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Chapter 4

IAT 343 Chapter Notes - Chapter 4: Levelup


Department
Interactive Arts & Tech
Course Code
IAT 343
Professor
Steve DiPaola
Chapter
4

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WK2:Chapter4
January24,2018 11:55PM
Chapter4:ModelingTechniquesPg.115‑138
4.2CurvedLines
FivePopularTypesofCurves
NURBScurve117
• Curvesarecataloguedbasedontheirmathematicaland
geometriccharacteristics
• 5populartypesofsplinesusedinmainstream3dmodeling:
○ Linearsplines
○ cardinalsplines
○ B‑splines
○ Beziercurves
○ NURBSornonuniformrationalb‑splines
• Splinesarecalledcontrolledcurvesbecausetheyaregenerated
fromadefiningpolygon
• Structuresthatcontrolthesplinesareinvisible–theyare
displayedonlywhileweshapethespline–theycontain
importantinfothatcanbeusedtoreshapethespline
• Controlsfoundinsplinesincludethecontrolsplineorcontrol
polygonorhull,thecontrolpointsorcontrolvertices,the
tangentpoints,theknots,andtheweights
• Eachsplinecurveischaracterizedbyhowitiscontrolledbythe
controlpointsorcontrolvertices
• Alinearsplinelookslikeaseriesofstraightlinesconnectingthe
controlpoints
• Acardinalsplinelookslikepassesthroughallofitscontrol
points
B‑splinelookslikeacurvedlinethatrarelypassesthroughthe
controlpoints
Beziercurvespassthroughallthecontrol
○ Onlycurvethathastangentpointsinadditiontocontrol
points
NURBSdoesnotpassthroughitscontrolpoints
○ Offersahighdegreeoflocalcurvecontrolbyusing
weightsandknots
○ Thesecontrolsallowaportionofthesplinetobemodified
withoutaffectingotherpartsofthespline
○ 1weightisattachedtoeachcontrolpointwhich
determinethedistanceb/wthecontrolpointandthe
apexofthecurve
• Controlpointscancontrolthecurvatureortensionofacurved
linemainlybyhowclosetheyaretooneanotherandbyhow
closetheirtangentpointsarefromthecurve
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• Allcontrolverticesonasplinehavethesameweightfactor
calledanonrationalcurve
Rationalcurve:whenthevaluesoftheweightsonthecurveare
modified
• ManipulatingweightsonaNURBScurvemayimprovethesubtle
shapingofaline
○ Canslowdowntherenderingofthefinalmodel
• Workingwithdifferentweightvaluesisthatmanysystemswill
ignorethedatawhenmodelfilesareexchanged
KnotsonaNURBSdeterminethedistributionandlocaldensity
ofpointsonacurve
• Min.#ofknowsrequiredtoformacurvesegment=tothe
degreeofacurve+1+#ofcontrolpoints
• Thehigherthedegreeofacurve=morecomputationis
requiredtocreateit
• Curvesofthefirstdegreecorrespondtoquadraticcurves
• Curvesofthe3rddegreecorrespondtocubiccurves
• Thehigherthedegreeofacurve,themorepointsandknotsare
requiredtoformacurvesegment
SimpleExtrusion121
Extrusionstandsfortheprocessofshapingamaterialbyforcing
itwithheatandpressurethroughadie
• Die:atoolusedforshapingorstampingdifferentmaterials
• Industrialextrusionisbasedonastationarydie;limitationsin
handlinghotmaterialsandheavydie
• 3dmodelingcomputerprogramsoffersimpleextrusiontools–
likeheavyindustrycounterparts‑create3dshapesbystarting
witha2doutlineandextrudingorextendingitalongastraight
pathalong1axis
• Simpleextrusionhappensalonganyoneaxis
• 2doutlinestobeextrudedcanbecreatedwithgeometric
primitivetoolsorexportedfromotherprogramsinhighly
portablefileformats
• Extrusionakalofting(2doutlinesareduplicatedandmoveda
levelup)
LatheorSurfacesofRevolution122
Lathe/revolve:aformofsweeping
• Alwayspresentedasastand‑alonetool,,separatefromthe
general‑purposesweepingtool
Surfaceofrevolution:thesurfacescreatedwiththistechnique
• Softwarebasedlathetoolsimulatesareallathe,whichisatool
composedofarotatingbaseonwhichyouplaceacylinderof
woodthatisshapedbyplacingasteelbladeonitssurfaceasthe
baserotatesarounditsverticalaxis
• Softwarelathesweepsa2doutlinearound1axis;the2doutline
maybeopenorclosed
• Anew3dshapeemergesasthe2doutlineissweptalonga
circularorradialpath;itusuallyremainsperpendiculartothe
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