# 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: pc = Poly3DCollection(vl[fl], alpha=alpha, linewidths=1, edgecolors='k') pc.set_facecolor(color) h = ax.add_collection3d(pc) 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: pc = Poly3DCollection(vl[fl], alpha=alpha, linewidths=1, edgecolors='k') pc.set_facecolor(color) h = ax.add_collection3d(pc) 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 V = np.array(initparams.V) # 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=8., azim=120.) # 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 xmin, xmax = initparams.env.boundary[0], initparams.env.boundary[3] ymin, ymax = initparams.env.boundary[1], initparams.env.boundary[4] zmin, zmax = initparams.env.boundary[2], initparams.env.boundary[5] dx, dy, dz = xmax - xmin, ymax - ymin, zmax - zmin ax.get_proj = make_get_proj(ax, 1 * dx, 1 * dy, 2 * dy) make_transparent(ax) #plt.xlabel('x') #plt.ylabel('y') ax.set_axis_off() plt.pause(0.0001) def make_get_proj(self, rx, ry, rz): ''' Return a variation on :func:`~mpl_toolkit.mplot2d.axes3d.Axes3D.getproj` that makes the box aspect ratio equal to *rx:ry:rz*, using an axes object *self*. ''' rm = max(rx, ry, rz) kx = rm / rx; ky = rm / ry; kz = rm / rz # Copied directly from mpl_toolkit/mplot3d/axes3d.py. New or modified lines are # marked by ## def get_proj(): relev, razim = np.pi * self.elev / 180, np.pi * self.azim / 180 xmin, xmax = self.get_xlim3d() ymin, ymax = self.get_ylim3d() zmin, zmax = self.get_zlim3d() # transform to uniform world coordinates 0-1.0,0-1.0,0-1.0 worldM = proj3d.world_transformation(xmin, xmax, ymin, ymax, zmin, zmax) ratio = 0.5 # adjust the aspect ratio ## aspectM = proj3d.world_transformation(-kx + 1, kx, ## -ky + 1, ky, ## -kz + 1, kz) ## # look into the middle of the new coordinates R = np.array([0.5, 0.5, 0.5]) xp = R[0] + np.cos(razim) * np.cos(relev) * self.dist * ratio yp = R[1] + np.sin(razim) * np.cos(relev) * self.dist * ratio zp = R[2] + np.sin(relev) * self.dist * ratio E = np.array((xp, yp, zp)) self.eye = E self.vvec = R - E self.vvec = self.vvec / np.linalg.norm(self.vvec) if abs(relev) > np.pi / 2: # upside down V = np.array((0, 0, -1)) else: V = np.array((0, 0, 1)) zfront, zback = -self.dist * ratio, self.dist * ratio viewM = proj3d.view_transformation(E, R, V) perspM = proj3d.persp_transformation(zfront, zback) M0 = np.dot(viewM, np.dot(aspectM, worldM)) ## M = np.dot(perspM, M0) return M return get_proj 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