Articles

Math- Sub Categories

  • Detecting collisions and locating impact points

  • Physics (0)

    Dynamics simulation in realtime

  • Algorithms to calculate random points on surfaces and in volumes

Collision Query between Moving AABB and AABB

Explains how to find the time of impact between a moving AABB and stationary AABB using the SAT (Seperating Axis Theorem). Also works with two moving AABBs, since you can simply subtract the velocity of one AABB from the other's to make it stationary.

Random Points within Cylinder

Code snippet that generates uniformly distributed random points within the volume of a 3D cylinder with arbitrary orientation.

Random Points on Cylinder Surface

This code snippet generates uniformly distributed random points on the surface of a 3D cylinder, either on its two caps or along the length of the cylinder, taking the surface area of each section into account.

Random Points within AABB

Code snippet for generating random points within an AABB (axis-aligned bounding box)

Random Points in Rectangle

Code snippet that generates random points within a 2D rectangle.

Random Points on Rectangle Perimeter

Shows how to generate random points along the perimeter of an arbitrary 2D rectangle.

Random Points in Disc

Simple code snippet that demonstrated how to generate random points on a flat disc that are uniformly distributed and do not become more dense near the disc's center.

Random Points on Disc Perimeter

Snippet for generating random points along the perimeter of a flat disc (or circle)

Random Points within Sphere

This code snippet generates random points inside a sphere with uniform distribution. Unlike commonly used rejection methods, this code generates only valid points, ensuring deterministic runtime performance.

Static Intersection Test Between Cylinder and Sphere

Shows how to do an intersection check between a freely oriented cylinder and a sphere

Determine Minimal AABB of OBB

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Explains how to efficiently determine a minimal AABB (axis-aligned bounding box) for any OBB (oriented bounding box)

Static Intersection Test Between OBB and Sphere

Explains how to check an OBB (oriented bounding box) for intersection with a sphere.

Static Intersection Test Between OBB and OBB

Explains how to determine whether two freely placed OBBs (oriented bounding boxes) are overlapping with each other.

Static Intersection Test Between AABB and OBB

Explains how to determine wether an AABB (axis-aligned bounding box) is overlapping with an OBB (oriented bounding box)

Static Intersection Test Between AABB and Sphere

Shows how to determine whether an AABB (axis-aligned bounding box) is intersecting with a sphere