diff --git a/src/app/calibration-ui.test.ts b/src/app/calibration-ui.test.ts
index 0f42a38..bae2934 100644
--- a/src/app/calibration-ui.test.ts
+++ b/src/app/calibration-ui.test.ts
@@ -1,22 +1,22 @@
 import { describe, it, expect } from 'vitest';
 import { residuals } from './calibration-ui';
-import { estimateHomography } from '../geometry/homography';
+import { estimatePolyWarp } from '../geometry/polywarp';
 import type { Vec2 } from '../types';
 
 describe('calibration residuals', () => {
-  it('reports near-zero error for a clean fit', () => {
+  it('reports near-zero error for a clean degree-1 fit', () => {
     const machine: Vec2[] = [[0, 0], [100, 0], [100, 100], [0, 100]];
-    const image: Vec2[] = [[10, 10], [210, 12], [208, 210], [8, 208]];
-    const H = estimateHomography(machine, image);
-    const errs = residuals(H, machine, image);
-    expect(Math.max(...errs)).toBeLessThan(1e-6);
+    const image: Vec2[] = machine.map((p): Vec2 => [p[0] * 0.5 + 5, p[1] * 0.5 + 5]);
+    const w = estimatePolyWarp(machine, image, 1);
+    const errs = residuals(w, machine, image);
+    expect(Math.max(...errs)).toBeLessThan(1e-4);
   });
 
   it('flags a mismatched point with a large residual', () => {
-    const machine: Vec2[] = [[0, 0], [100, 0], [100, 100], [0, 100], [50, 50]];
-    const image: Vec2[] = [[0, 0], [100, 0], [100, 100], [0, 100], [80, 20]]; // last is wrong
-    const H = estimateHomography(machine, image);
-    const errs = residuals(H, machine, image);
-    expect(errs[4]!).toBeGreaterThan(5);
+    const machine: Vec2[] = [[0, 0], [100, 0], [100, 100], [0, 100], [50, 50], [25, 75], [75, 25]];
+    const image: Vec2[] = [[0, 0], [50, 0], [50, 50], [0, 50], [25, 25], [12.5, 37.5], [90, 5]]; // last is wrong
+    const w = estimatePolyWarp(machine, image, 1);
+    const errs = residuals(w, machine, image);
+    expect(errs[6]!).toBeGreaterThan(5);
   });
 });
diff --git a/src/app/calibration-ui.ts b/src/app/calibration-ui.ts
index 68ed23a..554974b 100644
--- a/src/app/calibration-ui.ts
+++ b/src/app/calibration-ui.ts
@@ -1,11 +1,11 @@
-import type { Vec2, Mat3 } from '../types';
-import { estimateHomography, applyHomography } from '../geometry/homography';
+import type { Vec2, PolyWarp } from '../types';
+import { estimatePolyWarp, applyPolyWarp } from '../geometry/polywarp';
 
-/** Per-point reprojection error in pixels: |H·machine − image|. */
-export function residuals(H: Mat3, machine: Vec2[], image: Vec2[]): number[] {
+/** Per-point reprojection error in normalized units: |warp(machine) − image|. */
+export function residuals(warp: PolyWarp, machine: Vec2[], image: Vec2[]): number[] {
   if (machine.length !== image.length) throw new Error('residuals: machine/image length mismatch');
   return machine.map((m, i) => {
-    const p = applyHomography(H, m);
+    const p = applyPolyWarp(warp, m);
     return Math.hypot(p[0] - image[i]![0], p[1] - image[i]![1]);
   });
 }
@@ -18,16 +18,15 @@ interface CalibPoint {
 export interface CalibrationDeps {
   panel: HTMLElement;
   overlay: HTMLCanvasElement;
-  onHomography: (H: Mat3, points: CalibPoint[]) => void;
+  onWarp: (w: PolyWarp, points: CalibPoint[]) => void;
 }
 
 /**
  * Renders the calibration panel. Flow: enter machine X/Y → click "Click point in video" →
- * click the spindle tip in the video → repeat ≥4× → "Compute".
+ * click the spindle tip in the video → repeat ≥10× → choose degree → "Compute".
  *
- * Captured image points and the resulting homography are in normalized [0,1] camera-frame
- * coordinates (machine-mm → normalized image), so they are display-size independent.
- * The JSON output structure stays the same (imagePoints now hold normalized values).
+ * Image points and the resulting warp are in normalized [0,1] camera-frame coordinates
+ * (machine-mm ↔ normalized image), so they are display-size independent.
  */
 export function mountCalibration(deps: CalibrationDeps): void {
   const { panel, overlay } = deps;
@@ -36,7 +35,7 @@ export function mountCalibration(deps: CalibrationDeps): void {
 
   panel.innerHTML = `
     <h2>Calibration</h2>
-    <div class="row"><small>Jog the spindle to a known X/Y, enter it, then click the tip in the video.</small></div>
+    <div class="row"><small>Jog the spindle to a known X/Y, enter it, then click the tip in the video. ≥10 points (degree 3); spread them out incl. corners.</small></div>
     <div class="row">
       X <input id="cal-x" type="number" step="0.1" />
       Y <input id="cal-y" type="number" step="0.1" />
@@ -44,7 +43,8 @@ export function mountCalibration(deps: CalibrationDeps): void {
     </div>
     <ul id="cal-list"></ul>
     <div class="row">
-      <button id="cal-compute">Compute homography</button>
+      Degree <select id="cal-degree"><option value="2">2</option><option value="3" selected>3</option></select>
+      <button id="cal-compute">Compute warp</button>
       <button id="cal-clear">Clear</button>
     </div>
     <textarea id="cal-json" rows="6" style="width:100%" readonly placeholder="Calibration JSON appears here"></textarea>
@@ -54,6 +54,7 @@ export function mountCalibration(deps: CalibrationDeps): void {
   const yEl = panel.querySelector('#cal-y') as HTMLInputElement;
   const armBtn = panel.querySelector('#cal-arm') as HTMLButtonElement;
   const list = panel.querySelector('#cal-list') as HTMLUListElement;
+  const degreeEl = panel.querySelector('#cal-degree') as HTMLSelectElement;
   const jsonEl = panel.querySelector('#cal-json') as HTMLTextAreaElement;
 
   const renderList = (errs?: number[]) => {
@@ -74,8 +75,6 @@ export function mountCalibration(deps: CalibrationDeps): void {
   overlay.addEventListener('click', (ev) => {
     if (!pendingMachine || !overlay.classList.contains('interactive')) return;
     const rect = overlay.getBoundingClientRect();
-    // Store normalized [0,1] image coords (fraction of the displayed camera frame).
-    // This makes the calibration independent of display/canvas size.
     const px: Vec2 = [
       (ev.clientX - rect.left) / rect.width,
       (ev.clientY - rect.top) / rect.height,
@@ -93,24 +92,28 @@ export function mountCalibration(deps: CalibrationDeps): void {
   });
 
   (panel.querySelector('#cal-compute') as HTMLButtonElement).addEventListener('click', () => {
-    if (points.length < 4) {
-      jsonEl.value = 'Need at least 4 points.';
+    const degree = parseInt(degreeEl.value, 10);
+    const need = ((degree + 1) * (degree + 2)) / 2;
+    if (points.length < need) {
+      jsonEl.value = `Need at least ${need} points for degree ${degree}.`;
       return;
     }
     const machine = points.map((p) => p.machine);
     const image = points.map((p) => p.image);
-    const H = estimateHomography(machine, image);
-    // Per-axis pixel residual (normalized error scaled by canvas width/height) — used only for misclick display.
+    let warp: PolyWarp;
+    try {
+      warp = estimatePolyWarp(machine, image, degree);
+    } catch (e) {
+      jsonEl.value = `Fit failed: ${(e as Error).message}`;
+      return;
+    }
+    // Per-point pixel residual (normalized error scaled by canvas size) — for misclick display.
     const errsPx = machine.map((m, i) => {
-      const p = applyHomography(H, m);
+      const p = applyPolyWarp(warp, m);
       return Math.hypot((p[0] - image[i]![0]) * overlay.width, (p[1] - image[i]![1]) * overlay.height);
     });
     renderList(errsPx);
-    jsonEl.value = JSON.stringify(
-      { imagePoints: image, machinePoints: machine, homography: H },
-      null,
-      2,
-    );
-    deps.onHomography(H, [...points]);
+    jsonEl.value = JSON.stringify({ imagePoints: image, machinePoints: machine, warp }, null, 2);
+    deps.onWarp(warp, [...points]);
   });
 }