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Name

surfaces — A normal surface list packet

Synopsis

Content Model 
surfaces ::= (surface*,
              tag*,
              (container|textdata|script|attachment|
               tri|link|snappeadata|
               angles|surfaces|hypersurfaces|
               filtercomb|filterprop|filtertrivial|
               anon|anonref)*)
Attributes
NameType
algorithmNUMBER (required)
coordsNUMBER (required)
triCDATA (required)
typeNUMBER (required)
idCDATA
labelCDATA

Added in Regina 7.0

Description

This represents a normal surface list packet, one of the many types of packet that together form the packet tree that a user sees when they open a Regina data file.

A normal surface list stores a list of normal surfaces in a particular 3-manifold triangulation. This list will often contain the vertex surfaces whose convex span is the set of all normal surfaces in the triangulation that satisfy certain constraints, though other lists (such as fundamental surfaces, or other customised lists) can be stored also.

Since Regina 7.0, a normal surface list no longer needs to be a child packet of its underlying triangulation. Instead, the triangulation is denoted by the tri attribute. This must be the ID of a 3-dimensional triangulation packet that appears before this list in the packet tree, with respect to a pre-order depth-first traversal (i.e., the triangulation must appear before this list in the XML data file). The triangulation may be an anonymous packet (see anon).

The individual normal surfaces in this list are contained in the child surface elements. Since Regina 7.0, the parameters of the normal surface enumeration that created this list are stored in the attributes; there is no longer a child params element.

There are several child XML elements that are common to all packet types. The tag elements represent an arbitrary set of string “tags” that users can attach to a packet to help organise their data. The remaining child elements list all of Regina's packet types (container, textdata, etc.), and these represent the immediate children of this packet in the packet tree.

Parents

The following elements can contain any packet element (including this): angles, anon, anonref, attachment, container, filtercomb, filterprop, filtertrivial, hypersurfaces, link, regina, script, snappeadata, surfaces, textdata, tri. This list includes all packet types, as well as the top-level element regina.

Children

The following elements occur in surfaces, and are specific to the normal surface list packet type: surface.

The following children can occur in all packet elements: angles, anon, anonref, attachment, container, filtercomb, filterprop, filtertrivial, hypersurfaces, link, script, snappeadata, surfaces, tag, textdata, tri. This list includes all packet types, as well as the tag element for tagging individual packets.

Attributes

The following attributes are specific to normal surface lists:

algorithm

Specifies the algorithm that was used to enumerate these normal surfaces.

This must be an integer, formed as a bitwise OR combination of constants from the NormalAlgFlags enumeration in Regina's calculation engine.

An example of such an integer might be 17, which combines the NormalAlgFlags constants NS_VERTEX_VIA_REDUCED (1) and NS_TREE (16), indicating that the enumeration used the tree traversal method and did the bulk of its work in a smaller coordinate system.

coords

Specifies which coordinate system was used in the normal surface enumeration.

This must be a non-negative integer that matches one of the constants from the NormalCoords enumeration in Regina's calculation engine.

An example of such an integer might be 102, which is the constant NS_AN_QUAD_OCT that represents standard coordinates for octagonal almost normal surfaces.

tri

The ID of the triangulation in which these normal surfaces live. This must match the id attribute of a 3-dimensional triangulation that appears before this list in a pre-order depth-first traversal of the full packet tree.

type

Specifies exactly which normal surfaces this list contains. In particular, this flag indicates whether the list contains all vertex surfaces, all fundamental surfaces, or some other customised list. It also indicates whether the list is restricted to properly embedded surfaces.

This must be an integer, formed as a bitwise OR combination of constants from the NormalListFlags enumeration in Regina's calculation engine.

An example of such an integer might be 5, which combines the NormalListFlags constants NS_EMBEDDED_ONLY (1) and NS_VERTEX (4).

The following attributes are common to all packet types:

id

A unique identifier for this packet. Packets are not required to have IDs, but when they are present they must be distinct (i.e., no packets in the same file may share the same ID). IDs do not need to be human-readable, must not contain leading or trailing whitespace, and must not be empty strings. Currently, IDs are built from base 64 hashes of the underlying C++ pointers.

The purpose of these packet IDs is to allow other packets to reference this packet (for instance, so that a script packet can store references to its variables).

IDs are not required to stay the same across subsequent loads and saves of the same file. In other words, if you load a file and save it again, the packet IDs are allowed to change.

label

The name given by the user to this particular packet within the overall packet tree.

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