world transforms

World reconstruction is separate from local solving. Skip it when you only need to commit a Motor6D.Transform, AnimationConstraint.Transform, or Bone.Transform for playback.

solver.solve_prepared(rig, prepared)
local world = solver.compute_world_transforms(rig, character:GetPivot())

For optimal performance, manage the output array yourself:

local world = table.create(rig.desc.count)

solver.solve_prepared(rig, prepared)
solver.apply_delta_prepared(rig, deltas)
solver.compute_world_transforms(rig, character:GetPivot(), world)

When out is omitted, the first call allocates rig.world_transforms and later calls reuse it. Pass a preallocated array when you want that ownership explicit.

Formulas

Descriptor indices are parent before child, so reconstruction is one iterative pass with no Instance hierarchy traversal:

Motor6D/AnimationConstraint: parentWorld * C0 * localTransform * inverse(C1)
Bone:                        parentWorld * bindCFrame * localTransform

The supplied root CFrame is used for every descriptor target whose parent index is zero. Use the root transform from the same moment you are evaluating.

One call accepts one root transform. Descriptors with unrelated root hierarchies cannot use distinct root transforms in the same reconstruction pass.