Version 3.1.2
matplotlib
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Source code for mpl_toolkits.mplot3d.proj3d

"""
Various transforms used for by the 3D code
"""

import numpy as np
import numpy.linalg as linalg

from matplotlib import cbook


[docs]@cbook.deprecated("3.1") def line2d(p0, p1): """ Return 2D equation of line in the form ax+by+c = 0 """ # x + x1 = 0 x0, y0 = p0[:2] x1, y1 = p1[:2] # if x0 == x1: a = -1 b = 0 c = x1 elif y0 == y1: a = 0 b = 1 c = -y1 else: a = y0 - y1 b = x0 - x1 c = x0*y1 - x1*y0 return a, b, c
[docs]@cbook.deprecated("3.1") def line2d_dist(l, p): """ Distance from line to point line is a tuple of coefficients a, b, c """ a, b, c = l x0, y0 = p return abs((a*x0 + b*y0 + c) / np.hypot(a, b))
def _line2d_seg_dist(p1, p2, p0): """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
[docs]@cbook.deprecated("3.1") def line2d_seg_dist(p1, p2, p0): """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 """ return _line2d_seg_dist(p1, p2, p0)
[docs]@cbook.deprecated("3.1", alternative="np.linalg.norm") def mod(v): """3d vector length""" return np.sqrt(v[0]**2+v[1]**2+v[2]**2)
[docs]def world_transformation(xmin, xmax, ymin, ymax, zmin, zmax): dx, dy, dz = (xmax-xmin), (ymax-ymin), (zmax-zmin) 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]])
[docs]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)
[docs]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
[docs]@cbook.deprecated("3.1") def proj_transform_vec(vec, M): return _proj_transform_vec(vec, M)
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
[docs]@cbook.deprecated("3.1") def proj_transform_vec_clip(vec, M): return _proj_transform_vec_clip(vec, M)
[docs]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)])
[docs]@cbook.deprecated("3.1") def vec_pad_ones(xs, ys, zs): return _vec_pad_ones(xs, ys, zs)
[docs]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
[docs]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)
[docs]def proj_points(points, M): return np.column_stack(proj_trans_points(points, M))
[docs]def proj_trans_points(points, M): xs, ys, zs = zip(*points) return proj_transform(xs, ys, zs, M)
[docs]@cbook.deprecated("3.1") def proj_trans_clip_points(points, M): xs, ys, zs = zip(*points) return proj_transform_clip(xs, ys, zs, M)
[docs]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)