人家要我去学阿基米德螺旋线,但显然我是数学渣,根本领会到不到那些精神,转换不过来,就不要装着能转换。既然习题5说“或者其他种类的螺线”于是我就选择了在我理解范围内的斐波那契螺旋线,也就是黄金螺旋线。人家要我画螺旋线,我觉得要把方框也画出来才容易验证我自己有没有搞错。

为了完成方形和圆弧的两个循环,我笨蛋地把斐波那契数列算了两次……
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| import turtle, math
def arc(t, r, angle):
n = 20 # int(2*math.pi*r/4)+3 公式画图太细致太慢,直接赋值加速
step_length = int(2*math.pi*r)*angle/360/n
step_angle = angle/n
t.lt(step_angle/2) # 据说折腾一下角度能消除像素误差?
polygon(t, step_length, n, step_angle)
t.rt(step_angle/2)
def polygon(t, length, n, angle):
for i in range(n):
t.fd(length)
t.lt(angle)
def start(t): # 起点要先偏移一些,每次方向保持一致
t.pu()
t.home()
t.goto(160,-110)
def square(t, size): # 第一个正方形
for i in range(4):
t.lt(90)
t.fd(size)
t.rt(90)
def boxes(t, n, size): # n-1个正方形
a = b = 1
base = size
for i in range(n-1):
for i in range(6):
t.lt(90)
t.fd(size)
t.rt(90)
fibo = a+b # 计算斐波那契数列
a = b
b = fibo
size = base*fibo
def spiral(t, n, size): # 第一个正方形里没有弧线,所以弧线也是n-1
a = b = 1
base = size
for i in range(n-1):
arc(t, size, 90)
fibo = a+b # 在算一次斐波那契数列
a = b
b = fibo
size = base*fibo
bob = turtle.Turtle()
bob.pensize(2) # 笔迹粗点好看些
n = 8
size = 20
start(bob)
square(bob, size)
boxes(bob, n, size)
start(bob)
spiral(bob, n, size)
turtle.mainloop() |
import turtle, math
def arc(t, r, angle):
n = 20 # int(2*math.pi*r/4)+3 公式画图太细致太慢,直接赋值加速
step_length = int(2*math.pi*r)*angle/360/n
step_angle = angle/n
t.lt(step_angle/2) # 据说折腾一下角度能消除像素误差?
polygon(t, step_length, n, step_angle)
t.rt(step_angle/2)
def polygon(t, length, n, angle):
for i in range(n):
t.fd(length)
t.lt(angle)
def start(t): # 起点要先偏移一些,每次方向保持一致
t.pu()
t.home()
t.goto(160,-110)
def square(t, size): # 第一个正方形
for i in range(4):
t.lt(90)
t.fd(size)
t.rt(90)
def boxes(t, n, size): # n-1个正方形
a = b = 1
base = size
for i in range(n-1):
for i in range(6):
t.lt(90)
t.fd(size)
t.rt(90)
fibo = a+b # 计算斐波那契数列
a = b
b = fibo
size = base*fibo
def spiral(t, n, size): # 第一个正方形里没有弧线,所以弧线也是n-1
a = b = 1
base = size
for i in range(n-1):
arc(t, size, 90)
fibo = a+b # 在算一次斐波那契数列
a = b
b = fibo
size = base*fibo
bob = turtle.Turtle()
bob.pensize(2) # 笔迹粗点好看些
n = 8
size = 20
start(bob)
square(bob, size)
boxes(bob, n, size)
start(bob)
spiral(bob, n, size)
turtle.mainloop()