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| """ Organize some frequently used visualization functions. """ | |
| import cv2 | |
| import numpy as np | |
| import matplotlib | |
| import matplotlib.pyplot as plt | |
| import copy | |
| import seaborn as sns | |
| # Plot junctions onto the image (return a separate copy) | |
| def plot_junctions(input_image, junctions, junc_size=3, color=None): | |
| """ | |
| input_image: can be 0~1 float or 0~255 uint8. | |
| junctions: Nx2 or 2xN np array. | |
| junc_size: the size of the plotted circles. | |
| """ | |
| # Create image copy | |
| image = copy.copy(input_image) | |
| # Make sure the image is converted to 255 uint8 | |
| if image.dtype == np.uint8: | |
| pass | |
| # A float type image ranging from 0~1 | |
| elif image.dtype in [np.float32, np.float64, np.float] and image.max() <= 2.0: | |
| image = (image * 255.0).astype(np.uint8) | |
| # A float type image ranging from 0.~255. | |
| elif image.dtype in [np.float32, np.float64, np.float] and image.mean() > 10.0: | |
| image = image.astype(np.uint8) | |
| else: | |
| raise ValueError( | |
| "[Error] Unknown image data type. Expect 0~1 float or 0~255 uint8." | |
| ) | |
| # Check whether the image is single channel | |
| if len(image.shape) == 2 or ((len(image.shape) == 3) and (image.shape[-1] == 1)): | |
| # Squeeze to H*W first | |
| image = image.squeeze() | |
| # Stack to channle 3 | |
| image = np.concatenate([image[..., None] for _ in range(3)], axis=-1) | |
| # Junction dimensions should be N*2 | |
| if not len(junctions.shape) == 2: | |
| raise ValueError("[Error] junctions should be 2-dim array.") | |
| # Always convert to N*2 | |
| if junctions.shape[-1] != 2: | |
| if junctions.shape[0] == 2: | |
| junctions = junctions.T | |
| else: | |
| raise ValueError("[Error] At least one of the two dims should be 2.") | |
| # Round and convert junctions to int (and check the boundary) | |
| H, W = image.shape[:2] | |
| junctions = (np.round(junctions)).astype(np.int) | |
| junctions[junctions < 0] = 0 | |
| junctions[junctions[:, 0] >= H, 0] = H - 1 # (first dim) max bounded by H-1 | |
| junctions[junctions[:, 1] >= W, 1] = W - 1 # (second dim) max bounded by W-1 | |
| # Iterate through all the junctions | |
| num_junc = junctions.shape[0] | |
| if color is None: | |
| color = (0, 255.0, 0) | |
| for idx in range(num_junc): | |
| # Fetch one junction | |
| junc = junctions[idx, :] | |
| cv2.circle( | |
| image, tuple(np.flip(junc)), radius=junc_size, color=color, thickness=3 | |
| ) | |
| return image | |
| # Plot line segements given junctions and line adjecent map | |
| def plot_line_segments( | |
| input_image, | |
| junctions, | |
| line_map, | |
| junc_size=3, | |
| color=(0, 255.0, 0), | |
| line_width=1, | |
| plot_survived_junc=True, | |
| ): | |
| """ | |
| input_image: can be 0~1 float or 0~255 uint8. | |
| junctions: Nx2 or 2xN np array. | |
| line_map: NxN np array | |
| junc_size: the size of the plotted circles. | |
| color: color of the line segments (can be string "random") | |
| line_width: width of the drawn segments. | |
| plot_survived_junc: whether we only plot the survived junctions. | |
| """ | |
| # Create image copy | |
| image = copy.copy(input_image) | |
| # Make sure the image is converted to 255 uint8 | |
| if image.dtype == np.uint8: | |
| pass | |
| # A float type image ranging from 0~1 | |
| elif image.dtype in [np.float32, np.float64, np.float] and image.max() <= 2.0: | |
| image = (image * 255.0).astype(np.uint8) | |
| # A float type image ranging from 0.~255. | |
| elif image.dtype in [np.float32, np.float64, np.float] and image.mean() > 10.0: | |
| image = image.astype(np.uint8) | |
| else: | |
| raise ValueError( | |
| "[Error] Unknown image data type. Expect 0~1 float or 0~255 uint8." | |
| ) | |
| # Check whether the image is single channel | |
| if len(image.shape) == 2 or ((len(image.shape) == 3) and (image.shape[-1] == 1)): | |
| # Squeeze to H*W first | |
| image = image.squeeze() | |
| # Stack to channle 3 | |
| image = np.concatenate([image[..., None] for _ in range(3)], axis=-1) | |
| # Junction dimensions should be 2 | |
| if not len(junctions.shape) == 2: | |
| raise ValueError("[Error] junctions should be 2-dim array.") | |
| # Always convert to N*2 | |
| if junctions.shape[-1] != 2: | |
| if junctions.shape[0] == 2: | |
| junctions = junctions.T | |
| else: | |
| raise ValueError("[Error] At least one of the two dims should be 2.") | |
| # line_map dimension should be 2 | |
| if not len(line_map.shape) == 2: | |
| raise ValueError("[Error] line_map should be 2-dim array.") | |
| # Color should be "random" or a list or tuple with length 3 | |
| if color != "random": | |
| if not (isinstance(color, tuple) or isinstance(color, list)): | |
| raise ValueError("[Error] color should have type list or tuple.") | |
| else: | |
| if len(color) != 3: | |
| raise ValueError( | |
| "[Error] color should be a list or tuple with length 3." | |
| ) | |
| # Make a copy of the line_map | |
| line_map_tmp = copy.copy(line_map) | |
| # Parse line_map back to segment pairs | |
| segments = np.zeros([0, 4]) | |
| for idx in range(junctions.shape[0]): | |
| # if no connectivity, just skip it | |
| if line_map_tmp[idx, :].sum() == 0: | |
| continue | |
| # record the line segment | |
| else: | |
| for idx2 in np.where(line_map_tmp[idx, :] == 1)[0]: | |
| p1 = np.flip(junctions[idx, :]) # Convert to xy format | |
| p2 = np.flip(junctions[idx2, :]) # Convert to xy format | |
| segments = np.concatenate( | |
| (segments, np.array([p1[0], p1[1], p2[0], p2[1]])[None, ...]), | |
| axis=0, | |
| ) | |
| # Update line_map | |
| line_map_tmp[idx, idx2] = 0 | |
| line_map_tmp[idx2, idx] = 0 | |
| # Draw segment pairs | |
| for idx in range(segments.shape[0]): | |
| seg = np.round(segments[idx, :]).astype(np.int) | |
| # Decide the color | |
| if color != "random": | |
| color = tuple(color) | |
| else: | |
| color = tuple( | |
| np.random.rand( | |
| 3, | |
| ) | |
| ) | |
| cv2.line( | |
| image, tuple(seg[:2]), tuple(seg[2:]), color=color, thickness=line_width | |
| ) | |
| # Also draw the junctions | |
| if not plot_survived_junc: | |
| num_junc = junctions.shape[0] | |
| for idx in range(num_junc): | |
| # Fetch one junction | |
| junc = junctions[idx, :] | |
| cv2.circle( | |
| image, | |
| tuple(np.flip(junc)), | |
| radius=junc_size, | |
| color=(0, 255.0, 0), | |
| thickness=3, | |
| ) | |
| # Only plot the junctions which are part of a line segment | |
| else: | |
| for idx in range(segments.shape[0]): | |
| seg = np.round(segments[idx, :]).astype(np.int) # Already in HW format. | |
| cv2.circle( | |
| image, | |
| tuple(seg[:2]), | |
| radius=junc_size, | |
| color=(0, 255.0, 0), | |
| thickness=3, | |
| ) | |
| cv2.circle( | |
| image, | |
| tuple(seg[2:]), | |
| radius=junc_size, | |
| color=(0, 255.0, 0), | |
| thickness=3, | |
| ) | |
| return image | |
| # Plot line segments given Nx4 or Nx2x2 line segments | |
| def plot_line_segments_from_segments( | |
| input_image, line_segments, junc_size=3, color=(0, 255.0, 0), line_width=1 | |
| ): | |
| # Create image copy | |
| image = copy.copy(input_image) | |
| # Make sure the image is converted to 255 uint8 | |
| if image.dtype == np.uint8: | |
| pass | |
| # A float type image ranging from 0~1 | |
| elif image.dtype in [np.float32, np.float64, np.float] and image.max() <= 2.0: | |
| image = (image * 255.0).astype(np.uint8) | |
| # A float type image ranging from 0.~255. | |
| elif image.dtype in [np.float32, np.float64, np.float] and image.mean() > 10.0: | |
| image = image.astype(np.uint8) | |
| else: | |
| raise ValueError( | |
| "[Error] Unknown image data type. Expect 0~1 float or 0~255 uint8." | |
| ) | |
| # Check whether the image is single channel | |
| if len(image.shape) == 2 or ((len(image.shape) == 3) and (image.shape[-1] == 1)): | |
| # Squeeze to H*W first | |
| image = image.squeeze() | |
| # Stack to channle 3 | |
| image = np.concatenate([image[..., None] for _ in range(3)], axis=-1) | |
| # Check the if line_segments are in (1) Nx4, or (2) Nx2x2. | |
| H, W, _ = image.shape | |
| # (1) Nx4 format | |
| if len(line_segments.shape) == 2 and line_segments.shape[-1] == 4: | |
| # Round to int32 | |
| line_segments = line_segments.astype(np.int32) | |
| # Clip H dimension | |
| line_segments[:, 0] = np.clip(line_segments[:, 0], a_min=0, a_max=H - 1) | |
| line_segments[:, 2] = np.clip(line_segments[:, 2], a_min=0, a_max=H - 1) | |
| # Clip W dimension | |
| line_segments[:, 1] = np.clip(line_segments[:, 1], a_min=0, a_max=W - 1) | |
| line_segments[:, 3] = np.clip(line_segments[:, 3], a_min=0, a_max=W - 1) | |
| # Convert to Nx2x2 format | |
| line_segments = np.concatenate( | |
| [ | |
| np.expand_dims(line_segments[:, :2], axis=1), | |
| np.expand_dims(line_segments[:, 2:], axis=1), | |
| ], | |
| axis=1, | |
| ) | |
| # (2) Nx2x2 format | |
| elif len(line_segments.shape) == 3 and line_segments.shape[-1] == 2: | |
| # Round to int32 | |
| line_segments = line_segments.astype(np.int32) | |
| # Clip H dimension | |
| line_segments[:, :, 0] = np.clip(line_segments[:, :, 0], a_min=0, a_max=H - 1) | |
| line_segments[:, :, 1] = np.clip(line_segments[:, :, 1], a_min=0, a_max=W - 1) | |
| else: | |
| raise ValueError( | |
| "[Error] line_segments should be either Nx4 or Nx2x2 in HW format." | |
| ) | |
| # Draw segment pairs (all segments should be in HW format) | |
| image = image.copy() | |
| for idx in range(line_segments.shape[0]): | |
| seg = np.round(line_segments[idx, :, :]).astype(np.int32) | |
| # Decide the color | |
| if color != "random": | |
| color = tuple(color) | |
| else: | |
| color = tuple( | |
| np.random.rand( | |
| 3, | |
| ) | |
| ) | |
| cv2.line( | |
| image, | |
| tuple(np.flip(seg[0, :])), | |
| tuple(np.flip(seg[1, :])), | |
| color=color, | |
| thickness=line_width, | |
| ) | |
| # Also draw the junctions | |
| cv2.circle( | |
| image, | |
| tuple(np.flip(seg[0, :])), | |
| radius=junc_size, | |
| color=(0, 255.0, 0), | |
| thickness=3, | |
| ) | |
| cv2.circle( | |
| image, | |
| tuple(np.flip(seg[1, :])), | |
| radius=junc_size, | |
| color=(0, 255.0, 0), | |
| thickness=3, | |
| ) | |
| return image | |
| # Additional functions to visualize multiple images at the same time, | |
| # e.g. for line matching | |
| def plot_images(imgs, titles=None, cmaps="gray", dpi=100, size=6, pad=0.5): | |
| """Plot a set of images horizontally. | |
| Args: | |
| imgs: a list of NumPy or PyTorch images, RGB (H, W, 3) or mono (H, W). | |
| titles: a list of strings, as titles for each image. | |
| cmaps: colormaps for monochrome images. | |
| """ | |
| n = len(imgs) | |
| if not isinstance(cmaps, (list, tuple)): | |
| cmaps = [cmaps] * n | |
| figsize = (size * n, size * 3 / 4) if size is not None else None | |
| fig, ax = plt.subplots(1, n, figsize=figsize, dpi=dpi) | |
| if n == 1: | |
| ax = [ax] | |
| for i in range(n): | |
| ax[i].imshow(imgs[i], cmap=plt.get_cmap(cmaps[i])) | |
| ax[i].get_yaxis().set_ticks([]) | |
| ax[i].get_xaxis().set_ticks([]) | |
| ax[i].set_axis_off() | |
| for spine in ax[i].spines.values(): # remove frame | |
| spine.set_visible(False) | |
| if titles: | |
| ax[i].set_title(titles[i]) | |
| fig.tight_layout(pad=pad) | |
| def plot_keypoints(kpts, colors="lime", ps=4): | |
| """Plot keypoints for existing images. | |
| Args: | |
| kpts: list of ndarrays of size (N, 2). | |
| colors: string, or list of list of tuples (one for each keypoints). | |
| ps: size of the keypoints as float. | |
| """ | |
| if not isinstance(colors, list): | |
| colors = [colors] * len(kpts) | |
| axes = plt.gcf().axes | |
| for a, k, c in zip(axes, kpts, colors): | |
| a.scatter(k[:, 0], k[:, 1], c=c, s=ps, linewidths=0) | |
| def plot_matches(kpts0, kpts1, color=None, lw=1.5, ps=4, indices=(0, 1), a=1.0): | |
| """Plot matches for a pair of existing images. | |
| Args: | |
| kpts0, kpts1: corresponding keypoints of size (N, 2). | |
| color: color of each match, string or RGB tuple. Random if not given. | |
| lw: width of the lines. | |
| ps: size of the end points (no endpoint if ps=0) | |
| indices: indices of the images to draw the matches on. | |
| a: alpha opacity of the match lines. | |
| """ | |
| fig = plt.gcf() | |
| ax = fig.axes | |
| assert len(ax) > max(indices) | |
| ax0, ax1 = ax[indices[0]], ax[indices[1]] | |
| fig.canvas.draw() | |
| assert len(kpts0) == len(kpts1) | |
| if color is None: | |
| color = matplotlib.cm.hsv(np.random.rand(len(kpts0))).tolist() | |
| elif len(color) > 0 and not isinstance(color[0], (tuple, list)): | |
| color = [color] * len(kpts0) | |
| if lw > 0: | |
| # transform the points into the figure coordinate system | |
| transFigure = fig.transFigure.inverted() | |
| fkpts0 = transFigure.transform(ax0.transData.transform(kpts0)) | |
| fkpts1 = transFigure.transform(ax1.transData.transform(kpts1)) | |
| fig.lines += [ | |
| matplotlib.lines.Line2D( | |
| (fkpts0[i, 0], fkpts1[i, 0]), | |
| (fkpts0[i, 1], fkpts1[i, 1]), | |
| zorder=1, | |
| transform=fig.transFigure, | |
| c=color[i], | |
| linewidth=lw, | |
| alpha=a, | |
| ) | |
| for i in range(len(kpts0)) | |
| ] | |
| # freeze the axes to prevent the transform to change | |
| ax0.autoscale(enable=False) | |
| ax1.autoscale(enable=False) | |
| if ps > 0: | |
| ax0.scatter(kpts0[:, 0], kpts0[:, 1], c=color, s=ps, zorder=2) | |
| ax1.scatter(kpts1[:, 0], kpts1[:, 1], c=color, s=ps, zorder=2) | |
| def plot_lines( | |
| lines, line_colors="orange", point_colors="cyan", ps=4, lw=2, indices=(0, 1) | |
| ): | |
| """Plot lines and endpoints for existing images. | |
| Args: | |
| lines: list of ndarrays of size (N, 2, 2). | |
| colors: string, or list of list of tuples (one for each keypoints). | |
| ps: size of the keypoints as float pixels. | |
| lw: line width as float pixels. | |
| indices: indices of the images to draw the matches on. | |
| """ | |
| if not isinstance(line_colors, list): | |
| line_colors = [line_colors] * len(lines) | |
| if not isinstance(point_colors, list): | |
| point_colors = [point_colors] * len(lines) | |
| fig = plt.gcf() | |
| ax = fig.axes | |
| assert len(ax) > max(indices) | |
| axes = [ax[i] for i in indices] | |
| fig.canvas.draw() | |
| # Plot the lines and junctions | |
| for a, l, lc, pc in zip(axes, lines, line_colors, point_colors): | |
| for i in range(len(l)): | |
| line = matplotlib.lines.Line2D( | |
| (l[i, 0, 0], l[i, 1, 0]), | |
| (l[i, 0, 1], l[i, 1, 1]), | |
| zorder=1, | |
| c=lc, | |
| linewidth=lw, | |
| ) | |
| a.add_line(line) | |
| pts = l.reshape(-1, 2) | |
| a.scatter(pts[:, 0], pts[:, 1], c=pc, s=ps, linewidths=0, zorder=2) | |
| def plot_line_matches(kpts0, kpts1, color=None, lw=1.5, indices=(0, 1), a=1.0): | |
| """Plot matches for a pair of existing images, parametrized by their middle point. | |
| Args: | |
| kpts0, kpts1: corresponding middle points of the lines of size (N, 2). | |
| color: color of each match, string or RGB tuple. Random if not given. | |
| lw: width of the lines. | |
| indices: indices of the images to draw the matches on. | |
| a: alpha opacity of the match lines. | |
| """ | |
| fig = plt.gcf() | |
| ax = fig.axes | |
| assert len(ax) > max(indices) | |
| ax0, ax1 = ax[indices[0]], ax[indices[1]] | |
| fig.canvas.draw() | |
| assert len(kpts0) == len(kpts1) | |
| if color is None: | |
| color = matplotlib.cm.hsv(np.random.rand(len(kpts0))).tolist() | |
| elif len(color) > 0 and not isinstance(color[0], (tuple, list)): | |
| color = [color] * len(kpts0) | |
| if lw > 0: | |
| # transform the points into the figure coordinate system | |
| transFigure = fig.transFigure.inverted() | |
| fkpts0 = transFigure.transform(ax0.transData.transform(kpts0)) | |
| fkpts1 = transFigure.transform(ax1.transData.transform(kpts1)) | |
| fig.lines += [ | |
| matplotlib.lines.Line2D( | |
| (fkpts0[i, 0], fkpts1[i, 0]), | |
| (fkpts0[i, 1], fkpts1[i, 1]), | |
| zorder=1, | |
| transform=fig.transFigure, | |
| c=color[i], | |
| linewidth=lw, | |
| alpha=a, | |
| ) | |
| for i in range(len(kpts0)) | |
| ] | |
| # freeze the axes to prevent the transform to change | |
| ax0.autoscale(enable=False) | |
| ax1.autoscale(enable=False) | |
| def plot_color_line_matches(lines, correct_matches=None, lw=2, indices=(0, 1)): | |
| """Plot line matches for existing images with multiple colors. | |
| Args: | |
| lines: list of ndarrays of size (N, 2, 2). | |
| correct_matches: bool array of size (N,) indicating correct matches. | |
| lw: line width as float pixels. | |
| indices: indices of the images to draw the matches on. | |
| """ | |
| n_lines = len(lines[0]) | |
| colors = sns.color_palette("husl", n_colors=n_lines) | |
| np.random.shuffle(colors) | |
| alphas = np.ones(n_lines) | |
| # If correct_matches is not None, display wrong matches with a low alpha | |
| if correct_matches is not None: | |
| alphas[~np.array(correct_matches)] = 0.2 | |
| fig = plt.gcf() | |
| ax = fig.axes | |
| assert len(ax) > max(indices) | |
| axes = [ax[i] for i in indices] | |
| fig.canvas.draw() | |
| # Plot the lines | |
| for a, l in zip(axes, lines): | |
| # Transform the points into the figure coordinate system | |
| transFigure = fig.transFigure.inverted() | |
| endpoint0 = transFigure.transform(a.transData.transform(l[:, 0])) | |
| endpoint1 = transFigure.transform(a.transData.transform(l[:, 1])) | |
| fig.lines += [ | |
| matplotlib.lines.Line2D( | |
| (endpoint0[i, 0], endpoint1[i, 0]), | |
| (endpoint0[i, 1], endpoint1[i, 1]), | |
| zorder=1, | |
| transform=fig.transFigure, | |
| c=colors[i], | |
| alpha=alphas[i], | |
| linewidth=lw, | |
| ) | |
| for i in range(n_lines) | |
| ] | |
| def plot_color_lines(lines, correct_matches, wrong_matches, lw=2, indices=(0, 1)): | |
| """Plot line matches for existing images with multiple colors: | |
| green for correct matches, red for wrong ones, and blue for the rest. | |
| Args: | |
| lines: list of ndarrays of size (N, 2, 2). | |
| correct_matches: list of bool arrays of size N with correct matches. | |
| wrong_matches: list of bool arrays of size (N,) with correct matches. | |
| lw: line width as float pixels. | |
| indices: indices of the images to draw the matches on. | |
| """ | |
| # palette = sns.color_palette() | |
| palette = sns.color_palette("hls", 8) | |
| blue = palette[5] # palette[0] | |
| red = palette[0] # palette[3] | |
| green = palette[2] # palette[2] | |
| colors = [np.array([blue] * len(l)) for l in lines] | |
| for i, c in enumerate(colors): | |
| c[np.array(correct_matches[i])] = green | |
| c[np.array(wrong_matches[i])] = red | |
| fig = plt.gcf() | |
| ax = fig.axes | |
| assert len(ax) > max(indices) | |
| axes = [ax[i] for i in indices] | |
| fig.canvas.draw() | |
| # Plot the lines | |
| for a, l, c in zip(axes, lines, colors): | |
| # Transform the points into the figure coordinate system | |
| transFigure = fig.transFigure.inverted() | |
| endpoint0 = transFigure.transform(a.transData.transform(l[:, 0])) | |
| endpoint1 = transFigure.transform(a.transData.transform(l[:, 1])) | |
| fig.lines += [ | |
| matplotlib.lines.Line2D( | |
| (endpoint0[i, 0], endpoint1[i, 0]), | |
| (endpoint0[i, 1], endpoint1[i, 1]), | |
| zorder=1, | |
| transform=fig.transFigure, | |
| c=c[i], | |
| linewidth=lw, | |
| ) | |
| for i in range(len(l)) | |
| ] | |
| def plot_subsegment_matches(lines, subsegments, lw=2, indices=(0, 1)): | |
| """Plot line matches for existing images with multiple colors and | |
| highlight the actually matched subsegments. | |
| Args: | |
| lines: list of ndarrays of size (N, 2, 2). | |
| subsegments: list of ndarrays of size (N, 2, 2). | |
| lw: line width as float pixels. | |
| indices: indices of the images to draw the matches on. | |
| """ | |
| n_lines = len(lines[0]) | |
| colors = sns.cubehelix_palette( | |
| start=2, rot=-0.2, dark=0.3, light=0.7, gamma=1.3, hue=1, n_colors=n_lines | |
| ) | |
| fig = plt.gcf() | |
| ax = fig.axes | |
| assert len(ax) > max(indices) | |
| axes = [ax[i] for i in indices] | |
| fig.canvas.draw() | |
| # Plot the lines | |
| for a, l, ss in zip(axes, lines, subsegments): | |
| # Transform the points into the figure coordinate system | |
| transFigure = fig.transFigure.inverted() | |
| # Draw full line | |
| endpoint0 = transFigure.transform(a.transData.transform(l[:, 0])) | |
| endpoint1 = transFigure.transform(a.transData.transform(l[:, 1])) | |
| fig.lines += [ | |
| matplotlib.lines.Line2D( | |
| (endpoint0[i, 0], endpoint1[i, 0]), | |
| (endpoint0[i, 1], endpoint1[i, 1]), | |
| zorder=1, | |
| transform=fig.transFigure, | |
| c="red", | |
| alpha=0.7, | |
| linewidth=lw, | |
| ) | |
| for i in range(n_lines) | |
| ] | |
| # Draw matched subsegment | |
| endpoint0 = transFigure.transform(a.transData.transform(ss[:, 0])) | |
| endpoint1 = transFigure.transform(a.transData.transform(ss[:, 1])) | |
| fig.lines += [ | |
| matplotlib.lines.Line2D( | |
| (endpoint0[i, 0], endpoint1[i, 0]), | |
| (endpoint0[i, 1], endpoint1[i, 1]), | |
| zorder=1, | |
| transform=fig.transFigure, | |
| c=colors[i], | |
| alpha=1, | |
| linewidth=lw, | |
| ) | |
| for i in range(n_lines) | |
| ] | |