数学图形(1.4)心形线

心形线，是一个圆上的固定一点在它绕着与其相切且半径相同的另外一个圆周滚动时所形成的轨迹，因其形状像心形而得名。当然我觉得与其说它像心，还不如说它像屁股。

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极坐标方程:

水平方向： r=a(1-cosθ) 或 r=a(1+cosθ) (a>0)
垂直方向： r=a(1-sinθ) 或 r=a(1+sinθ) (a>0)

直角坐标方程:

心形线的平面直角坐标系方程表达式分别为 x^2+y^2+a*x=a*sqrt(x^2+y^2) 和 x^2+y^2-a*x=a*sqrt(x^2+y^2）

参数方程:

x=a*(2*cos(t)-cos(2*t))
y=a*(2*sin(t)-sin(2*t))

不过我觉得这种线怎么看都像屁股.

心脏线1

vertices = 1000

r = 10.0
t = from 0 to (2*PI)
p = 2*r*(1+cos(t));
x = p*sin(t)
y = p*cos(t)

 

心脏线2

vertices = 1000

r = 10.0
t = from 0 to (2*PI)
p = 2*r*(1-sin(t));
x = p*sin(t)
y = p*cos(t)

 

心脏线3

vertices = 1000

r = 10.0
t = from 0 to (2*PI)
p = 2*r*(1+sin(t));
x = p*sin(t)
y = p*cos(t)

 

心脏线4

vertices = 1000

r = 10.0
t = from 0 to (2*PI)
p = 2*r*(1-cos(t));
x = p*sin(t)
y = p*cos(t)

 

 心形线的另一种写法:

vertices = 1000

r = 10.0
t = from 0 to (2*PI)
x = r*[2*cos(t) - cos(2*t)]
y = r*[2*sin(t) - sin(2*t)]

不太像屁股的心形线:

vertices = 1000
r = 10.0
t = from 0 to (2*PI)
p = sin(t)*sqrt(abs(cos(t)))/(sin(t) + 7/5) - 2*sin(t) + 2
x = p*cos(t)
y = p*sin(t)

 心形面:

vertices = D1:360 D2:100
u = from (-PI) to (PI) D1
v = from 10 to 1000 D2

w = abs(u)
p = sqrt(w/(v + w))
r = 10

x = r*p*sin(u)
y = r*p*cos(u)