diff --git a/src/render/renderer.test.ts b/src/render/renderer.test.ts
new file mode 100644
index 0000000..68f2ec6
--- /dev/null
+++ b/src/render/renderer.test.ts
@@ -0,0 +1,39 @@
+import { describe, it, expect } from 'vitest';
+import { drawOverlay } from './renderer';
+import type { Segment, RenderStyle } from '../types';
+
+class FakeCtx {
+  calls: string[] = [];
+  strokeStyle = '';
+  lineWidth = 0;
+  beginPath() { this.calls.push('begin'); }
+  setLineDash(d: number[]) { this.calls.push(`dash:${d.length}`); }
+  moveTo(x: number, y: number) { this.calls.push(`move:${x},${y}`); }
+  lineTo(x: number, y: number) { this.calls.push(`line:${x},${y}`); }
+  stroke() { this.calls.push(`stroke:${this.strokeStyle}`); }
+}
+
+const STYLE: RenderStyle = { cutColor: '#cut', rapidColor: '#rapid', lineWidth: 2 };
+
+describe('drawOverlay', () => {
+  it('strokes a cut as a solid polyline in the cut colour', () => {
+    const ctx = new FakeCtx();
+    const segs: Segment[] = [{ kind: 'cut', points: [[0, 0], [5, 5], [10, 0]] }];
+    drawOverlay(ctx as unknown as CanvasRenderingContext2D, segs, STYLE);
+    expect(ctx.calls).toEqual(['begin', 'dash:0', 'move:0,0', 'line:5,5', 'line:10,0', 'stroke:#cut']);
+  });
+
+  it('strokes a rapid dashed in the rapid colour', () => {
+    const ctx = new FakeCtx();
+    const segs: Segment[] = [{ kind: 'rapid', points: [[0, 0], [5, 0]] }];
+    drawOverlay(ctx as unknown as CanvasRenderingContext2D, segs, STYLE);
+    expect(ctx.calls).toContain('dash:2');
+    expect(ctx.calls).toContain('stroke:#rapid');
+  });
+
+  it('skips degenerate segments', () => {
+    const ctx = new FakeCtx();
+    drawOverlay(ctx as unknown as CanvasRenderingContext2D, [{ kind: 'cut', points: [[1, 1]] }], STYLE);
+    expect(ctx.calls).toEqual([]);
+  });
+});
diff --git a/src/render/renderer.ts b/src/render/renderer.ts
new file mode 100644
index 0000000..0cf261c
--- /dev/null
+++ b/src/render/renderer.ts
@@ -0,0 +1,28 @@
+import type { Segment, RenderStyle } from '../types';
+
+/** Draw already-projected (image-pixel) segments onto a 2D context. */
+export function drawOverlay(
+  ctx: CanvasRenderingContext2D,
+  projected: Segment[],
+  style: RenderStyle,
+): void {
+  for (const seg of projected) {
+    if (seg.points.length < 2) continue;
+    ctx.beginPath();
+    ctx.setLineDash(seg.kind === 'rapid' ? [6, 4] : []);
+    ctx.strokeStyle = seg.kind === 'rapid' ? style.rapidColor : style.cutColor;
+    ctx.lineWidth = style.lineWidth;
+    const first = seg.points[0]!;
+    ctx.moveTo(first[0], first[1]);
+    for (let i = 1; i < seg.points.length; i++) {
+      ctx.lineTo(seg.points[i]![0], seg.points[i]![1]);
+    }
+    ctx.stroke();
+  }
+}
+
+/** Clear the whole canvas. */
+export function clearCanvas(ctx: CanvasRenderingContext2D, width: number, height: number): void {
+  ctx.setLineDash([]);
+  ctx.clearRect(0, 0, width, height);
+}