目的：求圓和線段的交點
網上搜出的代碼大多千篇一律，都是這樣：
千篇一律，或許根本運都沒運作就發出來了；
源代碼
# 計算圓 與 直接相交的點
def line_intersect_circle(p, lsp, esp):
# p is the circle parameter, lsp and lep is the two end of the line
x0, y0, r0 = p
x1, y1 = lsp
x2, y2 = esp
if r0 == 0:
return [[x1, y1]]
if x1 == x2:
if abs(r0) >= abs(x1 - x0):
p1 = x1, round(y0 - math.sqrt(r0 ** 2 - (x1 - x0) ** 2), 5)
p2 = x1, round(y0 + math.sqrt(r0 ** 2 - (x1 - x0) ** 2), 5)
inp = [p1, p2]
# select the points lie on the line segment
inp = [p for p in inp if p[0] >= min(x1, x2) and p[0] <= max(x1, x2)]
else:
inp = []
else:
k = (y1 - y2) / (x1 - x2)
b0 = y1 - k * x1
a = k ** 2 + 1
b = 2 * k * (b0 - y0) - 2 * x0
c = (b0 - y0) ** 2 + x0 ** 2 - r0 ** 2
delta = b ** 2 - 4 * a * c
if delta >= 0:
p1x = round((-b - math.sqrt(delta)) / (2 * a), 5)
p2x = round((-b + math.sqrt(delta)) / (2 * a), 5)
p1y = round(k * x1 + b0, 5)
p2y = round(k * x2 + b0, 5)
inp = [[p1x, p1y], [p2x, p2y]]
# select the points lie on the line segment
inp = [p for p in inp if p[0] >= min(x1, x2) and p[0] <= max(x1, x2)]
else:
inp = []
return inp if inp != [] else [[x1, y1]] 出現的問題
我輸入，求 圓心為（0,0），半徑為1的圓 與 線段（0.5，-0.5）（1.5，-1）的交點：
print(line_intersect_circle((0, 0, 1), (0.5, -0.5), (1.5, -1))) 結果輸出：
[[0.77178, -1.0]]
一般一眼就能看出結果 x 沒問題，但是 y 錯了；
x應該在0.5 和 1.5 之間，且還沒到1，y應該在-0.5到-1之間；
錯誤代碼
倒數第八行：
p1y = round(k * x1 + b0, 5)
p2y = round(k * x2 + b0, 5) 很明顯這裡的 p1y 和 p2y 還是用的函數一開始傳進去的 原始x坐标，而沒有用解方程得到的 交點x坐标，交點x坐标分别是p1x和p2x；
是以，這裡改為：
p1y = round(k * p1x + b0, 5)
p2y = round(k * p2x + b0, 5) 正确代碼
# 計算圓 與 直接相交的點
def line_intersect_circle(p, lsp, esp):
# p is the circle parameter, lsp and lep is the two end of the line
x0, y0, r0 = p
x1, y1 = lsp
x2, y2 = esp
if r0 == 0:
return [[x1, y1]]
if x1 == x2:
if abs(r0) >= abs(x1 - x0):
p1 = x1, round(y0 - math.sqrt(r0 ** 2 - (x1 - x0) ** 2), 5)
p2 = x1, round(y0 + math.sqrt(r0 ** 2 - (x1 - x0) ** 2), 5)
inp = [p1, p2]
# select the points lie on the line segment
inp = [p for p in inp if p[0] >= min(x1, x2) and p[0] <= max(x1, x2)]
else:
inp = []
else:
k = (y1 - y2) / (x1 - x2)
b0 = y1 - k * x1
a = k ** 2 + 1
b = 2 * k * (b0 - y0) - 2 * x0
c = (b0 - y0) ** 2 + x0 ** 2 - r0 ** 2
delta = b ** 2 - 4 * a * c
if delta >= 0:
p1x = round((-b - math.sqrt(delta)) / (2 * a), 5)
p2x = round((-b + math.sqrt(delta)) / (2 * a), 5)
p1y = round(k * p1x + b0, 5)
p2y = round(k * p2x + b0, 5)
inp = [[p1x, p1y], [p2x, p2y]]
# select the points lie on the line segment
inp = [p for p in inp if p[0] >= min(x1, x2) and p[0] <= max(x1, x2)]
else:
inp = []
return inp if inp != [] else [[x1, y1]]