Say when a drawing cannot be taken out of its box, rather than guessing

`lerp_inv` returns `Option`. Inverting a lerp over a range of zero
length has no one answer, and `div_or`'s fallback picked one: the start
of the range. Measured, that is not a wrong number so much as a
plausible one -- taking a part out of a box fixed at the top of the
window hands back exactly what went in, and out of a box fixed at the
middle hands back the parent's own `rel` of 0.5 as if it were the
child's fraction. Either way the caller cannot tell that nothing was
recovered, which is the defect; the previous commit's claim that it
"returns a rel of 0" is right only for the first case.

`UiScalar::outside` and `UiSpan::outside` follow it to `Option`, and
`Remap` is the answer at the region level: `new` says whether a drawing
in one box can be put in another and `apply` then cannot fail, so
`try_reuse` asks once for a whole subtree and `reusable` goes back to
reporting only what the widget claims. That replaces the predicate the
last commit put in `reusable`, which stated the same rule in a second
place.

`DivOr` existed only for the fallback and is gone, along with
`UiRegion::outside` and `UiVec2::outside`, which had no callers once
`Remap` owned the operation. `UiRegion::axis` took `&mut self` to
return a shared reference; `Remap::new` needs it on a shared one.

This does not redraw less. `Remap::new` refuses exactly what the
predicate refused; what it buys is one statement of the rule and a
remap that cannot half-apply. Counted on a resize, with the old
wipe-everything for comparison:

  20 padded rows, 101 widgets     101 draws -> 0
  the `tabs` example               73 draws -> 0
  the `text` example               49 draws -> 48

So the saving is whole where a resize does not change any widget's
size, and nil in `text`, where both paragraphs rewrap to a different
height and the relayout that forces reaches the root. The last commit's
message oversold that case.

Checked: fmt, clippy and 35 tests. `tabs` (with the image replay),
`view` and `minimal` still byte-identical to `upstream/main`, `text`
unchanged, and the live sway resize round trip still matches a cold
start at each size.

core/src/orientation/pos.rs

@@ -56,13 +56,6 @@ impl UiVec2 {
         }
     }
 
-    pub const fn outside(&self, region: &UiRegion) -> UiVec2 {
-        UiVec2 {
-            x: self.x.outside(&region.x),
-            y: self.y.outside(&region.y),
-        }
-    }
-
     pub fn axis_mut(&mut self, axis: Axis) -> &mut UiScalar {
         match axis {
             Axis::X => &mut self.x,
@@ -209,10 +202,12 @@ impl UiScalar {
         }
     }
 
-    pub const fn outside(&self, span: &UiSpan) -> Self {
-        let rel = self.rel.lerp_inv(span.start.rel, span.end.rel);
+    /// Undoes `within`, and `None` where the span has a fixed length: every
+    /// fraction of it lands on the same `rel`, so none can be told apart.
+    pub fn outside(&self, span: &UiSpan) -> Option<Self> {
+        let rel = self.rel.lerp_inv(span.start.rel, span.end.rel)?;
         let abs = self.abs - rel.lerp(span.start.abs, span.end.abs);
-        Self { rel, abs }
+        Some(Self { rel, abs })
     }
 
     pub fn within_len(&self, len: UiScalar) -> Self {
@@ -283,10 +278,10 @@ impl UiSpan {
         }
     }
 
-    pub const fn outside(&self, parent: &Self) -> Self {
-        Self {
-            start: self.start.outside(parent),
-            end: self.end.outside(parent),
+    pub fn outside(&self, parent: &Self) -> Option<Self> {
+        match (self.start.outside(parent), self.end.outside(parent)) {
+            (Some(start), Some(end)) => Some(Self { start, end }),
+            _ => None,
         }
     }
 
@@ -324,14 +319,7 @@ impl UiRegion {
             y: self.y.within(&parent.y),
         }
     }
-    pub const fn outside(&self, parent: &Self) -> Self {
-        Self {
-            x: self.x.outside(&parent.x),
-            y: self.y.outside(&parent.y),
-        }
-    }
-
-    pub const fn axis(&mut self, axis: Axis) -> &UiSpan {
+    pub const fn axis(&self, axis: Axis) -> &UiSpan {
         match axis {
             Axis::X => &self.x,
             Axis::Y => &self.y,
@@ -409,6 +397,50 @@ impl UiRegion {
     }
 }
 
+/// Taking a drawing out of one box and putting it in another, checked once
+/// for a whole subtree so that applying it cannot fail.
+///
+/// A box of a fixed length holds each part as an offset from its start rather
+/// than as a fraction of it, so those parts can be carried to a box of the
+/// same length but never stretched to a different one.
+#[derive(Debug, Copy, Clone, PartialEq)]
+pub struct Remap {
+    from: UiRegion,
+    to: UiRegion,
+}
+
+impl Remap {
+    pub fn new(from: UiRegion, to: UiRegion) -> Option<Self> {
+        [Axis::X, Axis::Y]
+            .into_iter()
+            .all(|axis| {
+                let (from, to) = (from.axis(axis), to.axis(axis));
+                from.start.rel != from.end.rel || from.len() == to.len()
+            })
+            .then_some(Self { from, to })
+    }
+
+    pub fn apply(&self, region: UiRegion) -> UiRegion {
+        UiRegion {
+            x: Self::span(region.x, self.from.x, self.to.x),
+            y: Self::span(region.y, self.from.y, self.to.y),
+        }
+    }
+
+    fn span(span: UiSpan, from: UiSpan, to: UiSpan) -> UiSpan {
+        match span.outside(&from) {
+            Some(out) => out.within(&to),
+            // `new` admits this only where the two are the same length, so
+            // the difference between their starts is the whole move.
+            None => {
+                let mut span = span;
+                span.shift(to.start - from.start);
+                span
+            }
+        }
+    }
+}
+
 impl Display for UiRegion {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
         write!(