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"# Sample Representation\n",
"\n",
"A core component of volumetric rendering is computing samples along a ray. The representation of these samples is important. We use conical frustums to represent samples. The conical frustums are defined via the following parameters:\n",
"\n",
"```{image} imgs/frustums.png\n",
":align: center\n",
":class: only-light\n",
":width: 600\n",
"```\n",
"\n",
"```{image} imgs/frustums-dark.png\n",
":align: center\n",
":class: only-dark\n",
":width: 600\n",
"```\n",
"\n",
"| Parameter | Dimension | Description |\n",
"| ---------- | :-------: | ----------------------------------------------------- |\n",
"| origin | 3 | The _x,y,z_ origin of the ray |\n",
"| direction | 3 | The direction of the ray represented as a unit vector |\n",
"| pixel area | 1 | The pixel's area a distance of 1 from the origin |\n",
"| start | 1 | The distance at which the frustum starts |\n",
"| end | 1 | The distance at which the frustums ends |\n",
"\n",
":::{note}\n",
"Why conical frustums and not pyramidal frustums? Those interested in this question may be interested in [_A Pixel Is Not A Little Square_](http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf) by Alvy Ray Smith.\n",
":::\n",
"\n",
":::{important}\n",
"This representation is only an approximation.\n",
"nerfstudio calculates $pixel area$ as $dx * dy$ where $dx$ and $dy$ are the distance between points neighboring rays in the $x$ and $y$ direction a distance of 1 from the origin.\n",
":::\n",
"\n",
"\n",
"## 3D Frustum\n"
]
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"# HIDDEN\n",
"import plotly.graph_objects as go\n",
"\n",
"webdocs_layout = go.Layout(\n",
" scene=dict(\n",
" aspectmode=\"data\",\n",
" xaxis=dict(showspikes=False),\n",
" yaxis=dict(showspikes=False),\n",
" zaxis=dict(showspikes=False),\n",
" xaxis_visible=False,\n",
" yaxis_visible=False,\n",
" zaxis_visible=False,\n",
" ),\n",
" scene_camera=dict(up=dict(x=0, y=1, z=0)),\n",
" margin=dict(r=0, b=10, l=0, t=10),\n",
" hovermode=False,\n",
" showlegend=False,\n",
" paper_bgcolor=\"rgba(0,0,0,0)\",\n",
")"
]
},
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"data": {
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" \n",
" "
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"source": [
"# COLLAPSED\n",
"import torch\n",
"from nerfstudio.cameras.cameras import Cameras, CameraType\n",
"from nerfstudio.utils import plotly_utils as vis\n",
"import plotly.graph_objects as go\n",
"\n",
"cx = 2.0\n",
"cy = 2.0\n",
"fx = 10.0\n",
"fy = 10.0\n",
"\n",
"num_samples = 3\n",
"near_plane = 1\n",
"far_plane = 3\n",
"\n",
"c2w = torch.eye(4)[None, :3, :]\n",
"camera = Cameras(fx=fx, fy=fy, cx=cx, cy=cy, camera_to_worlds=c2w, camera_type=CameraType.PERSPECTIVE)\n",
"ray_bundle = camera.generate_rays(camera_indices=0)\n",
"\n",
"bins = torch.linspace(near_plane, far_plane, num_samples + 1)[..., None]\n",
"ray_samples = ray_bundle.get_ray_samples(bin_starts=bins[:-1, :], bin_ends=bins[1:, :])\n",
"\n",
"vis_rays = vis.get_ray_bundle_lines(ray_bundle, color=\"teal\", length=far_plane)\n",
"\n",
"fig = go.Figure(data=[vis_rays] + vis.get_frustums_mesh_list(ray_samples.frustums), layout=webdocs_layout)\n",
"fig.show()"
]
},
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"metadata": {},
"source": [
"## Representing Frustums as Points\n",
"\n",
"These frustums can be converted into point samples using `frustum.get_positions()`.\n"
]
},
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"## Representing Frustums as Gaussians\n",
"\n",
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"# COLLAPSED\n",
"fig = go.Figure(\n",
" data=[vis_rays] + vis.get_gaussian_ellipsoids_list(ray_samples.frustums.flatten().get_gaussian_blob()),\n",
" layout=webdocs_layout,\n",
")\n",
"fig.show()"
]
}
],
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