1. 2008-04-14 Copyright LKSoftWare GmbH, 2008 1 Entities for Geometrically bounded wireframe ISO 10303-510: AIC Geometrically bounded wireframe ISO/TS 10303-1510: AM Geometrically bounded wireframe ISO 10303-503: AIC Geometrically bounded 2D wireframe ISO/TS 10303-1347: AM Wireframe 2D

2. 2008-04-14 Copyright LKSoftWare GmbH, 2008 2 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

3. 2008-04-14 Copyright LKSoftWare GmbH, 2008 3 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 …

4. 2008-04-14 Copyright LKSoftWare GmbH, 2008 4 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

5. 2008-04-14 Copyright LKSoftWare GmbH, 2008 5 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

6. 2008-04-14 Copyright LKSoftWare GmbH, 2008 6 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

7. 2008-04-14 Copyright LKSoftWare GmbH, 2008 7 Geometry for neighbouring surfaces x 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

8. 2008-04-14 Copyright LKSoftWare GmbH, 2008 8 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 VP2VP3 VP4VP5VP6 EC4EC5 EC2EC1 EC6EC7 OE3a OE3b OE1a OE1b OE2a OE2b OE5b OE5a OE6b OE4aOE4b OE7a OE6aOE7a FB-EL-A AF-AAF-B Closed_shell VP - Vertex_point EC - Edge_curve OE - Oriented_edge FB - Face_bound EL - Edge_loop AF - Advanced_face

9. 2008-04-14 Copyright LKSoftWare GmbH, 2008 9 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

10. 2008-04-14 Copyright LKSoftWare GmbH, 2008 10 Constructive Solid Geometry

11. 2008-04-14 Copyright LKSoftWare GmbH, 2008 11 CSG: Constructive Solid Geometry (3D)

12. 2008-04-14 Copyright LKSoftWare GmbH, 2008 12 Example from ISO 10303-523: AIC Curve swept solid (1/2) Ruled surface and directrix curveCross-section used to define swept solid

13. 2008-04-14 Copyright LKSoftWare GmbH, 2008 13 Example from ISO 10303-523: AIC Curve swept solid (2/2) Result as displayed by some from a viewing system

14. 2008-04-14 Copyright LKSoftWare GmbH, 2008 14 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