常用曲線方程

1、1.碟形彈簧圓柱坐標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+(t3)y=3*a*(t2)/(1+(t3)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*ts=2*pi*r*tx0=s*cos(ang)y0=s*sin(ang)x=x0+s*sin(ang)y=

2、y0-s*cos(ang)z=0  6.螺旋線.笛卡兒坐標x = 4 * cos ( t *(5*360)y = 4 * sin ( t *(5*360)z = 10*t  7.對數(shù)曲線笛卡爾坐標系z=0x = 10*ty = log(10*t+0.0001)  8.球面螺旋線球坐標系rho=4theta=t*180phi=t*360*209.雙弧外擺線卡迪爾坐標l=2.5b=2.5x=3*b*cos(t*360)+l*cos(3*t*360)Y=3*b*sin(t*360)+l*sin(3*t*360)10.星行線卡迪爾坐標a=5x

3、=a*(cos(t*360)3y=a*(sin(t*360)311.心臟線圓柱坐標a=10r=a*(1+cos(theta)theta=t*360  12.圓內螺旋線柱座標系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)+1theta=t*360z=0 15.費馬曲線（有點像螺紋線）數(shù)學方程：rr = a*a*theta圓柱坐標方程1: theta=360*t*5a=4r=a*sqrt(t

4、heta*180/pi)方程2: theta=360*t*5a=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*4x=25+(10-6)*cos(theta)+10*cos(10/6-1)*theta)y=25+(10-6)*sin(theta)-6

5、*sin(10/6-1)*theta)19. 拋物線笛卡兒坐標x =(4 * t)y =(3 * t) + (5 * t 2)z =020.螺旋線圓柱坐標r = 5theta = t*1800z =(cos(theta-90)+24*t21.三葉線圓柱坐標a=1theta=t*380b=sin(theta)r=a*cos(theta)*(4*b*b-1)22.外擺線迪卡爾坐標theta=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

6、 曲線theta=t*360a=1b=1c=100n=3x=a*sin(n*theta+c)y=b*sin(theta)24.長短幅圓內旋輪線卡笛爾坐標a=5b=7c=2.2theta=360*t*10x=(a-b)*cos(theta)+c*cos(a/b-1)*theta)y=(a-b)*sin(theta)-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

7、a=10x = 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-x2)28.箕舌線笛卡兒坐標系a = 1x = -5 + t*10y = 8*a3/(x2+4*a2)29.阿基米德螺線柱坐標a=100theta = t*400r = a*theta  30.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*100-50solvex3 = y2*(2*a

8、-x)for x32.tan曲線笛卡兒坐標系x = t*8.5 -4.25y = 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 = (exp(x)-exp(0-x)/235.雙曲正切x = 6*t-3y = (exp(x)-exp(0-x)/(exp(x)+exp(0-x)36.一峰三駐點曲線x = 3*t-1.5y=(x2-1)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)+1theta=10

9、+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*tphi=t*360*10  41.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*180)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)244

10、.橢圓曲線笛卡爾坐標系a = 10b = 20theta = t*360x = a*cos(theta)y = b*sin(theta)45.梅花曲線柱坐標theta = t*360r=10+(3*sin(theta*2.5)246.另一個花曲線theta = t*360r=10-(3*sin(theta*3)2z=4*sin(theta*3)247.改一下就成為空間感更強的花曲線了;)theta = t*360r=10-(3*sin(theta*3)2z=(r*sin(theta*3)248.螺旋上升的橢圓線a = 10b = 20theta = t*360*3x = a*cos(theta

11、)y = b*sin(theta)z=t*1249.甚至這種螺旋花曲線theta = t*360*4r=10+(3*sin(theta*2.5)2z = t*1650 鼓形線笛卡爾方程r=5+3.3*sin(t*180)+ttheta=t*360*10z=t*1051 長命鎖曲線笛卡爾方程：a=1*t*359.5b=q2*t*360c=q3*t*360rr1=w1rr2=w2rr3=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

12、*1053.螺旋上升曲線r=t10theta=t3*360*6*3+t3*360*3*3z=t3*(t+1)54.蘑菇曲線球坐標rho=t3+t*(t+1)theta=t*360phi=t2*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=t3+t*(t+1)theta=t*360phi=t2*360*10*1058.碟形彈簧圓柱坐r = 5the

13、ta = 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*3602)theta=t*360phi=log(1+t*360)*t*36061.正弦周彈簧笛卡爾：ang1=t*360ang2=t*360*20x=ang1*2*pi/360y=sin(ang1)*5+cos(ang2)z=sin(ang2)62.環(huán)形螺旋線笛卡爾：x=（50+10*sin(t*360*15)*cos(t*360)y=

14、(50+10*sin(t*360*15)*sin(t*360)z=10*cos(t*360*5)63.內接彈簧笛卡爾：x=2*cos(t*360*10)+cos(t*180*10)y=2*sin(t*360*10)+sin(t*180*10)z=t*664.多變內接式彈簧笛卡爾：x=3*cos(t*360*8)-1.5*cos(t*480*8)y=3*sin(t*360*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*202theta=t*log(30)*60phi=t*

15、720067. 手把曲線笛卡爾：thta0=t*360thta1=t*360*6r0=400r1=40r=r0+r1*cos(thta1)x=r*cos(thta0)y=r1*sin(thta1)z=068.籃子圓柱坐標r=5+0.3*sin(t*180)+ttheta=t*360*30z=t*569. 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/180*sin(afa)x=10*sin(afa)-pi*10*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=sqr

16、t(theta)theta=t*360*30z=071. 罩形線球坐標:rho=4theta=t*60phi=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：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*20theta=t*360*90phi=t*360*1076 雙元寶線笛卡爾：r=sin(t*360*10)+30theta=sin(t*360*15)z=sin(t*3)7

17、7 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*t*sin(ang)y=r*sin(ang)-2*pi*r*t*cos(ang)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=y0-s*cos(ang)z=079 雙魚曲線球坐標系rho=30+10*sin(t*360*10)theta=t*180*cos(

18、t*360*10)phi=t*360*3080 蝴蝶結曲線迪卡爾坐標x=200*t*sin(t*3600)y=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)+sin(5*t*360)83 彎月x=cos(t*360)+cos(2*t*360)Y=sin(t*360)*2+sin(t*360)*284 熱帶魚a=5x=(a*(cos(t*360*3)4)*ty

19、=(a*(sin(t*360*3)4)*t85 燕尾剪x=3*cos(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)+.2theta=10+t*(6*360)z=t*388 變化后的星形線迪卡爾坐標系theta=t*360x=10*cos(theta)3y=10*sin(theta)3z=cos(theta)89 小白兔theta=t*360-90r=cos(360*(t/(1+t(6.5)*6*t)*3.5+590 大家好柱坐標theta=t*360+180r=cos(360*t3*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)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 內五環(huán)笛卡爾theta=t*360*4x=