Create math_utils.py

we are flattening the directory, since HF only supports flat imports

math_utils.py

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+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the license found in the
+# LICENSE file in the root directory of this source tree.
+# MIT License
+
+# Copyright (c) 2022 Petr Kellnhofer
+
+# Permission is hereby granted, free of charge, to any person obtaining a copy
+# of this software and associated documentation files (the "Software"), to deal
+# in the Software without restriction, including without limitation the rights
+# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+# copies of the Software, and to permit persons to whom the Software is
+# furnished to do so, subject to the following conditions:
+
+# The above copyright notice and this permission notice shall be included in all
+# copies or substantial portions of the Software.
+
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+# SOFTWARE.
+
+import torch
+
+def transform_vectors(matrix: torch.Tensor, vectors4: torch.Tensor) -> torch.Tensor:
+    """
+    Left-multiplies MxM @ NxM. Returns NxM.
+    """
+    res = torch.matmul(vectors4, matrix.T)
+    return res
+
+
+def normalize_vecs(vectors: torch.Tensor) -> torch.Tensor:
+    """
+    Normalize vector lengths.
+    """
+    return vectors / (torch.norm(vectors, dim=-1, keepdim=True))
+
+def torch_dot(x: torch.Tensor, y: torch.Tensor):
+    """
+    Dot product of two tensors.
+    """
+    return (x * y).sum(-1)
+
+
+def get_ray_limits_box(rays_o: torch.Tensor, rays_d: torch.Tensor, box_side_length):
+    """
+    Author: Petr Kellnhofer
+    Intersects rays with the [-1, 1] NDC volume.
+    Returns min and max distance of entry.
+    Returns -1 for no intersection.
+    https://www.scratchapixel.com/lessons/3d-basic-rendering/minimal-ray-tracer-rendering-simple-shapes/ray-box-intersection
+    """
+    o_shape = rays_o.shape
+    rays_o = rays_o.detach().reshape(-1, 3)
+    rays_d = rays_d.detach().reshape(-1, 3)
+
+
+    bb_min = [-1*(box_side_length/2), -1*(box_side_length/2), -1*(box_side_length/2)]
+    bb_max = [1*(box_side_length/2), 1*(box_side_length/2), 1*(box_side_length/2)]
+    bounds = torch.tensor([bb_min, bb_max], dtype=rays_o.dtype, device=rays_o.device)
+    is_valid = torch.ones(rays_o.shape[:-1], dtype=bool, device=rays_o.device)
+
+    # Precompute inverse for stability.
+    invdir = 1 / rays_d
+    sign = (invdir < 0).long()
+
+    # Intersect with YZ plane.
+    tmin = (bounds.index_select(0, sign[..., 0])[..., 0] - rays_o[..., 0]) * invdir[..., 0]
+    tmax = (bounds.index_select(0, 1 - sign[..., 0])[..., 0] - rays_o[..., 0]) * invdir[..., 0]
+
+    # Intersect with XZ plane.
+    tymin = (bounds.index_select(0, sign[..., 1])[..., 1] - rays_o[..., 1]) * invdir[..., 1]
+    tymax = (bounds.index_select(0, 1 - sign[..., 1])[..., 1] - rays_o[..., 1]) * invdir[..., 1]
+
+    # Resolve parallel rays.
+    is_valid[torch.logical_or(tmin > tymax, tymin > tmax)] = False
+
+    # Use the shortest intersection.
+    tmin = torch.max(tmin, tymin)
+    tmax = torch.min(tmax, tymax)
+
+    # Intersect with XY plane.
+    tzmin = (bounds.index_select(0, sign[..., 2])[..., 2] - rays_o[..., 2]) * invdir[..., 2]
+    tzmax = (bounds.index_select(0, 1 - sign[..., 2])[..., 2] - rays_o[..., 2]) * invdir[..., 2]
+
+    # Resolve parallel rays.
+    is_valid[torch.logical_or(tmin > tzmax, tzmin > tmax)] = False
+
+    # Use the shortest intersection.
+    tmin = torch.max(tmin, tzmin)
+    tmax = torch.min(tmax, tzmax)
+
+    # Mark invalid.
+    tmin[torch.logical_not(is_valid)] = -1
+    tmax[torch.logical_not(is_valid)] = -2
+
+    return tmin.reshape(*o_shape[:-1], 1), tmax.reshape(*o_shape[:-1], 1)
+
+
+def linspace(start: torch.Tensor, stop: torch.Tensor, num: int):
+    """
+    Creates a tensor of shape [num, *start.shape] whose values are evenly spaced from start to end, inclusive.
+    Replicates but the multi-dimensional bahaviour of numpy.linspace in PyTorch.
+    """
+    # create a tensor of 'num' steps from 0 to 1
+    steps = torch.arange(num, dtype=torch.float32, device=start.device) / (num - 1)
+
+    # reshape the 'steps' tensor to [-1, *([1]*start.ndim)] to allow for broadcastings
+    # - using 'steps.reshape([-1, *([1]*start.ndim)])' would be nice here but torchscript
+    #   "cannot statically infer the expected size of a list in this contex", hence the code below
+    for i in range(start.ndim):
+        steps = steps.unsqueeze(-1)
+
+    # the output starts at 'start' and increments until 'stop' in each dimension
+    out = start[None] + steps * (stop - start)[None]
+
+    return out