3D Math: Linear Algebra, Quaternions

Understands basic 3D math concepts: coordinate systems, vectors, transformation matrices. Uses quaternions for rotation representation in Unity/Unreal. Works with the Transform API for object positioning.

Uses basic 3D math in Unity: Vector3, Quaternion, Transform. Understands coordinate systems and transformations. Works with Mathf for calculations in XR scenes.

Fluently applies linear algebra in AR/VR development: dot/cross product, projection matrices, rotation interpolation (slerp). Solves spatial geometry problems: ray-casting, intersection tests. Understands the difference between Euler angles and quaternions.

Fluently applies linear algebra in Unity XR: dot/cross product for spatial queries, Matrix4x4 for transformations, Quaternion.Slerp for smooth rotations. Implements ray-plane intersection for AR placement.

Develops mathematical algorithms for XR: spatial mapping, mesh reconstruction, ICP registration. Optimizes computations using SIMD instructions. Designs custom spatial data structures (octree, BVH) for XR scenes.

Develops mathematical algorithms for XR: ICP for mesh alignment, spatial hashing, frustum culling. Optimizes mathematical computations through Unity Mathematics (math library) and Burst Compiler.

Defines mathematical approaches for XR products. Mentors the team on 3D math. Conducts reviews of mathematical algorithms. Builds a library of reusable math utilities.

Defines mathematical approaches for XR product. Conducts review of mathematical algorithms. Mentors on 3D math for XR.

Researches new mathematical approaches for XR (neural radiance fields, differentiable rendering). Defines the long-term strategy for spatial computing usage.

Researches new mathematical approaches for XR (differentiable rendering, neural radiance fields). Shapes mathematical foundation for XR platform.