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         id="tspan7939-4-1">4. Spatial Data Structures</tspan></text>
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       style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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         id="tspan23964-4-3">There are different approaches for constructing hierarchical spatial data structures with bounding </tspan><tspan
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         x="48.834229"
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         style="font-size:12.5px"
         id="tspan24078-9">volumes. These approaches generally result in different types of spatial data structures, depending</tspan><tspan
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         x="48.834229"
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         style="font-size:12.5px"
         id="tspan24366">on the exact strategy that is used for the construction.</tspan><tspan
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         x="48.834229"
         y="640.21265"
         style="font-size:12.5px"
         id="tspan8865-1-6-1-7-3" /></text>
    <text
       xml:space="preserve"
       style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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       sodipodi:linespacing="125%"><tspan
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         x="50.032715"
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         id="tspan24380">The generic spatial data structures in 3D Tiles allow modeling the results of all these construction </tspan><tspan
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         x="50.032715"
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         style="font-size:12.5px"
         id="tspan24382">methods. Each tile is a node of the hierarchy that may optionally refer to geometry content or store </tspan><tspan
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         x="50.032715"
         y="987.79419"
         style="font-size:12.5px"
         id="tspan24384">only a bounding volume that encloses the content of all its descendants, and different types of </tspan><tspan
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         x="50.032715"
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         style="font-size:12.5px"
         id="tspan13138">bounding volumes can be stored in a single tileset.</tspan></text>
    <text
       xml:space="preserve"
       style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
       x="49.819824"
       y="644.99506"
       id="text16568-4-9-2-3-6-0"
       sodipodi:linespacing="125%"><tspan
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         x="49.819824"
         y="644.99506"
         style="font-size:12.5px"
         id="tspan24541">A simple spatial hierarchy can be constructed by recursively splitting the content of a tile along certain </tspan><tspan
         sodipodi:role="line"
         x="49.819824"
         y="660.62006"
         style="font-size:12.5px"
         id="tspan24662">axes, until a stopping criterion is met. When the content is only split along a single axis at each level, </tspan><tspan
         sodipodi:role="line"
         x="49.819824"
         y="676.24506"
         style="font-size:12.5px"
         id="tspan24666">then the result is a <tspan
   style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold'"
   id="tspan84671">k-d tree</tspan>. 3D Tiles also supports <tspan
   style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold'"
   id="tspan84673">multi-way k-d trees</tspan>, where each level has </tspan><tspan
         sodipodi:role="line"
         x="49.819824"
         y="691.87006"
         style="font-size:12.5px"
         id="tspan24668">multiple splits along one axis. When the content is split along the x, y, and the z-axis at each level, </tspan><tspan
         sodipodi:role="line"
         x="49.819824"
         y="707.49506"
         style="font-size:12.5px"
         id="tspan24545">then the result is an <tspan
   style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold'"
   id="tspan84675">octree</tspan>. When the content is split at the center of the content bounding volume, </tspan><tspan
         sodipodi:role="line"
         x="49.819824"
         y="723.12006"
         style="font-size:12.5px"
         id="tspan24593">then the result is a <tspan
   style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold'"
   id="tspan84677">uniform octree</tspan>. When the content is split at a different point, then the result is a</tspan><tspan
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         x="49.819824"
         y="738.74506"
         style="font-size:12.5px"
         id="tspan24759"><tspan
   style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold'"
   id="tspan84679">non-uniform </tspan>octree.</tspan><tspan
         sodipodi:role="line"
         x="49.819824"
         y="754.37006"
         style="font-size:12.5px"
         id="tspan24547" /></text>
    <text
       xml:space="preserve"
       style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
       x="49.103516"
       y="757.34436"
       id="text16568-4-9-2-3-6-0-6"
       sodipodi:linespacing="125%"><tspan
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         x="49.103516"
         y="757.34436"
         style="font-size:12.5px"
         id="tspan24576">At each level of the hierarchy, the bounding volumes can be created purely spatially from the bounding </tspan><tspan
         sodipodi:role="line"
         x="49.103516"
         y="772.96936"
         style="font-size:12.5px"
         id="tspan24545-7">volume of the parent node. Alternatively, the bounding volumes for each node can be computed from </tspan><tspan
         sodipodi:role="line"
         x="49.103516"
         y="788.59436"
         style="font-size:12.5px"
         id="tspan24601">the actual content of the node. This can be particularly useful for sparse datasets because it ensures</tspan><tspan
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         x="49.103516"
         y="804.21936"
         style="font-size:12.5px"
         id="tspan24603"><tspan
   style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold'"
   id="tspan84700">tightly-fitting bounding volumes</tspan> at each level of the hierarchy.</tspan><tspan
         sodipodi:role="line"
         x="49.103516"
         y="819.84436"
         style="font-size:12.5px"
         id="tspan24547-4" /></text>
    <text
       xml:space="preserve"
       style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
       x="49.696045"
       y="823.51233"
       id="text16568-4-9-2-3-8-7-5-3-1-0"
       sodipodi:linespacing="125%"><tspan
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         x="49.696045"
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         style="font-size:12.5px"
         id="tspan18050-2">It is sometimes not possible to divide a tile without splitting a single feature (model) of the content. It is </tspan><tspan
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         x="49.696045"
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         style="font-size:12.5px"
         id="tspan18058-9">therefore possible to construct <tspan
   style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold'"
   id="tspan84702">loose octrees</tspan> and <tspan
   style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold'"
   id="tspan84704">loose k-d trees</tspan>, where the bounding volumes of </tspan><tspan
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         x="49.696045"
         y="854.76233"
         style="font-size:12.5px"
         id="tspan18060-3">children overlap. These trees still maintain spatial coherence, in that the parent bounding volume still </tspan><tspan
         sodipodi:role="line"
         x="49.696045"
         y="870.38733"
         style="font-size:12.5px"
         id="tspan24650">encloses the content of all children.</tspan><tspan
         sodipodi:role="line"
         x="49.696045"
         y="886.01233"
         style="font-size:12.5px"
         id="tspan17980-0-5" /></text>
    <text
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       style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
       x="49.150879"
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       sodipodi:linespacing="125%"><tspan
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         x="49.150879"
         y="889.23712"
         style="font-size:12.5px"
         id="tspan24873">In the most general case, a tileset can be divided into a <tspan
   style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold'"
   id="tspan84714">non-uniform grid</tspan>. Since each node in the </tspan><tspan
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         x="49.150879"
         y="904.86212"
         style="font-size:12.5px"
         id="tspan13975">spatial hierarchy in 3D Tiles may have an arbitrary number of child nodes, and non-leaf tiles are not </tspan><tspan
         sodipodi:role="line"
         x="49.150879"
         y="920.48712"
         style="font-size:12.5px"
         id="tspan24869">required to contain renderable content, the grid cells can still be organized in a hierarchical structure</tspan><tspan
         sodipodi:role="line"
         x="49.150879"
         y="936.11212"
         style="font-size:12.5px"
         id="tspan24883">in order to support hierarchical culling.</tspan></text>
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