A self-contained reference book covering the linear algebra and geometry used in game development.
Number types, 3D space, left vs right-handed systems, radians, SohCahToa, and the trig identities that underpin all of game math.
Magnitude, normalization, distance, scalar multiplication, vector addition, and the dot product — the single most-used operation in real-time rendering and AI.
World, object, camera, clip, and screen space. Basis vectors, span, rank, and orthonormal bases — the machinery behind the vertex shader pipeline.
Matrix anatomy, identity, transposition, row vs column vectors, multiplication rules, and how matrices encode linear transformations through basis vectors.
Rotation (2D, 3D cardinal, arbitrary axis), scale, orthographic projection, reflection, shearing, and TRS matrix composition.
Computing perpendicular vectors, the right-hand rule, surface normals, camera right vectors, triangle area, and winding-order detection.
2D polar, aliasing, atan2, cylindrical and spherical coordinates, and the heading/pitch convention used by game engines for 3D directions.
Matrix form, Euler angles (heading/pitch/bank), gimbal lock, canonical sets, axis-angle, exponential map, and quaternions.
Lines, rays (parametric and implicit forms), spheres, AABBs, OBBs, and planes — the shapes that drive collision detection.
Closest-point queries and intersection tests: ray-sphere, ray-plane, ray-triangle, AABB-AABB, AABB-sphere, and the separating axis theorem.