fix(lambda-tiler): NZTM terrain been multiplied twice. BM-1122 (#3373)

### Motivation

Basemap terrain exaggeration for NZTM been multiplied twice.

![image](https://github.com/user-attachments/assets/4e7b4a77-431c-4f0e-be5d-206787ae2452)

![image](https://github.com/user-attachments/assets/e8a64789-7e70-4bb9-97f8-c8cac4e06e36)

### Modifications
We have manually multiplied the NZTM terrain exaggeration when
converting the style json earlier, however, we got default setting to
fix them as 4.4 in `DefaultExaggeration`, so we don't need to covert the
exaggeration twice to make it too large.

### Verification
Local test and unit test.

![image](https://github.com/user-attachments/assets/42f35f6f-6410-4ccd-87f6-c007f9faae7f)

Author: Wentao-Kuang

packages/lambda-tiler/src/routes/__tests__/tile.style.json.test.ts

@@ -2,7 +2,8 @@ import assert from 'node:assert';
 import { afterEach, before, beforeEach, describe, it } from 'node:test';
 
 import { ConfigProviderMemory, SourceRaster, StyleJson } from '@basemaps/config';
-import { Terrain } from '@basemaps/config/src/config/vector.style.js';
+import { DefaultExaggeration, Terrain } from '@basemaps/config/build/config/vector.style.js';
+import { Nztm2000QuadTms } from '@basemaps/geo';
 import { Env } from '@basemaps/shared';
 import { createSandbox } from 'sinon';
 
@@ -441,7 +442,7 @@ describe('/v1/styles', () => {
           },
         ],
         terrain: {
-          exaggeration: 1.1,
+          exaggeration: DefaultExaggeration[Nztm2000QuadTms.identifier],
         },
       },
     };

packages/lambda-tiler/src/routes/tile.style.json.ts

@@ -90,7 +90,7 @@ export interface StyleConfig {
 /**
  * Turn on the terrain setting in the style json
  */
-function setStyleTerrain(style: StyleJson, terrain: string, tileMatrix: TileMatrixSet): void {
+export function setStyleTerrain(style: StyleJson, terrain: string, tileMatrix: TileMatrixSet): void {
   const source = Object.keys(style.sources).find((s) => s === terrain);
   if (source == null) throw new LambdaHttpResponse(400, `Terrain: ${terrain} does not exists in the style source.`);
   style.terrain = {

packages/lambda-tiler/src/util/__test__/nztm.style.test.ts

@@ -2,7 +2,9 @@ import assert from 'node:assert';
 import { describe, it } from 'node:test';
 
 import { StyleJson } from '@basemaps/config';
+import { GoogleTms, Nztm2000QuadTms } from '@basemaps/geo';
 
+import { setStyleTerrain } from '../../routes/tile.style.json.js';
 import { convertStyleToNztmStyle } from '../nztm.style.js';
 
 describe('NZTM2000QuadStyle', () => {
@@ -25,9 +27,6 @@ describe('NZTM2000QuadStyle', () => {
 
     convertStyleToNztmStyle(baseStyle);
     assert.equal(baseStyle.terrain?.exaggeration, 1.1);
-
-    convertStyleToNztmStyle(baseStyle, false);
-    assert.equal(baseStyle.terrain?.exaggeration, 4.4);
   });
 
   it('should convert min/maxzooms', () => {
@@ -39,13 +38,24 @@ describe('NZTM2000QuadStyle', () => {
     assert.deepEqual(newStyle.layers[0], { minzoom: 3, maxzoom: 8, id: 'something', type: '' });
   });
 
-  it('should offset terrain', () => {
-    const newStyle = convertStyleToNztmStyle({
+  it('should not offset terrain for WebMecator', () => {
+    const testStyle: StyleJson = {
       ...fakeStyle,
-      terrain: { exaggeration: 1.1, source: 'abc' },
-    });
+      sources: { 'LINZ-Terrain': { type: 'raster-dem', tiles: ['https://example.com/{z}/{x}/{y}.png'] } },
+    };
+    setStyleTerrain(testStyle, 'LINZ-Terrain', GoogleTms);
+
+    assert.deepEqual(testStyle.terrain, { exaggeration: 1.2, source: 'LINZ-Terrain' });
+  });
+
+  it('should offset terrain for NZTM', () => {
+    const testStyle: StyleJson = {
+      ...fakeStyle,
+      sources: { 'LINZ-Terrain': { type: 'raster-dem', tiles: ['https://example.com/{z}/{x}/{y}.png'] } },
+    };
+    setStyleTerrain(testStyle, 'LINZ-Terrain', Nztm2000QuadTms);
 
-    assert.deepEqual(newStyle.terrain, { exaggeration: 4.4, source: 'abc' });
+    assert.deepEqual(testStyle.terrain, { exaggeration: 4.4, source: 'LINZ-Terrain' });
   });
 
   it('should convert stops inside of paint and layout', () => {

packages/lambda-tiler/src/util/nztm.style.ts

@@ -37,8 +37,5 @@ export function convertStyleToNztmStyle(inputStyle: StyleJson, clone: boolean =
     }
   }
 
-  /** Based on {@link DefaultExaggeration} offsetting by 2 two levels changes the exaggeration needed by approx 4x */
-  if (style.terrain) style.terrain.exaggeration = style.terrain.exaggeration * 4;
-
   return style;
 }