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Version 3.0.2
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Source code for mpl_toolkits.mplot3d.proj3d

# 3dproj.py
#
"""
Various transforms used for by the 3D code
"""
import numpy as np
import numpy.linalg as linalg



[docs]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]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.sqrt(a**2+b**2))
[docs]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.sqrt((x01 - u*x21)**2 + (y01 - u*y21)**2) return d
[docs]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([ [1.0/dx,0,0,-xmin/dx], [0,1.0/dy,0,-ymin/dy], [0,0,1.0/dz,-zmin/dz], [0,0,0,1.0]])
[docs]def view_transformation(E, R, V): n = (E - R) ## new # n /= mod(n) # u = np.cross(V,n) # u /= mod(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 / mod(n) u = np.cross(V, n) u = u / mod(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] ])
[docs]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]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]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]
[docs]def vec_pad_ones(xs, ys, zs): return np.array([xs, ys, zs, np.ones_like(xs)])
[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)
[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)
transform = proj_transform
[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]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)