Axis Aligned Bounding Box

AABBf

Work in progress

The Axis-Aligned Bounding Box (float) is an efficient tool for collision detection. A Bounding Box forms itself out of the minimal and the maximal x, y, z coordinates of an object. The min and max values of a cube in the center of a scene may look like this:

min = (-1, -1, -1); 
max = (1, 1, 1);

A Bounding Box draws a cuboid as tightly as possible around the targeted object. A sphere with radius 1 would have the same Bounding Box as the cube in the example above.

The Axis-Aligned Bounding Box is as the name suggests "axis-aligned", which means the Bounding Boxes are not able to rotate and if its object rotates the AABB has to be recalculated and may end up in a bad approximation of its former shape. Therefore the AABB is most useful when the objects principal axes are roughly aligned with the scenes coordinate system.

When two Bounding Boxes are tested for a collision, the minimum values of one box are compared to the maximum of the other and vice versa (A.min.y & B.max.y,..., A.max.z & B.min.z,...). So if a minimum value is greater than a maximum value / a maximum value is lesser than a minimum value, a collision occurs.

Components

Type	Name	Description
AABBf	AABBf()	Creates a new axis aligned bounding box
bool	Equals()	Indicates whether this plane is equal to another object
bool	Intersects()	Checks if this AABB intersects with another
AABBf	ReferenceEquals()	Determines whether the specified object instances are the same instance
AABBf	Union()	Calculates the bounding box around two existing bounding boxes
int	GetHashCode()	Returns the hash code for this instance
Type	GetType()	Gets the Type of the current instance
bool	InsideOrIntersectingFrustrum()	Checks if a viewing frustrum lies within or intersects this AABB
bool	InsideOrIntersectingPlane()	Checks if a viewing plane lies within or intersects this AABB
string	ToString()	Returns the fully qualified type name of this instance
float3	Size	Returns the width, height and depth of the box in x, y and z
float3	Center	Returns the center of the bounding box
float3	min	The minimum value of the axis aligned bounding box in x, y and z direction
float3	max	The maximum value of the axis aligned bounding box in x, y and z direction

Building your own Bounding Box

You can use the constructor 'AABBf' to build your own Bounding Box:

_min = new float3(-1, -1, -1);
_max = new float3(1, 1, 1):

AABBf bb1 = new AABBf
(
    _min,
    _max 
);

There is also a way to get the Bounding Box of an Asset or Object in the scene:

private Transform SphereTrans;
private Mesh SphereMesh;

SphereMesh = Scene.Children.FindNodes(node =>node.Name == "Sphere")?.FirstOrDefault()?.GetMesh();
bb2 = SphereMesh.BoundingBox;

If (at least) one of your objects moves you can multiplicate it with the Matrix of the moving Object:

AABBf movingBb = bb2 * SphereTrans.Matrix();

Now if you want to check for a collision between these two Bounding Boxes, you can use the Intersect Method:

if(bb1.Intersects(bb2))
{
    Console.WriteLine(Oh? You're intersecting me?);
}