曲線方程集合(無圖)

1、1 碟形彈簧rl柱坐標r = 5theta = t* 3600z = (sin (3.5* theta-90)+ 24* t2 葉形線笛卡兒坐標標a= 10x=3*a*t/(1 + (ta 3) y=3*a*(ta 2)/(1 + (ta 3) 3.螺旋線(helical curve)圓柱坐標(cylindrical)r= ttheta=10+t*(20*360) z=t*34 蝴蝶曲線球坐標rho = 8 * ttheta = 360 * t * 4phi =360 * t * 85 漸開線笛卡爾坐標系r= 1ang= 360* t s= 2* pi* r* t x0= s* cos(ang

2、) y0= s* sin(ang) x= x0+ s* sin(ang) y= yo-s* cos(a ng) z= 06螺旋線.笛卡兒坐標x = 4 * cos ( t *(5*360) y = 4 * sin ( t *(5*360) z = 10*t7 對數(shù)曲線笛卡爾坐標系z= 0x = 10*ty = log(10*t+0.0001)&球而螺旋線球坐標系rho= 4theta= t* 180 phi=t*360*209.雙弧外擺線卡迪爾坐標1=2.5b=2.5x= 3* b* cos(t* 360)+ i* cos(3* t* 360)y=3*b*sin(t*360)+l*si

3、n(3*t*360)10.星行線卡辿爾坐標a= 5x=a*(cos(t*360)a 3 y=a*(sin(t*360)a 3伯心臟線圓柱坐標a=10r= a* (14- cos(theta)theta= t* 36012.圓內(nèi)螺旋線柱座標系theta= t* 360r= 10+ 10* sin(6* theta) z= 2* sin(6* theta)13 正弦曲線 笛卡爾坐標系 x=50*ty=10*sin(t*360)z= 014 太陽線 柱坐標r= 1.5* cos(50* theta)+ 1 theta=t*360z= 015費馬曲線（有點像螺紋線）數(shù)學方程：r*r= a* a* th

4、eta圓柱坐標方程 1: theta= 360* t* 5a= 4r= a* sqrt(theta* 180/pi)方程 2: theta=360*t*53= 4r= -a* sqrt(theta* 180/pi)由于pro/e只能做連續(xù)的曲線，所以只能分兩次做16.talbot 曲線卡笛爾坐標theta=t* 360a= 1.1b=0.666c= sin(theta)f=1x = (a* a+ f* f* c* c)* cos(theta)/ay = (a* a-2* f+ f* f* c* c)* sin(theta)/b18. rhodonea 曲線笛卡爾坐標系theta= t* 360

5、* 4x= 25+ (10-6)* cos(theta)+ 1 0* cos(10/6-1 )* theta) y= 25+ (10-6)* sin(theta)-6* sin(1 0/6-1 )* theta)19. 拋物線 笛卡兒坐標x = (4 * t)y =(3 * t) + (5 * t a 2)z = 020 螺旋線圓柱坐標r = 5theta = t* 1 800z = (cos(theta-90) + 24* t21 三葉線圓柱坐標3= 1theta= t* 380b= sin(theta)r= a* cos(theta)* (4* b* b-1)22 外擺線迪卡爾坐標thet

6、a=t*720*5b= 8a= 5x= (a+ b)* cos(theta)-b* cos(a/b+ 1 )* theta) y= (a+ b)* sin(theta)-b* sin(a/b+ 1 )* theta) z= 023. lissajous 曲線theta=t*3603= 1b=1c=100n= 3x= a* sin(n* theta+ c)y= b* sin(theta)24 長短幅|員|內(nèi)旋輪線 卡笛爾坐標a= 5b=7c=2.2theta=360*t*10x= (a-b)* cos(theta) + c* cos(a/b-1 )* theta)y= (a-b)* sin(th

7、eta)-c* sin(a/b-1 )* theta)25 長短幅圓外旋輪線卡笛爾坐標theta=t*360* 10a= 5b= 3c= 5x= (a+ b)* cos(theta)-c* cos(a/b+ 1 )* theta) y= (a+ b)* sin(theta)-c* sin(a/b+ 1 )* theta)26.三尖瓣線3= 1 0x = a* (2*cos(t*360) + cos(2*t*360) y = a* (2*sin(t*360)-sin(2*t*360)27 概率曲線!笛卡兒坐標x = t* 10-5y = exp(0-xa 2)28 箕舌線笛卡兒坐標系a = 1x

8、 =5 + t* 10y = 8* aa 3/(xa 2+ 4* aa 2)29 阿基米德螺線 柱坐標a= 100theta = t* 400r = a* theta30 對數(shù)螺線柱坐標theta = t*360*2.2a = 0.005r = exp(a* theta)31 蔓葉線笛卡兒坐標系a= 10y=t* 100-50solvexa 3 = ya 2* (2* a-x)for x32.tan曲線 笛卡兒坐標系x = t*8.5 -4.25 y = tan(x* 20)33 雙曲余弦x = 6*t-3y = (exp(x)+ exp(0-x)/234 雙曲正弦x = 6*t-3y = (

9、exp(x)-exp(0-x)/235 雙曲正切x = 6*t-3y = (exp(x)-exp(o-x)/(exp(x)+ exp(o-x)36 峰三駐點曲線x = 3*t-1.5y=(xa 2-1)a 3+137 八字曲線x = 2 * cos ( t *(2*180) y = 2 * sin ( t *(5*360) z = 038 螺旋曲線r=t*(10*180)+1 theta=10+t*(20* 180) z= t39 圓x = cos ( t *(5*180) y = sin ( t *(5*180) z = 040 封閉球形環(huán)繞曲線rho=2theta= 360* t phi=

10、t*360* 1041 柱坐標螺旋曲線x = 100*t * cos ( t *(5*180) y = 100*t * sin ( t *(5*180) z = 042 蛇形曲線x = 2 * cos ( (t+ 1) * (2* 1 80) y = 2 * sin ( t *(5*360)z = t* (t+ 1) 43.8字形曲線柱坐標theta = t* 360r= 10+ (8* sin(theta)a 244.橢圓曲線笛卡爾坐標系3 = 1 0b = 20theta = t* 360x = a* cos(theta)y = b* sin(theta)45 梅花曲線柱坐標theta =

11、 t* 360r=10+(3*sin(theta*2.5)a 246 另一個花曲線theta = t* 360r=10-(3*sin(theta*3)a 2z=4*sin(thetr 3)八 247 改一下就成為空間感更強的花曲線了;)theta = t*360 r=10-(3*sin(theta*3)a 2 z= (r* sin(theta* 3)a 248 螺旋上升的橢|員i線a = 10b = 20theta = t*360*3x = a* cos(theta) y = b* sin(theta) z=t* 1249 甚至這種螺旋花曲線theta = t*360*4r=10+(3*sin

12、(theta*2.5)a 2 z = t* 1650鼓形線笛卡爾方程r=5+3.3*si n(t*1 80) + ttheta=t*360*10z=t* 1051長命鎖曲線 笛卡爾方程：a=1*t*359.5 b=q2*t*360 c=q3*t*360 rr1 = w1 rr2= w2 rr3= w3x= rr1 * cos(a)+ rr2* cos(b)+ rr3* cos(c) y = rr1 * sin(a)+ rr2* sin(b) + rr3* sin(c)52簪形線球坐標rho=200*ttheta= 900* tphi= t* 90* 1 053 螺旋上升曲線r=ta 10the

13、ta=ta 3*360* 6*3+ta 3*360*3*3 z=ta 3*(t+1)54 蘑菇曲線球坐標rho= ta 3+1* (t+ 1)theta= t* 360phi=ta 2*360*20*2055. 8字曲線 a= 1b= 1x= 3* b* cos(t* 360)+ a* cos(3* t* 360)y= b* sin(t* 360)+ a* sin(3* t* 360)56 梅花曲線theta=t*360r= 100+ 50* cos(5* theta) z= 2* cos(5* theta)57 桃形曲線 rho=ta 3+t*(t+1)theta= t* 360phi=ta

14、 2*360* 10* 1058 碟形彈簧圓柱坐r = 5theta = t*3600z = (sin(3.5* theta-90)+ 2459環(huán)形二次曲線笛卡兒方程：x= 50* cos(t* 360) y= 50* sin(t* 360) z= 10*cos(t*360*8)60蝶線球坐標：rho= 4* sin(t* 360) + 6* cos(t* 360a 2)theta= t* 360phi=log(1 + t*360)*t*36061 正弦周彈簧 笛卡爾：ang1 = t* 360an g2=t*360*20x= ang1 * 2* pi/360y= sin(ang1 )* 5+

15、 cos(ang2)z= sin(an g2)62 環(huán)形螺旋線笛卡爾：x= (50+ 10* sin(t* 360* 15)* cos(t* 360) y= (50+ 10* sin(t* 360* 15)* sin(t* 360)z= 10*cos(t*360*5)63 內(nèi)接彈簧笛卡爾：x= 2* cos(t* 360* 10) + cos(t* 180* 10) y= 2* sin(t* 360* 10) + sin(t* 180* 10) z=t*664 多變內(nèi)接式彈簧笛卡爾：x= 3* cos(t* 360* 8)-1.5* cos(t* 480* 8) y=3*sin(t*360&q

16、uot;8)1.5* sin(t”480* 8) z=t*865 柱面正弦波線 柱坐標r=30theta= t* 360z= 5* sin(5* theta-90)66.漩渦線球坐標：rho=t*20a 2theta= t* log(30)* 60phi=t*720067.手把曲線笛卡爾：thta0=t*360thta1 = t*360*6 r0=400r1 = 40r= r0+ r1 * cos(thta1) x= r* cos(thtao)y= r1 * sin(thtal) z= 068 籃子圓柱坐標r=5+0.3*sin(t* 180) + ttheta=t*360*30z= t* 5

17、69.圓柱齒輪齒廓的漸開線方程：笛卡爾坐標afa=60*tx= 10* cos(afa)+ pi* 10* afa/1 80* sin(afa)x= 10* sin(afa)-pi* 1 0* afa/180* cos(afa) z= 0注：afa為壓力角，取值范圍是0到60, 10為基圓半徑。70 對數(shù)螺旋曲線 柱坐標：r= sqrt(theta) theta=t*360*30 z= 071罩形線球坐標：rho= 4theta= t* 60 phi=t*360* 1072.向日葵線笛卡爾：theta= t* 360r= 30+ 10* sin(theta* 30) z= 073.太陽線笛卡爾

18、：r= 1.5* cos(50* theta)+ 1theta= t* 360z= 074塔形螺旋線笛卡爾：r=t*80+50theta=t*360* 10z=t*8075花瓣線 球坐標：rho=t*20 theta=t*360*90 phi=t*360* 1076雙元寶線笛卡爾：r=sin(t*360* 10)+30 theta= sin(t* 360* 15) z= sin(t* 3)77阿基米德螺線的變形 柱坐標theta=360*2*(t-0.5)r= 10* thetaz= 078改過來的漸開線方程r=20ang = t* 360x= r* cos(ang) + 2* pi* r*

19、t* sin(ang)y= r* sin (an g)-2* pi* r* t* cos(a ng) z= 0前面的方程是這樣的：(對比研究一下兩者有什么不同)采用笛卡爾坐標系r=1ang= 360* ts= 2* pi* r* tx0= s* cos(ang)y0= s* sin(ang)x= x0+ s* sin(ang)y= yo-s* cos(ang) z= 079雙魚曲線球坐標系rho=30+10*sin(t*360* 10) theta= t* 180* cos(t* 360* 10) phi=t*360*3080蝴蝶結(jié)曲線 迪卡爾坐標x=200*t*si n(t*3600) y=

20、250*t*cos(t*3600) z=300*t*sin(t* 1800)81 ”兩相望“曲線 球坐標系rho= 30theta= t* 360* cos(t* 360* 20) phi=t*360*2082小蜜蜂笛卡爾坐標系：x= cos(t* 360) + cos(3* t* 360)y=sin(t*360)+si n(5t360)83彎月x= cos(t* 360) + cos(2* t* 360)y=sin (t*360)*2+sin(t*360)*284熱帶魚3= 5x=(a*(cos(t*360*3)a 4)*ty=(a*(sin(t*360*3)a 4)*t85燕尾剪x=3*c

21、os(t*360*4) y=3*sin(t*360*3) z= t86天蠶絲柱坐標theta= t* 3600r=(cos(360*t*20)*.5*t+1)*t87心電圖圓柱坐標系：r=sin(t*360*2)+.2 theta=10+t*(6*360) z= t* 388變化后的星形線 迪卡爾坐標系theta= t* 360x= 1 0* cos(theta)a 3 y= 1 0* sin(theta)a 3 z= cos(theta)89小白兔theta=t*36 090r=cos(360* (t/(1 + ta (6.5)*6*t)*3.5+5 90大家好柱坐標theta=t*360+

22、 180 r=cos(360*ta 3*6)*2+591蛇形線笛卡爾坐標系：x=2*cos(t*360*3)*ty=2*sin(t*360*3)*tz= (sqrt(sqrt(sqrt(t)a 3* 592五環(huán)柱坐標：theta=t*360*4r=cos(t* 360* 5)+193蜘蛛網(wǎng)柱坐標：theta=t*360*5r=t*sin(t*360*25)*5+894次聲波笛卡爾：x=t*5y=t*cos(t*360*8)95十字漸開線柱坐標：theta=t*360*4r=(cos(t*360*16)*0.5*t+1)*t96內(nèi)五環(huán)笛卡爾theta=t*360*4x= 2+ (10-5)* cos(theta)+ 6* cos(10/6-1 )* theta) y= 2+ (10-5)* sin(theta)-6* sin(10/6-1 )* theta)97蝸