三维曲线方程大全

1、1. 碟形弹簧圓柱坐标方程：r = 5theta = t*3600z =(si n(3.5*theta-90)+24*t2. 葉形线.笛卡儿坐標标方程：a=10x=3*a*t/(1+(tA3)y=3*a*(tA2)/(1+(tA3)3. 螺旋线(Helical curve)圆柱坐标(cylindrical )方程：r=ttheta=10+t*(20*360)z=t*34.蝴蝶曲线球坐标方程：rho = 8 * ttheta = 360 * t * 4phi = -360 * t * 85.渐开线采用笛卡尔坐标系方程：r=1an g=360*ts=2*pi*r*txO=s*cos(a ng)y0

2、=s*s in(ang)x=x0+s*s in(ang)y=yO-s*cos(a ng)z=06. 螺旋线.笛卡儿坐标方程：x = 4 * cos ( t *(5*360)y = 4 * sin ( t *(5*360)z = 10*t7. 对数曲线笛卡尔坐标系方程：z=0x = 10*t8. 球面螺旋线 采用球坐标系方程：rho=4 theta=t*180 phi=t*360*209. 双弧外摆线卡迪尔坐标方程：1=2.5b=2.5x=3*b*cos(t*360)+l*cos(3*t*360)Y=3*b*si n(t*360)+l*si n(3*t*360)10.星行线卡迪尔坐标方程：a=5

3、x=a*(cos(t*360)A3y=a*(si n(t*360)A311.心脏线圓柱坐标方程：a=10r=a*(1+cos(theta)theta=t*36012.圆内螺旋线米用柱座标系方程：theta=t*360r=10+10*si n(6*theta)z=2*si n(6*theta)方程：x=50*ty=10*si n(t*360)15.费马曲线(有点像螺纹线)数学方程：r * r = a*a*theta圓柱坐标方程 1: theta=360*t*5a=4r=a*sqrt(theta*180/pi)方程 2: theta=360*t*5a=4r=-a*sqrt(theta*180/pi

4、)由于Pro/e只能做连续的曲线，所以只能分两次做卡笛尔坐标方程：theta=t*360a=1.1b=0.666c=s in( theta)f=1x = (a*a+f*f*c*c)*cos(theta)/ay = (a*a-2*f+f*f*c*c)*si n(theta)/b17.4叶线（一个方程做的，没有复制）方程：theta=t*360*4x=25+(10-6)*cos(theta)+10*cos(10/6-1)*theta)y=25+(10-6)*s in (theta)-6*si n( (10/6-1)*theta)19.抛物线笛卡儿坐标方程：x =(4 * t)y =(3 * t)

5、+ (5 * t A2)z =020.螺旋线圓柱坐标方程：r = 5theta = t*180021.三叶线圆柱坐标方程：a=1theta=t*380b=s in( theta)r=a*cos(theta)*(4*b*b-1)22.外摆线迪卡尔坐标方程：theta=t*720*5b=8a=5x=(a+b)*cos(theta)-b*cos(a/b+1)*theta)y=(a+b)*si n(theta)-b*si n(a/b+1)*theta)z=023. Lissajous 曲线theta=t*360a=1b=1c=100n=3x=a*s in(n *theta+c)卡笛尔坐标方程：a=5b

6、=7c=2.2theta=360*t*10x=(a-b)*cos(theta)+c*cos(a/b-1)*theta)y=(a-b)*si n(theta)-c*si n(a/b-1)*theta)25.长短幅圆外旋轮线卡笛尔坐标方程：theta=t*360*10a=5b=3c=5x=(a+b)*cos(theta)-c*cos(a/b+1)*theta)26.三尖瓣线a=10x = a*(2*cos(t*360)+cos(2*t*360)y = a*(2*si n(t*360)-si n(2*t*360)方程：笛卡儿坐标x = t*10-5y = exp(0-xA2)28.箕舌线笛卡儿坐标系

7、a = 1x = -5 + t*10y = 8*aA3/(xA2+4*aA2)29.阿基米德螺线柱坐标a=100theta = t*400r = a*theta30.对数螺线柱坐标theta = t*360*2.2a = 0.005r = exp(a*theta)31.蔓叶线笛卡儿坐标系a=10y=t*100-50solvexA3 = yA2*(2*a-x)for x32.ta n曲线笛卡儿坐标系x = t*8.5 -4.25y = tan( x*20)33.双曲余弦x = 6*t-3y = (exp(x)+exp(0-x)/234.双曲正弦x = 6*t-3y = (exp(x)-exp(0

8、-x)/235.双曲正切x = 6*t-3y = (exp(x)_exp(O_x)/(exp(x)+exp(O_x)36. 一峰三驻点曲线x = 3*t-1.5y=(xA2-1)A3+137.八字曲线x = 2 * cos ( t *(2*180)38.螺旋曲线r=t*(10*180)+1theta=10+t*(20*180)z=t39.圆x = cos ( t *(5*180)y = sin ( t *(5*180)rho=2theta=360*tphi=t*360*1041.柱坐标螺旋曲线x = 100*t * cos ( t *(5*180) y = 100*t * sin ( t *(

9、5*180)z = 042.蛇形曲线x = 2 * cos ( (t+1) *(2*180)y = 2 * sin ( t *(5*360)z = t*(t+1)43.8字形曲线柱坐标theta = t*360r=10+(8*si n(theta)A244.椭圆曲线笛卡尔坐标系a = 10b = 20theta = t*360x = a*cos(theta) y = b*s in( theta)45.梅花曲线柱坐标theta = t*360r=10+(3*si n(theta*2.5)A246.另一个花曲线theta = t*360r=10-(3*si n(theta*3)A2z=4*si n

10、(theta*3F247.改一下就成为空间感更强的花曲线了;)theta = t*360r=10-(3*si n( theta*3)A2z=(r*si n(theta*3)A248.螺旋上升的椭圆线a = 10b = 20theta = t*360*3x = a*cos(theta)y = b*s in( theta)z=t*1249.五星螺旋花曲线theta = t*360*4r=10+(3*si n(theta*2.5)A2z = t*1650鼓形线笛卡尔方程r=5+3.3*si n(t*180)+ttheta=t*360*10z=t*1051长命锁曲线笛卡尔方程：a=1*t*359.5b

11、=q2*t*360c=q3*t*360rr1=w1rr2=w2rr3=w3x=rr1*cos(a)+rr2*cos(b)+rr3*cos(c)y=rr1*si n( a)+rr2*si n( b)+rr3*si n(c)52簪形线球坐标方程：rho=200*ttheta=900*tphi=t*90*1053.螺旋上升曲线r=tA10theta=L3*360*6*3+tA3*360*3*3z=tA3*(t+1)54.蘑菇曲线rho=tA3+t*(t+1)theta=t*360phi=tA2*360*20*2055. 8字曲线a=1b=1x=3*b*cos(t*360)+a*cos(3*t*360

12、)Y=b*si n(t*360)+a*si n(3*t*360)09e*Eo£ (L+F+ev 芥 oil(eo£*9)soo*cxluz(eo£*9)soo*09+00u 09e*Eo£phi=L2*360*10*1058.名稱：碟形弹簧建立環境：pro/e圓柱坐r = 5theta = t*3600z =(si n(3.5*theta-90)+2459.环形二次曲线 笛卡儿方程：x=50*cos(t*360)y=50*s in (t*360)z=10*cos(t*360*8)60蝶线球坐标：rho=4*s in (t*360)+6*cos(t*360

13、A2) theta=t*360 phi=log(1+t*360)*t*36061.正弦周弹簧笛卡尔：ang仁 t*360an g2=t*360*20x=an g1*2*pi/360y=s in(an g1)*5+cos(a ng2)z=s in(an g2)62.环形螺旋线x= (50+10*si n(t*360*15)*cos(t*360)y=(50+10*si n(t*360*15)*si n(t*360)z=10*cos(t*360*5)63.内接弹簧x=2*cos(t*360*10)+cos(t*180*10)y=2*si n( t*360*10)+si n( 1*180*10)z=t

14、*664.多变内接式弹簧x=3*cos(t*360*8)-1.5*cos(t*480*8)y=3*si n(t*360*8)-1.5*si n( t*480*8)z=t*865.柱面正弦波线柱坐标：方程r=30theta=t*360z=5*si n(5*theta-90)66. ufo (漩涡线)球坐标：rho=t*20A2theta=t*log(30)*60phi=t*720067.手把曲线thta0=t*360thta1=t*360*6rO=4OOr1=40r=rO+r1*cos(thta1)x=r*cos(thtaO)y=r1*si n(thta1)z=068.篮子圆柱坐标r=5+0.3

15、*si n(t*180)+ttheta=t*360*30z=t*569.圆柱齿轮齿廓的渐开线方程：afa=60*tx=10*cos(afa)+pi*10*afa/180*si n(afa)x=10*si n(afa)-pi*10*afa/180*cos(afa)z=0注：afa为压力角，取值范围是0到60, 10为基圆半径。70.对数螺旋曲线柱坐标：r=sqrt(theta)theta=t*360*30z=071.罩形线 球坐标： rho=4 theta=t*60 phi=t*360*1072.向日葵线theta=t*360r=30+10*si n( theta*30)z=073.太阳线r=1

16、.5*cos(50*theta)+1theta=t*360z=074塔形螺旋线r=t*80+50theta=t*360*10z=t*8075花瓣线球坐标：rho=t*20theta=t*360*90phi=t*360*1076双元宝线r=si n(t*360*10)+30theta=si n(t*360*15)z=si n(t*3)77阿基米德螺线的变形(自己想得)不知前面有没有？:what柱坐标下：theta=360*2*(t-0.5)r=10*thetar=20ang = t*360x=r*cos(a ng)+2*pi*r*t*s in(ang)y=r*si n(an g)-2*pi*r*

17、t*cos(a ng)z=079双鱼曲线球坐标系rho=30+10*s in (t*360*10)theta=t*180*cos(t*360*10)phi=t*360*3080蝴蝶结曲线x=200*t*s in (t*3600)y=250*t*cos(t*3600)z=300*t*s in (t*1800)81 ”两相望“曲线球坐标系rho=30theta=t*360*cos(t*360*20)phi=t*360*2082小蜜蜂笛卡尔坐标系：x=cos(t*360)+cos(3*t*360)Y=si n(t*360)+si n(5*t*360)83弯月x=cos(t*360)+cos(2*t*

18、360)Y=si n(t*360)*2+si n(t*360)*284热带鱼a=5x=(a*(cos(t*360*3)M)*ty=(a*(si n(t*360*3)A4)*t85燕尾剪x=3*cos(t*360*4)y=3*si n(t*360*3)z=t86天蚕丝theta=t*3600r=(cos(360*t*20)*.5*t+1)*t87心电图 圆柱坐标系： r=si n(t*360*2)+.2 theta=10+t*(6*360)z=t*388变化后的星形线迪卡尔坐标系theta=t*360 x=10*cos(theta)A3 y=10*si n( theta)A3z=cos(theta)89小白兔theta=t*360-90r=cos(360*(t/(1+tA(6.5)*6*t)*3.5+590大家好theta=t*360+180r=cos(360*tA3*6)*2+591蛇形线笛卡尔坐标系：x=2*cos(t*360*3)*ty=2*si n(t*360*3)*tz=(sqrt(sqrt(sqrt(t)A3*592五环柱坐标：theta=t*360*4r=cos