[图形学]3d数学基础 图形与游戏开发(习题答案)

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1、AnswersChapter21)Givethecoordinatesofthefollowingpoints:a(-2.5,3)b(1,2)c(2.5,2)d(-1,1)e(0,0)f(2,-0.5)g(-0.5,-1.5)h(0,-2)j(-3,-2)12)Listthe48differentpossiblewaysthatthe3Daxesmaybeassignedtothedirections“north,”“east”and“up.”Identifywhichofthesecombinationsareleft-handed,andw

2、hichareright-handed.NorthEastUpHandNorthEastUpHand+x+y+zLeft+x+z+yRight+x+y–zRight+x+z–yLeft+x–y+zRight+x–z+yLeft+x–y–zLeft+x–z–yRight–x+y+zRight–x+z+yLeft–x+y–zLeft–x+z–yRight–x–y+zLeft–x–z+yRight–x–y–zRight–x–z–yLeft+y+x+zRight+y+z+xLeft+y+x–zLeft+y+z–xRight+y–x+zLeft+y–z+

3、xRight+y–x–zRight+y–z–xLeft–y+x+zLeft–y+z+xRight–y+x–zRight–y+z–xLeft–y–x+zRight–y–z+xLeft–y–x–zLeft–y–z–xRight+z+x+yLeft+z+y+xRight+z+x–yRight+z+y–xLeft+z–x+yRight+z–y+xLeft+z–x–yLeft+z–y–xRight–z+x+yRight–z+y+xLeft–z+x–yLeft–z+y–xRight–z–x+yLeft–z–y+xRight–z–x–yRight–z–y–x

4、Left3)Inapopularmodelingprogram3DStudioMax,thedefaultorientationoftheaxesisfor+xtopointright,+ytopointforward,and+ztopointup.Isthisaleft-orright-handedcoordinatespace?Right-handed.2Chapter31)DrawanestedspacehierarchytreeforthesheepdescribedinSection3.3,assumingthatitshead,ea

5、rs,upperlegs,lowerlegs,andbodymoveindemendently.2)Supposeourobjectaxesaretransformedtoworldaxesbyrotatingthemcounterclockwisearoundthey-axisby42ºandthentranslatingsixunitsalongthez-axisand12unitsalongthex-axis.Describethistransformationfromtheperspectiveoftheobject.Imagineap

6、ointontheobject,inobjectspace.Astheaxesarerotatingcounterclockwise,thepointisactuallyrotatingcounterclockwiserelativetotheaxes.Then,astheaxestranslateby[12,0,6],thepointtranslates[-12,0,-6]relativetotheaxes.3)Whichcoordinatespaceisthemostappropriateinwhichtoaskthefollowingqu

7、estions?a)Ismycomputerinfrontoforbehindme?Objectspace.Ifweknowthepositionofthecomputerwithinourobjectspace,thisquestionisatrivialmatterofcheckingforapositivezvalue.(AssumingtheconventionsfromSection2.3.4)b)Isthebookeastorwestofme?Inertialspaceistheeasiestspacetomakethistest.

8、Again,assumingtheconventionsfromSection2.3.4,thebookiseastofusifthex-coordi