Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

• Geometric Accuracy: Geometric Accuracy:

• Graphics Is Not Graphics Is Not the Only Show in Town! the Only Show in Town!

• Geometric Accuracy: Geometric Accuracy:

• Graphics Is Not Graphics Is Not the Only Show in Town! the Only Show in Town!

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

• Topology : Topology : ConnectivityConnectivity of Geometric Model of Geometric Model((particularly at surface intersectionsparticularly at surface intersections))

• Topology : Topology : ConnectivityConnectivity of Geometric Model of Geometric Model((particularly at surface intersectionsparticularly at surface intersections))

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

Robustness (with D. R. Ferguson, Boeing)Robustness (with D. R. Ferguson, Boeing)

• RobustnessRobustness

– Reliability of modeling tools , andReliability of modeling tools , and

– Usability of models across multiple applicationsUsability of models across multiple applications

Robustness (with D. R. Ferguson, Boeing)Robustness (with D. R. Ferguson, Boeing)

• RobustnessRobustness

– Reliability of modeling tools , andReliability of modeling tools , and

– Usability of models across multiple applicationsUsability of models across multiple applications

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

Original Goals for CAD SystemsOriginal Goals for CAD Systems

• Graphics DisplayGraphics Display

• Drafting SupportDrafting Support

• Link to CAMLink to CAM

• NotNot for sophisticated engineering simulations for sophisticated engineering simulations

Original Goals for CAD SystemsOriginal Goals for CAD Systems

• Graphics DisplayGraphics Display

• Drafting SupportDrafting Support

• Link to CAMLink to CAM

• NotNot for sophisticated engineering simulations for sophisticated engineering simulations

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

• IntersectionIntersection

– Two surfacesTwo surfaces

– Common Boundary CurveCommon Boundary Curve

– Curve on both Surfaces !!!Curve on both Surfaces !!!

• IntersectionIntersection

– Two surfacesTwo surfaces

– Common Boundary CurveCommon Boundary Curve

– Curve on both Surfaces !!!Curve on both Surfaces !!!

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

• SemanticsSemantics

– LowLow 11 degrees11 degrees

– HighHigh 10 degrees10 degrees

• SemanticsSemantics

– LowLow 11 degrees11 degrees

– HighHigh 10 degrees10 degrees

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

• Intersection Point (Intent)Intersection Point (Intent)• Intersection Point (Intent)Intersection Point (Intent)

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

• Intersection Point (Reality)Intersection Point (Reality)• Intersection Point (Reality)Intersection Point (Reality)

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

• Intersection Point (Approximation)Intersection Point (Approximation)

• Numerical SolutionNumerical Solution

– t approximately at intersectiont approximately at intersection

– s approximately at intersections approximately at intersection

– need for some tolerance factorneed for some tolerance factor

• Intersection Point (Approximation)Intersection Point (Approximation)

• Numerical SolutionNumerical Solution

– t approximately at intersectiont approximately at intersection

– s approximately at intersections approximately at intersection

– need for some tolerance factorneed for some tolerance factor

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

• Intersection Curve (Approximation)Intersection Curve (Approximation)

• Numerical SolutionNumerical Solution

– Curve-1 approximately at intersectionCurve-1 approximately at intersection

– Curve-2 approximately at intersectionCurve-2 approximately at intersection

– need for some tolerance factorneed for some tolerance factor

– Curve-1 NOT EQUAL Curve-2Curve-1 NOT EQUAL Curve-2

• Intersection Curve (Approximation)Intersection Curve (Approximation)

• Numerical SolutionNumerical Solution

– Curve-1 approximately at intersectionCurve-1 approximately at intersection

– Curve-2 approximately at intersectionCurve-2 approximately at intersection

– need for some tolerance factorneed for some tolerance factor

– Curve-1 NOT EQUAL Curve-2Curve-1 NOT EQUAL Curve-2

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 transfer Investigating 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 transfer Investigating technology transfer

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

• Just two bi-cubic surface Just two bi-cubic surface

– Can have degree 324 (Sederberg)Can have degree 324 (Sederberg)

– Approximate to reduce data volumeApproximate to reduce data volume

• Just two bi-cubic surface Just two bi-cubic surface

– Can have degree 324 (Sederberg)Can have degree 324 (Sederberg)

– Approximate to reduce data volumeApproximate to reduce data volume

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

• Gap Checking Tool for STEPGap Checking Tool for STEP

– Used DT_NURBS utilitiesUsed DT_NURBS utilities

– STEP Tools Conversion (from Express)STEP Tools Conversion (from Express)

– Prototype Research CodePrototype Research Code

– Paper submitted to CAD Robustness issuePaper submitted to CAD Robustness issue

• Gap Checking Tool for STEPGap Checking Tool for STEP

– Used DT_NURBS utilitiesUsed DT_NURBS utilities

– STEP Tools Conversion (from Express)STEP Tools Conversion (from Express)

– Prototype Research CodePrototype Research Code

– Paper submitted to CAD Robustness issuePaper submitted to CAD Robustness issue

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

Digits of accuracy for gaps by applicationDigits of accuracy for gaps by applicationDigits of accuracy for gaps by applicationDigits of accuracy for gaps by application

Surface Intersection

Electromagnetics

Fluid DynamicsVisualizaltion

2 8

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

Surface IntersectionsSurface Intersections

• 2 < Gap < 4 , for Visualization2 < Gap < 4 , for Visualization

• 5 < Gap < 8 , for Electromagnetics 5 < Gap < 8 , for Electromagnetics

Surface IntersectionsSurface Intersections

• 2 < Gap < 4 , for Visualization2 < Gap < 4 , for Visualization

• 5 < Gap < 8 , for Electromagnetics 5 < Gap < 8 , for Electromagnetics

?21 SS

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

Unique Representation -- Very ExpensiveUnique Representation -- Very ExpensiveUnique Representation -- Very ExpensiveUnique Representation -- Very Expensive

CEMVisualizeSS 21

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

Grandine-Klein Intersector (CAGD, 1997)Grandine-Klein Intersector (CAGD, 1997)

• Input: Two surfaces Input: Two surfaces and error boundand 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)Grandine-Klein Intersector (CAGD, 1997)

• Input: Two surfaces Input: Two surfaces and error boundand 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

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

Approximation CounterexampleApproximation 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 CounterexampleApproximation 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

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

Design NeighborhoodsDesign 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

– TopologicalTopological

– FunctionalFunctional

– ……..?????..?????

Design NeighborhoodsDesign 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

– TopologicalTopological

– FunctionalFunctional

– ……..?????..?????

Geometry and Graphics Accuracy T. J. Peters, UConn, CSE

Partially Defined Models and RobustnessPartially Defined Models and Robustness

• Proposed Models (Sketches) Proposed Models (Sketches)

• Partially Defined ModelsPartially Defined Models

• RobustnessRobustness

– Reliability of modeling tools , andReliability of modeling tools , and

– Usability of models across multiple applicationsUsability of models across multiple applications

Partially Defined Models and RobustnessPartially Defined Models and Robustness

• Proposed Models (Sketches) Proposed Models (Sketches)

• Partially Defined ModelsPartially Defined Models

• RobustnessRobustness

– Reliability of modeling tools , andReliability of modeling tools , and

– Usability of models across multiple applicationsUsability of models across multiple applications