這個方程如何在Python中工作？

Question

這是一個繪製簡單字符串藝術的基本程序。在下面的while循環中，我不明白fraction和reverse_fraction計算。

首先，爲什麼要計算這些值的公式？其次，我讀這個代碼會產生25行，最後一行是從(x2a, y2a)到(x1b, y1b)？如果函數和反函數的變量是正確的，那是真的嗎？在我看來，最後一個字符串實際上並沒有觸及第二行的端點。

# Function to make string art with two sticks, A and B. Stick A 
# has endpoints (x1a, y1a) and (x2a, y2a). Stick B has endpoints 
# (x1b, y1b), (x2a, y2b). The parameter strings says how many 
# strings to put between the two sticks. 
def make_string_art(x1a, y1a, x2a, y2a, x1b, y1b, x2b, y2b, strings): 
    # Start by making the background black. 
    set_clear_color(0, 0, 0) 
    clear() 

    enable_smoothing() 

    # Draw the sticks in red, 3 pixels wide. 
    set_stroke_color(1, 0, 0) 
    set_stroke_width(3) 
    draw_line(x1a, y1a, x2a, y2a) # draw stick A 
    draw_line(x1b, y1b, x2b, y2b) # draw stick B 

    set_stroke_width(1)    # strings should be thin 

    # Variables red, green, and blue give the color combination for each string.  
    red = 0 
    green = 0 
    blue = 1 

    # The variable s indicates which string. It runs from 0 to strings-1, so 
    # that it takes on strings different values. 
    s = 0 
    while s < strings: 
     fraction = float(s)/float(strings - 1) # how far from (x1a, y1a) on stick A 
     reverse_fraction = 1.0 - fraction   # how far from (x1b, y1b) on stick B 

     # Compute the points where the strings attach on sticks A and B. 
     attach1_x = x1a + fraction * (x2a - x1a) 
     attach1_y = y1a + fraction * (y2a - y1a) 
     attach2_x = x1b + reverse_fraction * (x2b - x1b) 
     attach2_y = y1b + reverse_fraction * (y2b - y1b) 

     # The string color changes as the strings progress down the sticks. 
     # It always has no red. It starts with no green and all blue, and 
     # each string has a little more green and a little less blue than the 
     # string before it. By the time we draw the last string, it has all 
     # green and no blue. 
     green = fraction 
     blue = reverse_fraction 
     set_stroke_color(red, green, blue) 

     # Now that we have the attachment points and the color set, draw 
     # the string. 
     draw_line(attach1_x, attach1_y, attach2_x, attach2_y) 

     # Go on to the next string. 
     s = s + 1  

    # Main function. Just calls make_string_art with parameters. 
def main(): 
    make_string_art(25, 50, 50, 200, 350, 180, 200, 350, 25) 

start_graphics(main) 

Answer 1

此代碼是（X1A，Y1A）和（X2A，Y2A）之間linearly interpolating和反向內插從（X2B，Y2B）至（X1B，Y1B）。

它這樣做是爲了讓線條交叉，並且看起來不錯。