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import torch
def area(a, b, c):
return (c[1] - a[1]) * (b[0] - a[0]) - (b[1] - a[1]) * (c[0] - a[0])
def triangle_area(A, B, C):
out = (C - A).flip([-1]) * (B - A)
out = out[..., 1] - out[..., 0]
return out
def compute_sine_theta(s1, s2): # s1 and s2 aret two segments to be uswed
# s1, s2 (2, 2)
v1 = s1[1, :] - s1[0, :]
v2 = s2[1, :] - s2[0, :]
# print(v1, v2)
sine_theta = (v1[0] * v2[1] - v1[1] * v2[0]) / (torch.norm(v1) * torch.norm(v2))
return sine_theta
def xing_loss_fn(x_list, scale=1e-3): # x[npoints, 2]
loss = 0.
# print(f"points_len: {len(x_list)}")
for x in x_list:
# print(f"x: {x}")
seg_loss = 0.
N = x.size()[0]
assert N % 3 == 0, f'The segment number ({N}) is not correct!'
x = torch.cat([x, x[0, :].unsqueeze(0)], dim=0) # (N+1,2)
segments = torch.cat([x[:-1, :].unsqueeze(1), x[1:, :].unsqueeze(1)], dim=1) # (N, start/end, 2)
segment_num = int(N / 3)
for i in range(segment_num):
cs1 = segments[i * 3, :, :] # start control segs
cs2 = segments[i * 3 + 1, :, :] # middle control segs
cs3 = segments[i * 3 + 2, :, :] # end control segs
# print('the direction of the vectors:')
# print(compute_sine_theta(cs1, cs2))
direct = (compute_sine_theta(cs1, cs2) >= 0).float()
opst = 1 - direct # another direction
sina = compute_sine_theta(cs1, cs3) # the angle between cs1 and cs3
seg_loss += direct * torch.relu(- sina) + opst * torch.relu(sina)
# print(direct, opst, sina)
seg_loss /= segment_num
templ = seg_loss
loss += templ * scale # area_loss * scale
return loss / (len(x_list))
if __name__ == "__main__":
# x = torch.rand([6, 2])
# x = torch.tensor([[0,0], [1,1], [2,1], [1.5,0]])
x = torch.tensor([[0, 0], [1, 1], [2, 1], [0.5, 0]])
# x = torch.tensor([[1,0], [2,1], [0,1], [2,0]])
scale = 1 # 0.5
y = xing_loss_fn([x], scale)
print(y)
x = torch.tensor([[0, 0], [1, 1], [2, 1], [2., 0]])
# x = torch.tensor([[1,0], [2,1], [0,1], [2,0]])
scale = 1 # 0.5
y = xing_loss_fn([x], scale)
print(y)
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