各种曲线PROE的参数方程

1、各种曲线 PROE 的参数方程1. 碟形弹簧(柱坐标 方程:r = 5theta = t*3600 z =(sin(3.5*theta-90+24*t 2. 葉形线 .方程:a=10x=3*a*t/(1+(t3 y=3*a*(t2/(1+(t3 3.锥形螺旋线 (Helical curve 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 * 4 phi = -360 * t * 8 5. 渐开线方程:r=1ang=360*ts=2*pi*r*tx0=s*cos(angy0=s*sin(angx=x0

2、+s*sin(ang y=y0-s*cos(ang z=0(相似形:69、 786. 圆柱螺旋线 .方程:x = 4 * cos ( t *(5*360 y = 4 * sin ( t *(5*360 z = 10*t7. 对数曲线方程:z=0x = 10*ty = log(10*t+0.0001 8. 球面螺旋线方程:rho=4theta=t*180phi=t*360*209. 双弧外摆线方程: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*36010. 星形线方程:a=5x=a*(cos(t*3603 y=

3、a*(sin(t*3603 11. 心脏线方程:a=10 r=a*(1+cos(theta theta=t*360 12. 圆内螺旋线方程:theta=t*360 r=10+10*sin(6*theta z=2*sin(6*theta 13. 正弦线方程:x=50*t y=10*sin(t*360 z=014. 太阳线(发光的太阳,见 73 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*5 a=4r= a*sqrt(theta*180/pi方程 2: theta=360*t*5a=4r= -a*sqrt(theta*18

4、0/piPro/e只能做连续的曲线,所以要分两次做 16.Talbot 曲线方程:theta=t*360a=1.1b=0.666c=sin(thetaf=1x = (a*a+f*f*c*c*cos(theta/a y = (a*a-2*f+f*f*c*c*sin(theta/b 17. 四叶线(一个方程,比三叶线多一个叶子 18.Rhodonea 曲线方程:theta=t*360*4x=25+(10-6*cos(theta+10*cos(10/6-1*theta y=25+(10-6*sin(theta-6*sin(10/6-1*theta 19. 抛物线方程:x =(4 * ty =(3 *

5、 t + (5 * t 2z =020. 螺旋线方程:r = 5theta = t*1800z =(cos(theta-90+24*t 21. 三叶线方程:a=1theta=t*380b=sin(thetar=a*cos(theta*(4*b*b-1 22. 外摆线方程: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 曲线方程:theta=t*360a=1b=1c=100n=3x=a*sin(n*theta+cy=b*sin(the

6、ta24.长短幅圆内旋轮线方程: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 z=0 (?25. 长短幅圆外旋轮线方程: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 z=0 (? (与 22线同? 26. 三尖瓣线方程:a=10x = a*(2*cos(t*360+cos(2*t*360 y = a*(2*sin(

7、t*360-sin(2*t*36027. 概率曲线!方程:x = t*10-5y = exp(0-x2方程:a = 1x = -5 + t*10y = 8*a3/(x2+4*a2 29. 阿基米德螺线 方程:a=100theta = t*400 r = a*theta30. 对数螺线方程:theta = t*360*2.2 a = 0.005r = exp(a*theta 31. 蔓叶线方程:a=10y=t*100-50solvex3 = y2*(2*a-x for x32. 正切线方程:x = t*8.5 -4.25 y = tan(x*20 33. 双曲余弦方程:x = 6*t-3 y =

8、 (exp(x+exp(0-x/2方程:x = 6*t-3y = (exp(x-exp(0-x/235. 双曲正切方程:x = 6*t-3y = (exp(x-exp(0-x/(exp(x+exp(0-x 36. 一峰三驻点曲线方程:x = 3*t-1.5y=(x2-13+137.”8” 字曲线方程:x = 2 * cos ( t *(2*180y = 2 * sin ( t *(5*360 z = 0(同形:55,相似:4338. 螺旋线方程:r=t*(10*180+1theta=10+t*(20*180z=t(其它螺旋线方程:3、 6、 20、 41、 53、 62 39. 圆方程:x=c

9、os(t*5*180y=sin(t*5*180z=040. 封闭球形环绕曲线方程:rho=2theta=360*tphi=t*360*10(相似形:22、 24、 2541. 螺旋线方程:x = 100*t * cos ( t *(5*180 y = 100*t * sin ( t *(5*180 z = 0(其它螺旋线方程:3、 6、 20、 38、 53、 62 42. 蛇形线方程:x = 2 * cos ( (t+1 *(2*180 y = 2 * sin ( t *(5*360 z = t*(t+143. 墨镜线方程:theta = t*360r=10+(8*sin(theta2(相似

10、形:37、 5544. 椭圆线方程:a = 10b = 20theta = t*360x = a*cos(thetay = b*sin(theta45. 梅花线 (圆角五星 方程:theta = t*360 r=10+(3*sin(theta*2.52 46. 直叶六叶线方程:theta = t*360 r=10-(3*sin(theta*32 z=4*sin(theta*32 47. 弯叶六叶线方程:theta = t*360 r=10-(3*sin(theta*32 z=(r*sin(theta*32 48. 空间螺旋椭圆线 方程:a = 10 b = 20theta = t*360*3x

11、 = a*cos(theta y = b*sin(thetaz=t*1249. 空间螺旋梅花线 方程:theta = t*360*4 r=10+(3*sin(theta*2.52 z = t*1650 鼓形线方程:r=5+3.3*sin(t*180+t theta=t*360*10z=t*1051. 长命锁线方程: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 簪形线方程:rho=200*ttheta=900*t

12、phi=t*90*1053. 锁呐线方程:r=t10theta=t3*360*6*3+t3*360*3*3 z=t3*(t+1(其它螺旋线方程:3、 6、 20、 38、 41、 62 54. 蘑菇线方程:rho=t3+t*(t+1theta=t*360phi=t2*360*20*2055.“ 8” 字线方程:a=1b=1x=3*b*cos(t*360+a*cos(3*t*360 y=b*sin(t*360+a*sin(3*t*360 (同形:37,相似:43 56. 梅花线方程:theta=t*360r=100+50*cos(5*theta z=2*cos(5*theta(同形:4557.

13、桃形线方程:rho=t3+t*(t+1theta=t*360phi=t2*360*10*10 (相似形:5458.:碟簧方程:r = 5theta = t*3600z =(sin(3.5*theta-90+2459. 环形二次曲线方程:x=50*cos(t*360 y=50*sin(t*360z=10*cos(t*360*860 蝶线方程:rho=4*sin(t*360+6*cos(t*3602 theta=t*360phi=log(1+t*360*t*36061. 正弦周弹簧方程:ang1=t*360ang2=t*360*20x=ang1*2*pi/360y=sin(ang1*5+cos(a

14、ng2z=sin(ang262. 环形螺旋线方程: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(其它螺旋线方程:3、 6、 20、 38、 41、 53 63. 内接弹簧方程:x=2*cos(t*360*10+cos(t*180*10 y=2*sin(t*360*10+sin(t*180*10 z=t*664. 多变内接式弹簧方程: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

15、正弦波线方程:r=30theta=t*360z=5*sin(5*theta-9066. UFO(漩涡线方程:rho=t*202theta=t*log(30*60phi=t*720067. 手把曲线方程:theta=t*360theta1=t*360*6r0=400r1=40r=r0+r1*cos(theta1x=r*cos(thta0y=r1*sin(thta1z=068. 无底篮子方程:r=5+0.3*sin(t*180+t theta=t*360*30z=t*569. 圆柱齿轮齿廓的渐开线方程:方程:afa=60*tx=10*cos(afa+pi*10*afa/180*sin(afax=1

16、0*sin(afa-pi*10*afa/180*cos(afa z=0注:afa 为压力角, 060, 10为基圆半径 70. 对数螺旋曲线 (唱片 方程:r=sqrt(thetatheta=t*360*30z=071. 球面螺旋线 (罩形 方程:rho=4theta=t*60phi=t*360*1072. 向日葵线方程:theta=t*360r=30+10*sin(theta*30z=073. 太阳线方程:r=1.5*cos(50*theta+1 theta=t*360z=074 塔形螺旋线方程:r=t*80+50theta=t*360*10z=t*8075. 九瓣花方程:rho=t*20t

17、heta=t*360*90phi=t*360*1076 双元宝线方程:r=sin(t*360*10+30 theta=sin(t*360*15z=sin(t*377 变形阿基米德螺线 (双向 方程:theta=360*2*(t-0.5 r=10*thetaz=0(相似形:2978渐开线方程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(相似形:5、 6979 双鱼曲线方程:rho=30+10*sin(t*360*10 theta=t*180*cos(t*360*10 phi=t*360*3

18、080 蝴蝶结曲线方程:x=200*t*sin(t*3600 y=250*t*cos(t*3600z=300*t*sin(t*180081.“ 两相望 ” 曲线方程:rho=30theta=t*360*cos(t*360*20 phi=t*360*2082 小蜜蜂方程:x=cos(t*360+cos(3*t*360 y=sin(t*360+sin(5*t*360 83 弯月方程:x=cos(t*360+cos(2*t*360 y=sin(t*360*2+sin(t*360*2 84 热带鱼方程:a=5x=(a*(cos(t*360*34*t y=(a*(sin(t*360*34*t 85 燕尾

19、剪方程:x=3*cos(t*360*4 y=3*sin(t*360*3z=t86 天蚕丝方程:theta=t*3600 r=(cos(360*t*20*.5*t+1*t87 心电图方程:r=sin(t*360*2+.2 theta=10+t*(6*360z=t*388. 变化后的星形线方程:theta=t*360 x=10*cos(theta3y=10*sin(theta3z=cos(theta89. 小白兔方程:theta=t*360+180 r=cos(360*t3*6*2+5 91. 锁呐线方程:x=2*cos(t*360*3*t y=2*sin(t*360*3*tz=(sqrt(sqr

20、t(sqrt(t3*5 (同形:5392. 五环方程:theta=t*360*4 r=cos(t*360*5+193. 蜘蛛网方程:theta=t*360*5r=t*sin(t*360*25*5+894. 次声波方程:x=t*5y=t*cos(t*360*895. 十字渐开线方程:theta=t*360*4r=(cos(t*360*16*0.5*t+1*t96. 内五环方程: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. 蜗轨线方程:theta=t*36

21、0*2r=cos(t*360*30*t*0.5+t*2星形线:数学方程:x=a*cos3(ty=a*sin3(t心脏线:数学方程:r = 2a(1+cos(悬链线:数学方程:y=a*cosh(x/a克莱线:数学方程:r=4a*cos3(/3蜗牛线:数学方程:r=a*sin(/(做不出来? Why 蔓叶线:数学方程:r=2a*tan(sin( (分 2段做曳物线:数学方程:x=1/cosh(ty=t-tanh(t(分两段做 平摆线:数学方程:x=at-h*sin(ty=a-h*cos(t(做出来形状不对? 外摆线:数学方程:x=(a+bcos-lcos(a+b/by=(a+bsin-lsin(a

22、+b/b (abl基圆、滚圆、摆点半径, 公转角 内摆线:数学方程:x=(a-bcos+lcos(b-a/by=(a-bsin+lsin(b-a/b (abl基圆、滚圆、摆点半径, 公转角 蚌线:数学方程:a(r*cos-a=k2cos2(做不出全 360度的? 三尖瓣线:数学方程:x=a(2cost+cos2t y=a(2sint-sin2t(将 2变为 n-1即扩展为 n 尖瓣线 Devils 曲线:数学方程:r=(25-24tan2/(1-tan21/2 (做不出 8字曲线:数学方程:r2=a2cos2sec4(做不出 双叶线:数学方程:r=4a*cos*sin2费马线 :数学方程:r2=a2(分两段做 对数螺线 (等角螺线 :数学方程:r=aem阿基米德螺线 (等径螺线 数学方程:r=a叶形线:数学方程:r=4a*cossin2-bcos迪卡尔叶形线:数学方程:x=3at/(1+t3 y=3at2/(1+t3 肾形线:数学方程:r=a(1+2sin(/2双曲螺线:数学方程:r=a/ (做不出? 渐开线:数学方程:x=a(co