用Python海龟制作圆圈函数

Question

我有一项学校的作业：

构建一个不含海龟circle函数的雪人circle

雪人应该在蓝色的背景上，画得满是白色。

雪人的轮廓应该是黑色的。

雪人的身体应该由三个装满的圆圈组成。

每个圆的轮廓应该是3个像素宽。

底部圆圈的半径应为100像素。

中间圆圈的半径应为70像素。

顶部圆圈的半径应为40像素。

每个圆圈都应该在它下面的那个上面(除了底部的圆圈，它可以在任何地方)。

两个圈子之间不应该有任何差距。

给雪人一个嘴巴，眼睛和鼻子(帽子是可选的)。

确保每只手都有两根棍子和至少两根手指.

到目前为止，我创建了这个，但是在我继续前进之前，我似乎还不能正确地得到这个圆圈。而且，不知道如何将涂成圆圈，或者为眼睛做点。请帮帮我，第一次编码。

import turtle                               # allows us to use turtle library
wn = turtle.Screen()                        # allows us to create a graphics window
wn.bgcolor("blue")                          # sets gtaphics windows background color to blue
import math                                 # allows us to use math functions
quinn = turtle.Turtle()                     # sets up turtle quinn
quinn.setpos(0,0)
quinn.pensize(3)
quinn.up()

# drawing first circle middle
quinn.forward(70)
quinn.down()
quinn.left(90)

# calculation of cicumference of a circle
a = (math.pi*140.00/360)

#itineration for first circle
for i in range (1,361,1):
    quinn.left(a)
    quinn.forward (1)

# drawing second circle bottom
quinn.up()
quinn.home()
quinn.right(90)
quinn.forward(70)
quinn.left(90)
quinn.down()

b = (math.pi*200.00/360)

for i in range (1,361,1):
    quinn.right(b)
    quinn.forward(1)

# drawing third circle head top

quinn.up ()
quinn.goto(0,70)
quinn.right(90)
quinn.down()

c =(math.pi*80/360)

for i in range (1,361,1):
    quinn.left(c)
    quinn.forward(1)

wn.exitonclick()

Answer 1

下面是一个绘制蓝色圆圈的示例函数：

def draw_circle(radius):    
    turtle.up()
    turtle.goto(0,radius) # go to (0, radius)
    turtle.begin_fill() # start fill
    turtle.down() # pen down
    turtle.color('blue')
    times_y_crossed = 0
    x_sign = 1.0
    while times_y_crossed <= 1:
        turtle.forward(2*math.pi*radius/360.0) # move by 1/360
        turtle.right(1.0)
        x_sign_new = math.copysign(1, turtle.xcor())        
        if(x_sign_new != x_sign):
            times_y_crossed += 1
        x_sign = x_sign_new
    turtle.up() # pen up
    turtle.end_fill() # end fill.
    return

然后您可以修改上面的函数，为圆心的位置(x，y)添加参数：

def draw_circle(radius, x, y):    
    turtle.up()
    turtle.goto(x,y+radius) # go to (x, y + radius)
    turtle.begin_fill() # start fill
    turtle.down() # pen down
    turtle.color('blue')
    times_y_crossed = 0
    x_sign = 1.0
    while times_y_crossed <= 1:
        turtle.forward(2*math.pi*radius/360.0) # move by 1/360
        turtle.right(1.0)
        x_sign_new = math.copysign(1, turtle.xcor())        
        if(x_sign_new != x_sign):
            times_y_crossed += 1
        x_sign = x_sign_new
    turtle.up() # pen up
    turtle.end_fill() # end fill.
    return

您可以轻松地添加点，例如：

turtle.goto(-20,10)
turtle.color('red')
turtle.dot(20)
turtle.goto(40,10)
turtle.dot(20)

汇集在一起：

import turtle
import math

def draw_circle(radius, x, y):    
    turtle.up()
    turtle.goto(x,y+radius) # go to (0, radius)
    turtle.begin_fill() # start fill
    turtle.down() # pen down
    turtle.color('blue')
    times_y_crossed = 0
    x_sign = 1.0
    while times_y_crossed <= 1:
        turtle.forward(2*math.pi*radius/360.0) # move by 1/360
        turtle.right(1.0)
        x_sign_new = math.copysign(1, turtle.xcor())        
        if(x_sign_new != x_sign):
            times_y_crossed += 1
        x_sign = x_sign_new
    turtle.up() # pen up
    turtle.end_fill() # end fill.
    return


draw_circle(100, 10, 10)
turtle.goto(-20,10)
turtle.color('red')
turtle.dot(20)
turtle.goto(40,10)
turtle.dot(20)
turtle.pen(shown=False)
turtle.done()

你应该尝试自己完成作业的其余部分。;)

Answer 2

很抱歉没有给出解释。第一部分是Ramanujan对pi的近似，但不是很好，因为它只在循环的大约300,000次迭代之后才到达pi的近似，并且它只精确到小数点5位。这部分将是：

    r += (1 / k) * (-1)**i
    pi = (4 * (1 - r))

然后我用圆周：

t.forward(2*5*pi)

最后，我只让乌龟走到了20点钟。

import turtle 
t = turtle.Turtle()
t.right(90)
t.penup()
t.goto(100, 0)
t.pendown()

i = 0
r = 0
k = 3

while i <= 360:
    r += (1 / k) * (-1)**i
    pi = (4 * (1 - r))
    t.write(pi)
    t.forward(2*5*pi)
    t.right(20)

    i += 1
    k += 2

turtle.done()

Answer 3

“无海龟圆函数”的大多数解决方案都涉及到编写与海龟的圆函数相当的内容。但是已经有另外两种方法可以画出轮廓，满是海龟的圆圈。

一个是你可以使用同心圆点。

turtle.color('black')
turtle.dot(200 + 3)
turtle.color('white')
turtle.dot(200 - 3)

请记住，dot()需要一个直径，而circle()需要一个半径：

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然而，我更喜欢使用加盖印花来解决这类问题：

''' Build a Snowman without turtle circle function '''

from turtle import Turtle, Screen

# The snowman’s body should be made of 3 filled circles.

# The bottom circle should have a radius of 100 pixels.
# The middle circle should have a radius of 70 pixels.
# The top circle should have a radius of 40 pixels.

RADII = (100, 70, 40)

STAMP_SIZE = 20

# The snowman should be on a blue background
screen = Screen()
screen.bgcolor('blue')

quinn = Turtle('circle')
quinn.setheading(90)
quinn.up()

# The outline of the snowman should be in black, and should be drawn filled with white.
quinn.color('black', 'white')

for not_first, radius in enumerate(RADII):

    if not_first:
        quinn.forward(radius)

    # The outline of each circle should be 3 pixels wide.
    quinn.shapesize((radius * 2) / STAMP_SIZE, outline=3)

    quinn.stamp()

    # Each circle should be centered above the one below it
    # There should be no gap between the circles.
    quinn.forward(radius)

# Give the snowman eyes

quinn.shapesize(15 / STAMP_SIZE)
quinn.color('black')
quinn.backward(3 * RADII[-1] / 4)

for x in (-RADII[-1] / 3, RADII[-1] / 3):
    quinn.setx(x)
    quinn.stamp()

# Give the snowman a mouth, and a nose (a hat is optional).

pass

# Make sure to include two stick-arms and at least two fingers on each hand.

pass

quinn.hideturtle()

screen.exitonclick()

这个想法是你把海龟光标本身扭曲到你需要的地方，在屏幕上拍一张它的快照，然后把它扭曲到你需要画的下一件东西上。

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