Manipulator geometry

The maths a manipulator needs, as pure functions. No scene, no engine, no pointer — so the part most likely to be subtly wrong is the part that can be tested without a browser.

Each grip answers one question: given where the pointer is aiming now, what value should this handle have?

• translate — the point on the axis closest to the pointer's ray
• planar — where the ray crosses the plane the grip lies in, as a point
• rotate — the angle around the axis where the ray crosses its plane
• scale — the same projection as translate, read as a ratio
• uniform — the ray's distance from the widget centre, read as a ratio

A grip, not a mode

The widget shows every enabled affordance AT ONCE and lets the grip you grab say what the drag means — the shape Cheetah 3D's universal manipulator made its reputation on. A mode switch asks the author to declare their intent twice: once to the toolbar, and again to the handle. Here Grip is the whole vocabulary, and it is what a pick returns.

Snapping quantises the VALUE, not the movement

A drag that snaps by stepping the delta accumulates error: sixty frames of round(delta) is not round(sixty deltas), and a piece walks off the grid over a long drag. Quantising the resulting absolute value instead means a snapped piece is always exactly on the grid, however it got there.