2008-04-14 copyright lksoftware gmbh, 2008 1 iso 10303 step representation and geometry - a detailed...

2008-04-14 Copyright LKSoftWare GmbH, 2008 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


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


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('',…);


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


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 forma directed acyclic graph


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 = ?


Generic representation_items (p43)

• Details on measure, value and units are not provided here.


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


Associating representation datawith 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


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)


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…);


Instance pattern (2/2) for representation_relationship_with_transformation

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 !!!

#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(…);


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


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


Entities forGeometrically bounded wireframe

• ISO 10303-510: AIC Geometrically bounded wireframeISO/TS 10303-1510: AM Geometrically bounded wireframe

• ISO 10303-503: AIC Geometrically bounded 2D wireframeISO/TS 10303-1347: AM Wireframe 2D


Example for Geometrically bounded wireframe with composite_curve (2D)

#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.));

#100: 0 / 0

#110: 1 / 0

#120: 0 / 1


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 …


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


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


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


Geometry for neighbouring surfaces

• x

CP - Cartesian_pointC - 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 surfacesAs a result the receiver can't be sure what is meant


Wrapping geometry by topology

• 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)

VP1

EC3

VP2 VP3

VP4 VP5 VP6

EC4 EC5

EC2EC1

EC6 EC7

OE3a

OE3b

OE1a

OE1b

OE2a

OE2b

OE5b

OE5a

OE6b

OE4a OE4b

OE7a

OE6a OE7a

FB-EL-A FB-EL-A

AF-A AF-B

Closed_shell

VP - Vertex_pointEC - Edge_curveOE - Oriented_edge

FB - Face_boundEL - Edge_loopAF - Advanced_face


Example from ISO 10303-521: AIC Manifold 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)

subedge

Second subsurface

First subsurface

subface

Advance BREP


Constructive Solid Geometry


CSG: Constructive Solid Geometry (3D)


Example from ISO 10303-523:AIC Curve swept solid (1/2)

Ruled surface and directrix curveCross-section used to define swept solid


Example from ISO 10303-523:AIC Curve swept solid (2/2)

Result as displayed by some from a viewing system


Geometry not covered here

• ISO 10303-41 Units & quantities• ISO 10303-42

• Volume models with inner parametric point formulas• …

• ISO 10303-55 Procedural and hybrid representation• ISO 10303-59 Quality of product shape data• ISO 10303-101 Construction history• ISO 10303-108 Parameterization and constraints for explicit geometric

product models

• see http://www.wikistep.org for• ISO 10303-46 Visual presentation• ISO 10303-47 Shape variation tolerance• ISO 10303-101 Draughting• And other presentation related AICs

2008-04-14 copyright lksoftware gmbh, 2008 1 iso 10303 step representation and geometry - a detailed...

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