1. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Geometric Accuracy: Geometric Accuracy: Graphics Is Not the Only Show in Town!Graphics Is Not the Only Show in Town! Geometric Accuracy: Geometric Accuracy: Graphics Is Not the Only Show in Town!Graphics Is Not the Only Show in Town!

2. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Topology : Connectivity of Geometric Model (particularly at surface intersections) Topology : Connectivity of Geometric Model (particularly at surface intersections)

3. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Robustness (with D. R. Ferguson, Boeing) RobustnessRobustness –Reliability of modeling tools, and –Usability of models across multiple applications Robustness (with D. R. Ferguson, Boeing) RobustnessRobustness –Reliability of modeling tools, and –Usability of models across multiple applications

4. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Original Goals for CAD Systems Graphics DisplayGraphics Display Drafting SupportDrafting Support Link to CAMLink to CAM Not for sophisticated engineering simulationsNot for sophisticated engineering simulations Original Goals for CAD Systems Graphics DisplayGraphics Display Drafting SupportDrafting Support Link to CAMLink to CAM Not for sophisticated engineering simulationsNot for sophisticated engineering simulations

5. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE IntersectionIntersection –Two surfaces –Common Boundary Curve –Curve on both Surfaces !!! IntersectionIntersection –Two surfaces –Common Boundary Curve –Curve on both Surfaces !!!

6. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE SemanticsSemantics –Low11 degrees –High10 degrees SemanticsSemantics –Low11 degrees –High10 degrees

7. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Intersection Point (Intent)Intersection Point (Intent)

8. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Intersection Point (Reality)Intersection Point (Reality)

9. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Intersection Point (Approximation)Intersection Point (Approximation) Numerical SolutionNumerical Solution –t approximately at intersection –s approximately at intersection –need for some tolerance factor Intersection Point (Approximation)Intersection Point (Approximation) Numerical SolutionNumerical Solution –t approximately at intersection –s approximately at intersection –need for some tolerance factor

12. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Intersection Curve (Approximation)Intersection Curve (Approximation) Numerical SolutionNumerical Solution –Curve-1 approximately at intersection –Curve-2 approximately at intersection –need for some tolerance factor –Curve-1 NOT EQUAL Curve-2 Intersection Curve (Approximation)Intersection Curve (Approximation) Numerical SolutionNumerical Solution –Curve-1 approximately at intersection –Curve-2 approximately at intersection –need for some tolerance factor –Curve-1 NOT EQUAL Curve-2

13. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Even ‘gaps’ for line segment intersectionEven ‘gaps’ for line segment intersection More complex for surface intersectionsMore complex for surface intersections STEP surface gap detection prototypeSTEP surface gap detection prototype Investigating technology transferInvestigating technology transfer Even ‘gaps’ for line segment intersectionEven ‘gaps’ for line segment intersection More complex for surface intersectionsMore complex for surface intersections STEP surface gap detection prototypeSTEP surface gap detection prototype Investigating technology transferInvestigating technology transfer

14. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Just two bi-cubic surfaceJust two bi-cubic surface –Can have degree 324 (Sederberg) –Approximate to reduce data volume Just two bi-cubic surfaceJust two bi-cubic surface –Can have degree 324 (Sederberg) –Approximate to reduce data volume

15. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Gap Checking Tool for STEPGap Checking Tool for STEP –Used DT_NURBS utilities –STEP Tools Conversion (from Express) –Prototype Research Code –Paper submitted to CAD Robustness issue Gap Checking Tool for STEPGap Checking Tool for STEP –Used DT_NURBS utilities –STEP Tools Conversion (from Express) –Prototype Research Code –Paper submitted to CAD Robustness issue

17. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Digits of accuracy for gaps by application Surface Intersection Electromagnetics Fluid Dynamics Visualizaltion 2 8

18. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Surface Intersections 2 < Gap < 4, for Visualization2 < Gap < 4, for Visualization 5 < Gap < 8, for Electromagnetics5 < Gap < 8, for Electromagnetics Surface Intersections 2 < Gap < 4, for Visualization2 < Gap < 4, for Visualization 5 < Gap < 8, for Electromagnetics5 < Gap < 8, for Electromagnetics

19. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Unique Representation -- Very Expensive

20. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Grandine-Klein Intersector (CAGD, 1997) Input: Two surfaces and error boundInput: Two surfaces and error bound Bound in parameter space (vs. hiding by vendors)Bound in parameter space (vs. hiding by vendors) Permits use of differing tolerancesPermits use of differing tolerances DT_NURBS/GEML libraryDT_NURBS/GEML library Possible technology transfer with BoeingPossible technology transfer with Boeing Grandine-Klein Intersector (CAGD, 1997) Input: Two surfaces and error boundInput: Two surfaces and error bound Bound in parameter space (vs. hiding by vendors)Bound in parameter space (vs. hiding by vendors) Permits use of differing tolerancesPermits use of differing tolerances DT_NURBS/GEML libraryDT_NURBS/GEML library Possible technology transfer with BoeingPossible technology transfer with Boeing

24. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Approximation Counterexample PW-linearPW-linear Preserve curvaturePreserve curvature Use of Pasting Lemma & homeomorphismsUse of Pasting Lemma & homeomorphisms Need ambient isotopyNeed ambient isotopy Maekawa, Patrikalakis, Sakkalis & Yu, CAGD, 1998Maekawa, Patrikalakis, Sakkalis & Yu, CAGD, 1998 Approximation Counterexample PW-linearPW-linear Preserve curvaturePreserve curvature Use of Pasting Lemma & homeomorphismsUse of Pasting Lemma & homeomorphisms Need ambient isotopyNeed ambient isotopy Maekawa, Patrikalakis, Sakkalis & Yu, CAGD, 1998Maekawa, Patrikalakis, Sakkalis & Yu, CAGD, 1998

26. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Design Neighborhoods Proposed Partial Models (Sketch with intersection)Proposed Partial Models (Sketch with intersection) Within some design neighborhoodWithin some design neighborhood Limited by constraintsLimited by constraints –Topological –Functional –…..????? Design Neighborhoods Proposed Partial Models (Sketch with intersection)Proposed Partial Models (Sketch with intersection) Within some design neighborhoodWithin some design neighborhood Limited by constraintsLimited by constraints –Topological –Functional –…..?????

28. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE Partially Defined Models and Robustness Proposed Models (Sketches)Proposed Models (Sketches) Partially Defined ModelsPartially Defined Models RobustnessRobustness –Reliability of modeling tools, and –Usability of models across multiple applications Partially Defined Models and Robustness Proposed Models (Sketches)Proposed Models (Sketches) Partially Defined ModelsPartially Defined Models RobustnessRobustness –Reliability of modeling tools, and –Usability of models across multiple applications