colab elements of cvxnet

PiperOrigin-RevId: 438883571

Author: taiya

tensorflow_graphics/projects/cvxnet/colab/blender.py

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+# Copyright 2020 The TensorFlow Authors
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#    https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""Example of conversion between convex hyperplanes and mesh."""
+
+# --- being forgiving as this is a colab
+# pylint: disable=invalid-name
+# pylint: disable=redefined-outer-name
+# pylint: disable=missing-function-docstring
+# pylint: disable=using-constant-test
+
+import os
+import shutil
+
+import matplotlib.pyplot as plt
+from mpl_toolkits.mplot3d import Axes3D
+import numpy as np
+from scipy.spatial import HalfspaceIntersection
+import trimesh
+
+
+def load_npz(path):
+  """Load a halfspace definition from a numpy file."""
+  data = np.load(path)
+  trans = data['trans']
+  planes = data['planes']
+  T, C, H = planes.shape[0:3]
+  return T, C, H, trans, planes
+
+
+def load_cube():
+  """A dummy halfspace definition of a cube."""
+  T = 1  #< temporal
+  C = 3  #< num convexes
+  H = 6  #< num planes
+  trans = np.zeros([T, C, 3])
+  planes = np.zeros([T, C, H, 4])
+  cube = np.array([[-1., 0., 0., -.1], [1., 0., 0., -.1], [0., -1., 0., -.1],
+                   [0., 1., 0., -.1], [0., 0., -1., -.1], [0., 0., 1., -.1]])
+  planes[0, 0, ...] = cube
+  planes[0, 1, ...] = cube
+  planes[0, 2, ...] = cube
+  trans[0, 0, ...] = np.array([0, 0, 0])
+  trans[0, 1, ...] = np.array([+.25, 0, 0])
+  trans[0, 2, ...] = np.array([-.25, 0, 0])
+  return T, C, H, trans, planes
+
+
+T, C, H, trans, planes = load_npz('example.npz')
+T, C, H, trans, planes = load_cube()
+
+
+def halfspaces_to_vertices(halfspaces):
+  # pre-condition: euclidean origin is within the halfspaces
+  # Input: Hx(D+1) numpy array of halfplane constraints
+  # Output: convex hull vertices
+  n_dims = halfspaces.shape[1]-1
+  feasible_point = np.zeros([n_dims,])
+  hs = HalfspaceIntersection(halfspaces, feasible_point)
+  return hs.intersections
+
+
+def vertices_to_convex(vertices):
+  mesh = trimesh.Trimesh(vertices=vertices, faces=None)
+  return mesh.convex_hull.vertices, mesh.convex_hull.faces
+
+
+def plot_wireframe(ax, vertices, triangles):
+  xs, ys, zs = zip(*vertices)
+  ax.plot_trisurf(
+      xs,
+      ys,
+      zs,
+      triangles=triangles,
+      shade=True,
+      linewidth=0.1,
+      edgecolors=(0, 0, 0),
+      antialiased=True)
+  ax.set_xlim(-.5, .5)
+  ax.set_ylim(-.5, .5)
+  ax.set_zlim(-.5, .5)
+
+
+def makedirs(path):
+  os.makedirs(path)
+
+
+def deletedirs(path):
+  if os.path.isdir(path):
+    shutil.rmtree(path)
+
+
+def export_mesh(path, vertices, faces):
+  mesh = trimesh.Trimesh(vertices=vertices, faces=faces)
+  mesh.export(path)
+
+
+# --- Reset environment
+deletedirs('data/')
+fig = plt.figure()
+ax = Axes3D(fig)
+
+
+for iT in range(T):
+  iT_folder = 'data/frame_{0:02d}/'.format(iT)
+  makedirs(iT_folder)
+  obj_shape = planes[iT, ...]
+  obj_trans = trans[iT, ...]
+
+  combo = list()
+  for iC in range(C):
+    cvx_halfspaces = obj_shape[iC, ...]
+    cvx_translation = obj_trans[iC, ...]
+    vertices = halfspaces_to_vertices(cvx_halfspaces)
+    vertices, faces = vertices_to_convex(vertices)
+    vertices += cvx_translation
+    plot_wireframe(ax, vertices, faces)
+
+    if True:
+      iC_folder = iT_folder+'cvx_{0:02d}.obj'.format(iC)
+      export_mesh(iC_folder, vertices, faces)
+      plot_wireframe(ax, vertices, faces)
+
+    combo.append(trimesh.Trimesh(vertices=vertices, faces=faces))
+
+  if False:
+    combo = np.sum(combo)
+    combo.export(iT_folder+'/mesh.obj')
+    plot_wireframe(ax, combo.vertices, combo.faces)
+
+  plt.show()

tensorflow_graphics/projects/cvxnet/colab/cvxdec.py

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+# Copyright 2020 The TensorFlow Authors
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#    https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""A simple 2D demo of the differentiable convex function."""
+
+# --- being forgiving as this is a colab
+# pylint: skip-file
+
+#%% Load the data (from point picker)
+import numpy as np
+import matplotlib.pyplot as plt
+import numpy as np
+import matplotlib.image as mpimg
+
+# --- Equations of hyperplanes in the 'hyperplanes.png' image
+h0 = np.array([(223.84848484848487, 55.04545454545456),
+               (97.78787878787875, 91.4848484848485)])
+h1 = np.array([(96.80303030303028, 91.4848484848485),
+               (62.333333333333286, 239.21212121212125)])
+h2 = np.array([(62.333333333333286, 239.21212121212125),
+               (134.2272727272727, 311.1060606060606)])
+h3 = np.array([(134.2272727272727, 311.1060606060606),
+               (264.22727272727275, 161.40909090909093)])
+h4 = np.array([(264.22727272727275, 161.40909090909093),
+               (223.84848484848487, 55.04545454545456)])
+h5 = np.array([(234.6818181818182, 327.8484848484849),
+               (333.1666666666667, 159.43939393939394)])
+hs = [h0, h1, h2, h3, h4, h5]
+
+# --- Load base image
+img = mpimg.imread('hyperplanes.png')
+
+if False:
+  #--- Check lines match PNG
+  plt.figure(0)
+  imgplot = plt.imshow(img)
+
+  def ploth(h):
+    plt.plot(h[0][0], h[0][1], '.r')
+    plt.plot(h[1][0], h[1][1], '.r')
+
+  for h in hs:
+    ploth(h)
+
+
+def pointnormal(h):
+  ROT = np.array([[0, -1], [1, 0]])
+  p1 = np.array(h[0][:])
+  p2 = np.array(h[1][:])
+  n = (p2 - p1) / np.linalg.norm(p2 - p1)
+  return p1, np.dot(ROT, n)
+
+
+#--- Define sampling domain
+x = np.linspace(0, 364, 364)
+y = np.linspace(0, 364, 364)
+XX, YY = np.meshgrid(x, y)
+
+#--- Compute the SDFs
+D = np.zeros((len(hs), img.shape[0], img.shape[1]))
+for i, hi in enumerate(hs):
+  p0, n0 = pointnormal(hi)
+  XY = np.stack([XX, YY])
+  p0 = np.reshape(p0, [2, 1, 1])  # (2,1,1)
+  n0 = np.reshape(n0, [2, 1, 1])
+  off = (XY - p0)  #< broadcat (2,W,H)
+  d = np.linalg.norm(off, axis=0)
+  d = np.einsum('i...,i...', n0, off)
+  D[i, ...] = d
+
+# softmax = lambda x, delta: np.exp(delta*x) / np.sum(np.exp(delta*x), axis=0)
+softmax = lambda x, delta=1: np.log(np.sum(np.exp(delta * x), axis=0)) / delta
+Dmax = softmax(D)
+
+# Dmax = D.max(axis=0)
+D_clim = np.maximum(D.max(), -D.min())
+Dmax_clim = np.maximum(Dmax.max(), -Dmax.min())
+Dshift = Dmax  #< ?what was this?
+
+sigmoid = lambda x, sigma: 1 / (1 + np.exp(sigma * x))
+Dout = sigmoid(Dshift, 1 / 10.)
+
+#%%
+#--- individual
+get_ipython().system('mkdir cvxdec')
+for i, hi in enumerate(hs):
+  d = D[i, ...]
+  plt.figure(i)
+  plt.imshow(d, cmap=plt.get_cmap('coolwarm'), clim=(-D_clim, +D_clim))
+  plt.contour(d, [0])
+  plt.axis('off')
+  plt.gca().xaxis.set_major_locator(plt.NullLocator())
+  plt.gca().yaxis.set_major_locator(plt.NullLocator())
+  plt.savefig(
+      'cvxdec/sdf_{}.png'.format(i), bbox_inches='tight', pad_inches=-.1)
+
+#%%
+#--- Display a single one + the colormap beside it
+for i, hi in enumerate(hs):
+  d = D[i, ...]
+  plt.figure(i)
+  imaxis = plt.imshow(d, cmap=plt.get_cmap('coolwarm'), clim=(-D_clim, +D_clim))
+  plt.contour(d, [0])
+  plt.gcf().colorbar(imaxis)
+  plt.axis('off')
+  plt.gca().xaxis.set_major_locator(plt.NullLocator())
+  plt.gca().yaxis.set_major_locator(plt.NullLocator())
+  plt.savefig(
+      'cvxdec/sdf_{}_cmap.png'.format(i), bbox_inches='tight', pad_inches=-.1)
+  break
+
+#%%
+#--- max / union
+plt.figure()
+imaxis = plt.imshow(
+    Dmax, cmap=plt.get_cmap('coolwarm'), clim=(-Dmax_clim, +Dmax_clim))
+plt.contour(Dmax, [0])
+plt.axis('off')
+plt.gcf().colorbar(imaxis)
+plt.gca().xaxis.set_major_locator(plt.NullLocator())
+plt.gca().yaxis.set_major_locator(plt.NullLocator())
+plt.savefig('cvxdec/maxoperator_cmap.png', bbox_inches='tight', pad_inches=0)
+plt.show()
+
+#%%
+#--- max / union with different thresholds
+Dmax_news = list()
+for idelta, delta in enumerate([0.040, 0.060, 0.080, 1]):
+  Dmax_new = softmax(D, delta)
+  Dmax_news.append(Dmax_new)
+  if True:
+    print(delta)
+    plt.figure(idelta, frameon=False)
+    imaxis = plt.imshow(
+        Dmax, cmap=plt.get_cmap('coolwarm'), clim=(-Dmax_clim, +Dmax_clim))
+    plt.contour(Dmax_new, [0])
+    # plt.gcf().colorbar(imaxis)
+    plt.axis('off')
+    plt.gca().xaxis.set_major_locator(plt.NullLocator())
+    plt.gca().yaxis.set_major_locator(plt.NullLocator())
+    plt.savefig(
+        'cvxdec/softmax_{}.png'.format(delta),
+        bbox_inches='tight',
+        pad_inches=-.1)
+    plt.show()
+
+#%%
+#--- sigmoid
+Dshift = Dmax_news[2]
+for isigma, sigma in enumerate([1 / 5]):
+  Dout = sigmoid(Dshift, sigma)
+  if True:
+    plt.figure(isigma, frameon=False)
+    imaxis = plt.imshow(Dout, cmap=plt.get_cmap('coolwarm'), clim=(0, 1))
+    plt.contour(Dout, [0.5])
+    plt.axis('off')
+    # plt.gcf().colorbar(imaxis)
+    plt.gca().xaxis.set_major_locator(plt.NullLocator())
+    plt.gca().yaxis.set_major_locator(plt.NullLocator())
+    plt.savefig(
+        'cvxdec/sigmoid_{}.png'.format(sigma),
+        bbox_inches='tight',
+        pad_inches=-.1)
+    plt.show()
+
+#%%
+#--- 2D visualization
+plt.figure()
+plt.plot(Dout[182, :])