A node has a pivot

Rotation and scale are composed about `[:xform :pivot]`, a point in the
node's own coordinates:

    local = T(pos) · T(piv) · R · K · S · T(-piv)

Schema 7 deleted this field, on the argument that an anchor is a peg. The
algebra was right and the conclusion was not. The identity holds between a
pivot and a peg THAT ALREADY EXISTS; it says nothing about what a node
turns about when nobody has made one, and that default is what a person
meets. With no pivot in the composition, a turn about anything but the
node's own origin has to be paid for by solving `pos` per frame —
`gesture/about` — and that solution is an arc in the angle while `pos`
tweens along the chord. Right on the frame it is written, wrong on every
frame between two keys.

A drawing escaped it: `paint/centred` puts a shape's origin on the middle
of what it draws. A symbol instance cannot — its origin is its symbol's,
and a symbol is drawn on the stage, so its origin is the top-left corner
of the stage. Off the document this was reported on: a symbol's content
centred 161 px from its own origin, and one instance of it keyed rot 0→60
put the drawing where it was put on both keys and at (-88, 121) halfway
between, a stage and a half away. The advice on offer was "make a peg
first", for wanting to spin a drawing.

So a turn now writes `rot` and nothing else, always, and the pivot is held
exactly between two keys because the matrix is built about it on every
frame. The default, and the way back to it, are the parts the old anchor
was missing:

  - a node nobody has pivoted turns about the middle of what it draws,
    `pick/bounds-of` — the same bounds the selection box comes from
  - the first turn or scale writes that middle down, in the same edit,
    with the `pos` that holds the picture still (`gesture/with-pivot`)
  - `clip/place-symbol` stores the middle of what a symbol draws as the
    instance's pivot, so a drop spins in place from the start
  - ⌃/⌘-drag the cross on the stage to put the pivot anywhere, moving
    nothing — on any node now, not pegs alone
  - ⌖ beside the pivot row in the inspector puts it back on the middle of
    what the node draws NOW (`gesture/centred`)

A pivot is a CHOICE and does not follow the drawing: once it is the node's
own, adding a shape inside a symbol cannot re-aim a keyed spin of any
instance of it. `instance-test` has asserted both answers to that now, and
the stored one is right.

A peg stays a peg, for the three things a node's own pivot is not: a pivot
SHARED between nodes, a SECOND transform on one node, and a hand transform
over a measured one. `nest/repivot` is gone — a pivot inside the node's own
transform has nothing to correct in anybody else's `:pinv`, so the gesture
works on every node and is no longer refused on an animated one. A measured
node's pivot is authored like any other, so a traced mouth can be told
where to turn without a peg.

Schema 8, and the first version that converts rather than refusing: an
absent pivot reads as [0 0] and T(pos)·T(0)·M·T(-0) is T(pos)·M to the
bit, so every stored document composes to exactly the matrices it did and
the migration only restamps the version.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

clips/migrations/0017_a_node_has_a_pivot.py

@@ -0,0 +1,45 @@
+"""Schema 8: a node has a pivot.
+
+`[:xform :pivot]` is back in the transform, as the point rotation and scale are
+composed about: `local = T(pos)·T(piv)·R·K·S·T(-piv)`. Schema 7 deleted it, on
+the argument that an anchor is a peg — true as algebra, and not true as a feature.
+A peg is a node, and a turn about a point that is not the turning node's own
+origin still has to solve for a position to hold that point still; that solution
+is an arc in the angle while a position channel tweens along the chord, so it is
+right on the frame it is written and wrong on every frame between two keys. A
+drawing escaped it, since its origin is the middle of what it draws. A symbol
+instance could not: its origin is its symbol's, which is the top-left corner of
+the stage, so one keyed turn of an instance swung its drawing round that corner
+on an orbit the size of the stage.
+
+CONVERTED, unlike 6 and 7, because adding this one is exact. A schema-7 node has
+no pivot; an absent pivot reads as [0 0]; and T(pos)·T(0)·M·T(-0) is T(pos)·M to
+the last bit of the mantissa. Every stored document therefore composes to exactly
+the matrices it composed to before, dense tier-2 transforms included, so there is
+nothing to guess at and no node a conversion could silently move. The version is
+restamped and nothing else is touched.
+
+What a converted document does NOT get is a pivot somebody chose: nodes placed
+before this carry none, so they still turn about their own origin until the first
+turn or scale writes one — `gesture/with-pivot`, from the middle of what the node
+draws at that moment — or until the cross is dragged (ctrl/cmd-drag on the stage).
+"""
+
+from django.db import migrations, models
+
+
+def forwards(apps, schema_editor):
+    apps.get_model("clips", "Project").objects.update(schema_version=8)
+
+
+class Migration(migrations.Migration):
+    dependencies = [("clips", "0016_an_anchor_is_a_peg")]
+
+    operations = [
+        migrations.AlterField(
+            model_name="project",
+            name="schema_version",
+            field=models.PositiveIntegerField(default=8),
+        ),
+        migrations.RunPython(forwards, migrations.RunPython.noop),
+    ]