常用曲线函数图例

1.碟形弹簧圓柱坐标方程：r=5theta=t*3600z=(sin(3.5*theta-90))+24*t 2 . 叶形线.笛卡儿坐标方程：a=10x=3*a*t/(1+(t^3))y=3*a*(t^2)/(1+(t^3))  3.螺旋线(Helical curve)圆柱坐标（cylindrical）方程：r=ttheta=10+t*(20*360)z=t*3  4.蝴蝶曲线球坐标方程：rho=8*ttheta=360*t*4phi=-360*t*8  5.渐开线采用笛卡尔坐标系方程：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=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*ty=log(10*t+0.0001)8..球面螺旋线采用球坐标系方程：rho=4theta=t*180phi=t*360*209.双弧外摆线卡迪尔坐标方程：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*360)10.星行线卡迪尔坐标方程：a=5x=a*(cos(t*360))^3y=a*(sin(t*360))^311.心脏线圓柱坐标方程：a=10r=a*(1+cos(theta))theta=t*36012.圆内螺旋线采用柱座标系方程：theta=t*360r=10+10*sin(6*theta)z=2*sin(6*theta)13.正弦曲线笛卡尔坐标系方程：x=50*ty=10*sin(t*360)z=014.太阳线 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)由于Pro/e只能做连续的曲线，所以只能分两次做16.Talbot 曲线卡笛尔坐标方程：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)/b17.4叶线 18.Rhodonea 曲线 采用笛卡尔坐标系方程：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)*theta19.抛物线 笛卡儿坐标方程：x=(4*t)y=(3*t)+(5*t^2)z=020.螺旋线圓柱坐标方程：r=5theta=t*1800z=(cos(theta-90))+24*t21.三叶线圆柱坐标方程：a=1theta=t*380b=sin(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)*sin(theta)-b*sin((a/b+1)*theta)z=023.Lissajous 曲线theta=t*360a=1b=1c=100n=3x=a*sin(n*theta+c)y=b*sin(theta)24.长短幅圆内旋轮线卡笛尔坐标方程：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)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)y=(a+b)*sin(theta)-c*sin((a/b+1)*theta)26.三尖瓣线a=10x=a*(2*cos(t*360)+cos(2*t*360))y=a*(2*sin(t*360)-sin(2*t*360))]27.概率曲线！方程：笛卡儿坐标x=t*10-5y=exp(0-x^2)28.箕舌线笛卡儿坐标系a=1x=-5+t*10y=8*a^3/(x^2+4*a^2)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*100-50solvex^3=y^2*(2*a-x)forx32.tan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-x))/235.双曲正切x=6*t-3y=(exp(x)-exp(0-x))/(exp(x)+exp(0-x))36.一峰三驻点曲线x=3*t-1.5y=(x^2-1)^3+137.八字曲线x=2*cos(t*(2*180))y=2*sin(t*(5*360))z=038.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))z=040.封闭球形环绕曲线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*(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*sin(theta))^244.椭圆曲线笛卡尔坐标系a=10b=20theta=t*360x=a*cos(theta)y=b*sin(theta)45.梅花曲线柱坐标theta=t*360r=10+(3*sin(theta*2.5))^246.另一个花曲线theta=t*360r=10-(3*sin(theta*3))^2z=4*sin(theta*3)^247.改一下就成为空间感更强的花曲线了theta=t*360r=10-(3*sin(theta*3))^2z=(r*sin(theta*3))^248.螺旋上升的椭圆线a=10b=20theta=t*360*3x=a*cos(theta)y=b*sin(theta)z=t*1249.甚至这种螺旋花曲线theta=t*360*4r=10+(3*sin(theta*2.5))^2z=t*1650.鼓形线     r=5+3.3*sin(t*180)+ttheta=t*360*10z=t*1051 长命锁曲线 笛卡尔方程：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     球坐标方程：rho=200*ttheta=900*tphi=t*90*1053．螺旋上升曲线r=t^10theta=t^3*360*6*3+t^3*360*3*3z=t^3*(t+1)54. 蘑菇曲线rho=t^3+t*(t+1)theta=t*360phi=t^2*360*20*2055.  8字曲线a=1b=1x=3*b*cos(t*360)+a*cos(3*t*360)Y=b*sin(t*360)+a*sin(3*t*360)56.梅花曲线theta=t*360r=100+50*cos(5*theta)z=2*cos(5*theta)57.桃形曲线rho=t^3+t*(t+1)theta=t*360phi=t^2*360*10*1058.碟形弹簧 建立環境:pro/e圓柱坐r=5theta=t*3600z=(sin(3.5*theta-90))+2459.环形二次曲线笛卡儿方程：x=50*cos(t*360)y=50*sin(t*360)z=10*cos(t*360*8)60 蝶线球        坐标：rho=4*sin(t*360)+6*cos(t*360^2)theta=t*360phi=log(1+t*360)*t*36061.正弦周弹簧 笛卡尔： ang1=t*360 ang2=t*360*20 x=ang1*2*pi/360 y=sin(ang1)*5+cos(ang2) z=sin(ang2) 62.环形螺旋线 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.内接弹簧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.柱面正弦波线       柱坐标：方程r=30theta=t*360z=5*sin(5*theta-90)66. ufo （漩涡线） 球坐标：rho=t*20^2theta=t*log(30)*60phi=t*7200图6669.圆柱齿轮廓的渐开线方程: 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=4theta=t*60phi=t*360*1072. 向日葵线theta=t*360r=30+10*sin(theta*30)z=073. 太阳线r=1.5*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=sin(t*360*10)+30theta=sin(t*360*15)z=sin(t*3)77 阿基米德螺线的变形不知前面有没有？？:what柱坐标下：theta=360*2*(t-0.5)r=10*thetaz=078 改过来的渐开线方程r=20ang=t*360x=r*cos(ang)+2*pi*r*t*sin(ang)y=r*sin(ang)-2*pi*r*t*cos(ang)z=079 双鱼曲线球坐标系rho=30+10*sin(t*360*10)theta=t*180*cos(t*360*10)phi=t*360*3080 蝴蝶结曲线x=200*t*sin(t*3600)y=250*t*cos(t*3600)z=300*t*sin(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=sin(t*360)+sin(5*t*360)83 弯月 x=cos(t*360)+cos(2*t*360)Y=sin(t*360)*2+sin(t*360)*284 热带鱼a=5x=(a*(cos(t*3