1. ISO 10303 STEP representation and geometry - a detailed introduction
Lothar Klein,
LKSoftWare GmbH
This work is done as part of the European funded DEPUIS project within the EUROPE INNOVA program.
Some pictures and explanations are taken from Wikipedia
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2. ISO 10303-43: Representation structures
A representation is a collection of elements of representation (representation_item) within a specified context (representation_context)
Representation_items must exisit within at least one representation_context via a representation, either
directly by being referenced from „representation.items S[1:?]“ or
indirectly by being referenced from a specialization of representation_item or
indirectly by being referenced from a specialized founded_item
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3. ISO 10303-43 Representation structures: Instance example
#1=REPRESENTATION_CONTEXT('iii','ttt');
#2=REPRESENTATION('rrr', (#3,#4), ,#1);
#3=YYY('',…);
#4=XXX('',#5,#6);
#5=YYY('',…);
#6=FFF('',#6)
#7=ZZZ('',…);
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4. representation_item with some specializations from other schema
representaion_items have only meaning when used within a representation that applies a context, either directly or indirectly
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5. Representation Example (1/2)
Given entity instances:
representations A, B, C
r. contexts X, Y
a graph of several representation_items
cartesian_points 1, 2
Note:
Representation_items form
a directed acyclic graph
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6. Representation Example (2/2)
Defined distances:
A/1 – A/2 = 1
B/1 – B/2 = 1
B/1 – C/2 = 1
B/1 – C/1 = 0
Undefined distances:
cp_1 – cp_2 = ?
A/1 – B/1 = ?
A/1 – C/2 = ?
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7. Generic representation_items (p43)
Details on measure, value and units are not provided here.
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8. Relations between representations
sharing the same context (see previous slides)
not definitional but …
representation_relationship /_with_transformation + item_defined_transformation
definitional only if within assembly structure or complex with definitional_
mapped_item + representation_map
definitional by default
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9. Associating representation data with other product data
property_definition_representation / shape_definition_representation
default for the geometry model of a product and other property data
context_dependent_shape_representation
only used for the shape of a product within a product structure
item_identified_representation_usage
only used for an aspect of a product
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10. Instance pattern for mapped_item + representation_map
#1=XXX_REPRESENTATION('',(#3,…),#2);
#2=(REPRESENTATION_CONTEXT(….) …);
#3=MAPPED_ITEM('',#5,#4);
#4=AXIS2_PLACEMENT_3D(…some trans+rot…);
#5=REPRESENTATION_MAP(#8,#6);
#6=XXX_REPRESENTATION('',(#8,…),#7)
#7=(REPRESENTATION_CONTEXT(…) …);
#8=AXIS2_PLACEMENT_3D(… typical 0/0/0 no rot…);
Note:
representation #6 is definitional part of representation #1
representations have different contexts, #2 and #7
representation_map #5 is not a representation_item and so #8 is not founded via #3 in rep. #1 (it is only founded in rep. #6)
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11. Copyright LKSoftWare GmbH, 2008
Instance pattern (1/2) for representation_relationship_with_transformation
Note:
Not definitional by default
#1=XXX_REPRESENTATION('',(#3,…),#2);
#2=(REPRESENTATION_CONTEXT(….) …);
#3=AXIS2_PLACEMENT_3D(…some trans+rot…);
#3=REP_REL_WITH_TRANSFORMATION('',#1,#6);
#5=ITEM_DEFINED_TRANSFORMATION(#3,#8);
#6=XXX_REPRESENTATION('',(#8,…),#7)
#7=(REPRESENTATION_CONTEXT(…) …);
#8=AXIS2_PLACEMENT_3D(… typical 0/0/0 no rot…);
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12. Copyright LKSoftWare GmbH, 2008
Instance pattern (2/2) for representation_relationship_with_transformation
#1=XXX_REPRESENTATION('',(#3,…),#2);
#2=(REPRESENTATION_CONTEXT(….) …);
#3=CARTESIAN_TRANSFORMATION_OPERATOR_3D(…);
#3=REPRESENTATION_RELATIONSHIP_WITH_TRANSFORMATION('',#1,#3);
#6=XXX_REPRESENTATION('',(#8,…),#7)
#7=(REPRESENTATION_CONTEXT(…) …);
#8=XXX(…);
Note:
cartesian_transformation_operator allows scaling and mirroring
For assembly of parts use only placement because you can't scaled or mirror the shape of a part !!!
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13. Some special usage from CAX-IF
Goal is to combine several specialized shape_representations into a single one (left) and then to include it in a bigger one (left) with some transformation
Used e.g. to combine topological bounded representation:
advanced_brep_shape_representation
manifold_surface_shape_representation
edge_based_wireframe_shape_representation
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14. Basic geometric entities, placement and transformation
Note:
In STEP all geometric representation contexts are right hand
All axis and ref_direction attributes are optional. If not given a default value applies
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15. Entities for Geometrically bounded wireframe
ISO : AIC Geometrically bounded wireframe ISO/TS : AM Geometrically bounded wireframe
ISO : AIC Geometrically bounded 2D wireframe ISO/TS : AM Wireframe 2D
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16. Example for Geometrically bounded wireframe with composite_curve (2D)
#110: 1 / 0
#100: 0 / 0
#120: 0 / 1
#10=GEOMETRICALLY_BOUNDED_2D_WIREFRAME_REPRESENTATION('',(#30),#20);
#20=GEOMETRIC_REPRESENTATION_CONTEXT('','', 2);
#30=COMPOSITE_CURVE('',(#40,#80),.T.);
#40=COMPOSITE_CURVE_SEGMENT(.CONTINUOUS.,.F.,#50);
#50=TRIMMED_CURVE('',#60,(#110),(#120),.F.,.CARTESIAN.);
#60=CIRCLE('',#70,1.);
#70=AXIS2_PLACEMENT_2D('',#110,$);
#80=COMPOSITE_CURVE_SEGMENT(.CONTINUOUS.,.T.,#80);
#90=POLYLINE('',(#110,#100,#120));
#100=CARTESIAN_POINT('',(0.,0.));
#110=CARTESIAN_POINT('',(1.,0.));
#120=CARTESIAN_POINT('',(0.,1.));
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17. Geometrically bounded surface shape representation
All surfaces must be bounded, either b_spline_surface or curve_bounded_surface or …
The boundary_curve is either a pcurve (complex) or …
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18. Advanced boundary representation
For the precise representation of complex objects
Combination of geometrical and topological elements
Extensivly tested within the CAX-IF
Most widely used for STEP geometry exchange
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19. Topologically bounded geometry (1/2)
A vertex_point represents both, a vertex and a point => cartesian_point
An edge_curve connects two vertex_points and associates with a curve. The curve is bounded by the vertex_points
One or two oriented edges for each edge_curve (for open or closed shell …)
A face_surface is a face with one or more bounds and associated with a surface. Advanced_face adds constraints for surface, curve, point and bounds
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20. Topologically bounded geometry (2/2)
elementary_-(AIC 513) and advanced_brep_shape_representation (AIC514) are using closed_shell, edge_loop, and advanced_face (AIC 511)
faceted_brep_shape_representation (AIC 512) is using closed_shell and poly_loop
manifold_surface_shape_representation (AIC 509) is using open_shell, edge_loop and advanced_face
manifold_subsurface_shape_representation (AIC 521) is similar, but allows also subedge, subface, and connected_face_sub_set
edge_based_wireframe_shape_representation (AIC 501) uses connected_edge_set
shell_based_wireframe_shape_representation (AIC 502) uses vertex_shell or wire_shell or open_shell or closed_shell
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21. Geometry for neighbouring surfaces
CP - Cartesian_point
C - Curve
Numerical problems:
Cartesian_points are not exactly on the curves
Cartesian_points are not exaclty on the surfaces
Curves are not exactly on the surfaces
As a result the receiver can't be sure what is meant x
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22. Wrapping geometry by topology
VP - Vertex_point
EC - Edge_curve
OE - Oriented_edge
FB - Face_bound
EL - Edge_loop
AF - Advanced_face
OE1a
OE2a
VP1
EC1
VP2
EC2
VP3
OE1b
OE2b
OE3b
OE5a
EC3
OE3a
FB-EL-A
OE4a
EC4
OE4b
FB-EL-A
OE5b
EC5
AF-A
AF-B
OE6b
OE7a
VP4
EC6
VP5
EC7
VP6
OE6a
Closed_shell
OE7a
Topological structure can be verified whether it is closed, open or non-manifold (> 2 )
Neighbourhood is explicitly expressed without geometrical inaccuracy
Orientation of edge, oriented_edge must be arranged for a unique direction in the edge_loops (not shown here)
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23. Example from ISO 10303-521: AIC Manifold subsurface
subedge
subface
Second subsurface
Advance BREP
First subsurface
The first manifold_subsurface_shape_representation is defined on the shell of an advanced_brep_shape_representation
The second one is defined within the first one (connected_face_sub_set)
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24. Constructive Solid Geometry
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25. CSG: Constructive Solid Geometry (3D)
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26. Example from ISO 10303-523: AIC Curve swept solid (1/2)
Cross-section used to
define swept solid
Ruled surface and directrix curve
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27. Example from ISO 10303-523: AIC Curve swept solid (2/2)
Result as displayed
by some from a
viewing system
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28. Geometry not covered here
ISO Units & quantities
ISO
Volume models with inner parametric point formulas …
ISO Procedural and hybrid representation
ISO Quality of product shape data
ISO Construction history
ISO Parameterization and constraints for explicit geometric product models
see for
ISO Visual presentation
ISO Shape variation tolerance
ISO Draughting
And other presentation related AICs
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