-
-
Notifications
You must be signed in to change notification settings - Fork 7.5k
/
proj3d.py
179 lines (139 loc) · 4.31 KB
/
proj3d.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
"""
Various transforms used for by the 3D code
"""
import numpy as np
import numpy.linalg as linalg
def _line2d_seg_dist(p1, p2, p0):
"""
Return the distance(s) from line defined by p1 - p2 to point(s) p0.
p0[0] = x(s)
p0[1] = y(s)
intersection point p = p1 + u*(p2-p1)
and intersection point lies within segment if u is between 0 and 1.
If p1 and p2 are identical, the distance between them and p0 is returned.
"""
x01 = np.asarray(p0[0]) - p1[0]
y01 = np.asarray(p0[1]) - p1[1]
if np.all(p1[0:2] == p2[0:2]):
return np.hypot(x01, y01)
x21 = p2[0] - p1[0]
y21 = p2[1] - p1[1]
u = (x01*x21 + y01*y21) / (x21**2 + y21**2)
u = np.clip(u, 0, 1)
d = np.hypot(x01 - u*x21, y01 - u*y21)
return d
def world_transformation(xmin, xmax,
ymin, ymax,
zmin, zmax, pb_aspect=None):
"""
Produce a matrix that scales homogeneous coords in the specified ranges
to [0, 1], or [0, pb_aspect[i]] if the plotbox aspect ratio is specified.
"""
dx = xmax - xmin
dy = ymax - ymin
dz = zmax - zmin
if pb_aspect is not None:
ax, ay, az = pb_aspect
dx /= ax
dy /= ay
dz /= az
return np.array([[1/dx, 0, 0, -xmin/dx],
[0, 1/dy, 0, -ymin/dy],
[0, 0, 1/dz, -zmin/dz],
[0, 0, 0, 1]])
def view_transformation(E, R, V):
n = (E - R)
## new
# n /= np.linalg.norm(n)
# u = np.cross(V, n)
# u /= np.linalg.norm(u)
# v = np.cross(n, u)
# Mr = np.diag([1.] * 4)
# Mt = np.diag([1.] * 4)
# Mr[:3,:3] = u, v, n
# Mt[:3,-1] = -E
## end new
## old
n = n / np.linalg.norm(n)
u = np.cross(V, n)
u = u / np.linalg.norm(u)
v = np.cross(n, u)
Mr = [[u[0], u[1], u[2], 0],
[v[0], v[1], v[2], 0],
[n[0], n[1], n[2], 0],
[0, 0, 0, 1]]
#
Mt = [[1, 0, 0, -E[0]],
[0, 1, 0, -E[1]],
[0, 0, 1, -E[2]],
[0, 0, 0, 1]]
## end old
return np.dot(Mr, Mt)
def persp_transformation(zfront, zback):
a = (zfront+zback)/(zfront-zback)
b = -2*(zfront*zback)/(zfront-zback)
return np.array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, a, b],
[0, 0, -1, 0]])
def ortho_transformation(zfront, zback):
# note: w component in the resulting vector will be (zback-zfront), not 1
a = -(zfront + zback)
b = -(zfront - zback)
return np.array([[2, 0, 0, 0],
[0, 2, 0, 0],
[0, 0, -2, 0],
[0, 0, a, b]])
def _proj_transform_vec(vec, M):
vecw = np.dot(M, vec)
w = vecw[3]
# clip here..
txs, tys, tzs = vecw[0]/w, vecw[1]/w, vecw[2]/w
return txs, tys, tzs
def _proj_transform_vec_clip(vec, M):
vecw = np.dot(M, vec)
w = vecw[3]
# clip here.
txs, tys, tzs = vecw[0] / w, vecw[1] / w, vecw[2] / w
tis = (0 <= vecw[0]) & (vecw[0] <= 1) & (0 <= vecw[1]) & (vecw[1] <= 1)
if np.any(tis):
tis = vecw[1] < 1
return txs, tys, tzs, tis
def inv_transform(xs, ys, zs, M):
iM = linalg.inv(M)
vec = _vec_pad_ones(xs, ys, zs)
vecr = np.dot(iM, vec)
try:
vecr = vecr / vecr[3]
except OverflowError:
pass
return vecr[0], vecr[1], vecr[2]
def _vec_pad_ones(xs, ys, zs):
return np.array([xs, ys, zs, np.ones_like(xs)])
def proj_transform(xs, ys, zs, M):
"""
Transform the points by the projection matrix
"""
vec = _vec_pad_ones(xs, ys, zs)
return _proj_transform_vec(vec, M)
transform = proj_transform
def proj_transform_clip(xs, ys, zs, M):
"""
Transform the points by the projection matrix
and return the clipping result
returns txs, tys, tzs, tis
"""
vec = _vec_pad_ones(xs, ys, zs)
return _proj_transform_vec_clip(vec, M)
def proj_points(points, M):
return np.column_stack(proj_trans_points(points, M))
def proj_trans_points(points, M):
xs, ys, zs = zip(*points)
return proj_transform(xs, ys, zs, M)
def rot_x(V, alpha):
cosa, sina = np.cos(alpha), np.sin(alpha)
M1 = np.array([[1, 0, 0, 0],
[0, cosa, -sina, 0],
[0, sina, cosa, 0],
[0, 0, 0, 1]])
return np.dot(M1, V)