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| from __future__ import absolute_import, division | |
| import numpy as np | |
| from scipy.special import comb | |
| def bezier_curve(points, nb_points=1000): | |
| """ Given a list of points compute a bezier curve from it. | |
| # Arguments | |
| points: ndarray. Array of points with shape (N, 2) with N being the | |
| number of points and the second dimension representing the | |
| (x, y) coordinates. | |
| nb_points: Integer. Number of points to sample from the bezier curve. | |
| This value must be larger than the number of points given in | |
| `points`. Maximum value 10000. | |
| # Returns | |
| ndarray: Array of shape (1000, 2) with the bezier curve of the | |
| given path of points. | |
| """ | |
| nb_points = min(nb_points, 1000) | |
| points = np.asarray(points, dtype=np.float) | |
| if points.ndim != 2 or points.shape[1] != 2: | |
| raise ValueError( | |
| '`points` should be two dimensional and have shape: (N, 2)') | |
| n_points = len(points) | |
| if n_points > nb_points: | |
| # We are downsampling points | |
| return points | |
| t = np.linspace(0., 1., nb_points).reshape(1, -1) | |
| # Compute the Bernstein polynomial of n, i as a function of t | |
| i = np.arange(n_points).reshape(-1, 1) | |
| n = n_points - 1 | |
| polynomial_array = comb(n, i) * (t**(n - i)) * (1 - t)**i | |
| bezier_curve_points = polynomial_array.T.dot(points) | |
| return bezier_curve_points | |
| def bresenham(points): | |
| """ Apply Bresenham algorithm for a list points. | |
| More info: https://en.wikipedia.org/wiki/Bresenham's_line_algorithm | |
| # Arguments | |
| points: ndarray. Array of points with shape (N, 2) with N being the number | |
| if points and the second coordinate representing the (x, y) | |
| coordinates. | |
| # Returns | |
| ndarray: Array of points after having applied the bresenham algorithm. | |
| """ | |
| points = np.asarray(points, dtype=np.int) | |
| def line(x0, y0, x1, y1): | |
| """ Bresenham line algorithm. | |
| """ | |
| d_x = x1 - x0 | |
| d_y = y1 - y0 | |
| x_sign = 1 if d_x > 0 else -1 | |
| y_sign = 1 if d_y > 0 else -1 | |
| d_x = np.abs(d_x) | |
| d_y = np.abs(d_y) | |
| if d_x > d_y: | |
| xx, xy, yx, yy = x_sign, 0, 0, y_sign | |
| else: | |
| d_x, d_y = d_y, d_x | |
| xx, xy, yx, yy = 0, y_sign, x_sign, 0 | |
| D = 2 * d_y - d_x | |
| y = 0 | |
| line = np.empty((d_x + 1, 2), dtype=points.dtype) | |
| for x in range(d_x + 1): | |
| line[x] = [x0 + x * xx + y * yx, y0 + x * xy + y * yy] | |
| if D >= 0: | |
| y += 1 | |
| D -= 2 * d_x | |
| D += 2 * d_y | |
| return line | |
| nb_points = len(points) | |
| if nb_points < 2: | |
| return points | |
| new_points = [] | |
| for i in range(nb_points - 1): | |
| p = points[i:i + 2].ravel().tolist() | |
| new_points.append(line(*p)) | |
| new_points = np.concatenate(new_points, axis=0) | |
| return new_points | |