176 lines
4.2 KiB
Python
176 lines
4.2 KiB
Python
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"""
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Various transforms used for by the 3D code
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"""
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import numpy as np
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import numpy.linalg as linalg
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def _line2d_seg_dist(p1, p2, p0):
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"""
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Return the distance(s) from line defined by p1 - p2 to point(s) p0.
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p0[0] = x(s)
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p0[1] = y(s)
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intersection point p = p1 + u*(p2-p1)
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and intersection point lies within segment if u is between 0 and 1
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"""
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x21 = p2[0] - p1[0]
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y21 = p2[1] - p1[1]
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x01 = np.asarray(p0[0]) - p1[0]
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y01 = np.asarray(p0[1]) - p1[1]
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u = (x01*x21 + y01*y21) / (x21**2 + y21**2)
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u = np.clip(u, 0, 1)
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d = np.hypot(x01 - u*x21, y01 - u*y21)
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return d
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def world_transformation(xmin, xmax,
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ymin, ymax,
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zmin, zmax, pb_aspect=None):
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"""
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Produce a matrix that scales homogeneous coords in the specified ranges
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to [0, 1], or [0, pb_aspect[i]] if the plotbox aspect ratio is specified.
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"""
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dx = xmax - xmin
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dy = ymax - ymin
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dz = zmax - zmin
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if pb_aspect is not None:
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ax, ay, az = pb_aspect
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dx /= ax
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dy /= ay
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dz /= az
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return np.array([[1/dx, 0, 0, -xmin/dx],
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[0, 1/dy, 0, -ymin/dy],
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[0, 0, 1/dz, -zmin/dz],
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[0, 0, 0, 1]])
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def view_transformation(E, R, V):
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n = (E - R)
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## new
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# n /= np.linalg.norm(n)
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# u = np.cross(V, n)
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# u /= np.linalg.norm(u)
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# v = np.cross(n, u)
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# Mr = np.diag([1.] * 4)
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# Mt = np.diag([1.] * 4)
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# Mr[:3,:3] = u, v, n
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# Mt[:3,-1] = -E
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## end new
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## old
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n = n / np.linalg.norm(n)
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u = np.cross(V, n)
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u = u / np.linalg.norm(u)
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v = np.cross(n, u)
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Mr = [[u[0], u[1], u[2], 0],
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[v[0], v[1], v[2], 0],
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[n[0], n[1], n[2], 0],
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[0, 0, 0, 1]]
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#
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Mt = [[1, 0, 0, -E[0]],
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[0, 1, 0, -E[1]],
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[0, 0, 1, -E[2]],
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[0, 0, 0, 1]]
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## end old
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return np.dot(Mr, Mt)
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def persp_transformation(zfront, zback):
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a = (zfront+zback)/(zfront-zback)
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b = -2*(zfront*zback)/(zfront-zback)
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return np.array([[1, 0, 0, 0],
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[0, 1, 0, 0],
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[0, 0, a, b],
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[0, 0, -1, 0]])
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def ortho_transformation(zfront, zback):
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# note: w component in the resulting vector will be (zback-zfront), not 1
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a = -(zfront + zback)
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b = -(zfront - zback)
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return np.array([[2, 0, 0, 0],
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[0, 2, 0, 0],
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[0, 0, -2, 0],
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[0, 0, a, b]])
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def _proj_transform_vec(vec, M):
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vecw = np.dot(M, vec)
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w = vecw[3]
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# clip here..
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txs, tys, tzs = vecw[0]/w, vecw[1]/w, vecw[2]/w
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return txs, tys, tzs
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def _proj_transform_vec_clip(vec, M):
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vecw = np.dot(M, vec)
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w = vecw[3]
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# clip here.
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txs, tys, tzs = vecw[0] / w, vecw[1] / w, vecw[2] / w
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tis = (0 <= vecw[0]) & (vecw[0] <= 1) & (0 <= vecw[1]) & (vecw[1] <= 1)
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if np.any(tis):
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tis = vecw[1] < 1
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return txs, tys, tzs, tis
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def inv_transform(xs, ys, zs, M):
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iM = linalg.inv(M)
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vec = _vec_pad_ones(xs, ys, zs)
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vecr = np.dot(iM, vec)
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try:
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vecr = vecr / vecr[3]
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except OverflowError:
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pass
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return vecr[0], vecr[1], vecr[2]
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def _vec_pad_ones(xs, ys, zs):
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return np.array([xs, ys, zs, np.ones_like(xs)])
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def proj_transform(xs, ys, zs, M):
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"""
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Transform the points by the projection matrix
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"""
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vec = _vec_pad_ones(xs, ys, zs)
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return _proj_transform_vec(vec, M)
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transform = proj_transform
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def proj_transform_clip(xs, ys, zs, M):
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"""
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Transform the points by the projection matrix
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and return the clipping result
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returns txs, tys, tzs, tis
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"""
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vec = _vec_pad_ones(xs, ys, zs)
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return _proj_transform_vec_clip(vec, M)
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def proj_points(points, M):
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return np.column_stack(proj_trans_points(points, M))
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def proj_trans_points(points, M):
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xs, ys, zs = zip(*points)
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return proj_transform(xs, ys, zs, M)
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def rot_x(V, alpha):
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cosa, sina = np.cos(alpha), np.sin(alpha)
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M1 = np.array([[1, 0, 0, 0],
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[0, cosa, -sina, 0],
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[0, sina, cosa, 0],
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[0, 0, 0, 1]])
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return np.dot(M1, V)
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