非正则equivolumetric偏置曲线曲面的分析

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1、、≮≯，l一一．’_tV一，，f、：t，≈，．f非正则Equivolumetric偏置曲线曲面的研究AbstractOffsettingofcurvesandsurfacesisoneofthemostimportantgeometricoperationsinComputerAidedGeometricDesign：CAGD．Theoffsetapproximationmayhaveself-intersectionseventhoughtheoriginalcurveorsurfacehasnoself-intersection--anoffsetcurveors

2、urfacehasself-intersectionslocallyduetoregionsofhighcurvatureintheoriginalcurveorsurfaceandtheglobalSelf-intersectionresultsfromtwodifferentpointsofthecurveorsurfacethatareOf．fSettothesame10cation．Theseself-intersectionsmustbedetectedandtrimmedawaytoobtainaproperoffset．Theself-intersect

3、ionsproblemofvariableradiusoffsetsurfacespresentsmorecomplexformbecauseofthevariousrealradiusfunctionandhighdimensions．Inordertocompletethetheoryofoffsetcurves／surfaces，inouritem，theirregularinvari—distanceoffsetcurves／surfacesiSresearchedwhichiStheextensionofequi—distanceoffset．Conside

4、radisk(ofradiusequaloffsetradius)movingalongtheoriginalcurve．Ifanoffsetcurvepointiscontainedinaninstanceofthemovingdisk’Sinterior，thepointbelongstoaself-intersecting．Thenrealself-intersectpointsareconfinedbythenormal．Bysolvingasystemofpolynomialequationsforoffsetcurves／surface，alllocala

5、ndglobalself-intersectionregionsinoffsetcurvescanbedetectedandtrimmedeffectivelybythealgorithm，thentheself-intersectionsiSvanishedinvari．distanceoffsetCurves．Theself_intersectionsinthevariableradiusoffsetcurvesaredetectedandtrimmingeffectivelybythealgorithm．Next，thealgorithmforvari-dist

6、anceoffsetcurveisextenttothevari—distanceoffsetsurfaces．Consideradisk(ofradiusequaloffsetradius)movingalongtheoriginalsurface．Ifanoffsetsurfacepointiscontainedinaninstanceofthemovingdisk’Sinterior，thepointbelongstoaself-intersecting．Thenrealself-intersectpointsareconfinedbythenormal．Bys

7、olvingasystemofpolynomialequationsforoffsetsurfaces，alllocalandglobalself-intersectionregionsinoffsetsurfacescanbedetectedandtrimmedeffectivelybythealgorithm．thentheself二intersectionsisvanishedinvari—distanceoffsetcurves．Finally，theirregularinEquivolumetriccurves／surfaces，which