How the volume of a solid is calculated

The method Surpac uses to calculate solid volume is outlined below.

1. A datum plane is chosen with a z value below all the z values in the solid.
2. The vertices of each triangle of the solid are projected onto the datum plane. For each triangle, a column is formed by joining the triangle to the datum plane.
3. The volume of each of these columns is calculated and added together to give a total.

Surpac uses a reference point above the solid to perform this calculation. This is important because it means that:

• the triangles at the top of the solid have a clockwise orientation and have positive solid volumes.
• the triangles on the underside of the solid have an anti-clockwise orientation and have negative solid volumes.

So the total of the columns formed from the triangles at the top of the solid give the volume between the top of the solid and the datum plane as a positive value. The total of the columns formed from the triangles on the underside of the solid give the volume between the underside of the solid and the datum plane as a negative value. The sum of all columns then is the volume of the solid.

Note: From this, you can see that it does not matter exactly which z value is chosen for the datum line, provided it is lower than the lowest z value in the solid.