def calc_seg_intersect(xa, ya, xb, yb, xc, yc, xd, yd): s_abc = cross(xb - xa, yb - ya, xc - xa, yc - ya) c_abc = dblcmp(s_abc) c_cda = dblcmp(cross(xd - xc, yd - yc, xa - xc, ya - yc)) if c_abc == 0: f = between(xc, yc, xa, ya, xb, yb) if f is not None: return xc, yc, f, 0.0, (c_cda == 1), False if c_cda == 0: f = between(xa, ya, xc, yc, xd, yd) if f is not None: return xa, ya, 0.0, f, False, (c_abc == 1) s_abd = cross(xb - xa, yb - ya, xd - xa, yd - ya) c_abd = dblcmp(s_abd) c_cdb = dblcmp(cross(xd - xc, yd - yc, xb - xc, yb - yc)) if c_abd * c_abc < 0 and c_cda * c_cdb < 0: i = 1.0 * s_abc / (s_abc - s_abd) j = 1.0 - i res_x = xc * j + xd * i res_y = yc * j + yd * i return res_x, res_y, between(res_x, res_y, xa, ya, xb, yb), i, (c_cda == 1), (c_abc == 1) return None, None, None, None, (c_cda == 1), (c_abc == 1)
def get_seg_proper_intersect(xa, ya, xb, yb, xc, yc, xd, yd): s_abd = cross(xb - xa, yb - ya, xd - xa, yd - ya) c_abd = dblcmp(s_abd) s_abc = cross(xb - xa, yb - ya, xc - xa, yc - ya) c_abc = dblcmp(s_abc) c_cda = dblcmp(cross(xd - xc, yd - yc, xa - xc, ya - yc)) c_cdb = dblcmp(cross(xd - xc, yd - yc, xb - xc, yb - yc)) if c_abd * c_abc >= 0 or c_cda * c_cdb >= 0: return None i = 1.0 * s_abd / (s_abd - s_abc) j = 1.0 - i return xd * i + xc * j, yd * i + yc * j
def is_seg_intersect(xa, ya, xb, yb, xc, yc, xd, yd): c_abd = dblcmp(cross(xb - xa, yb - ya, xd - xa, yd - ya)) if c_abd == 0 and between(xd, yd, xa, ya, xb, yb) <= 0: return True c_abc = dblcmp(cross(xb - xa, yb - ya, xc - xa, yc - ya)) if c_abc == 0 and between(xc, yc, xa, ya, xb, yb) <= 0: return True c_cda = dblcmp(cross(xd - xc, yd - yc, xa - xc, ya - yc)) if c_cda == 0 and between(xa, ya, xc, yc, xd, yd) <= 0: return True c_cdb = dblcmp(cross(xd - xc, yd - yc, xb - xc, yb - yc)) if c_cdb == 0 and between(xb, yb, xc, yc, xd, yd) <= 0: return True return c_abd * c_abc < 0 and c_cda * c_cdb < 0
def between(xc, yc, xa, ya, xb, yb): if math.fabs(xb - xa) > math.fabs(yb - ya): da = xa - xc db = xb - xc else: da = ya - yc db = yb - yc sa = dblcmp(da) if sa == 0: return 0.0 sb = dblcmp(db) if sb == 0: return None if sa * sb < 0: return 1.0 * da / (da - db) return None
def get_seg_intersect(xa, ya, xb, yb, xc, yc, xd, yd): res = [] s_abd = cross(xb - xa, yb - ya, xd - xa, yd - ya) c_abd = dblcmp(s_abd) if c_abd == 0 and between(xd, yd, xa, ya, xb, yb) <= 0: res.append((xd, yd)) s_abc = cross(xb - xa, yb - ya, xc - xa, yc - ya) c_abc = dblcmp(s_abc) if c_abc == 0 and between(xc, yc, xa, ya, xb, yb) <= 0: res.append((xc, yc)) c_cda = dblcmp(cross(xd - xc, yd - yc, xa - xc, ya - yc)) if c_cda == 0 and between(xa, ya, xc, yc, xd, yd) < 0: res.append((xa, ya)) c_cdb = dblcmp(cross(xd - xc, yd - yc, xb - xc, yb - yc)) if c_cdb == 0 and between(xb, yb, xc, yc, xd, yd) < 0: res.append((xb, yb)) # 如果至少有一个点与另一条线段共线，那么此时可以断定交点已经全部求完 if len(res) > 0: return res if c_abd * c_abc < 0 and c_cda * c_cdb < 0: i = 1.0 * s_abd / (s_abd - s_abc) j = 1.0 - i res.append((xd * i + xc * j, yd * i + yc * j)) return res
def is_seg_proper_intersect(xa, ya, xb, yb, xc, yc, xd, yd): c_abd = dblcmp(cross(xb - xa, yb - ya, xd - xa, yd - ya)) c_abc = dblcmp(cross(xb - xa, yb - ya, xc - xa, yc - ya)) c_cda = dblcmp(cross(xd - xc, yd - yc, xa - xc, ya - yc)) c_cdb = dblcmp(cross(xd - xc, yd - yc, xb - xc, yb - yc)) return c_abd * c_abc < 0 and c_cda * c_cdb < 0
def between(xc, yc, xa, ya, xb, yb): if math.fabs(xb - xa) > math.fabs(yb - ya): return dblcmp(xa - xc) * dblcmp(xb - xc) else: return dblcmp(ya - yc) * dblcmp(yb - yc)
def decal_2d(rect, tri):
p0, p1, p2, p3 = rect
pa, pb, pc = tri
cw = dblcmp(cross(pb[0] - pa[0], pb[1] - pa[1], pc[0] - pb[0], pc[1] - pb[1]))
if cw == 0: # 三角形面积为0
return ()
if cw < 0:
pb, pc = pc, pb
tri = (pa, pb, pc)
rect_e = ((p0, p1), (p1, p2), (p2, p3), (p3, p0))
tri_e = ((pa, pb), (pb, pc), (pc, pa))
rect_p_seq = ([], [], [], [])
tri_p_seq = ([], [], [])
rp_inside = [True] * 4
pid = 0
for j, te in enumerate(tri_e):
tp_inside = True # 三角形的顶点是否在矩形的内部
for i, re in enumerate(rect_e):
x, y, f1, f2, tp_on_left, rp_on_left = calc_seg_intersect(
te[0][0], te[0][1], te[1][0], te[1][1],
re[0][0], re[0][1], re[1][0], re[1][1],)
if x is not None:
tri_p_seq[j].append((f1, (x, y), pid, i))
rect_p_seq[i].append((f2, (x, y), pid, j))
pid += 1
if not tp_on_left: # 只要有不在任意一条边的左侧，都out
tp_inside = False
if not rp_on_left:
rp_inside[i] = False
if tp_inside:
tri_p_seq[j].append((0.0, tri[j], pid, None))
pid += 1
for i in range(4):
if rp_inside[i]:
rect_p_seq[i].append((0.0, rect[i], pid, None))
pid += 1
if pid < 3:
return ()
# 排序，并找一个点作为起始点
start_pid = None
seq = None
p_index = None
for i, seg_p_seq in enumerate(tri_p_seq):
seg_p_seq.sort()
if start_pid is None and seg_p_seq:
start_pid = seg_p_seq[0][2]
seq = tri_p_seq
p_index = (i, 0)
for i, seg_p_seq in enumerate(rect_p_seq):
seg_p_seq.sort()
if start_pid is None and seg_p_seq:
start_pid = seg_p_seq[0][2]
seq = rect_p_seq
p_index = (i, 0)
ret = []
while True:
i, j = p_index
f, p, pid, rev_i = seq[i][j]
ret.append(p)
# 需要切换到另外一个序列上
if rev_i is not None and j == len(seq[i]) - 1:
next_p_seq = seq[(i + 1) % len(seq)]
if not next_p_seq or dblcmp(next_p_seq[0][0]) != 0:
if seq == tri_p_seq:
seq = rect_p_seq
else:
seq = tri_p_seq
for k, (_f, _p, _pid, _rev_i) in enumerate(seq[rev_i]):
if pid == _pid:
i, j = p_index = (rev_i, k)
break
# 找下一个顶点，此时可以允许换边
j += 1
if j < len(seq[i]):
p_index = (i, j)
else:
i = i + 1
if i >= len(seq):
i = 0
j = 0
p_index = (i, j)
try:
pid = seq[i][j][2]
except IndexError:
print ("f*****g algorithm error")
return ()
if pid == start_pid:
break
return ret