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weighted.py
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weighted.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.
"""This module implements weighted interpolation for point sets."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import tensorflow as tf
from tensorflow_graphics.math import vector
from tensorflow_graphics.util import asserts
from tensorflow_graphics.util import export_api
from tensorflow_graphics.util import safe_ops
from tensorflow_graphics.util import shape
from tensorflow_graphics.util import type_alias
def interpolate(points: type_alias.TensorLike,
weights: type_alias.TensorLike,
indices: type_alias.TensorLike,
normalize: bool = True,
allow_negative_weights: bool = False,
name: str = "weighted_interpolate") -> type_alias.TensorLike:
"""Weighted interpolation for M-D point sets.
Given an M-D point set, this function can be used to generate a new point set
that is formed by interpolating a subset of points in the set.
Note:
In the following, A1 to An, and B1 to Bk are optional batch dimensions.
Args:
points: A tensor with shape `[B1, ..., Bk, M]` and rank R > 1, where M is
the dimensionality of the points.
weights: A tensor with shape `[A1, ..., An, P]`, where P is the number of
points to interpolate for each output point.
indices: A tensor of dtype tf.int32 and shape `[A1, ..., An, P, R-1]`, which
contains the point indices to be used for each output point. The R-1
dimensional axis gives the slice index of a single point in `points`. The
first n+1 dimensions of weights and indices must match, or be broadcast
compatible.
normalize: A `bool` describing whether or not to normalize the weights on
the last axis.
allow_negative_weights: A `bool` describing whether or not negative weights
are allowed.
name: A name for this op. Defaults to "weighted_interpolate".
Returns:
A tensor of shape `[A1, ..., An, M]` storing the interpolated M-D
points. The first n dimensions will be the same as weights and indices.
"""
with tf.name_scope(name):
points = tf.convert_to_tensor(value=points)
weights = tf.convert_to_tensor(value=weights)
indices = tf.convert_to_tensor(value=indices)
shape.check_static(
tensor=points, tensor_name="points", has_rank_greater_than=1)
shape.check_static(
tensor=indices,
tensor_name="indices",
has_rank_greater_than=1,
has_dim_equals=(-1, points.shape.ndims - 1))
shape.compare_dimensions(
tensors=(weights, indices),
axes=(-1, -2),
tensor_names=("weights", "indices"))
shape.compare_batch_dimensions(
tensors=(weights, indices),
last_axes=(-2, -3),
tensor_names=("weights", "indices"),
broadcast_compatible=True)
if not allow_negative_weights:
weights = asserts.assert_all_above(weights, 0.0, open_bound=False)
if normalize:
sums = tf.reduce_sum(input_tensor=weights, axis=-1, keepdims=True)
sums = asserts.assert_nonzero_norm(sums)
weights = safe_ops.safe_signed_div(weights, sums)
point_lists = tf.gather_nd(points, indices)
return vector.dot(
point_lists, tf.expand_dims(weights, axis=-1), axis=-2, keepdims=False)
def get_barycentric_coordinates(
triangle_vertices: type_alias.TensorLike,
pixels: type_alias.TensorLike,
name: str = "rasterizer_get_barycentric_coordinates"
) -> type_alias.TensorLike:
"""Computes the barycentric coordinates of pixels for 2D triangles.
Barycentric coordinates of a point `p` are represented as coefficients
$(w_1, w_2, w_3)$ corresponding to the masses placed at the vertices of a
reference triangle if `p` is the center of mass. Barycentric coordinates are
normalized so that $w_1 + w_2 + w_3 = 1$. These coordinates play an essential
role in computing the pixel attributes (e.g. depth, color, normals, and
texture coordinates) of a point lying on the surface of a triangle. The point
`p` is inside the triangle if all of its barycentric coordinates are positive.
Note:
In the following, A1 to An are optional batch dimensions.
Args:
triangle_vertices: A tensor of shape `[A1, ..., An, 3, 2]`, where the last
two dimensions represents the `x` and `y` coordinates for each vertex of a
2D triangle.
pixels: A tensor of shape `[A1, ..., An, N, 2]`, where `N` represents the
number of pixels, and the last dimension represents the `x` and `y`
coordinates of each pixel.
name: A name for this op that defaults to
"rasterizer_get_barycentric_coordinates".
Returns:
barycentric_coordinates: A float tensor of shape `[A1, ..., An, N, 3]`,
representing the barycentric coordinates.
valid: A boolean tensor of shape `[A1, ..., An, N], which is `True` where
pixels are inside the triangle, and `False` otherwise.
"""
with tf.name_scope(name):
triangle_vertices = tf.convert_to_tensor(value=triangle_vertices)
pixels = tf.convert_to_tensor(value=pixels)
shape.check_static(
tensor=triangle_vertices,
tensor_name="triangle_vertices",
has_dim_equals=((-1, 2), (-2, 3)))
shape.check_static(
tensor=pixels, tensor_name="pixels", has_dim_equals=(-1, 2))
shape.compare_batch_dimensions(
tensors=(triangle_vertices, pixels),
last_axes=(-3, -3),
broadcast_compatible=True)
vertex_1, vertex_2, vertex_3 = tf.unstack(
tf.expand_dims(triangle_vertices, axis=-3), axis=-2)
vertex_x1, vertex_y1 = tf.unstack(vertex_1, axis=-1)
vertex_x2, vertex_y2 = tf.unstack(vertex_2, axis=-1)
vertex_x3, vertex_y3 = tf.unstack(vertex_3, axis=-1)
pixels_x, pixels_y = tf.unstack(pixels, axis=-1)
x1_minus_x3 = vertex_x1 - vertex_x3
x3_minus_x2 = vertex_x3 - vertex_x2
y3_minus_y1 = vertex_y3 - vertex_y1
y2_minus_y3 = vertex_y2 - vertex_y3
x_minus_x3 = pixels_x - vertex_x3
y_minus_y3 = pixels_y - vertex_y3
determinant = y2_minus_y3 * x1_minus_x3 - x3_minus_x2 * y3_minus_y1
coordinate_1 = y2_minus_y3 * x_minus_x3 + x3_minus_x2 * y_minus_y3
coordinate_1 = safe_ops.safe_signed_div(coordinate_1, determinant)
coordinate_2 = y3_minus_y1 * x_minus_x3 + x1_minus_x3 * y_minus_y3
coordinate_2 = safe_ops.safe_signed_div(coordinate_2, determinant)
coordinate_3 = 1.0 - (coordinate_1 + coordinate_2)
barycentric_coordinates = tf.stack(
(coordinate_1, coordinate_2, coordinate_3), axis=-1)
valid = tf.logical_and(
tf.logical_and(coordinate_1 >= 0.0, coordinate_2 >= 0.0),
coordinate_3 >= 0.0)
return barycentric_coordinates, valid
# API contains all public functions and classes.
__all__ = export_api.get_functions_and_classes()