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!(

core/src/ui/render_state.rs

@@ -1,5 +1,5 @@
 use crate::{
-    ActiveData, Axis, DrawLayers, IdLike, MaskIdx, OnResize, Painter, PixelRegion, Size,
+    ActiveData, Axis, DrawLayers, IdLike, MaskIdx, OnResize, Painter, PixelRegion, Remap, Size,
     StrongWidget, UiRegion, UiRsc, WidgetId, Widgets,
     util::{HashMap, HashSet, Vec2, forget_ref},
 };
@@ -183,38 +183,29 @@ impl UiRenderState {
             return Some(size);
         }
         // TODO: epsilon?
-        if old.size() == region.size() {
-            self.mov(id, old, region);
-            return Some(size);
+        if old.size() != region.size() && !self.reusable(id, region, rsc) {
+            return None;
         }
-        if self.reusable(id, region, rsc) {
-            // Its drawing stands; the new box is remapped into the primitives.
-            self.mov(id, old, region);
-            return Some(size);
-        }
-        None
+        // Its drawing stands, if the new box can be reached from the old one.
+        self.mov(id, &Remap::new(old, region)?);
+        Some(size)
     }
 
     /// Whether the widget can keep the drawing it has and be given `region`
     /// instead, asked one axis at a time: a change on an axis it does not
     /// depend on costs nothing, whatever it depends on elsewhere.
-    fn reusable(&self, id: WidgetId, mut region: UiRegion, rsc: &dyn UiRsc) -> bool {
+    fn reusable(&self, id: WidgetId, region: UiRegion, rsc: &dyn UiRsc) -> bool {
         let Some(active) = self.active.get(&id) else {
             return false;
         };
         let Some(widget) = rsc.widgets().get_dyn(id) else {
             return false;
         };
-        let mut old = active.region;
         [Axis::X, Axis::Y].into_iter().all(|axis| {
-            let offered = region.axis_mut(axis).len();
-            let had = old.axis_mut(axis).len();
+            let offered = region.axis(axis).len();
+            let had = active.region.axis(axis).len();
             match widget.on_resize(axis) {
-                // Remapping out of the old box only scales while that box
-                // had a relative extent; inside a fixed one every part became
-                // an offset from its start, which `mov` carries but cannot
-                // stretch.
-                OnResize::Scale => offered == had || had.rel != 0.0,
+                OnResize::Scale => true,
                 // `Translate` is not acted on yet, and cannot be until a
                 // drawing can sit somewhere other than its box. `region` is
                 // both the box a widget was given and the box its primitives
@@ -237,17 +228,17 @@ impl UiRenderState {
         })
     }
 
-    fn mov(&mut self, id: WidgetId, from: UiRegion, to: UiRegion) {
+    fn mov(&mut self, id: WidgetId, remap: &Remap) {
         let active = self.active.get_mut(&id).unwrap();
         for h in &active.primitives {
             let region = self.layers[h.layer].region_mut(h);
-            *region = region.outside(&from).within(&to);
+            *region = remap.apply(*region);
         }
-        active.region = active.region.outside(&from).within(&to);
+        active.region = remap.apply(active.region);
         // SAFETY: children cannot be recursive
         let children = unsafe { forget_ref(&active.children) };
         for child in children {
-            self.mov(*child, from, to);
+            self.mov(*child, remap);
         }
     }
 

core/src/util/math.rs

@@ -1,33 +1,21 @@
-use std::ops::*;
-
-pub const trait LerpUtil {
+pub const trait LerpUtil: Sized {
     fn lerp(self, from: Self, to: Self) -> Self;
-    fn lerp_inv(self, from: Self, to: Self) -> Self;
+    fn lerp_inv(self, from: Self, to: Self) -> Option<Self>;
 }
 
-pub const trait DivOr {
-    fn div_or(self, rhs: Self, other: Self) -> Self;
-}
-
-const impl DivOr for f32 {
-    fn div_or(self, rhs: Self, other: Self) -> Self {
-        let res = self / rhs;
-        if res.is_nan() { other } else { res }
-    }
-}
-
-const impl<
-    T: const Add<Output = T> + const Sub<Output = T> + const Mul<Output = T> + const DivOr + Copy,
-> LerpUtil for T
-{
+const impl LerpUtil for f32 {
     /// linear interpolation
     /// from * (1.0 - self) + to * self
     fn lerp(self, from: Self, to: Self) -> Self {
         from + (to - from) * self
     }
-    /// inverse of lerp
-    fn lerp_inv(self, from: Self, to: Self) -> Self {
-        (self - from).div_or(to - from, from)
+    /// inverse of lerp, and `None` where `from` and `to` are the same point:
+    /// every input lerps to it, so there is no one answer to come back to.
+    fn lerp_inv(self, from: Self, to: Self) -> Option<Self> {
+        match to == from {
+            true => None,
+            false => Some((self - from) / (to - from)),
+        }
     }
 }
 

core/src/util/vec2.rs

@@ -1,4 +1,4 @@
-use crate::util::{DivOr, impl_op};
+use crate::util::impl_op;
 use std::{hash::Hash, ops::*};
 
 #[repr(C)]
@@ -67,15 +67,6 @@ impl_op!(Vec2 Sub sub; x y);
 impl_op!(Vec2 Mul mul; x y);
 impl_op!(Vec2 Div div; x y);
 
-const impl DivOr for Vec2 {
-    fn div_or(self, rhs: Self, other: Self) -> Self {
-        Self {
-            x: self.x.div_or(rhs.x, other.x),
-            y: self.y.div_or(rhs.y, other.y),
-        }
-    }
-}
-
 impl Neg for Vec2 {
     type Output = Self;
 

tests/remap.rs

@@ -0,0 +1,27 @@
+//! What a drawing can be taken out of, and what it cannot.
+
+use iris::core::{Remap, UiRegion, UiScalar, UiSpan};
+
+/// A box `size` tall whose top is `rel` of the way down the window.
+fn fixed(rel: f32, size: f32) -> UiRegion {
+    UiRegion::new(
+        UiSpan::FULL,
+        UiSpan::new(UiScalar { rel, abs: 0.0 }, UiScalar { rel, abs: size }),
+    )
+}
+
+#[test]
+fn a_fixed_box_can_be_carried_but_not_stretched() {
+    let from = fixed(0.0, 164.0);
+    assert!(Remap::new(from, UiRegion::FULL).is_none());
+    assert!(Remap::new(from, fixed(0.5, 164.0)).is_some());
+    assert!(Remap::new(from, fixed(0.0, 98.0)).is_none());
+}
+
+#[test]
+fn a_relative_box_can_be_stretched_to_any_other() {
+    let remap = Remap::new(UiRegion::FULL, fixed(0.0, 98.0)).expect("relative boxes remap");
+    // A part that filled the window keeps filling what replaced it, which is
+    // exactly what `outside` could not say for a box of a fixed length.
+    assert_eq!(remap.apply(UiRegion::FULL), fixed(0.0, 98.0));
+}