86 3D: Spatial maps and homotopies🔗ℹ

3D reference map · First 3D picture

Spatial map requests use the ordinary immutable scene timeline. Every target is a rooted spatial path, and every map procedure is authored in world coordinates. This makes a map applied to a nested child mean the same thing as applying it to an equivalent top-level child. A surrounding parent map must therefore be invertible when the result is rebased into that parent’s local coordinate system.

apply-linear3 and apply-affine3 retain the original spatial subtree and attach a full affine map to it. They consequently preserve the indexed topology exactly, even for a shear, reflection, or singular map. A named child of a transformed group3d remains addressable. The canonical linear-transformation-diagram3d groups coordinate planes, a unit cube, basis arrows, and an arbitrary vector so one map applies to all of them coherently.

(scene-play

(scene-add (make-scene) world)

(apply-linear3 '(world diagram)

(linear3 1 0 1

0 1 0

0 0 1))

(apply-homotopy3

'(world sheet)

(lambda (point phase)

(vec3 (vec3-x point)

(* (cos phase) (vec3-y point))

(* (sin phase) (vec3-y point)))))

#:duration 2)

An example is "examples/3d/spatial-maps-and-homotopies.rkt".