diff --git a/libs/lightbox/src/geometry.test.ts b/libs/lightbox/src/geometry.test.ts
new file mode 100644
index 0000000..82e19d2
--- /dev/null
+++ b/libs/lightbox/src/geometry.test.ts
@@ -0,0 +1,86 @@
+import { describe, it, expect } from 'vitest';
+import { fitCentered, transformFor, originalUrl, type Rect } from './geometry';
+
+describe('fitCentered', () => {
+  // 大图受 maxW=vw*0.92 / maxH=vh*0.88 约束,scale 取较小者
+  it('宽图被视口宽度卡住(横向受限)', () => {
+    // 2000x1000 in 1000x800: maxW=920, maxH=704
+    // scale = min(920/2000, 704/1000, 1) = min(0.46, 0.704, 1) = 0.46
+    const r = fitCentered(2000, 1000, 1000, 800);
+    expect(r.w).toBeCloseTo(920, 5);
+    expect(r.h).toBeCloseTo(460, 5);
+    expect(r.x).toBeCloseTo((1000 - 920) / 2, 5); // 40
+    expect(r.y).toBeCloseTo((800 - 460) / 2, 5); // 170
+  });
+
+  it('高图被视口高度卡住(纵向受限)', () => {
+    // 1000x2000 in 1000x800: maxW=920, maxH=704
+    // scale = min(920/1000, 704/2000, 1) = min(0.92, 0.352, 1) = 0.352
+    const r = fitCentered(1000, 2000, 1000, 800);
+    expect(r.w).toBeCloseTo(352, 5);
+    expect(r.h).toBeCloseTo(704, 5);
+  });
+
+  it('小图不被放大(scale 钳到 1)', () => {
+    // 300x200 in 1000x800: scale = min(920/300, 704/200, 1) = 1
+    const r = fitCentered(300, 200, 1000, 800);
+    expect(r.w).toBe(300);
+    expect(r.h).toBe(200);
+    expect(r.x).toBeCloseTo((1000 - 300) / 2, 5); // 350
+    expect(r.y).toBeCloseTo((800 - 200) / 2, 5); // 300
+  });
+
+  it('正方形图按 maxW/maxH 中较小者缩放', () => {
+    // 1000x1000 in 1000x800: maxW=920, maxH=704
+    // scale = min(0.92, 0.704, 1) = 0.704
+    const r = fitCentered(1000, 1000, 1000, 800);
+    expect(r.w).toBeCloseTo(704, 5);
+    expect(r.h).toBeCloseTo(704, 5);
+  });
+});
+
+describe('transformFor', () => {
+  it('居中态(base=target):scale=1,translate 到目标左上角', () => {
+    const target: Rect = { x: 40, y: 170, w: 920, h: 460 };
+    const t = transformFor(target, 920, 460);
+    expect(t).toBe('translate(40px,170px) scale(1,1)');
+  });
+
+  it('缩小态(rect 比 base 小):scale<1', () => {
+    // 原图位置小,base=居中尺寸 920x460
+    const origin: Rect = { x: 100, y: 500, w: 400, h: 200 };
+    const t = transformFor(origin, 920, 460);
+    // 400/920 = 0.43478260869565216（JS 浮点完整精度）
+    expect(t).toBe('translate(100px,500px) scale(0.43478260869565216,0.43478260869565216)');
+  });
+
+  it('baseW=0 守卫:scale 守卫为 1(不产生 NaN/Infinity)', () => {
+    const rect: Rect = { x: 0, y: 0, w: 0, h: 0 };
+    const t = transformFor(rect, 0, 0);
+    expect(t).toBe('translate(0px,0px) scale(1,1)');
+  });
+
+  it('字符串格式为 translate(Xpx,Ypx) scale(SX,SY)', () => {
+    const rect: Rect = { x: 10, y: 20, w: 100, h: 50 };
+    const t = transformFor(rect, 200, 100);
+    expect(t).toMatch(/^translate\(\d+(\.\d+)?px,\d+(\.\d+)?px\) scale\(\d+(\.\d+)?,\d+(\.\d+)?\)$/);
+  });
+});
+
+describe('originalUrl', () => {
+  it('去 query string', () => {
+    expect(originalUrl('/uploads/x.webp?w=800')).toBe('/uploads/x.webp');
+  });
+
+  it('无 query 原样返回', () => {
+    expect(originalUrl('/uploads/x.webp')).toBe('/uploads/x.webp');
+  });
+
+  it('null 输入返回空串', () => {
+    expect(originalUrl(null)).toBe('');
+  });
+
+  it('空串输入返回空串', () => {
+    expect(originalUrl('')).toBe('');
+  });
+});
diff --git a/libs/lightbox/src/geometry.ts b/libs/lightbox/src/geometry.ts
new file mode 100644
index 0000000..7c1c64c
--- /dev/null
+++ b/libs/lightbox/src/geometry.ts
@@ -0,0 +1,48 @@
+export interface Rect {
+  x: number;
+  y: number;
+  w: number;
+  h: number;
+}
+
+// 计算图片在视口居中、contain 适配后的目标 rect。
+// naturalW/H: 图片真实像素尺寸；vw/vh: 视口尺寸。
+export function fitCentered(naturalW: number, naturalH: number, vw: number, vh: number): Rect {
+  var maxW = vw * 0.92;
+  var maxH = vh * 0.88;
+  var scale = Math.min(maxW / naturalW, maxH / naturalH, 1);
+  var w = naturalW * scale;
+  var h = naturalH * scale;
+  return {
+    x: (vw - w) / 2,
+    y: (vh - h) / 2,
+    w: w,
+    h: h,
+  };
+}
+
+// 把目标 rect 转成 transform 字符串。
+// baseW/baseH 是 img 元素的布局尺寸（=居中目标尺寸），scale 相对它缩放。
+// transform-origin 为 top left（见 CSS），translate 到 rect 左上角后 scale。
+// - 居中态：scale=1（base 就是居中尺寸）
+// - originRect 态：scale = originRect.w / base.w（缩小）
+export function transformFor(rect: Rect, baseW: number, baseH: number): string {
+  var sx = baseW > 0 ? rect.w / baseW : 1;
+  var sy = baseH > 0 ? rect.h / baseH : 1;
+  return (
+    "translate(" +
+    rect.x +
+    "px," +
+    rect.y +
+    "px) scale(" +
+    sx +
+    "," +
+    sy +
+    ")"
+  );
+}
+
+// 原图 URL = data-src 去 query。data-src 形如 "/uploads/x.webp?w=800"。
+export function originalUrl(dataSrc: string | null): string {
+  return (dataSrc || "").split("?")[0];
+}