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Application module:
Elemental topology |
ISO/TS 10303-1005:2021(E)
© ISO
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This clause specifies the information requirements for the
Elemental topology
application module. The information requirements are specified as the
Application Reference Model (ARM) of this application module.
NOTE 1 A graphical representation of the information
requirements is given in
Annex C.
NOTE 2 The mapping specification is specified in
5.1. It shows how
the information requirements are met by using common resources and
constructs defined or imported in the MIM schema of this application
module.
This clause defines the information requirements to which implementations shall
conform using the EXPRESS language as defined in ISO 10303-11.
The following begins the
Elemental_topology_arm
schema and identifies the necessary external references.
EXPRESS specification:
*)
SCHEMA Elemental_topology_arm;
(*
The following EXPRESS interface statement specifies the elements
imported from the ARM of another application module.
EXPRESS specification:
*)
USE FROM
Foundation_representation_arm;
--
ISO/TS 10303-1006
(*
NOTE 1
The schemas referenced above are specified in the following
part of ISO 10303:
| Foundation_representation_arm |
ISO/TS 10303-1006 |
NOTE 2
See Annex C,
Figures
C.1and C.2
for a graphical representation of this schema.
This subclause specifies the ARM entities for this
module. Each ARM application entity is an atomic element that
embodies a unique application concept and contains attributes
specifying the data elements of the entity. The ARM
entities and definitions are specified below.
A Connected_edge_set is a type of
Detailed_topological_model_element
that is a set of edges arcwise connected via their common vertices.
EXPRESS specification:
*)
ENTITY Connected_edge_set
SUBTYPE OF (Detailed_topological_model_element);
connected_edges : SET[1:?] OF Edge;
END_ENTITY;
(*
Attribute definitions:
connected_edges:
a set of Edges arcwise connected at common Vertexs. The domains of the connected_edges shall not intersect.
A Connected_edge_sub_set is a type of
Connected_edge_set
that represents a subset of a parent
Connected_edge_set.
EXPRESS specification:
*)
ENTITY Connected_edge_sub_set
SUBTYPE OF (Connected_edge_set);
parent_edge_set : Connected_edge_set;
END_ENTITY;
(*
Attribute definitions:
parent_edge_set:
specifies the parent
Connected_edge_set.
A Connected_face_set is a type of
Detailed_topological_model_element that is a set of faces such that the domain of the faces together with their bounding edges and vertices is connected.
EXPRESS specification:
*)
ENTITY Connected_face_set
SUBTYPE OF (Detailed_topological_model_element);
connected_faces : SET[1:?] OF Face;
END_ENTITY;
(*
Attribute definitions:
connected_faces:
a set of Faces arcwise connected along common Edges or Vertexs. The domains of the connected_faces shall not overlap.
A Connected_face_sub_set is a type of
Connected_face_set.
EXPRESS specification:
*)
ENTITY Connected_face_sub_set
SUBTYPE OF (Connected_face_set);
parent_face_set : Connected_face_set;
END_ENTITY;
(*
Attribute definitions:
parent_face_set:
specifies a role of the
Connected_face_set
for the Connected_face_sub_set.
A Detailed_topological_model_element is a type of
Representation_item
that represents a single element of
the topology, or connectivity, of the entities that make up the representation of an object.
A Detailed_topological_model_element is either a
Connected_edge_set
or a
Connected_face_set,
or an
Edge,
or a
Face,
or a
Face_bound,
or a
Vertex,
or a
Loop,
or a
Loop
and a
Path,
or a
Path.
EXPRESS specification:
*)
ENTITY Detailed_topological_model_element
ABSTRACT SUPERTYPE
OF (ONEOF (Connected_edge_set,
Connected_face_set,
Edge,
Face,
Face_bound,
Vertex, (
Loop
ANDOR Path)))
SUBTYPE OF (Representation_item);
permanent_id :
OPTIONAL
identifier;
permanent_aggregate_id :
OPTIONAL
identifier;
END_ENTITY;
(*
Attribute definitions:
permanent_id:
an identifier that is invariant over the life cycle of the product model.
The permanent_id is optional and need not be provided.
NOTE
An application protocol may wish to enforce uniqueness constraints on the value of this attribute to ensure there is
no sharing of the identifier among Detailed_topological_model_element in
the context of a product model version.
permanent_aggregate_id:
an identifier that is invariant over the life cycle of the product model.
This attribute is designed to support the use case where more than one member of Detailed_topological_model_element
may share the same identifier within the context of a specific product model version.
The permanent_aggregate_id is optional and need not be provided.
An Edge is a type of
Detailed_topological_model_element
that is an oriented bounded one dimensional manifold connecting two vertices.
The topological sense of the edge is from the
edge_start to the edge_end.
EXPRESS specification:
*)
ENTITY Edge
SUBTYPE OF (Detailed_topological_model_element);
edge_start : Vertex;
edge_end : Vertex;
END_ENTITY;
(*
Attribute definitions:
edge_start:
the
Vertex
defining the start point of the edge.
edge_end:
the
Vertex
defining the end point of the edge; this may coincide with the start point if the edge forms a closed loop.
An Edge_loop is a type of
Loop
with a non-zero extent. It is also a type of Path with the property that the start and end vertices coincide.
EXPRESS specification:
*)
ENTITY Edge_loop
SUBTYPE OF (Loop, Path);
DERIVE
ne : INTEGER := SIZEOF(SELF\Path.edge_list);
WHERE
WR1: (SELF\Path.edge_list[1].edge_start) :=:
(SELF\Path.edge_list[ne].edge_end);
END_ENTITY;
(*
Attribute definitions:
ne:
the number of
Edges defining the path of the loop.
Formal propositions:
WR1:
The edge_start of the first edge shall be the same as the edge_end of the last edge. This ensures
that the path is closed to form a loop.
A Face is a type of
Detailed_topological_model_element
that is a topological entity of dimensionality 2 corresponding to the intuitive notion of a piece of
surface bounded by loops. Its domain, if present, is an oriented, connected, finite 2-manifold. A
face domain shall not have handles, but it may have holes, each hole bounded by a loop.
NOTE
The full semantics of this entity is defined in the corresponding MIM object from ISO 10303-42; this has additional constraints
in the form of informal propositions.
EXPRESS specification:
*)
ENTITY Face
SUBTYPE OF (Detailed_topological_model_element);
bounds : SET[1:?] OF Face_bound;
WHERE
WR1: SIZEOF(QUERY(temp <* bounds | 'ELEMENTAL_TOPOLOGY_ARM.FACE_OUTER_BOUND' IN
TYPEOF(temp))) <= 1;
END_ENTITY;
(*
Attribute definitions:
bounds:
the set of Face_bounds which define all the boundaries of the face.
Formal propositions:
WR1:
At most, one of the bounds shall be of type Face_outer_bound.
A Face_bound is a type of
Detailed_topological_model_element
that is the usage of a loop for bounding a Face.
EXPRESS specification:
*)
ENTITY Face_bound
SUBTYPE OF (Detailed_topological_model_element);
bound : Loop;
orientation : BOOLEAN;
END_ENTITY;
(*
Attribute definitions:
bound:
the Loop which will be used as a face boundary.
orientation:
an indicator of whether (TRUE), or not (FALSE) the Loop has the same sense when used to
bound the face as when first defined. If orientation is FALSE, the senses of all its component oriented
edges are implicitly reversed when used in the Face.
A Face_outer_bound is a type of
Face_bound
which carries the additional semantics of defining
an outer boundary on the face. A Face_outer_bound shall separate the interior of the face from the exterior and shall enclose the interior domain of the face. No more than
one boundary of a face shall be of this type.
EXPRESS specification:
*)
ENTITY Face_outer_bound
SUBTYPE OF (Face_bound);
END_ENTITY;
(*
A Loop is a type of
Detailed_topological_model_element
constructed from a single Vertex,
or by stringing together connected
edges beginning and ending at the same
Vertex.
A Loop has dimensionality 0 or 1.
A Loop may be either a
Vertex_loop
or an
Edge_loop.
EXPRESS specification:
*)
ENTITY Loop
SUPERTYPE OF (ONEOF (Vertex_loop,
Edge_loop))
SUBTYPE OF (Detailed_topological_model_element);
END_ENTITY;
(*
An Oriented_edge is a type of
Edge
constructed from another edge which contains a BOOLEAN orientation
flag to indicate whether or not the orientation of the constructed edge agrees with the orientation of
the original edge. Except for possible re-orientation, the Oriented_edge is equivalent to the original edge.
EXPRESS specification:
*)
ENTITY Oriented_edge
SUBTYPE OF (Edge);
edge_definition : Edge;
orientation : BOOLEAN;
DERIVE
SELF\Edge.edge_start : Vertex := boolean_choice (SELF.orientation,
SELF.edge_definition.edge_start,
SELF.edge_definition.edge_end);
SELF\Edge.edge_end : Vertex := boolean_choice (SELF.orientation,
SELF.edge_definition.edge_end,
SELF.edge_definition.edge_start);
WHERE
WR1: NOT ('ELEMENTAL_TOPOLOGY_ARM.ORIENTED_EDGE' IN TYPEOF (SELF.edge_definition));
END_ENTITY;
(*
Attribute definitions:
edge_definition:
the
Edge
defining the domain of the Oriented_edge
orientation:
a BOOLEAN flag. If TRUE, the topological orientation as used coincides with the orientation,
from start vertex to end vertex, of the edge_definition, if FALSE the vertices are reversed in order.
edge_start:
the start vertex of the Oriented_edge. This is derived from the vertices of the edge_definition after taking account of the orientation.
edge_end:
the end vertex of the Oriented_edge. This is derived from the vertices of the edge_definition
after taking account of the orientation.
Formal propositions:
WR1:
The edge_definition shall not be of type Oriented_edge.
A Path is a type of
Detailed_topological_model_element
consisting of an ordered collection of Oriented_edges, such that the
start vertex of each edge coincides with the end vertex of its predecessor. The path is ordered from the edge_start
of its first Oriented_edge to the edge_end of its last edge. The BOOLEAN value
orientation in the Oriented_edge indicates whether the Edge direction agrees with the direction of the
Path (TRUE) or is in the opposite direction (FALSE).
An individual edge can only be referenced once by an individual path.
An edge can be referenced by multiple paths. An edge can exist independently of a path.
EXPRESS specification:
*)
ENTITY Path
SUBTYPE OF (Detailed_topological_model_element);
edge_list : LIST[1:?] OF
UNIQUE
Oriented_edge;
WHERE
WR1: path_aligned(SELF);
END_ENTITY;
(*
Attribute definitions:
edge_list:
the list of unique Oriented_edge entities which are concatenated together to form this Path.
Formal propositions:
WR1:
The end vertex of each Oriented_edge shall be the same as the start vertex of its successor. This is checked by the function path_aligned.
A Subedge is a type of
Edge,
whose domain is a connected portion of the domain of an existing
Edge.
The topological constraints on a Subedge are the same as those on an
Edge.
EXPRESS specification:
*)
ENTITY Subedge
SUBTYPE OF (Edge);
parent_edge : Edge;
END_ENTITY;
(*
Attribute definitions:
parent_edge:
the
Edge,
or
Subedge, which contains the Subedge.
A Subpath is a type of Path,
whose domain is a connected portion of the domain of an existing Path.
An instance of Subpath may contain a combination of
Edges
and Subedges
such that the resulting domain of
Edges and
Subedges,
together with their bounding vertices, is an arcwise connected, non-intersecting (except at common vertices),
and 1-dimensional subdomain of the domain defined by the parent_path.
EXPRESS specification:
*)
ENTITY Subpath
SUBTYPE OF (Path);
parent_path : Path;
END_ENTITY;
(*
Attribute definitions:
parent_path:
the Path,
which contains the Subpath.
A Vertex is a type of
Detailed_topological_model_element
is a point of interest in topological space, it has dimensionality 0.
EXPRESS specification:
*)
ENTITY Vertex
SUBTYPE OF (Detailed_topological_model_element);
END_ENTITY;
(*
A Vertex_loop is a type of
Loop
of zero extent consisting of a single vertex.
EXPRESS specification:
*)
ENTITY Vertex_loop
SUBTYPE OF (Loop);
loop_vertex : Vertex;
END_ENTITY;
(*
Attribute definitions:
loop_vertex:
the Vertex which defines the entire Loop.
This subclause specifies the ARM functions for
this module. The ARM functions and definitions are
specified below.
The boolean_choice function returns one of 2 possible values from the input as determined by the value of a BOOLEAN input argument.
EXPRESS specification:
*)
FUNCTION boolean_choice (b : BOOLEAN; choice1 : GENERIC : item; choice2 : GENERIC : item) : GENERIC : item;
IF b THEN
RETURN (choice1);
ELSE
RETURN (choice2);
END_IF;
END_FUNCTION;
(*
Argument definitions:
b:
(input) the BOOLEAN value used to select the element choice1 (TRUE) or choice2 (FALSE).
choice1:
the first item which may be selected and returned.
choice2:
the second item which may be selected and returned.
The path_aligned function returns TRUE if, for the edges of the input Path, the end vertex of each edge is the same as the start vertex of its successor.
EXPRESS specification:
*)
FUNCTION path_aligned (a_path : Path) : LOGICAL;
LOCAL
n : INTEGER;
p : LOGICAL := TRUE;
END_LOCAL;
n := SIZEOF (a_path.edge_list);
REPEAT i := 2 TO n;
p := p AND (a_path.edge_list[i-1].edge_end :=:
a_path.edge_list[i].edge_start);
END_REPEAT;
RETURN (p);
END_FUNCTION;
(*
Argument definitions:
a_path:
(input) the Path for which it is required to verify that its component edges are arranged consecutively head-to-tail.
*)
END_SCHEMA; -- Elemental_topology_arm
(*
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