最全的UG方程曲線詳細(xì)表達(dá)式

1、在UG中利用【規(guī)律曲線】|【根據(jù)方程】繪制各種方程曲線：1、極坐標(biāo)或柱坐標(biāo)r,Z與直角坐標(biāo)系x,y,z的轉(zhuǎn)換關(guān)系：x=r*cosQy=r*singz=z2、球坐標(biāo)系r,0與£直角坐標(biāo)系x,y,z的轉(zhuǎn)換關(guān)系：x=rsin0cosy=rsin0sinz=rcos0在UG表達(dá)式中輸入的theta=0;phi=|;r=rho【注：所有UG表達(dá)式中,必須先在名稱欄輸入t,公式欄輸入0,類型為恒定的,即無單位.t是UG自帶的系統(tǒng)變量,其取值為01之間的連續(xù)數(shù)】1 .直線直線的數(shù)學(xué)方程為y-y0=tan8*x-x0,假設(shè)直線經(jīng)過點(diǎn)10,20,傾角8為30°,長度L為40,即UG表達(dá)式為：

2、theta=30L=40xt=10+L*costheta*tyt=20+L*sintheta*tzt=0效果如圖12 .圓和圓弧圓的數(shù)學(xué)方程為(x-x0)A2+(y-y0)A2=rA2,假設(shè)圓心坐標(biāo)為(50,40),半徑r為30,即UG表達(dá)式為：r=30theta=t*360xt=50+r*cos(theta)yt=40+r*sin(theta)zt=0效果如圖23 .橢圓和橢圓弧橢圓的數(shù)學(xué)方程為(x-x0)A2/aA2+(y-y0)A2/bA2=1,假設(shè)橢圓中央坐標(biāo)為(50,40),長半軸a為30(在X軸上),短半軸b為20,即UG表達(dá)式為：a=30b=20theta=t*360xt=50+

3、a*cos(theta)yt=40+b*sin(theta)zt=0效果如圖3圖3圖44 .雙曲線雙曲線的數(shù)學(xué)方程為x2/a2-y2/b2=1,假設(shè)中央坐標(biāo)為(0,0),實(shí)長半軸a為4(在x軸上),虛半軸b為3,y的取值范圍為-5+5內(nèi)的一段,即UG表達(dá)式為：a=4b=3yt=10*t-5xt=a/b*sqrt(bA2+ytA2)或xt=-a/b*sqrt(bA2+ytA2)zt=0做出一半后進(jìn)行鏡像復(fù)制,效果如圖45 .拋物線拋物線I的數(shù)學(xué)方程為y2=2px,假設(shè)拋物線的頂點(diǎn)為(30,20)焦點(diǎn)到準(zhǔn)線的距離p=8,y的取值范圍為-25+25,即UG表達(dá)式為：p=8yt=50*t-25+20x

4、t=(yt-20)A2/(2*p)+30zt=0效果如圖5-1拋物線II數(shù)學(xué)參數(shù)方程：x=2pt2,y=2pt(其中t為參數(shù)).UG表達(dá)式為：p=8tt=t*4-2xt=2*p*ttA2yt=2*p*ttzt=0效果如圖5-26 .正弦曲線假設(shè)正弦曲線一個周期X方向長度為50,振幅為10,即UG表達(dá)式為:theta=t*360xt=50*tyt=10*sin(theta)zt=0效果如圖67 .余弦曲線假設(shè)余弦曲線一個周期X方向長度為50,振幅為10,即UG表達(dá)式為:theta=t*360xt=50*tyt=10*cos(theta)zt=0效果如圖78.圓柱螺旋線假設(shè)圓柱螺旋線半徑r為20,

5、螺距p為10,圈數(shù)n為5,即UG表達(dá)式為:r=20p=10n=5theta=t*360xt=r*cos(theta*n)yt=r*sin(theta*n)zt=p*n*t或zt=cos(theta*n)+p*n*t效果如圖8圖89 .碟形彈簧假設(shè)碟形彈簧半徑r為20,螺距p為10,圈數(shù)n為5,即UG表達(dá)式為:r=20p=10n=5theta=t*360xt=r*cos(theta*n)yt=r*sin(theta*n)zt=cos(theta*nA2)+p*n*t或zt=cos(theta*nA2.4)+p*n*t效果如圖910 .圓錐螺旋線和圓臺螺旋線假設(shè)圓錐螺旋線底圓半徑r為20,螺距p為

6、5,圈數(shù)n為10,即UG表達(dá)式為:r=20*(1-t),假設(shè)圓臺上端半徑為5,那么r=20*(1-t*0.75)p=5n=10theta=t*360xt=r*cos(theta*n)yt=r*sin(theta*n)zt=p*n*t效果如圖10-1、10-2圖10-1圖10-211三尖瓣線三尖瓣線數(shù)學(xué)方程：x=r(2cos(+cos2肌y=r(2sinasin2.假設(shè)將2變?yōu)閚即擴(kuò)展為n+1尖瓣線.假設(shè)r=20,即UG表達(dá)式為：r=20n=2theta=t*360xt=r*(n*cos(theta)+cos(n*theta)yt=r*(n*sin(theta)-sin(n*theta)zt=0

7、效果如圖1112 .星形線【四尖瓣線】星形線的數(shù)學(xué)方程：x=r*cos3&y=r*sin3自【由n+1尖瓣線通式：x=r(n*cos(+cos(n*.)；y=r(n*sin&sin(n*9)當(dāng)n=3時的情況.三角函數(shù)公式:sin38=3sin04sin3gcos38=4803cos0假設(shè)r=20,即UG表達(dá)式為：r=20theta=t*360xt=r*(cos(theta)A3yt=r*(sin(theta)A3zt=0效果如圖1213 .漸開線漸開線的數(shù)學(xué)方程：x=r(cos+fsin肌y=r(sina&cos肌假設(shè)漸開線的基圓半徑r為10,展開角度8為360*2,即

8、UG表達(dá)式為：r=10theta=360*2*ts=r*rad(theta)=r*(2*pi()/360)*theta=2*pi()*r*t*2xt=r*cos(theta)+s*sin(theta)yt=r*sin(theta)-s*cos(theta)zt=0效果如圖1314 .阿基米德螺線(等徑螺線)阿基米德螺線(等徑螺線)數(shù)學(xué)方程：r=a*8(極坐標(biāo)),假設(shè)a=10,0=360*2,即UG表達(dá)式為：a=10theta=t*360*2r=a*thetaxt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖1415 .對數(shù)螺線(等角螺線)對數(shù)螺線(等角螺線)數(shù)學(xué)方程：

9、r=aem9o對數(shù)螺線的定義和性質(zhì)：運(yùn)動方向始終與極徑保持定角入的動點(diǎn)軌跡稱為對數(shù)螺線.假設(shè)a=0.005,即UG表達(dá)式為：a=0.005theta=t*360*2r=exp(a*theta)xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖1516雙曲螺線數(shù)學(xué)方程：r=a/0o假設(shè)a=10,即UG表達(dá)式為：a=100theta=t*360*2+1r=a/thetaxt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖1617.連鎖螺線數(shù)學(xué)方程：r2=a2/9假設(shè)a=10,即UG表達(dá)式為:a=10theta=t*360*2+1r=a/sqrt(t

10、heta)xt=r*cos(theta)yt=r*sin(theta)zt=018 .心臟線(腎形線)心臟線數(shù)學(xué)方程：r=2a(1+cos肌腎形線數(shù)學(xué)方程：r=a(1+2sin(0/2)假設(shè)a=10,0=360°,即UG表達(dá)式為：a=10theta=360*tr=2*a*(1+cos(theta)【或r=a*(1+sin(theta)l【或r=a*(1+2*sin(theta/2)xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖1819 .雙弧外擺線雙弧外擺線的數(shù)學(xué)方程：x=3b*cos(+a*cos38,y=3b*sinOa*sin30b即UG表達(dá)式為:

11、a=10b=10theta=t*360xt=3*b*cos(theta)+a*cos(3*theta)yt=3*b*sin(theta)+a*sin(3*theta)zt=0效果如圖1920 .腎臟線數(shù)學(xué)方程：x=a(3cost-cos3t);y=a(3sint-sin3t)a=10theta=360*txt=a*(3*cos(theta)-cos(3*theta)yt=a*(3*sin(theta)-sin(3*theta)zt=0效果如圖2021 .Talbot曲線【？x=(a2+f2+sin2t)cost/a,y=(a2+f2sin2t-2f2)sint/b】Talbot曲線數(shù)學(xué)方程：x

12、=(a2+f2sin29cos(/a,y=(a2+f2sin20-2f)sin(/bo假設(shè)a=1.1,b=0.666,0=360°,f=1,即UG表達(dá)式為：theta=360*ta=1.1b=0.666c=sin(theta)f=1xt=(aA2+fA2*cA2)*cos(theta)/ayt=(aA2-2*f+fA2*cA2)*sin(theta)/bzt=0效果如圖2122 .四葉線四葉線數(shù)學(xué)方程：r=a*cos20,假設(shè)a=10,(=360°,即UG表達(dá)式為：a=10theta=t*360r=a*cos(2*theta)xt=r*cos(theta)yt=r*sin(

13、theta)zt=0效果如圖2223 .三葉線三葉線數(shù)學(xué)方程：r=a*cos30=a*cos0*(41s時),假設(shè)a=10,0=180°,即UG表達(dá)式為:a=10theta=t*180r=a*cos(3*theta)xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖23iTj24雙葉線雙葉線數(shù)學(xué)方程：r=4a*cos8*sin2,假設(shè)a=10,k89.999°,即UG表達(dá)式為:a=10theta=t*89.999r=4*a*cos(theta)*sin(2*theta)xt=r*cos(theta)yt=r*sin(theta)zt=0繪制一半后利

14、用y軸鏡像,效果如圖2425.Rhodonea曲線Rhodonea曲線數(shù)學(xué)方程：r=a*sin(k0,)假設(shè)UG表達(dá)式為:theta=t*360*3xt=(10-6)*cos(theta)+10*cos(10/6-1)*theta)yt=(10-6)*sin(theta)-6*sin(10/6-1)*theta)zt=0那么效果如圖25-1假設(shè)UG表達(dá)式為：theta=t*360*5xt=4*cos(theta)+10*cos(0.8*theta)yt=4*sin(theta)-10*sin(0.8*theta)zt=0那么效果如圖25-226 .外擺線外擺線數(shù)學(xué)方程：x=(a+b)cos6c

15、os(a+b)/b;0y=(a+b)sin-rsin(a+b)/b8)【其中a、b、r分別是基圓、滾圓、擺點(diǎn)半徑,8為公轉(zhuǎn)角.UG表達(dá)式為:theta=360*t*10a=5b=8r=8xt=(a+b)*cos(theta)-r*cos(a/b+1)*theta)yt=(a+b)*sin(theta)-r*sin(a/b+1)*theta)zt=0效果如圖2627 .內(nèi)擺線內(nèi)擺線數(shù)學(xué)方程：x=(a-b)cos(+rcos(b-a)/b9;y=(a-b)sinOrsin(b-a)/b.【其中a、b、r分別是基圓、滾圓、擺點(diǎn)半徑,8為公轉(zhuǎn)角.UG表達(dá)式為:theta=360*t*10a=5b=8r

16、=10xt=(a-b)*cos(theta)+r*cos(1-a/b)*theta)yt=(a-b)*sin(theta)+r*sin(1-a/b)*theta)zt=0效果如圖2728 .長短幅圓內(nèi)旋輪線UG表達(dá)式為：a=5b=7c=2.2theta=360*t*10xt=(a-b)*cos(theta)+c*cos(a/b-1)*theta)yt=(a-b)*sin(theta)-c*sin(a/b-1)*theta)zt=0效果如圖28圖28圖2929 .長短幅圓外旋輪線UG表達(dá)式為：theta=360*t*10a=5b=3c=5xt=(a+b)*cos(theta)-c*cos(a/b

17、+1)*theta)yt=(a+b)*sin(theta)-c*sin(a/b+1)*theta)zt=0效果如圖2930封閉球形環(huán)繞曲線r=10theta=360*tphi=360*t*10xt=r*sin(theta)*cos(phi)yt=r*sin(theta)*sin(phi)zt=r*cos(theta)效果如圖30圖30圖3131 .費(fèi)馬線(有點(diǎn)像螺紋線)費(fèi)馬線數(shù)學(xué)方程：r2=a20(需分兩段做).UG表達(dá)式為：a=4theta=t*360*5r=a*sqrt(rad(theta)xt=r*cos(theta)yt=r*sin(theta)zt=0繪制一半后,繞原點(diǎn)旋轉(zhuǎn)180復(fù)制

18、,效果如圖3132 .球面螺旋線球面螺旋線采用球坐標(biāo)系的方程：rho=10,theta=t*180,phi=t*360*20.假設(shè)UG表達(dá)式為：r=10theta=t*180phi=t*360*20xt=r*sin(theta)*cos(phi)yt=r*sin(theta)*sin(phi)zt=r*cos(theta)那么效果如圖32-1球面螺旋線(罩形)UG表達(dá)式為：r=10theta=t*120phi=t*360*20xt=r*sin(theta)*cos(phi)yt=r*sin(theta)*sin(phi)zt=r*cos(theta)那么效果如圖32-2圖32-1圖32-233

19、 .圓內(nèi)螺旋線圓內(nèi)螺旋線的UG表達(dá)式為:theta=t*360r=10+10*sin(6*theta)xt=r*cos(theta)yt=r*sin(theta)zt=2*sin(6*theta)效果如圖33-1、33-234 .蝴蝶曲線蝴蝶曲線球坐標(biāo)方程：rho=8*t,theta=360*t*4,phi=-360*t*8.UG表達(dá)式為:theta=t*360*4r=8*tphi=-360*t*8xt=r*sin(theta)*cos(phi)yt=r*sin(theta)*sin(phi)zt=r*cos(theta)效果如圖34-1、34-2圖34-1圖34-235 .太陽線太陽線柱坐標(biāo)

20、方程：r=1.5*cos(50*theta)+1,theta=t*360,z=0.即UG表達(dá)式為:theta=t*360r=1.5*cos(50*theta)+1xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖35圖35圖3636 .九瓣花九瓣花的UG表達(dá)式為:r=20*ttheta=t*360*90phi=t*360*10xt=r*sin(theta)*cos(phi)yt=r*sin(theta)*sin(phi)zt=r*cos(theta)俯視圖效果如圖3637 .蝶線蝶線球坐標(biāo)方程：rho=4*sin(t*360)+6*cos(t*360A2),theta

21、=t*360,phi=log(1+t*360)*t*360.即UG表達(dá)式為：theta=t*360phi=log(1+t*360)*t*360r=4*sin(t*360)+6*cos(t*360A2)xt=r*sin(theta)*cos(phi)yt=r*sin(theta)*sin(phi)zt=r*cos(theta)效果如圖3738 .無底籃子曲線無底籃子曲線方程：r=5+0.3*sin(t*180)+t,theta=t*360*30,z=t*5.即UG表達(dá)式為:theta=360*t*30r=5+0.3*sin(t*180)+txt=r*cos(theta)yt=r*sin(thet

22、a)zt=t*5效果如圖38圖37圖3839飛蝶曲線UFO(漩渦線)漩渦線的UG表達(dá)式為：r=20A2*ttheta=30*log(30)*tphi=360*t*20xt=r*sin(theta)*cos(phi)yt=r*sin(theta)*sin(phi)zt=r*cos(theta)那么效果如圖39-1圖39-1圖39-2UFO的球坐標(biāo)方程：rho=t*20A2,theta=t*log(30)*60,phi=t*7200.即UG表達(dá)式為:r=20A2*ttheta=60*log(30)*tphi=360*t*20xt=r*sin(theta)*cos(phi)yt=r*sin(thet

23、a)*sin(phi)zt=r*cos(theta)效果如圖39-240 .蘑菇曲線蘑菇曲線的球坐標(biāo)：rho=tA3+t*(t+1)theta=60*log(60)*tphi=tA2*360*100xt=r*sin(theta)*cos(phi)yt=r*sin(theta)*sin(phi)zt=-r*cos(theta)效果如圖40-1、40-2圖40-1圖40-241 .葉妁形線葉(妁形線I的數(shù)學(xué)方程：x=3at/(1+t3)；y=3at2/(1+t3).假設(shè)a=10,即UG表達(dá)式為:a=10xt=3*a*t/(1+(tA3)yt=3*a*(tA2)/(1+(tA3)zt=0效果如圖41

24、-1葉形線II數(shù)學(xué)方程：r=4a*cosesin2abcos6假設(shè)a=10,b=2,依89°即UG表達(dá)式為：a=10b=2theta=89r=4*a*cos(theta)*(sin(theta)A2-b*cos(theta)xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖41-242概率曲線概率曲線UG表達(dá)式為:xt=t*10-5yt=exp(0-xtA2)zt=0效果如圖4243.箕舌線(魔線)箕舌線I的UG表達(dá)式為：a=10xt=t*100-50yt=8*aA3/(xtA2+4*aA2)zt=0效果如圖43-1箕舌線II數(shù)學(xué)方程：x=tan0,y=co

25、s28.UG表達(dá)式為:theta=160*t-80xt=tan(theta)yt=(cos(theta)A2zt=0效果如圖43-2魔線數(shù)學(xué)方程：x=a0；y=a/(1+2)a=10theta=t*360-180xt=a*rad(theta)yt=a/(1+(rad(theta)A2)zt=0效果如圖43-3圖43-2圖43-344.正切曲線正切曲線方程：x=t*8.5-4.25,y=tan(x*20).即UG表達(dá)式為：xt=t*8.5-4.25yt=tan(xt*20)zt=0效果如圖4445雙曲正弦曲線雙曲正弦曲線方程：x=6*t-3,y=(exp(x)-exp(0-x)/2.即UG表達(dá)式

26、為:xt=t*6-3yt=(exp(xt)-exp(-xt)/2zt=0效果如圖45圖44圖4546雙曲余弦曲線雙曲余弦曲線方程：x=6*t-3,y=(exp(x)+exp(0-x)/2.即UG表達(dá)式為:xt=t*6-3yt=(exp(xt)+exp(-xt)/2zt=0效果如圖4647雙曲正切曲線雙曲正切曲線方程：x=6*t-3,y=(exp(x)-exp(0-x)/(exp(x)+exp(0-x).即UG表達(dá)式為:xt=t*6-3yt=(exp(xt)-exp(0-xt)/(exp(xt)+exp(0-xt)zt=0效果如圖4748 .蔓葉線蔓葉線數(shù)學(xué)方程：r=2a*tanfsin8(分2

27、段做),假設(shè)a=10,0=75,即UG表達(dá)式為：theta=75a=10r=2*a*tan(theta)*sin(theta)xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖48圖48圖4949 .Lissajous曲線Lissajous曲線數(shù)學(xué)方程：x=a*sin(n0+c)=b*sin給假設(shè)a=10,b=10,c=100,n=3,=360,即UG表達(dá)式為：theta=t*360a=10b=10c=100n=3xt=a*sin(n*theta+c)yt=b*sin(theta)zt=0效果如圖4950 .“8字線“8字線方程I:x=a*cos(t*360),y=b

28、*sin(t*(2*360).假設(shè)a=2,b=1,即UG表達(dá)式theta=360*ta=2b=3xt=a*cos(theta)yt=b*sin(2*theta)zt=0效果如圖50-1“8字線方程IIGernono曲線數(shù)學(xué)方程:theta=360*txt=cos(theta)yt=sin(theta)*cos(theta)zt=0效果如圖50-2“8字線方程III(墨鏡線)的UG表達(dá)式為:theta=360*tr=10+(8*sin(theta)A2xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖50-3“8字線方程IV的UG表達(dá)式為:theta=360*ta=10

29、b=10xt=3*b*cos(theta)+a*cos(3*theta)yt=b*sin(theta)+a*sin(3*theta)zt=0效果如圖50-451 .一峰三駐點(diǎn)曲線一峰三駐點(diǎn)曲線方程：x=3*t-1.5,y=(xA2-1)A3+1.即UG表達(dá)式為:xt=3*t-1.5yt=(xtA2-1)A3+1zt=0效果如圖51圖51圖5252 .蛇形線蛇形線UG表達(dá)式為：xt=2*cos(t+1)*360)yt=2*sin(t*(5*360)zt=t*(t+1)效果如圖5253梅花線(圓角五星)梅花線1(圓角五星)的UG表達(dá)式為:theta=360*tr=10+(3*sin(theta*2

30、.5)A2xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖53-1梅花線II的UG表達(dá)式為：theta=t*360r=100+50*cos(5*theta)xt=r*cos(theta)yt=r*sin(theta)zt=2*cos(5*theta)效果如圖53-254手掌手掌的UG表達(dá)式為:theta=360*t+180r=cos(360*tA3*6)*2+5xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖5455直葉六葉線直葉六葉線的UG表達(dá)式為:theta=360*tr=10-(3*sin(theta*3)A2xt=r*cos(th

31、eta)yt=r*sin(theta)zt=-4*sin(theta*3)A2效果如圖55圖54圖5556.彎葉六葉線彎葉六葉線的UG表達(dá)式為:theta=360*tr=10-(3*sin(theta*3)A2xt=r*cos(theta)yt=r*sin(theta)zt=-(r*sin(theta*3)A2效果如圖56圖56圖5757 .六葉花形theta=t*360r=5-(3*sin(theta*3)A2xt=r*cos(theta)yt=r*sin(theta)zt=(r*sin(theta*3)A2效果如圖5758 .空間螺旋橢圓線a=10b=20theta=t*360*3xt=a

32、*cos(theta)yt=b*sin(theta)zt=t*3*4效果如圖5859.空間螺旋梅花線theta=t*360*4r=10+(3*sin(theta*2.5)A2xt=r*cos(theta)yt=r*sin(theta)zt=t*16效果如圖5960 .鼓形線(燈籠形)r=5+3.3*sin(t*180)+ttheta=t*360*10xt=r*cos(theta)yt=r*sin(theta)zt=t*10效果如圖60圖60圖6161 .鼓鼓形線r=6*sin(t*360)+ttheta=t*360*40xt=r*cos(theta)yt=r*sin(theta)zt=t*20

33、效果如圖6162 .蝴蝶結(jié)曲線(簪形線)蝴蝶結(jié)曲線方程：xt=200*t*sin(t*3600)yt=250*t*cos(t*3600)zt=300*t*sin(t*1800)效果如圖62-1簪形線方程：r=200*ttheta=900*tphi=t*900xt=r*sin(theta)*cos(phi)yt=r*sin(theta)*sin(phi)zt=r*cos(theta)效果如圖62-263 .鎖吶線鎖吶線I方程：r=tA10theta=tA3*360*6*3+tA3*360*3*3xt=r*cos(theta)yt=r*sin(theta)zt=tA3*(t+1)效果如圖63-1鎖

34、吶線II方程：xt=2*cos(t*360*3)*tyt=2*sin(t*360*3)*tzt=(sqrt(sqrt(sqrt(t)A3*5效果如圖63-2圖63-1圖63-264手把曲線theta0=t*360theta1=t*360*6r0=400r1=40r=r0+r1*cos(theta1)xt=r*cos(theta0)yt=r1*sin(theta1)zt=0效果如圖6465 .向日葵線theta=t*360r=30+10*sin(theta*30)xt=r*cos(theta)yt=r*sin(theta)zt=0圖6566 .環(huán)形二次曲線xt=50*cos(t*360)yt=5

35、0*sin(t*360)zt=10*cos(t*360*8)效果如圖6667 .柱面正弦波線r=30theta=t*360xt=r*cos(theta)yt=r*sin(theta)zt=5*sin(5*theta-90)效果如圖6768.環(huán)形螺旋線n=15theta=t*360xt=(50+10*sin(theta*n)*cos(theta)yt=(50+10*sin(theta*n)*sin(theta)zt=10*cos(theta*n)效果如圖6869.內(nèi)接彈簧xt=2*cos(t*360*10)+cos(t*180*10)yt=2*sin(t*360*10)+sin(t*180*10

36、)zt=t*6效果如圖69圖68圖6970多變內(nèi)接式彈簧xt=3*cos(t*360*8)-1.5*cos(t*480*8)yt=3*sin(t*360*8)-1.5*sin(t*480*8)zt=t*8效果如圖7071 .正弦周彈簧theta1=t*360theta2=t*360*20xt=2*theta1*2*pi/360【注：在UG中可輸入xt=2*rad(theta1)lyt=sin(theta1)*5+cos(theta2)zt=sin(theta2)效果如圖7172 .雙元寶線r=sin(t*360*10)+30theta=sin(t*360*15)xt=r*cos(theta)y

37、t=r*sin(theta)zt=sin(t*3)*10效果如圖7273 .變形阿基米德螺線(雙向)theta=360*2*(t-0.5)r=10*thetaxt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖73圖72圖7374雙魚曲線r=30+10*sin(t*360*10)theta=t*180*cos(t*360*10)phi=t*360*30xt=r*sin(theta)*cos(phi)yt=r*sin(theta)*sin(phi)zt=r*cos(theta)效果如圖74圖74圖7575.兩相望曲線r=30+10*sin(t*360*10)theta=t

38、*180*cos(t*360*10)phi=t*360*20xt=r*sin(theta)*cos(phi)yt=r*sin(theta)*sin(phi)zt=r*cos(theta)效果如圖7576 .小蜜蜂xt=cos(t*360)+cos(3*t*360)yt=sin(t*360)+sin(5*t*360)zt=0效果如圖7677 .彎月xt=cos(t*360)+cos(2*t*360)yt=sin(t*360)*2+sin(t*360)*2zt=0效果如圖7778 .熱帶魚a=5xt=(a*(cos(t*360*3)A4)*tyt=(a*(sin(t*360*3)A4)*tzt=0

39、效果如圖7879 .燕尾剪xt=3*cos(t*360*4)yt=3*sin(t*360*3)zt=t效果如圖79圖78圖7980 .天蠶絲theta=t*3600r=(cos(360*t*20)*0.5*t+1)*txt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖80圖8081 .蝸軌線theta=t*360*2r=cos(t*360*30)*t*0.5+t*2xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖8182 .變化后的星形線theta=t*360xt=10*cos(theta)A3yt=10*sin(theta)A3zt=co

40、s(theta)效果如圖82圖82圖8383 .心電圖r=sin(t*360*2)+0.2theta=10+t*(6*360)xt=r*cos(theta)yt=r*sin(theta)zt=t*3效果如圖8384 .次聲波xt=t*5yt=t*cos(t*360*8)zt=0效果如圖8485 .小白兔theta=t*360-90r=cos(360*(t/(1+tA(6.5)*6*t)*3.5+5xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖8586蜘蛛網(wǎng)theta=t*360*5r=t*sin(t*360*25)*5+8xt=r*cos(theta)yt=r*s

41、in(theta)zt=0效果如圖86圖8687.十字漸開線theta=t*360*4r=(cos(t*360*16)*0.5*t+1)*t*10xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖8788五環(huán)theta=t*360*4r=(cos(t*360*5)+1)*10xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖8889 .蝸牛線蝸牛線數(shù)學(xué)方程：r=a*sin(*&UG表達(dá)式為:a=10theta=360*t*5+0.001r=a*sin(theta)/rad(theta)xt=r*cos(theta)yt=r*sin(t

42、heta)zt=0效果如圖8990 .內(nèi)五環(huán)theta=t*360*4xt=2+(10-5)*cos(theta)+6*cos(10/6-1)*theta)yt=2+(10-5)*sin(theta)-6*sin(10/6-1)*theta)zt=0效果如圖90-1內(nèi)五角星a=5b=3s=t*19*180/pi(尸t*deg(19)xt=(a-b)*cos(s)+b*cos(a/b-1)*s)yt=(a-b)*sin(s)-b*sin(a/b-1)*s)zt=0效果如圖90-2圖90-1圖90-291梨形線梨形線數(shù)學(xué)方程：x=1+sint;y=a*cost*(1+sint).即UG表達(dá)式:th

43、eta=t*360a=0.8xt=1+sin(theta)yt=a*cos(theta)*(1+sin(theta)zt=0a=10b=6xt=10*tyt=sqrt(xtA3*(a-xt)/bA2)zt=0繪制后鏡像,效果如圖91-292 .空間梅花形the=t*360r=10+(3*sin(theta*2.5)A2xt=r*cos(theta)yt=r*sin(theta)zt=5*sin(6*theta)效果如圖9293 .一*朵小化theta=t*360r=3*cos(360*(t/(1+tA6)*6)+5xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖93

44、94 .紅十字theta=t*360r=cos(360*t*4)*0.5+1xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖94圖94圖9595 .波浪花環(huán)r=5theta=t*720xt=r*cos(theta)yt=r*sin(theta)zt=sin(3.5*theta-90)效果如圖9596 .正弦波帶xt=5*tA2yt=sin(t*8*360)*0.5zt=0效果如圖96圖9697 .懸鏈線數(shù)學(xué)方程：y=a*cosh(x/a)a=5xt=t*10-5yt=a*(exp(xt/a)+exp(-xt/a)/2zt=0效果如圖9798 .塔形螺旋線r=t*80

45、+50theta=t*360*10z=t*80效果如圖98圖98圖9999 .鈴鐺形線r=tA3+t*(t+1)theta=t*360phi=tA2*360*50xt=r*cos(phi)yt=r*sin(phi)zt=-r*cos(theta)效果如圖99100 .克萊線數(shù)學(xué)方程：r=4a*cos3(8/3)a=5theta=359*tr=4*a*(cos(theta/3)A3xt=r*cos(theta)yt=r*sin(theta)zt=0效果如圖100圖100圖101101對數(shù)曲線對數(shù)函數(shù)的數(shù)學(xué)方程：y=log(x),假設(shè)x的取值范圍從0.000110.0001,即對數(shù)曲線的UG表達(dá)式

46、為：xt=10*tyt=log(10*t+0.0001)zt=0效果如圖101102 .正環(huán)索線數(shù)學(xué)方程：r=a*cos(2f)/cos0a=10theta=t*178-89或【theta=t*178+91】r=a*cos(2*theta)/cos(theta)xt=r*cos(theta)yt=r*sin(theta)zt=0當(dāng)theta=t*120-60時的效果如圖102103三等分角線數(shù)學(xué)方程：r=2a*sin3f/sin20a=10theta=89*t+0.1和theta=89*t+90.1r=2*a*sin(3*theta)/sin(2*theta)xt=r*cos(theta)yt

47、=r*sin(theta)zt=0效果如圖103104 .平擺線數(shù)學(xué)方程：x=at-h*sin(t);y=a-h*cos(t)a=3h=6theta=360*t*5xt=a*rad(theta)-h*sin(theta)yt=a-h*cos(theta)zt=0效果如圖104105 .平穩(wěn)曲線數(shù)學(xué)方程：x=a*sin(m+n)t/sin(m-n)t;y=2a*sin(mt)sin(nt)/sin(m-n)ta=10m=8n=7theta=179.9*t+0.01xt=a*sin(m+n)*theta)/sin(m-n)*theta)yt=2*a*sin(m*theta)*sin(n*theta)/sin(m-n)*theta)zt=0效果如圖105106 .半立方拋物線數(shù)學(xué)方程：y3=ax2a=10xt=15*tyt=aA(1/3)*xtA(2/3)zt=0【或yt=15*t,xt=sqrt(ytA3/a),zt=0效果如圖