Let a shader move the corners of the picture it wears (#79)

A shader could only say what colour a pixel has. Where the picture
is drawn was fixed to the four corners of its rectangle, so nothing
could wave, bend or wobble.

- The new node Vertex output takes x and y, in pixels of the
  picture, and moves every corner of the wearer's grid by them. The
  UVs stay with the corners, so the picture bends along.
- Subdivisions on that node says how fine the grid is: cells per
  axis, 1 to 64, 8 by default. 1 is the plain quad. A shader without
  the node keeps the quad every sprite shares.
- A graph holds one Vertex output at most. UV, Time, Property,
  Number and the math nodes may feed it, and one node may feed both
  outputs.
- Texture color, Texture alpha, Sample texture, Texture size and
  Color cannot feed it. The node says "Not available per corner"
  and the shader does not compile.
- Sprites, texts and the preview in the shader tab wear the grid.
  A nine-slice sprite and particles draw as if the node were not
  there.
- Picking, the selection frame, the size and colliders stay with
  the rectangle. A wearer with a Vertex output is never culled, as
  with Padding, and with Padding the grid covers the room around
  the picture too.
- tools/perf-shaders.mjs takes GM_PERF_SUBDIVISIONS to measure a
  grid against the plain quad.

Measured on stein2 (Intel HD 630), frames per second, one run per
row: at 800 sprites 58 with a shader on the quad, 46 with 8 cells,
41 with 32. Up to 400 sprites a grid hardly shows. Every sprite
holds its own grid.

Tests:
- Gate on melektaus-atx: 220 files, 3416 tests, CHECK EXIT 0.
- 15 new unit tests for the compiler and the grid.
- Four new e2e checks in modules 28 and 30: a fixed offset moves
  the picture, 8 cells bend only the lower half where 1 cell shears
  it all, Texture alpha is refused at the node, a text moves.
- e2e 28,30 on melektaus-atx: 110 checks, all pass.
- The e2e total of 1699 is counted (1695 + 4), the full suite did
  not run.
- No counter-probe, no screenshot. Not looked at: the preview, Time
  in the browser, flipped sprites, Padding together with the grid.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tools/e2e/28-shader.mjs

@@ -854,6 +854,77 @@ export async function shader(t) {
   );
   await shot('28-shader-padding-scene');
 
+  // 28l-iv. A Vertex output moves the corners of the sprite's grid (#79), in pixels of the picture:
+  //         16 of this 32-px one is half the sprite. A constant moves the whole picture; a cut on v
+  //         bends it only where the grid has corners, and with one cell there is just a shear.
+  const cornered = (cornerNodes, cornerEdges, subdivisions) =>
+    graph(
+      [
+        node('texel', 'ShaderTextureColor'),
+        node('out', 'ShaderOutput', { edge: 'transparent' }, 780, 0),
+        ...cornerNodes,
+        node('vout', 'ShaderVertexOutput', { subdivisions }, 780, 260),
+      ],
+      [edge('texel', 'color', 'out', 'color'), ...cornerEdges],
+    );
+  await cornered(
+    [node('by', 'ShaderNumber', { value: 16 }, 260, 260)],
+    [edge('by', 'value', 'vout', 'x')],
+    8,
+  );
+  const moved = {
+    left: await pixel(-0.3, -0.3),
+    right: await pixel(0.3, -0.3),
+    past: await pixel(0.8, -0.3),
+  };
+  check(
+    'a Vertex output fed 16 moves the picture half a sprite to the right, past its rectangle',
+    colourDistance(moved.left, LEFT) > 60 &&
+      colourDistance(moved.right, LEFT) < 12 &&
+      colourDistance(moved.past, RIGHT) < 12 &&
+      colourDistance(bare.left, LEFT) < 12,
+    { moved, bare },
+  );
+  const lowerHalf = async (subdivisions) => {
+    await cornered(
+      [
+        node('uv', 'ShaderUV', {}, 0, 260),
+        node('cut', 'ShaderStep', { edge: 0.5 }, 260, 260),
+        node('far', 'ShaderMultiply', { b: 16 }, 520, 260),
+      ],
+      [
+        edge('uv', 'v', 'cut', 'value'),
+        edge('cut', 'result', 'far', 'a'),
+        edge('far', 'result', 'vout', 'x'),
+      ],
+      subdivisions,
+    );
+    return { upper: await pixel(0.6, -0.2), lower: await pixel(0.8, 0.35) };
+  };
+  const bent = await lowerHalf(8);
+  const sheared = await lowerHalf(1);
+  await shot('28-shader-vertex-scene');
+  check(
+    'with 8 subdivisions only the lower half moves; with 1 there are four corners, and the upper half leans along',
+    colourDistance(bent.lower, RIGHT) < 12 &&
+      colourDistance(bent.upper, RIGHT) > 60 &&
+      colourDistance(sheared.upper, RIGHT) < 12,
+    { bent, sheared },
+  );
+  await cornered(
+    [node('opacity', 'ShaderTextureAlpha', {}, 260, 260)],
+    [edge('opacity', 'value', 'vout', 'x')],
+    8,
+  );
+  const perCorner = await json("__gm.shader.nodeProblem('vout')");
+  const perCornerReadout = await info();
+  check(
+    'what reads the picture cannot feed the Vertex output: the node says so, and the shader does not compile',
+    perCorner === 'Not available per corner: Texture alpha' &&
+      JSON.stringify(perCornerReadout).includes(perCorner),
+    { perCorner, perCornerReadout },
+  );
+
   // 28l-ii. The sprite wears a picture and a shader: both open from the object's menu, from the
   //         asset's menu and from the inspector, whose Texture and Shader labels are links (#221).
   const shadedProps = await json("__gm.state.project.assets.find((a) => a.id === 'shade-sprite').props");

tools/e2e/30-font.mjs

@@ -321,10 +321,25 @@ export async function font(t) {
       Math.abs(textRoomy.last - textTight.last - reach) <= 2,
     JSON.stringify({ textTight, textRoomy, reach }),
   );
+  // 30i-iii. A shader's Vertex output moves a text's corners as it does a sprite's (#79), in the
+  //          text's own units: six of them to the right, and the filled quad stands six further on.
+  await filled(0);
   await mutate(`
     const graph = ${shaderGraph};
-    graph.nodes = graph.nodes.filter((n) => n.id !== 'ft-red-full');
-    graph.edges = graph.edges.filter((e) => e.id !== 'ft-red-e2');
+    graph.nodes.push(${JSON.stringify(node('ft-red-by', 'ShaderNumber', 0, 320, { value: 6 }))});
+    graph.nodes.push(${JSON.stringify(node('ft-red-vout', 'ShaderVertexOutput', 260, 320, { subdivisions: 4 }))});
+    graph.edges.push(${JSON.stringify(edge('ft-red-e3', 'ft-red-by', 'value', 'ft-red-vout', 'x'))});`);
+  const textMoved = await redSpan();
+  check(
+    'a Vertex output fed 6 draws the text six units to the right of where it stands',
+    Math.abs(textMoved.first - textTight.first - reach) <= 2 &&
+      Math.abs(textMoved.last - textTight.last - reach) <= 2,
+    JSON.stringify({ textTight, textMoved, reach }),
+  );
+  await mutate(`
+    const graph = ${shaderGraph};
+    graph.nodes = graph.nodes.filter((n) => !['ft-red-full', 'ft-red-by', 'ft-red-vout'].includes(n.id));
+    graph.edges = graph.edges.filter((e) => !['ft-red-e2', 'ft-red-e3'].includes(e.id));
     Object.assign(graph.nodes.find((n) => n.id === 'ft-red-out').params, { edge: 'clamp', padding: 0 });`);
 
   // 30j. The game draws a text through the same picture, shader included. In front of everything: