Unreal Engine’s colliders are not as intuitive as those in Unity. Particularly, it has colliders named N-DOP Simplified Collision, that may seem confusing at first.
collider_types

Basically, how the official document describes each option is pretty accurate. However, without background knowledge, it may be difficult to fully understand the behaviour.

The original paper on K-DOP (Discrete Oriented Polytope) is publicly available and I think this is sufficient to understand K-DOP in Unreal Engine.

TLDR summary for those without time and my future-self: K-DOP first creates an AABB (Axis-Aligned Bounding Box), and bevels its edges only (18-DOP) or vertices and edges altogether (26-DOP). The 10-DOP options only bevel the 4 edges parallel to the X, Y or Z axis.

Slightly More Detailed Explanation

Suppose in a 2D space, we were to create a bounding-box representation of a shape by doing the following:

  1. Locate the ‘minimum’ and ‘maximum’ pixel of the shape along the x-axis. Draw vertical lines on those points.
  2. Locate the ‘minimum’ and ‘maximum’ pixel of the shape along the y-axis. Draw horizontal lines on those points.
  3. Create a rectangular bounding box from the intersecting points

This is basically 4-DOF in 2D space, also known as AABB.

the K in the name represents the number of orientations. It first encapsulates objects with H halfspaces. a halfspace H_i, whose normal is parallel to K_i direction, is placed on the ‘maximum’ point along the direction. It then creates a bounding representation by taking the intersection of all.

As such, 4-DOF in 2D space is AABB if the 4 directions are <1, 0>, <-1, 0>, <0, 1>, <0, -1>.

To optimise computation, Half of the K directions are the opposite to the other half. This essentially creates K/2 unique axes and hyperplanes with one axis constrained by the min and max points.

Conventionally, the standard axes of D dimensional space are contained in the K directions. Therefore, What modifies the AABB created by the standard-axis hyperplanes are the hyperplanes along (K - 2 * D)/2 different axes.

In the paper, the author describes 14-DOP (4 add. axes), 18-DOP (6 add. axes) and 26-DOP (10 add. axes) in 3D space. The 4 additional axes in 14-DOP penetrate the 8 vertices of a cube, 6 additional axes in 18-DOP penetrate the 12 edges and the 10 axes in 26-DOP are the combination of 14-DOP and 18-DOP. cube Each axis represented by a different colour.

As such, Unreal Engine’s 18DOF Simplified Collision cannot accurately encapsulate a cube whose edges and vertices are beveled: 18DOF

Whereas 26DOP Simplified Collision can because it bevels both vertices and edges: 26DOF

The 10-DOP options are similar: they bevel the 4 edges of a cube that are parallel to a particular axis.