<p>You can use CGAL's <a href="https://doc.cgal.org/latest/Convex_hull_3/group__PkgConvexHull3Functions.html#gade99e8e830ff439ae242b7ab04de06c8" rel="nofollow noreferrer">half_space_intersection_3</a> or <a href="https://doc.cgal.org/latest/Convex_hull_3/group__PkgConvexHull3Functions.html#ga7517c4cbbef41338397eda273af75eb1" rel="nofollow noreferrer">half_space_intersection_with_construction_3</a> functions, where the half-spaces are defined by the faces of the cuboids.</p>

CC BY-SA 4.0
2018-05-21T13:59:30.817Z
2018-05-21T13:59:30.817Z
Iddo Hanniel
<p>Given two cuboids in 3D space (8 vertex coordinates each) that are arbitrarily oriented, how can we find the volume of overlap between them in the fastest manner? </p>

<3d><mathematics><volumetric>
How to compute volume of intersection of non-axis-aligned cuboids in 3D?
tejaskhot
# How to compute volume of intersection of non-axis-aligned cuboids in 3D?

(Asked by: username_0 on 2018-05-12)

Given two cuboids in 3D space (8 vertex coordinates each) that are arbitrarily oriented, how can we find the volume of overlap between them in the fastest manner?

**Tags:** 3d, mathematics, volumetric


---

## 1 answers

### Answer by username_1 on 2018-05-21. Score: 1

You can use CGAL's [half\_space\_intersection\_3](https://doc.cgal.org/latest/Convex_hull_3/group__PkgConvexHull3Functions.html#gade99e8e830ff439ae242b7ab04de06c8) or [half\_space\_intersection\_with\_construction\_3](https://doc.cgal.org/latest/Convex_hull_3/group__PkgConvexHull3Functions.html#ga7517c4cbbef41338397eda273af75eb1) functions, where the half-spaces are defined by the faces of the cuboids.


---

