Game Dev Math

Mathematical Principles & Theorems

Applies vector algebra, kinematics, and geometric computational algorithms to real-time simulation: 2D/3D Vector dot product (\(\mathbf{u}\cdot\mathbf{v} = |\mathbf{u}||\mathbf{v}|\cos\theta\)) for surface illumination and projection; Cross product (\(\mathbf{u}\times\mathbf{v}\)) for surface normals; Bézier curves \(B(t) = \sum_{i=0}^n \binom{n}{i}(1-t)^{n-i}t^i P_i\) for smooth spline interpolation; Axis-Aligned Bounding Box (AABB) separating axis intersection testing; Ray-plane intersection algorithms.

Operating Instructions

• Select a game math module: Bézier Splines, Vector Reflection, AABB Collision, or Raymarching.
• Adjust the interpolation parameter \(t \in [0, 1]\) using the numeric input value box.
• Drag control points on the visual canvas to alter spline tangents and collision geometry.
• Observe real-time vector normal reflections, intersection points, and bounding box overlap flags.