diff --git a/src/app/state.test.ts b/src/app/state.test.ts
index 73bb312..4dbacd3 100644
--- a/src/app/state.test.ts
+++ b/src/app/state.test.ts
@@ -1,8 +1,11 @@
 import { describe, it, expect } from 'vitest';
 import { createState } from './state';
-import type { Mat3 } from '../types';
+import { estimatePolyWarp } from '../geometry/polywarp';
+import type { Vec2 } from '../types';
 
-const IDENT: Mat3 = [1, 0, 0, 0, 1, 0, 0, 0, 1];
+// Identity warp: image == machine.
+const square: Vec2[] = [[0, 0], [10, 0], [10, 10], [0, 10]];
+const IDENT = estimatePolyWarp(square, square, 1);
 
 describe('app state', () => {
   it('starts with no segments and a zero alignment', () => {
@@ -20,12 +23,12 @@ describe('app state', () => {
 
   it('projected() returns image-space segments when calibrated', () => {
     const s = createState();
-    s.setHomography(IDENT);
+    s.setWarp(IDENT);
     s.loadGcode('G21 G90\nG1 X10 Y0');
     s.alignment.tx = 2;
     const proj = s.projected();
-    expect(proj[0]!.points[0]).toEqual([2, 0]);
-    expect(proj[0]!.points[1]).toEqual([12, 0]);
+    expect(proj[0]!.points[0]![0]).toBeCloseTo(2, 4);
+    expect(proj[0]!.points[1]![0]).toBeCloseTo(12, 4);
   });
 
   it('projected() returns [] when not calibrated', () => {
diff --git a/src/app/state.ts b/src/app/state.ts
index b08f67c..c57f65a 100644
--- a/src/app/state.ts
+++ b/src/app/state.ts
@@ -1,13 +1,13 @@
-import type { Segment, Alignment, Mat3 } from '../types';
+import type { Segment, Alignment, PolyWarp } from '../types';
 import { parseGcode } from '../gcode/parser';
 import { projectSegments } from '../geometry/transform';
 
 export interface AppState {
   segments: Segment[];
   alignment: Alignment;
-  homography: Mat3 | null;
+  warp: PolyWarp | null;
   loadGcode(text: string): string[];
-  setHomography(H: Mat3 | null): void;
+  setWarp(w: PolyWarp | null): void;
   projected(): Segment[];
 }
 
@@ -15,18 +15,18 @@ export function createState(): AppState {
   const state: AppState = {
     segments: [],
     alignment: { tx: 0, ty: 0, rot: 0 },
-    homography: null,
+    warp: null,
     loadGcode(text: string): string[] {
       const { segments, warnings } = parseGcode(text);
       state.segments = segments;
       return warnings;
     },
-    setHomography(H: Mat3 | null): void {
-      state.homography = H;
+    setWarp(w: PolyWarp | null): void {
+      state.warp = w;
     },
     projected(): Segment[] {
-      if (!state.homography) return [];
-      return projectSegments(state.segments, state.alignment, state.homography);
+      if (!state.warp) return [];
+      return projectSegments(state.segments, state.alignment, state.warp);
     },
   };
   return state;