forked from 170010011/fr
176 lines
4.2 KiB
Python
176 lines
4.2 KiB
Python
"""
|
|
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
|
|
"""
|
|
|
|
x21 = p2[0] - p1[0]
|
|
y21 = p2[1] - p1[1]
|
|
x01 = np.asarray(p0[0]) - p1[0]
|
|
y01 = np.asarray(p0[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)
|