曲线方程的公式是什么 高中数学中,曲线方程的公式是啥?
\u66f2\u7ebf\u65b9\u7a0b\u7684\u516c\u5f0f\uff0c\u662f\u4ec0\u4e481.\u789f\u5f62\u5f39\u7c27\u5706\u67f1\u5750\u6807 \u65b9\u7a0b\uff1ar = 5 theta = t*3600 z =(sin(3.5*theta-90))+24*t2.\u53f6\u5f62\u7ebf.\u7b1b\u5361\u513f\u5750\u6807\u6807\u65b9\u7a0b\uff1aa=10 x=3*a*t/(1+(t^3)) y=3*a*(t^2)/(1+(t^3))3.\u87ba\u65cb\u7ebf(Helical curve)\u5706\u67f1\u5750\u6807\uff08cylindrical\uff09 \u65b9\u7a0b\uff1a r=t theta=10+t*(20*360) z=t*34.\u8774\u8776\u66f2\u7ebf\u7403\u5750\u6807 \u65b9\u7a0b\uff1arho = 8 * t theta = 360 * t * 4 phi = -360 * t * 85.\u6e10\u5f00\u7ebf\u91c7\u7528\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u65b9\u7a0b\uff1ar=1 ang=360*t s=2*pi*r*t x0=s*cos(ang) y0=s*sin(ang) x=x0+s*sin(ang) y=y0-s*cos(ang) z=06.\u87ba\u65cb\u7ebf.\u7b1b\u5361\u513f\u5750\u6807 \u65b9\u7a0b\uff1ax = 4 * cos ( t *(5*360)) y = 4 * sin ( t *(5*360)) z = 10*t7.\u5bf9\u6570\u66f2\u7ebf\u7b1b\u5361\u5c14\u5750\u6807\u7cfb \u65b9\u7a0b\uff1az=0 x = 10*t y = log(10*t+0.0001)8.\u7403\u9762\u87ba\u65cb\u7ebf\u91c7\u7528\u7403\u5750\u6807\u7cfb\u65b9\u7a0b\uff1arho=4 theta=t*180 phi=t*360*209.\u53cc\u5f27\u5916\u6446\u7ebf\u5361\u8fea\u5c14\u5750\u6807 \u65b9\u7a0b\uff1a l=2.5 b=2.5 x=3*b*cos(t*360)+l*cos(3*t*360) Y=3*b*sin(t*360)+l*sin(3*t*360)\u56fe910.\u661f\u884c\u7ebf\u5361\u8fea\u5c14\u5750\u6807 \u65b9\u7a0b\uff1aa=5 x=a*(cos(t*360))^3y=a*(sin(t*360))^3\u56fe1011.\u5fc3\u810f\u7ebf\u5706\u67f1\u5750\u6807\u65b9\u7a0b\uff1aa=10 r=a*(1+cos(theta)) theta=t*360\u56fe1112.\u5706\u5185\u87ba\u65cb\u7ebf\u91c7\u7528\u67f1\u5ea7\u6807\u7cfb \u65b9\u7a0b\uff1atheta=t*360 r=10+10*sin(6*theta) z=2*sin(6*theta)\u56fe1213.\u6b63\u5f26\u66f2\u7ebf\u7b1b\u5361\u5c14\u5750\u6807\u7cfb \u65b9\u7a0b\uff1ax=50*t y=10*sin(t*360) z=0\u56fe1314.\u592a\u9633\u7ebf\uff08\u8fd9\u672c\u6765\u662f\u505a\u522b\u7684\u66f2\u7ebf\u7684\uff0c\u7ed3\u679c\u505a\u9519\u4e86\uff0c\u5c31\u53d8\u6210\u8fd9\u6837\u4e86\uff0915.\u8d39\u9a6c\u66f2\u7ebf\uff08\u6709\u70b9\u50cf\u87ba\u7eb9\u7ebf\uff09\u6570\u5b66\u65b9\u7a0b\uff1ar\uff0ar = a*a*theta\u5706\u67f1\u5750\u6807\u65b9\u7a0b1: theta=360*t*5a=4r=a*sqrt(theta*180/pi)\u65b9\u7a0b2: theta=360*t*5a=4r=-a*sqrt(theta*180/pi)\u7531\u4e8ePro/e\u53ea\u80fd\u505a\u8fde\u7eed\u7684\u66f2\u7ebf\uff0c\u6240\u4ee5\u53ea\u80fd\u5206\u4e24\u6b21\u505a16.Talbot \u66f2\u7ebf\u5361\u7b1b\u5c14\u5750\u6807\u65b9\u7a0b\uff1atheta=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\u53f6\u7ebf\uff08\u4e00\u4e2a\u65b9\u7a0b\u505a\u7684\uff0c\u6ca1\u6709\u590d\u5236\uff0918.Rhodonea \u66f2\u7ebf \u91c7\u7528\u7b1b\u5361\u5c14\u5750\u6807\u7cfb \u65b9\u7a0b\uff1atheta=t*360*4 x=25+(10-6)*cos(theta)+10*cos((10/6-1)*theta) y=25+(10-6)*sin(theta)-6*sin((10/6-1)*theta)19. \u629b\u7269\u7ebf \u7b1b\u5361\u513f\u5750\u6807\u65b9\u7a0b\uff1ax =(4 * t) y =(3 * t) + (5 * t ^2) z =020.\u87ba\u65cb\u7ebf\u5706\u67f1\u5750\u6807\u65b9\u7a0b\uff1ar = 5 theta = t*1800 z =(cos(theta-90))+24*t
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\u94fe\u63a5\uff1ahttps://pan.baidu.com/s/1znmI8mJTas01m1m03zCRfQ
?pwd=1234
\u63d0\u53d6\u7801\uff1a1234
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圆柱坐标
方程:r = 5
theta = t*3600
z =(sin(3.5*theta-90))+24*t
2.叶形线.
笛卡儿坐标标
方程:a=10
x=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=t
theta=10+t*(20*360)
z=t*3
4.蝴蝶曲线
球坐标
方程:rho = 8 * t
theta = 360 * t * 4
phi = -360 * t * 8
5.渐开线
采用笛卡尔坐标系
方程:r=1
ang=360*t
s=2*pi*r*t
x0=s*cos(ang)
y0=s*sin(ang)
x=x0+s*sin(ang)
y=y0-s*cos(ang)
z=0
6.螺旋线.
笛卡儿坐标
方程:x = 4 * cos ( t *(5*360))
y = 4 * sin ( t *(5*360))
z = 10*t
7.对数曲线
笛卡尔坐标系
方程:z=0
x = 10*t
y = log(10*t+0.0001)
8.球面螺旋线
采用球坐标系
方程:rho=4
theta=t*180
phi=t*360*20
9.双弧外摆线
卡迪尔坐标
方程: l=2.5
b=2.5
x=3*b*cos(t*360)+l*cos(3*t*360)
Y=3*b*sin(t*360)+l*sin(3*t*360)
图9
10.星行线
卡迪尔坐标
方程:a=5
x=a*(cos(t*360))^3
y=a*(sin(t*360))^3
图10
11.心脏线
圆柱坐标
方程:a=10
r=a*(1+cos(theta))
theta=t*360
图11
12.圆内螺旋线
采用柱座标系
方程:theta=t*360
r=10+10*sin(6*theta)
z=2*sin(6*theta)
图12
13.正弦曲线
笛卡尔坐标系
方程:x=50*t
y=10*sin(t*360)
z=0
图13
14.太阳线(这本来是做别的曲线的,结果做错了,就变成这样了)
15.费马曲线(有点像螺纹线)
数学方程:r*r = a*a*theta
圆柱坐标
方程1: theta=360*t*5
a=4
r=a*sqrt(theta*180/pi)
方程2: theta=360*t*5
a=4
r=-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*360
a=1.1
b=0.666
c=sin(theta)
f=1
x = (a*a+f*f*c*c)*cos(theta)/a
y = (a*a-2*f+f*f*c*c)*sin(theta)/b
17.4叶线(一个方程做的,没有复制)
18.Rhodonea 曲线
采用笛卡尔坐标系
方程:theta=t*360*4
x=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
笛卡儿坐标
方程:x =(4 * t)
y =(3 * t) + (5 * t ^2)
z =0
20.螺旋线
圆柱坐标
方程:r = 5
theta = t*1800
z =(cos(theta-90))+24*t
y=gx�0�5/2v�0�5
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