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Advancing Geometric Accuracy in Intersection Modeling for Engineering Applications

Explore geometric accuracy in intersection modeling, covering topology, robustness, semantics, and approximation for CAD systems. Investigate gaps, curves, and surfaces with advanced techniques. Address unique representations and proposed partial models, aiming to enhance reliability and usability across various applications.

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Advancing Geometric Accuracy in Intersection Modeling for Engineering Applications

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  1. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE • Geometric Accuracy: • 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)

  3. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE • Robustness (with D. R. Ferguson, Boeing) • Robustness • 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 Display • Drafting Support • Link to CAM • Not for sophisticated engineering simulations

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

  6. Geometry and Graphics Accuracy T. J. Peters, UConn, CSE • Semantics • Low 11 degrees • High 10 degrees

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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