3D graphics literacy

Frames, vectors, TRS, camera, winding

• Coordinate frame — an origin plus three axes. World space is the shared stage; each object has a local frame glued to it.
• Point vs vector — a point is a location (transforms with translation). A vector is a direction/offset (rotation and scale only). Confusing them is how “normals drift after you move the mesh.”
• TRS order — engines usually compose as Scale → Rotate → Translate when going local→world (matrix multiply order depends on row/column convention). Scale first so rotation spins the already-sized axes; translate last so you move the whole thing.
• Camera look-at — build a view from eye position, a target point, and an up vector. The camera looks along −Z or +Z depending on the API’s clip space; the look-at matrix orthonormalizes those three directions.
• Winding — triangle vertices declared clockwise or counter-clockwise when viewed from the front. Cull mode uses that to drop back faces. Flip winding and your mesh vanishes or shows inside-out.

Rotation about a point

To spin around a pivot that is not the origin: translate so the pivot sits at the origin, rotate, translate back. In code that is often T(pivot) · R · T(−pivot) (column-vector convention).

Local pivot — defined in the object’s own space (a door hinge on the door). World pivot — a fixed point in the stage (spin around a world origin marker). Same math; different which frame supplies the pivot coordinates.

Left hand vs right hand

Point thumb along +X, index along +Y: the middle finger shows +Z for that hand rule. Right-handed: +Z comes toward you when +X is right and +Y is up (common in mathematics and many OpenGL-style tutorials). Left-handed: +Z goes into the screen in that same picture (common in some Direct3D samples historically).

API tendencies (with disclaimers) — these are starting points, not laws:

• OpenGL / many Vulkan samples — traditionally taught as right-handed view/world with clip volume variations; NDC and Y-flip differ by pipeline. See the OpenGL 4.6 core spec (Khronos) and the Vulkan vertex post-processing chapter.
• Direct3D / DirectX — historical docs and many samples use a left-handed look-at; modern DirectXMath offers both LH and RH helpers. See Microsoft’s Direct3D coordinate systems note and DirectXMath.

Engines (Unity, Unreal, custom) pick conventions explicitly. Always read the engine’s matrix docs before porting shaders.