一类保形的有理三次插值样条

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1、山东大学硬士学位论文ASIU心EPRESERVl[NGRArIONALCUBIC玳TERPOLATIONSPLINEAsmoothcurveint日polationschemeforthevisuMiTmtionofscieⅡtificdatahasbeendevelopedinthisthesis，which咖preservetheinheritedfeaturesdadlapeddata．Twofamih'esofparameters，inthedescriptionofthepiecewiserationalc

2、ubicinterpolate她havebeenconstrainedtopreservetheshapeofthedatamshapeconstraintsarerestrictedonshapeparameterstoassuretheshapepreserva-fionofthedata啾．mrational搬schemehas8uniquerepresentatiommdegreeofsmoothnessattainedis伊．Thjsthesisiscomposedoffiveparts．Inchapter

3、1，theauthorgiv氆^concisedepictofthehistoryofinterpolationsadthecurrentsituationofshapepreservingstudy．Themostimportantproblemsrestrictingtherationalspline’Susagea弛ddicieacyofautomation,additionalre-strictionOildataetc．‘Inchapt口2，theauthorputsforwardthedefinition

4、ofthepiecewiserationalfunction：S∽=(1-o)3q^+0(1一∞2【(2t‘‘q+地)五+q乜列+萨(I一口)【(2t‘‘q+蛳)^+l一％乜c“I】+萨地^+l(1一日)2t￡I+2啦地口(1一∞+萨珥here口；0一向)／～，t‘I，tlIaleshapeparametersandt‘l，q>0，whichcanchangetheshapeofcurve．Inmostapplications。thederivativeparametersdiarenotgivenandhencem

5、ustbedeterminedfromthedataSotwoch9icesarementionedinthesecondsection．Inthethirdsectionwegett‘‘；q-+co，最(功-．五(1一口)+五+lp，80theeffectivenessfortheshapecontrolcanbes嘲hereandthatisthetheoreticalfoundationofshape-preservinganalym．Theshapepreservationoftheinterpolation

6、splineisstressedinchapter3．hadditionaltodiscusstheshape-preservingofmonotonicdata,COnVeXdataandpo争itivedata,theproblemstoconstraintherationalinterpohtionCU_rV器toliestrictlyIII山东大学硕士学位论文aboveorbelow矗细piecewiselinearcurveandbetweentwogivenpiecewisefin-earcurvesal

7、esolved．When越k}dcurvetokeepmonotone，F(z)≥(≤)Oreqllir蕾shapep咖ete聃tlI≥老，q≥％}．Inthe姗eway,，(z)≥o(so)rd{u晒蜥p8跚et_哪t‘‘≥环等暑幻，仉≥揣．s(而>0requiresshapeparametemtI‘>瑚x(o，一纽2‘16‘)，q>max(o，生瓣)．Aftergettingtheseresults，we静hancorestrictionOnt‘‘，仉thatkeepsthecurvebetweentwogive

8、npiec耐selinearcurves．Thus耽getitthatputtingtheshape-preservingcurvebetweentwogivenpiecewiselinearcurves．Theapproximatioupropertiesoftherationalcubicsplinearestudiedinchap-ter