def lookat_matrix(up, lookat_direction):
"""Construct a matrix that "looks at" a direction."""
# lookat_direction [Batch, 3]
# return [Batch, 3, 3] colomn major cam2world lookat matrix.
# z is the forward direction. x is the right vector. y is the up vector.
# Stack x, y, z vectors by colomn to get the lookat matrix.
# [[x.x y.x z.x]
# [x.y y.y z.y]
# [x.z y.z z.z]]
z = tf.linalg.l2_normalize(-lookat_direction, axis=-1)
x = tf.linalg.l2_normalize(tf.cross(up, z), axis=-1)
y = tf.cross(z, x)
lookat = tf.stack([x, y, z], axis=-1)
return lookat
def setup_v_rot_(links):
r = links.thickness[:-1, newaxis]
dl = (links.points[:-1] - links.points[1:]) / 2
dlh = dl / (tf.norm(dl, axis=1)[:, newaxis] + 1e-10)
idx = tf.argmin(dlh, 1)
r0 = tf.one_hot(idx, 3)
r1h = tf.cross(dlh, r0)
r2h = tf.cross(dlh, r1h)
r1 = r * r1h
r2 = r * r2h
vi = tf.concat(
(dl[:, :, newaxis], r1[:, :, newaxis], r2[:, :, newaxis]), axis=2)
ri = tf.concat(
(dlh[:, :, newaxis], r1h[:, :, newaxis], r2h[:, :, newaxis]),
axis=2)
links.v_rot = tf.matmul(vi, ri, transpose_b=True)
def ref_point(self, v):
if v.shape.ndims > self.rot.shape.ndims:
rot = self.rot[None] * (tf.zeros_like(v) + 1.)
vel = self.vel + tf1.cross(rot, v)
elif v.shape.ndims < self.rot.shape.ndims:
n = self.rot.shape[0].value
vel = self.vel + tf1.cross(self.rot, v[None] * tf.ones((n, 1)))
rot = self.rot
else:
vel = self.vel + tf1.cross(self.rot, v)
rot = self.rot
if self.is_batch or v.shape.ndims == 2:
return Twist(tf.concat([vel, rot], 1))
else:
return Twist(tf.concat([vel, rot], 0))
def lookat_matrix(up, lookat_direction):
"""Return rotation matrices given camera's lookat directions and up vectors.
Using OpenGL's coordinate system: -Z is the camera's lookat and +Y is up.
Args:
up: [BATCH, 3] the up vectors.
lookat_direction: [BATCH, 3] the lookat directions.
Returns:
[BATCH, 3, 3] the rotation matrices (from camera to world frame).
"""
z = tf.linalg.l2_normalize(-lookat_direction, axis=-1)
x = tf.linalg.l2_normalize(tf.cross(up, z), axis=-1)
y = tf.cross(z, x)
# Stack x, y, z basis vectors by colomn.
return tf.stack([x, y, z], axis=-1)
def Compute_norm(self, face_shape, facemodel):
shape = face_shape
face_id = facemodel.face_buf
point_id = facemodel.point_buf
# face_id and point_id index starts from 1
face_id = tf.cast(face_id - 1, tf.int32)
point_id = tf.cast(point_id - 1, tf.int32)
#compute normal for each face
v1 = tf.gather(shape, face_id[:, 0], axis=1)
v2 = tf.gather(shape, face_id[:, 1], axis=1)
v3 = tf.gather(shape, face_id[:, 2], axis=1)
e1 = v1 - v2
e2 = v2 - v3
face_norm = tf.cross(e1, e2)
face_norm = tf.nn.l2_normalize(face_norm,
dim=2) # normalized face_norm first
face_norm = tf.concat(
[face_norm, tf.zeros([tf.shape(face_shape)[0], 1, 3])], axis=1)
#compute normal for each vertex using one-ring neighborhood
v_norm = tf.reduce_sum(tf.gather(face_norm, point_id, axis=1), axis=2)
v_norm = tf.nn.l2_normalize(v_norm, dim=2)
return v_norm
def rotation_between_vectors(v1, v2):
"""Get the rotation matrix to align v1 with v2 (v2 = R * v1).
The rotation is computed by Rodrigues' rotation formula given an axis-angle.
The function returns an identity matrix when v1 = v2. When v1 = -v2, this
gives an 180-degree rotation around any axis perpendicular to v1 or v2 . The
function is discontinuous in this case.
Args:
v1: [BATCH, 3] 3d vectors.
v2: [BATCH, 3] 3d vectors.
Returns:
[BATCH, 3, 3] rotation matrices.
Raises:
Input has the wrong dimensions.
"""
with tf.name_scope(None, 'rotation_between_vectors', [v1, v2]):
if v1.shape[-1] != 3 or v2.shape[-1] != 3:
raise ValueError('Input has the wrong dimensions.')
batch = v1.shape.as_list()[0]
v1 = tf.linalg.l2_normalize(v1, -1)
v2 = tf.linalg.l2_normalize(v2, -1)
cross = tf.cross(v1, v2)
cos_angle = tf.reduce_sum(v1 * v2, -1, keepdims=True)
sin_angle = tf.norm(cross, axis=-1)
x_axis = tf.tile(tf.constant([[1., 0., 0.]]), [batch, 1])
y_axis = tf.tile(tf.constant([[0., 1., 0.]]), [batch, 1])
z_axis = tf.tile(tf.constant([[0., 0., 1.]]), [batch, 1])
identity = tf.eye(3, batch_shape=[batch])
rotation_axis = tf.where(
tf.abs(tf.tile(cos_angle, [1, 3]) - (-tf.ones([batch, 3]))) < 1e-6,
tf.cross(v1, x_axis) + tf.cross(v1, y_axis) + tf.cross(v1, z_axis),
cross)
rotation_axis = tf.linalg.l2_normalize(rotation_axis, -1)
ss = skew_symmetric(rotation_axis)
sin_angle = sin_angle[:, tf.newaxis, tf.newaxis]
cos_angle = cos_angle[:, tf.newaxis]
rotation_matrix = identity + sin_angle * ss + (
1 - cos_angle) * tf.matmul(ss, ss)
return rotation_matrix
def __mul__(self, other):
if isinstance(other, Twist):
# TODO check
rot = matvecmul(self.m, other.rot)
vel = matvecmul(self.m, other.vel) + tf1.cross(
self.p, rot) # should be cross product
return Twist(tf.concat([vel, rot], 0))
elif isinstance(other, tf.Tensor) or isinstance(other, tf.Variable):
if other.shape[-1].value == 3: # only position
if self.is_batch:
# return tf.einsum('aij,bj->abi', self.m, other) + self.p[:, None]
return tf.linalg.LinearOperatorFullMatrix(
self.m[:, None]).matvec(other[None]) + self.p[None]
else:
return tf.linalg.LinearOperatorFullMatrix(
self.m).matvec(other) + self.p[None]
else:
raise NotImplementedError('Only position supported yet')
else:
return Frame(p=matvecmul(self.m, other.p) + self.p,
m=matmatmul(self.m, other.m))
def get_edge_cross_feature(point_cloud, nn_idx, k=20):
"""Construct edge feature for each point
Args:
point_cloud: (batch_size, num_points, 1, num_dims)
nn_idx: (batch_size, num_points, k)
k: int
Returns:
edge features: (batch_size, num_points, k, num_dims)
"""
og_batch_size = point_cloud.get_shape().as_list()[0]
point_cloud = tf.squeeze(point_cloud)
if og_batch_size == 1:
point_cloud = tf.expand_dims(point_cloud, 0)
point_cloud_central = point_cloud
point_cloud_shape = point_cloud.get_shape()
batch_size = point_cloud_shape[0].value
num_points = point_cloud_shape[1].value
num_dims = point_cloud_shape[2].value
idx_ = tf.range(batch_size) * num_points
idx_ = tf.reshape(idx_, [batch_size, 1, 1])
point_cloud_flat = tf.reshape(point_cloud, [-1, num_dims])
point_cloud_neighbors = tf.gather(point_cloud_flat, nn_idx + idx_)
point_cloud_central = tf.expand_dims(point_cloud_central, axis=-2)
point_cloud_central = tf.tile(point_cloud_central, [1, 1, k, 1])
edge_feature = tf.concat([
point_cloud_central, point_cloud_neighbors - point_cloud_central,
tf.cross(point_cloud_central,
point_cloud_neighbors - point_cloud_central)
],
axis=-1)
return edge_feature
return sampling_module.farthest_point_sample(inp, npoint)
ops.NoGradient('FarthestPointSample')
if __name__ == '__main__':
import numpy as np
np.random.seed(100)
triangles = np.random.rand(1, 5, 3, 3).astype('float32')
with tf.device('/gpu:1'):
inp = tf.constant(triangles)
tria = inp[:, :, 0, :]
trib = inp[:, :, 1, :]
tric = inp[:, :, 2, :]
areas = tf.sqrt(
tf.reduce_sum(tf.cross(trib - tria, tric - tria)**2, 2) + 1e-9)
randomnumbers = tf.random_uniform((1, 8192))
triids = prob_sample(areas, randomnumbers)
tria_sample = gather_point(tria, triids)
trib_sample = gather_point(trib, triids)
tric_sample = gather_point(tric, triids)
us = tf.random_uniform((1, 8192))
vs = tf.random_uniform((1, 8192))
uplusv = 1 - tf.abs(us + vs - 1)
uminusv = us - vs
us = (uplusv + uminusv) * 0.5
vs = (uplusv - uminusv) * 0.5
pt_sample = tria_sample + (trib_sample - tria_sample) * tf.expand_dims(
us, -1) + (tric_sample - tria_sample) * tf.expand_dims(vs, -1)
print('pt_sample: ', pt_sample)
reduced_sample = gather_point(pt_sample,
