knowledge base/practices

The XZ plane seen from above is left-handed, so a yaw written as (cos, sin) is the mirror of a scene-graph rotation

added 2026-09-20·view source

3dgraphicsgeometryscene-graph

Fact

In a right-handed Y-up world, a rotation of r about +Y maps the local +X axis to

(cos r, 0, -sin r)

because the rotation matrix about +Y carries +X toward -Z. But the obvious way to place something "yawed by y" in the ground plane is to write a 2D circle in (x, z):

right = (cos y, 0, sin y)

Those two differ by a reflection. Both are called yaw, both are a single angle, and each is the natural expression in its own context — so a world layout, a collision routine and a renderer can each be internally correct and still disagree by a mirror.

The cause is that the (x, z) pair, viewed from +Y, is a left-handed 2D frame. Ordinary 2D intuition about (cos, sin) silently flips a sign when it is applied there.

Why it matters

The symptom is geometry drawn in the wrong place, not geometry missing, so nothing errors: the mesh exists, is positioned, is parented, is lit and is drawn. A gate's crossbars rendered ninety degrees out from the uprights they join, while the collidable gate stayed where the layout put it — you could fly through a gate that was not where it looked.

Worse, the error is invisible at exactly the angles anything gets checked at. At yaw 0 and yaw π the two expressions agree, so an axis-aligned test object, a screenshot of the first item in a list, and any hand-placed debugging case all look perfect. It only appears off-axis, where it reads as "the artist rotated it wrong".

How to apply

  • Keep one conversion, in one place, and route every call site through it: meshYaw(y) => -y for a right-handed Y-up scene graph, alongside rightVector(y) and facingVector(y) used by the layout and the physics.
  • Test it without a renderer: assert that the local +X direction implied by the scene-graph rotation equals the layout's right vector, over a spread of angles that excludes 0 and π, and separately assert that those two angles are the ones that hide it.
  • When a rotation looks wrong, compare a derived direction vector rather than the angle. Two mirrored conventions print the same number.
  • Related: [[mirrored-scale-inverts-rotation]], and [[yaw-derivatives-flip-with-the-yaw-axis]] for the same handedness trap where it reaches a physics table rather than a transform.