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import numpy as np |
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import math |
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def make_triangle(sx, sy, dx, dy, delta): |
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'''Create a right rectangle, alinged with X and Y axes, with x-side size sX |
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and y-side size sY. Triangle is offset by dX and dY.''' |
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x1 = np.arange(0, sx, delta) |
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y1 = np.zeros(x1.shape) |
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y2 = np.arange(0, sy, delta) |
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x2 = np.zeros(y2.shape) |
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x3 = np.arange(0, sx, delta) |
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y3 = sy - x3 * sy / sx |
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xs = np.hstack([x1, x2, x3]) - dx |
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ys = np.hstack([y1, y2, y3]) - dy |
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return xs, ys |
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def make_tri_pyramid(sx, sy, sz, dx, dy, dz, delta): |
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'''Create a right rectangle triangular pyramid, alinged with X and Y axes, |
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with x-side at the base size of sX and y-side size at the base of sY. |
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Pyramid has high sZ. It is offset by dX, dY and dZ.''' |
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points = [] |
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for z in np.arange(0, sz, delta): |
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ai = sx - z * sx / sz |
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bi = sy - z * sy / sz |
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xs, ys = make_triangle(ai, bi, dx, dy, delta) |
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points.append((xs, ys, z * np.ones(xs.shape))) |
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xs = np.hstack([x for x, y, z in points]) |
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ys = np.hstack([y for x, y, z in points]) |
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zs = np.hstack([z for x, y, z in points]) - dz |
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points = np.vstack([xs, ys, zs]).T |
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return points |
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def make_tri_pyramid_footprint(sx, sy, sz, dx, dy, dz): |
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'''Create the footprint of a pyramid created by make_tri_pyramid''' |
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footprint = np.array([ |
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[0, 0, 0], |
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[0, sy, 0], |
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[sx, 0, 0], |
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[0, 0, 0], |
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]) |
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footprint[:, 0] -= dx |
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footprint[:, 1] -= dy |
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footprint[:, 2] -= dz |
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return footprint |
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def make_tri_pyramid_with_base(side, delta, offset): |
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'''Create a pyramid as per make_tri_pyramid, suroundeded by a triangular |
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flat base.''' |
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rng = np.random.RandomState(0) |
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sx = side / 2 |
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sy = side |
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sz = side / 4 |
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dx = offset[0] + side / 2 |
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dy = offset[1] + side / 2 |
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dz = offset[2] |
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points = make_tri_pyramid(sx, sy, sz, dx, dy, dz, delta) |
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_add_noise(points, 0.1, rng) |
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for s in np.arange(0, side * 0.05, delta): |
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xs, ys = make_triangle(sx * (1 + s), sy * (1 + s), dx + s, dy + s, |
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delta) |
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zs = np.zeros(xs.shape) - dz |
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tmp = np.vstack([xs, ys, zs]).T |
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points = np.vstack([points, tmp]) |
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footprint = make_tri_pyramid_footprint(sx, sy, sz, dx, dy, dz) |
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return points, footprint |
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def _add_noise(points, size, rng): |
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'''Add noise to an array of 2D points''' |
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points += (rng.rand(points.shape[0], points.shape[1]) - 0.5) * size |
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def perpendicular_2d(a): |
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'''Create a vector perpendicular to the original''' |
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b = np.zeros(a.shape) |
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b[0] = -a[1] |
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b[1] = a[0] |
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return b |
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def rotation_around_axis(axis, theta): |
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''' |
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Return the rotation matrix associated with counterclockwise rotation about |
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the given axis by theta radians. |
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''' |
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axis = np.asarray(axis) |
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theta = np.asarray(theta) |
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axis = axis / math.sqrt(np.dot(axis, axis)) |
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a = math.cos(theta / 2) |
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b, c, d = -axis * math.sin(theta / 2) |
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aa, bb, cc, dd = a * a, b * b, c * c, d * d |
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bc, ad, ac, ab, bd, cd = b * c, a * d, a * c, a * b, b * d, c * d |
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return np.array([[aa + bb - cc - dd, 2 * (bc + ad), 2 * (bd - ac)], |
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[2 * (bc - ad), aa+cc-bb-dd, 2 * (cd + ab)], |
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[2 * (bd + ac), 2 * (cd - ab), aa + dd - bb - cc]]) |
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def make_half_red_stick(point_from, point_to, width=0.04, num_pts_per_line=50, |
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num_lines_per_stick=25): |
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''' Make a hollow red-white-red-white stick ''' |
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point_from = np.asarray(point_from, dtype=float)[:3] |
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point_to = np.asarray(point_to, dtype=float)[:3] |
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length = np.linalg.norm(point_to - point_from) |
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width = length * 0.04 |
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axis = (point_to - point_from) * 1.0 / length |
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origin = perpendicular_2d(axis) * width |
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points = np.zeros((num_pts_per_line * num_lines_per_stick, 6)) |
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points[:, 3:6] = 255 |
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idx = 0 |
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unitline = np.linspace(0, 1, num_pts_per_line) |
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for theta in np.linspace(0, math.pi, num_lines_per_stick): |
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src = np.dot(rotation_around_axis(axis, theta), origin) |
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# straight slope [0, 1] |
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line = np.array((unitline, unitline, unitline)).T |
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# linear function with slope |
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line = point_from + src + (point_to - point_from) * line |
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points[idx:idx + num_pts_per_line, :3] = line |
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points[idx:idx + num_pts_per_line/2, 3:6] = [210, 25, 30] |
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idx += num_pts_per_line |
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return points |
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def make_red_stick(point_from, point_to, **kwargs): |
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''' Make a hollow red-white-red-white stick ''' |
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point_from = np.asarray(point_from, dtype=float)[:3] |
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point_to = np.asarray(point_to, dtype=float)[:3] |
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halfway = (point_to + point_from)/2 |
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half1 = make_half_red_stick(point_from, halfway, **kwargs) |
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half2 = make_half_red_stick(halfway, point_to, **kwargs) |
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return np.concatenate((half1, half2), axis=0) |
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NLeSC /
PattyAnalytics
