====== 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.