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--- visual3d:documentation:modeling:segments:segment_volume [2024/07/17 15:42] – removed sgranger
+++ visual3d:documentation:modeling:segments:segment_volume [2026/06/12 17:29] (current) – Cleaned up page, added links, and added reference to Set_Model_Metric. wikisysop
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+====== Segment Volume ======
+Visual3D models segments as [[visual3d:documentation:modeling:segments:segment_geometry|cones, cylinders, spheres, and ellipsoids]]. Visual3D doesn't compute the volume of a segment based on these geometries, but the calculations are straightforward in each case.
+===== Volume Equations =====
+==== Volume of a Conical Frustrum ====
+One of the Visual3D segment geometries is labeled a [[visual3d:documentation:modeling:segments:segment_geometry#cones_-_frusta_of_right_cones|Cone]] or, to be precise, a **conical frustrum.** A **frustra of right cones** is created by cutting the top off of a cone such that the cut is parallel to the base of the cone. Given a conical frustrum defined as below:
+{{:frustraOfRightCones1.gif}}
+Its volume is calculated as: {{:Volume_Frustrum.jpg?350}}
+==== Volume of an Ellipsoid ====
+In Visual3D the inertial properties of an [[visual3d:documentation:modeling:segments:segment_geometry#ellipsoids|ellipsoid]] (sphere) are calculated using only the distal radius. For an ellipsoid defined as below, where L is the line between the segment's proximal end and its centre of mass,
+{{:sphere.gif}}
+Its volume is calculated as: {{:Volume_Ellipsoid.jpg?300}}
+==== Volume of an Elliptical Cylinder ====
+Finally, for an [[visual3d:documentation:modeling:segments:segment_geometry#cylinders_-_right_elliptical_cylinders|eliptical cylinder]] defined as:
+{{:Cylinder.gif}}
+Visual3D uses the radius at the distal end of the segment as the radius of the cylinder and calculates its volume as: {{:Volume_Cylinder.jpg?300}}
+===== Specifying Segment Volume as a Model Metric =====
+This segment volumes are not computed by default, but they can be added by the user as [[visual3d:documentation:modeling:model_metrics|Model Metrics]].
+This can be done through the interface, for example for a segment with **Cone** geometry:
+{{:Volume_Frustrum_Metric.png?400}}
+Or through the [[visual3d:documentation:pipeline:model_commands:set_model_metric|Set_Model_Metric]] pipeline command, for example for a segment with **Elliptical Cylinder** geometry:
+<code>
+Set_Model_Metric
+/METRIC_NAME=Pelvis_Volume
+! /METRIC_VALUE=PI*RPV_Seg_Length*RPV_Distal_Radius*RPV_Proximal_Radius/4
+;
+</code>
+===== See Also =====
+Go back to the [[visual3d:documentation:modeling:segments:segment_overview|Segment Overview]] for more information about segments in Visual3D.