# plotting import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D from mpl_toolkits.mplot3d.art3d import Poly3DCollection import mpl_toolkits.mplot3d as plt3d from mpl_toolkits.mplot3d import proj3d import numpy as np def CreateSphere(center, r): u = np.linspace(0, 2 * np.pi, 30) v = np.linspace(0, np.pi, 30) x = np.outer(np.cos(u), np.sin(v)) y = np.outer(np.sin(u), np.sin(v)) z = np.outer(np.ones(np.size(u)), np.cos(v)) x, y, z = r * x + center[0], r * y + center[1], r * z + center[2] return (x, y, z) def draw_Spheres(ax, balls): for i in balls: (xs, ys, zs) = CreateSphere(i[0:3], i[-1]) ax.plot_wireframe(xs, ys, zs, alpha=0.15, color="b") def draw_block_list(ax, blocks, color=None, alpha=0.15): ''' drawing the blocks on the graph ''' v = np.array([[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0], [0, 0, 1], [1, 0, 1], [1, 1, 1], [0, 1, 1]], dtype='float') f = np.array([[0, 1, 5, 4], [1, 2, 6, 5], [2, 3, 7, 6], [3, 0, 4, 7], [0, 1, 2, 3], [4, 5, 6, 7]]) n = blocks.shape[0] d = blocks[:, 3:6] - blocks[:, :3] vl = np.zeros((8 * n, 3)) fl = np.zeros((6 * n, 4), dtype='int64') for k in range(n): vl[k * 8:(k + 1) * 8, :] = v * d[k] + blocks[k, :3] fl[k * 6:(k + 1) * 6, :] = f + k * 8 if type(ax) is Poly3DCollection: ax.set_verts(vl[fl]) else: h = ax.add_collection3d(Poly3DCollection(vl[fl], facecolors='black', alpha=alpha, linewidths=1, edgecolors='k')) return h def obb_verts(obb): # 0.017004013061523438 for 1000 iters ori_body = np.array([[1, 1, 1], [-1, 1, 1], [-1, -1, 1], [1, -1, 1], \ [1, 1, -1], [-1, 1, -1], [-1, -1, -1], [1, -1, -1]]) # P + (ori * E) ori_body = np.multiply(ori_body, obb.E) # obb.O is orthornormal basis in {W}, aka rotation matrix in SO(3) verts = (obb.O @ ori_body.T).T + obb.P return verts def draw_obb(ax, OBB, color=None, alpha=0.15): f = np.array([[0, 1, 5, 4], [1, 2, 6, 5], [2, 3, 7, 6], [3, 0, 4, 7], [0, 1, 2, 3], [4, 5, 6, 7]]) n = OBB.shape[0] vl = np.zeros((8 * n, 3)) fl = np.zeros((6 * n, 4), dtype='int64') for k in range(n): vl[k * 8:(k + 1) * 8, :] = obb_verts(OBB[k]) fl[k * 6:(k + 1) * 6, :] = f + k * 8 if type(ax) is Poly3DCollection: ax.set_verts(vl[fl]) else: h = ax.add_collection3d(Poly3DCollection(vl[fl], facecolors='black', alpha=alpha, linewidths=1, edgecolors='k')) return h def draw_line(ax, SET, visibility=1, color=None): if SET != []: for i in SET: xs = i[0][0], i[1][0] ys = i[0][1], i[1][1] zs = i[0][2], i[1][2] line = plt3d.art3d.Line3D(xs, ys, zs, alpha=visibility, color=color) ax.add_line(line) def visualization(initparams): if initparams.ind % 100 == 0 or initparams.done: #----------- list structure # V = np.array(list(initparams.V)) # E = initparams.E #----------- end # edges = initparams.E Path = np.array(initparams.Path) start = initparams.env.start goal = initparams.env.goal # edges = E.get_edge() #----------- list structure edges = [] for i in initparams.Parent: edges.append([i,initparams.Parent[i]]) #----------- end # generate axis objects ax = plt.subplot(111, projection='3d') # ax.view_init(elev=0.+ 0.03*initparams.ind/(2*np.pi), azim=90 + 0.03*initparams.ind/(2*np.pi)) # ax.view_init(elev=0., azim=90.) ax.view_init(elev=65., azim=60.) # ax.view_init(elev=-8., azim=180) ax.clear() # drawing objects draw_Spheres(ax, initparams.env.balls) draw_block_list(ax, initparams.env.blocks) if initparams.env.OBB is not None: draw_obb(ax, initparams.env.OBB) draw_block_list(ax, np.array([initparams.env.boundary]), alpha=0) draw_line(ax, edges, visibility=0.75, color='g') draw_line(ax, Path, color='r') # if len(V) > 0: # ax.scatter3D(V[:, 0], V[:, 1], V[:, 2], s=2, color='g', ) ax.plot(start[0:1], start[1:2], start[2:], 'go', markersize=7, markeredgecolor='k') ax.plot(goal[0:1], goal[1:2], goal[2:], 'ro', markersize=7, markeredgecolor='k') # adjust the aspect ratio ax.dist = 15 set_axes_equal(ax) make_transparent(ax) #plt.xlabel('s') #plt.ylabel('y') ax.set_axis_off() plt.pause(0.0001) def set_axes_equal(ax): '''Make axes of 3D plot have equal scale so that spheres appear as spheres, cubes as cubes, etc.. This is one possible solution to Matplotlib's ax.set_aspect('equal') and ax.axis('equal') not working for 3D. https://stackoverflow.com/questions/13685386/matplotlib-equal-unit-length-with-equal-aspect-ratio-z-axis-is-not-equal-to Input ax: a matplotlib axis, e.g., as output from plt.gca(). ''' x_limits = ax.get_xlim3d() y_limits = ax.get_ylim3d() z_limits = ax.get_zlim3d() x_range = abs(x_limits[1] - x_limits[0]) x_middle = np.mean(x_limits) y_range = abs(y_limits[1] - y_limits[0]) y_middle = np.mean(y_limits) z_range = abs(z_limits[1] - z_limits[0]) z_middle = np.mean(z_limits) # The plot bounding box is a sphere in the sense of the infinity # norm, hence I call half the max range the plot radius. plot_radius = 0.5*max([x_range, y_range, z_range]) ax.set_xlim3d([x_middle - plot_radius, x_middle + plot_radius]) ax.set_ylim3d([y_middle - plot_radius, y_middle + plot_radius]) ax.set_zlim3d([z_middle - plot_radius, z_middle + plot_radius]) def make_transparent(ax): # make the panes transparent ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0)) # make the grid lines transparent ax.xaxis._axinfo["grid"]['color'] = (1,1,1,0) ax.yaxis._axinfo["grid"]['color'] = (1,1,1,0) ax.zaxis._axinfo["grid"]['color'] = (1,1,1,0) if __name__ == '__main__': pass