diff --git a/src/geometry/transform.test.ts b/src/geometry/transform.test.ts
index 1617c98..8b75e6a 100644
--- a/src/geometry/transform.test.ts
+++ b/src/geometry/transform.test.ts
@@ -1,5 +1,5 @@
 import { describe, it, expect } from 'vitest';
-import { applyAlignment, projectSegments, imageToMachine, alignmentFromOrigin } from './transform';
+import { applyAlignment, projectSegments, imageToMachine, alignmentFromOrigin, subdivideSegment } from './transform';
 import { estimatePolyWarp } from './polywarp';
 import type { Vec2, Segment, Alignment, PolyWarp } from '../types';
 
@@ -37,4 +37,36 @@ describe('transform', () => {
     const a = alignmentFromOrigin([7, 9], 0);
     expect(close(applyAlignment(a, [0, 0]), [7, 9])).toBe(true);
   });
+
+  it('subdivideSegment splits a long edge into <=stepMm pieces, preserving endpoints', () => {
+    const seg: Segment = { kind: 'cut', points: [[0, 0], [100, 0]] };
+    const out = subdivideSegment(seg, 25);
+    expect(out.points.length).toBe(5); // 0,25,50,75,100
+    expect(close(out.points[0]!, [0, 0])).toBe(true);
+    expect(close(out.points[4]!, [100, 0])).toBe(true);
+    expect(close(out.points[2]!, [50, 0])).toBe(true);
+    expect(out.kind).toBe('cut');
+  });
+
+  it('subdivideSegment leaves a short edge as just its endpoints', () => {
+    const out = subdivideSegment({ kind: 'cut', points: [[0, 0], [5, 0]] }, 25);
+    expect(out.points.length).toBe(2);
+  });
+
+  it('projectSegments subdivides straight moves so they follow the warp curvature', () => {
+    // A warp where straight machine lines bow in image-y: image = (x/100, y/100 + 0.3·s·(1−s)), s=x/100.
+    const grid: Vec2[] = [[0, 0], [100, 0], [100, 100], [0, 100], [50, 50], [50, 0], [0, 50]];
+    const curved = (p: Vec2): Vec2 => {
+      const s = p[0] / 100;
+      return [s, p[1] / 100 + 0.3 * s * (1 - s)];
+    };
+    const warp = estimatePolyWarp(grid, grid.map(curved), 2);
+    const a: Alignment = { tx: 0, ty: 0, rot: 0 };
+    const out = projectSegments([{ kind: 'cut', points: [[0, 0], [100, 0]] }], a, warp);
+    // The single straight move must become a multi-vertex polyline...
+    expect(out[0]!.points.length).toBeGreaterThan(2);
+    // ...whose interior bows well away from the straight chord (endpoints both have y≈0).
+    const maxY = Math.max(...out[0]!.points.map((p) => Math.abs(p[1])));
+    expect(maxY).toBeGreaterThan(0.05);
+  });
 });
diff --git a/src/geometry/transform.ts b/src/geometry/transform.ts
index ea73451..21c8e37 100644
--- a/src/geometry/transform.ts
+++ b/src/geometry/transform.ts
@@ -1,6 +1,15 @@
 import type { Vec2, Segment, Alignment, PolyWarp } from '../types';
 import { applyPolyWarp, applyPolyWarpInverse } from './polywarp';
 
+/**
+ * Max length (machine mm) of a sub-edge before the warp is applied. The polynomial warp
+ * bends a path only at its vertices, so a straight 2-point move would render as a straight
+ * chord — hiding the lens curvature. Resampling long edges to this step makes the warped
+ * polyline follow the curve. 20 mm keeps the per-sub-edge deviation well under a pixel even
+ * on the most strongly-bowed lines, while leaving already-short moves (most toolpaths) untouched.
+ */
+const SUBDIVIDE_STEP_MM = 20;
+
 /** Apply per-job alignment to a point: rotate by rot, then translate by (tx,ty). */
 export function applyAlignment(a: Alignment, p: Vec2): Vec2 {
   const c = Math.cos(a.rot);
@@ -8,11 +17,43 @@ export function applyAlignment(a: Alignment, p: Vec2): Vec2 {
   return [a.tx + c * p[0] - s * p[1], a.ty + s * p[0] + c * p[1]];
 }
 
-/** Project work-coordinate segments to image: work → (alignment) → machine → (warp) → image. */
-export function projectSegments(segments: Segment[], a: Alignment, warp: PolyWarp): Segment[] {
+/**
+ * Resample a polyline (work mm) so no sub-edge exceeds `stepMm`. Endpoints and existing
+ * vertices are preserved; edges already shorter than the step are left as-is. This is what
+ * lets the nonlinear warp curve a straight machine move instead of drawing a chord.
+ */
+export function subdivideSegment(seg: Segment, stepMm: number = SUBDIVIDE_STEP_MM): Segment {
+  const src = seg.points;
+  if (src.length < 2) return seg;
+  const out: Vec2[] = [];
+  for (let i = 0; i < src.length - 1; i++) {
+    const a = src[i]!;
+    const b = src[i + 1]!;
+    const len = Math.hypot(b[0] - a[0], b[1] - a[1]);
+    const n = Math.max(1, Math.ceil(len / stepMm));
+    for (let k = 0; k < n; k++) {
+      const t = k / n;
+      out.push([a[0] + (b[0] - a[0]) * t, a[1] + (b[1] - a[1]) * t]);
+    }
+  }
+  out.push(src[src.length - 1]!);
+  return { kind: seg.kind, points: out };
+}
+
+/**
+ * Project work-coordinate segments to image: work → (subdivide) → (alignment) → machine →
+ * (warp) → image. Subdivision happens in work space so the warp can bend each straight move
+ * along the camera's distortion instead of collapsing it to a chord.
+ */
+export function projectSegments(
+  segments: Segment[],
+  a: Alignment,
+  warp: PolyWarp,
+  stepMm: number = SUBDIVIDE_STEP_MM,
+): Segment[] {
   return segments.map((seg) => ({
     kind: seg.kind,
-    points: seg.points.map((p) => applyPolyWarp(warp, applyAlignment(a, p))),
+    points: subdivideSegment(seg, stepMm).points.map((p) => applyPolyWarp(warp, applyAlignment(a, p))),
   }));
 }