Collision Detection and Resolution

An attribute of a physics body, defining its basic shape.

Used to determine when two objects overlap.

Spherical collision volume

Has position and radius around position

Rectangular collision volume

Defined in two ways:
-Width, Length and Height
-Half Size along each axis from centre

Bounding Box where half sizes will always point in the direction of the global coordinate axes, no matter the orientation of the physics body.
Easier calculation of collisions

Bounding Box where the axes change direction to match the orientation.
Harder calculation of collisions, as it could be the y axis of one box hitting the x axis of another

A pair of collision bodies that are overlapping, generated for each set during the detection phase

Runs in two phases to allow for better performance.
Broad Phase: Determines objects that could never collide and culls them from each others collision sets.
Narrow Phase: Runs actual detection using the potential collision pairs from the broad phase.

Sorts bodies so they are spatially coherent, either just along one axis or along all axes.

-As the algorithm sweeps across the axis, adds objects to a list as it reaches its minimum extent on that axis
-If there are two or more objects now in the list, adds them to a list of possible collision pairs
-Removes items when the maximum extent on the axis is reached

Subdivides the area into quarters in order to group collision pairs. Has a maximum node volume (how many objects a node can hold before splitting) and maximum depth (how many nodes deep the tree can go).
The overall area is the root node, represented as a square, if the maximum node volume is reached, the area is split into equally sized smaller nodes.

Only volumes in the same leaf node are considered in detection

3D QuadTree, splitting into 8 cubes rather than 4 squares on node creation

How much two objects are overlapping each other

Direction of a collision

Calculate distance d between the two spheres.
If d < sum of the radii, spheres are colliding

Penetration Distance: Difference between the sum of the radii and d
Collision Normal: Normalised direction vector between the two bodies

Calculate if, on every axis, the distance between the objects is less than the sum of the half sizes.

Penetration Distance: The smallest difference between two axes
Collision Normal: Whichever side has the least amount of intersection

Find the closest point on AABB to the sphere (by clamping the sphere's position on each axis between the min and max of the AABB). If this is less than the sphere's radius away from the sphere's centre, they're colliding.

Penetration Distance: Difference between sphere's radius and the distance between the closest point and the sphere's origin
Collision Normal: Direction vector between the closest point and the sphere's position.

A tree of sphere or box colliders, the parent encapsulating all child colliders. Used for complex shapes with complex collision areas.

Calculate if the root collides first, if it does, check the children, etc.

Makes sure the objects are no longer overlapping by directly moving them (projecting them).

Calculation:
-collision normal * collision penetration * (inverse mass of object/total inverse mass)

Need to conserve momentum and apply forces to the objects to change acceleration accordingly.

Impulse Calculation:
J = -(1+e) vr.normal/total inverse mass

vr = vb - va

We apply this directly to the velocity in order to apply the force correctly.

new velocity = velocity +/- inverse mass * J * collision normal

Number that serves as an index of elasticity for colliding bodies, e.
If an object is entirely elastic, e = 1.0
If an object is entirely inelastic, e = 0

Physics objects that never move. These are never tested against each other for collision detection.

Placed into a static quad/octree when the level is built.

Use the static quad/octree, and move down the tree to find the leaf nodes that it may be overlapping with.

Large performance speed up

Dynamic objects that aren't moving (speed = 0). Ignored in collision detection against each other.

Awoken when speed > 0