad coordinates will have length 7T, and a vector encoded in quad coordinates will have length 3T.

Warning

Since Regina 7.0, the specific vector encoding being used is now explicitly specified in the enc attribute. This might or might not be deducible from the coordinate system specified in the parent surfaces. The parent list's coordinate system should only be used as a fallback if the enc attribute is not present.

The normal surface vector is stored as the character data of this XML element as follows. Since a normal surface 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.

Parents

The following elements contain surface: surfaces.

Children

The following elements occur in surface: compact, connected, euler, orbl, realbdry, twosided.

Attributes

enc

The specific vector encoding used to represent this normal surface. This will be given as an opaque integer; it is not meant to be interpreted manually, but instead should be passed to Regina's NormalEncoding::fromIntValue() function.

len

The length of the underlying normal surface vector. This depends upon both the underlying triangulation and the specific vector encoding being used.

name

A human-readable name given to this surface. Surface names need not be distinct and exist merely for the convenience of the user.

Example

The following XML snippet represents a normal surface in a 4-tetrahedron triangulation. The normal surface vector is: 

(0, 0, 0, 0, 0, 2, 0,
 0, 0, 1, 1, 1, 0, 0,
 1, 1, 0, 0, 1, 0, 0,
 0, 0, 0, 0, 0, 2, 0)

The child elements of this normal surface indicate that the surface has Euler characteristic -2 and real boundary, and is compact, connected, orientable and two-sided. 

<surface enc="279" len="28"> 5 2 9 1 10 1 11 1 14 1 15 1 18 1 26 2
    <euler value="-2"/>
    <realbdry value="T"/>
    <compact value="T"/>
    <connected value="1"/>
    <orbl value="1"/>
    <twosided value="1"/> </surface>
PrevContentsNext
struct Up surfaces