1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
import AxisAlignedBoundingBox from "./AxisAlignedBoundingBox.js";
import BoundingSphere from "./BoundingSphere.js";
import Cartesian2 from "./Cartesian2.js";
import Cartesian3 from "./Cartesian3.js";
import defaultValue from "./defaultValue.js";
import defined from "./defined.js";
import DeveloperError from "./DeveloperError.js";
import Ellipsoid from "./Ellipsoid.js";
import EllipsoidalOccluder from "./EllipsoidalOccluder.js";
import CesiumMath from "./Math.js";
import Matrix4 from "./Matrix4.js";
import OrientedBoundingBox from "./OrientedBoundingBox.js";
import Rectangle from "./Rectangle.js";
import TerrainEncoding from "./TerrainEncoding.js";
import Transforms from "./Transforms.js";
import WebMercatorProjection from "./WebMercatorProjection.js";
/**
* Contains functions to create a mesh from a heightmap image.
*
* @namespace HeightmapTessellator
*
* @private
*/
var HeightmapTessellator = {};
/**
* The default structure of a heightmap, as given to {@link HeightmapTessellator.computeVertices}.
*
* @constant
*/
HeightmapTessellator.DEFAULT_STRUCTURE = Object.freeze({
heightScale: 1.0,
heightOffset: 0.0,
elementsPerHeight: 1,
stride: 1,
elementMultiplier: 256.0,
isBigEndian: false,
});
var cartesian3Scratch = new Cartesian3();
var matrix4Scratch = new Matrix4();
var minimumScratch = new Cartesian3();
var maximumScratch = new Cartesian3();
/**
* Fills an array of vertices from a heightmap image.
*
* @param {Object} options Object with the following properties:
* @param {Int8Array|Uint8Array|Int16Array|Uint16Array|Int32Array|Uint32Array|Float32Array|Float64Array} options.heightmap The heightmap to tessellate.
* @param {Number} options.width The width of the heightmap, in height samples.
* @param {Number} options.height The height of the heightmap, in height samples.
* @param {Number} options.skirtHeight The height of skirts to drape at the edges of the heightmap.
* @param {Rectangle} options.nativeRectangle A rectangle in the native coordinates of the heightmap's projection. For
* a heightmap with a geographic projection, this is degrees. For the web mercator
* projection, this is meters.
* @param {Number} [options.exaggeration=1.0] The scale used to exaggerate the terrain.
* @param {Number} [options.exaggerationRelativeHeight=0.0] The height from which terrain is exaggerated.
* @param {Rectangle} [options.rectangle] The rectangle covered by the heightmap, in geodetic coordinates with north, south, east and
* west properties in radians. Either rectangle or nativeRectangle must be provided. If both
* are provided, they're assumed to be consistent.
* @param {Boolean} [options.isGeographic=true] True if the heightmap uses a {@link GeographicProjection}, or false if it uses
* a {@link WebMercatorProjection}.
* @param {Cartesian3} [options.relativeToCenter=Cartesian3.ZERO] The positions will be computed as <code>Cartesian3.subtract(worldPosition, relativeToCenter)</code>.
* @param {Ellipsoid} [options.ellipsoid=Ellipsoid.WGS84] The ellipsoid to which the heightmap applies.
* @param {Object} [options.structure] An object describing the structure of the height data.
* @param {Number} [options.structure.heightScale=1.0] The factor by which to multiply height samples in order to obtain
* the height above the heightOffset, in meters. The heightOffset is added to the resulting
* height after multiplying by the scale.
* @param {Number} [options.structure.heightOffset=0.0] The offset to add to the scaled height to obtain the final
* height in meters. The offset is added after the height sample is multiplied by the
* heightScale.
* @param {Number} [options.structure.elementsPerHeight=1] The number of elements in the buffer that make up a single height
* sample. This is usually 1, indicating that each element is a separate height sample. If
* it is greater than 1, that number of elements together form the height sample, which is
* computed according to the structure.elementMultiplier and structure.isBigEndian properties.
* @param {Number} [options.structure.stride=1] The number of elements to skip to get from the first element of
* one height to the first element of the next height.
* @param {Number} [options.structure.elementMultiplier=256.0] The multiplier used to compute the height value when the
* stride property is greater than 1. For example, if the stride is 4 and the strideMultiplier
* is 256, the height is computed as follows:
* `height = buffer[index] + buffer[index + 1] * 256 + buffer[index + 2] * 256 * 256 + buffer[index + 3] * 256 * 256 * 256`
* This is assuming that the isBigEndian property is false. If it is true, the order of the
* elements is reversed.
* @param {Number} [options.structure.lowestEncodedHeight] The lowest value that can be stored in the height buffer. Any heights that are lower
* than this value after encoding with the `heightScale` and `heightOffset` are clamped to this value. For example, if the height
* buffer is a `Uint16Array`, this value should be 0 because a `Uint16Array` cannot store negative numbers. If this parameter is
* not specified, no minimum value is enforced.
* @param {Number} [options.structure.highestEncodedHeight] The highest value that can be stored in the height buffer. Any heights that are higher
* than this value after encoding with the `heightScale` and `heightOffset` are clamped to this value. For example, if the height
* buffer is a `Uint16Array`, this value should be `256 * 256 - 1` or 65535 because a `Uint16Array` cannot store numbers larger
* than 65535. If this parameter is not specified, no maximum value is enforced.
* @param {Boolean} [options.structure.isBigEndian=false] Indicates endianness of the elements in the buffer when the
* stride property is greater than 1. If this property is false, the first element is the
* low-order element. If it is true, the first element is the high-order element.
*
* @example
* var width = 5;
* var height = 5;
* var statistics = Cesium.HeightmapTessellator.computeVertices({
* heightmap : [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0],
* width : width,
* height : height,
* skirtHeight : 0.0,
* nativeRectangle : {
* west : 10.0,
* east : 20.0,
* south : 30.0,
* north : 40.0
* }
* });
*
* var encoding = statistics.encoding;
* var position = encoding.decodePosition(statistics.vertices, index);
*/
HeightmapTessellator.computeVertices = function (options) {
//>>includeStart('debug', pragmas.debug);
if (!defined(options) || !defined(options.heightmap)) {
throw new DeveloperError("options.heightmap is required.");
}
if (!defined(options.width) || !defined(options.height)) {
throw new DeveloperError("options.width and options.height are required.");
}
if (!defined(options.nativeRectangle)) {
throw new DeveloperError("options.nativeRectangle is required.");
}
if (!defined(options.skirtHeight)) {
throw new DeveloperError("options.skirtHeight is required.");
}
//>>includeEnd('debug');
// This function tends to be a performance hotspot for terrain rendering,
// so it employs a lot of inlining and unrolling as an optimization.
// In particular, the functionality of Ellipsoid.cartographicToCartesian
// is inlined.
var cos = Math.cos;
var sin = Math.sin;
var sqrt = Math.sqrt;
var atan = Math.atan;
var exp = Math.exp;
var piOverTwo = CesiumMath.PI_OVER_TWO;
var toRadians = CesiumMath.toRadians;
var heightmap = options.heightmap;
var width = options.width;
var height = options.height;
var skirtHeight = options.skirtHeight;
var hasSkirts = skirtHeight > 0.0;
var isGeographic = defaultValue(options.isGeographic, true);
var ellipsoid = defaultValue(options.ellipsoid, Ellipsoid.WGS84);
var oneOverGlobeSemimajorAxis = 1.0 / ellipsoid.maximumRadius;
var nativeRectangle = Rectangle.clone(options.nativeRectangle);
var rectangle = Rectangle.clone(options.rectangle);
var geographicWest;
var geographicSouth;
var geographicEast;
var geographicNorth;
if (!defined(rectangle)) {
if (isGeographic) {
geographicWest = toRadians(nativeRectangle.west);
geographicSouth = toRadians(nativeRectangle.south);
geographicEast = toRadians(nativeRectangle.east);
geographicNorth = toRadians(nativeRectangle.north);
} else {
geographicWest = nativeRectangle.west * oneOverGlobeSemimajorAxis;
geographicSouth =
piOverTwo -
2.0 * atan(exp(-nativeRectangle.south * oneOverGlobeSemimajorAxis));
geographicEast = nativeRectangle.east * oneOverGlobeSemimajorAxis;
geographicNorth =
piOverTwo -
2.0 * atan(exp(-nativeRectangle.north * oneOverGlobeSemimajorAxis));
}
} else {
geographicWest = rectangle.west;
geographicSouth = rectangle.south;
geographicEast = rectangle.east;
geographicNorth = rectangle.north;
}
var relativeToCenter = options.relativeToCenter;
var hasRelativeToCenter = defined(relativeToCenter);
relativeToCenter = hasRelativeToCenter ? relativeToCenter : Cartesian3.ZERO;
var includeWebMercatorT = defaultValue(options.includeWebMercatorT, false);
var exaggeration = defaultValue(options.exaggeration, 1.0);
var exaggerationRelativeHeight = defaultValue(
options.exaggerationRelativeHeight,
0.0
);
var hasExaggeration = exaggeration !== 1.0;
var includeGeodeticSurfaceNormals = hasExaggeration;
var structure = defaultValue(
options.structure,
HeightmapTessellator.DEFAULT_STRUCTURE
);
var heightScale = defaultValue(
structure.heightScale,
HeightmapTessellator.DEFAULT_STRUCTURE.heightScale
);
var heightOffset = defaultValue(
structure.heightOffset,
HeightmapTessellator.DEFAULT_STRUCTURE.heightOffset
);
var elementsPerHeight = defaultValue(
structure.elementsPerHeight,
HeightmapTessellator.DEFAULT_STRUCTURE.elementsPerHeight
);
var stride = defaultValue(
structure.stride,
HeightmapTessellator.DEFAULT_STRUCTURE.stride
);
var elementMultiplier = defaultValue(
structure.elementMultiplier,
HeightmapTessellator.DEFAULT_STRUCTURE.elementMultiplier
);
var isBigEndian = defaultValue(
structure.isBigEndian,
HeightmapTessellator.DEFAULT_STRUCTURE.isBigEndian
);
var rectangleWidth = Rectangle.computeWidth(nativeRectangle);
var rectangleHeight = Rectangle.computeHeight(nativeRectangle);
var granularityX = rectangleWidth / (width - 1);
var granularityY = rectangleHeight / (height - 1);
if (!isGeographic) {
rectangleWidth *= oneOverGlobeSemimajorAxis;
rectangleHeight *= oneOverGlobeSemimajorAxis;
}
var radiiSquared = ellipsoid.radiiSquared;
var radiiSquaredX = radiiSquared.x;
var radiiSquaredY = radiiSquared.y;
var radiiSquaredZ = radiiSquared.z;
var minimumHeight = 65536.0;
var maximumHeight = -65536.0;
var fromENU = Transforms.eastNorthUpToFixedFrame(relativeToCenter, ellipsoid);
var toENU = Matrix4.inverseTransformation(fromENU, matrix4Scratch);
var southMercatorY;
var oneOverMercatorHeight;
if (includeWebMercatorT) {
southMercatorY = WebMercatorProjection.geodeticLatitudeToMercatorAngle(
geographicSouth
);
oneOverMercatorHeight =
1.0 /
(WebMercatorProjection.geodeticLatitudeToMercatorAngle(geographicNorth) -
southMercatorY);
}
var minimum = minimumScratch;
minimum.x = Number.POSITIVE_INFINITY;
minimum.y = Number.POSITIVE_INFINITY;
minimum.z = Number.POSITIVE_INFINITY;
var maximum = maximumScratch;
maximum.x = Number.NEGATIVE_INFINITY;
maximum.y = Number.NEGATIVE_INFINITY;
maximum.z = Number.NEGATIVE_INFINITY;
var hMin = Number.POSITIVE_INFINITY;
var gridVertexCount = width * height;
var edgeVertexCount = skirtHeight > 0.0 ? width * 2 + height * 2 : 0;
var vertexCount = gridVertexCount + edgeVertexCount;
var positions = new Array(vertexCount);
var heights = new Array(vertexCount);
var uvs = new Array(vertexCount);
var webMercatorTs = includeWebMercatorT ? new Array(vertexCount) : [];
var geodeticSurfaceNormals = includeGeodeticSurfaceNormals
? new Array(vertexCount)
: [];
var startRow = 0;
var endRow = height;
var startCol = 0;
var endCol = width;
if (hasSkirts) {
--startRow;
++endRow;
--startCol;
++endCol;
}
var skirtOffsetPercentage = 0.00001;
for (var rowIndex = startRow; rowIndex < endRow; ++rowIndex) {
var row = rowIndex;
if (row < 0) {
row = 0;
}
if (row >= height) {
row = height - 1;
}
var latitude = nativeRectangle.north - granularityY * row;
if (!isGeographic) {
latitude =
piOverTwo - 2.0 * atan(exp(-latitude * oneOverGlobeSemimajorAxis));
} else {
latitude = toRadians(latitude);
}
var v = (latitude - geographicSouth) / (geographicNorth - geographicSouth);
v = CesiumMath.clamp(v, 0.0, 1.0);
var isNorthEdge = rowIndex === startRow;
var isSouthEdge = rowIndex === endRow - 1;
if (skirtHeight > 0.0) {
if (isNorthEdge) {
latitude += skirtOffsetPercentage * rectangleHeight;
} else if (isSouthEdge) {
latitude -= skirtOffsetPercentage * rectangleHeight;
}
}
var cosLatitude = cos(latitude);
var nZ = sin(latitude);
var kZ = radiiSquaredZ * nZ;
var webMercatorT;
if (includeWebMercatorT) {
webMercatorT =
(WebMercatorProjection.geodeticLatitudeToMercatorAngle(latitude) -
southMercatorY) *
oneOverMercatorHeight;
}
for (var colIndex = startCol; colIndex < endCol; ++colIndex) {
var col = colIndex;
if (col < 0) {
col = 0;
}
if (col >= width) {
col = width - 1;
}
var terrainOffset = row * (width * stride) + col * stride;
var heightSample;
if (elementsPerHeight === 1) {
heightSample = heightmap[terrainOffset];
} else {
heightSample = 0;
var elementOffset;
if (isBigEndian) {
for (
elementOffset = 0;
elementOffset < elementsPerHeight;
++elementOffset
) {
heightSample =
heightSample * elementMultiplier +
heightmap[terrainOffset + elementOffset];
}
} else {
for (
elementOffset = elementsPerHeight - 1;
elementOffset >= 0;
--elementOffset
) {
heightSample =
heightSample * elementMultiplier +
heightmap[terrainOffset + elementOffset];
}
}
}
heightSample = heightSample * heightScale + heightOffset;
maximumHeight = Math.max(maximumHeight, heightSample);
minimumHeight = Math.min(minimumHeight, heightSample);
var longitude = nativeRectangle.west + granularityX * col;
if (!isGeographic) {
longitude = longitude * oneOverGlobeSemimajorAxis;
} else {
longitude = toRadians(longitude);
}
var u = (longitude - geographicWest) / (geographicEast - geographicWest);
u = CesiumMath.clamp(u, 0.0, 1.0);
var index = row * width + col;
if (skirtHeight > 0.0) {
var isWestEdge = colIndex === startCol;
var isEastEdge = colIndex === endCol - 1;
var isEdge = isNorthEdge || isSouthEdge || isWestEdge || isEastEdge;
var isCorner =
(isNorthEdge || isSouthEdge) && (isWestEdge || isEastEdge);
if (isCorner) {
// Don't generate skirts on the corners.
continue;
} else if (isEdge) {
heightSample -= skirtHeight;
if (isWestEdge) {
// The outer loop iterates north to south but the indices are ordered south to north, hence the index flip below
index = gridVertexCount + (height - row - 1);
longitude -= skirtOffsetPercentage * rectangleWidth;
} else if (isSouthEdge) {
// Add after west indices. South indices are ordered east to west.
index = gridVertexCount + height + (width - col - 1);
} else if (isEastEdge) {
// Add after west and south indices. East indices are ordered north to south. The index is flipped like above.
index = gridVertexCount + height + width + row;
longitude += skirtOffsetPercentage * rectangleWidth;
} else if (isNorthEdge) {
// Add after west, south, and east indices. North indices are ordered west to east.
index = gridVertexCount + height + width + height + col;
}
}
}
var nX = cosLatitude * cos(longitude);
var nY = cosLatitude * sin(longitude);
var kX = radiiSquaredX * nX;
var kY = radiiSquaredY * nY;
var gamma = sqrt(kX * nX + kY * nY + kZ * nZ);
var oneOverGamma = 1.0 / gamma;
var rSurfaceX = kX * oneOverGamma;
var rSurfaceY = kY * oneOverGamma;
var rSurfaceZ = kZ * oneOverGamma;
var position = new Cartesian3();
position.x = rSurfaceX + nX * heightSample;
position.y = rSurfaceY + nY * heightSample;
position.z = rSurfaceZ + nZ * heightSample;
Matrix4.multiplyByPoint(toENU, position, cartesian3Scratch);
Cartesian3.minimumByComponent(cartesian3Scratch, minimum, minimum);
Cartesian3.maximumByComponent(cartesian3Scratch, maximum, maximum);
hMin = Math.min(hMin, heightSample);
positions[index] = position;
uvs[index] = new Cartesian2(u, v);
heights[index] = heightSample;
if (includeWebMercatorT) {
webMercatorTs[index] = webMercatorT;
}
if (includeGeodeticSurfaceNormals) {
geodeticSurfaceNormals[index] = ellipsoid.geodeticSurfaceNormal(
position
);
}
}
}
var boundingSphere3D = BoundingSphere.fromPoints(positions);
var orientedBoundingBox;
if (defined(rectangle)) {
orientedBoundingBox = OrientedBoundingBox.fromRectangle(
rectangle,
minimumHeight,
maximumHeight,
ellipsoid
);
}
var occludeePointInScaledSpace;
if (hasRelativeToCenter) {
var occluder = new EllipsoidalOccluder(ellipsoid);
occludeePointInScaledSpace = occluder.computeHorizonCullingPointPossiblyUnderEllipsoid(
relativeToCenter,
positions,
minimumHeight
);
}
var aaBox = new AxisAlignedBoundingBox(minimum, maximum, relativeToCenter);
var encoding = new TerrainEncoding(
relativeToCenter,
aaBox,
hMin,
maximumHeight,
fromENU,
false,
includeWebMercatorT,
includeGeodeticSurfaceNormals,
exaggeration,
exaggerationRelativeHeight
);
var vertices = new Float32Array(vertexCount * encoding.stride);
var bufferIndex = 0;
for (var j = 0; j < vertexCount; ++j) {
bufferIndex = encoding.encode(
vertices,
bufferIndex,
positions[j],
uvs[j],
heights[j],
undefined,
webMercatorTs[j],
geodeticSurfaceNormals[j]
);
}
return {
vertices: vertices,
maximumHeight: maximumHeight,
minimumHeight: minimumHeight,
encoding: encoding,
boundingSphere3D: boundingSphere3D,
orientedBoundingBox: orientedBoundingBox,
occludeePointInScaledSpace: occludeePointInScaledSpace,
};
};
export default HeightmapTessellator;