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import BoundingSphere from "./BoundingSphere.js";
import Cartesian2 from "./Cartesian2.js";
import Cartesian3 from "./Cartesian3.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
*/
const 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,
});
const cartesian3Scratch = new Cartesian3();
const matrix4Scratch = new Matrix4();
const minimumScratch = new Cartesian3();
const 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.default] 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
* const width = 5;
* const height = 5;
* const 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
* }
* });
*
* const encoding = statistics.encoding;
* const 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.
const cos = Math.cos;
const sin = Math.sin;
const sqrt = Math.sqrt;
const atan = Math.atan;
const exp = Math.exp;
const piOverTwo = CesiumMath.PI_OVER_TWO;
const toRadians = CesiumMath.toRadians;
const heightmap = options.heightmap;
const width = options.width;
const height = options.height;
const skirtHeight = options.skirtHeight;
const hasSkirts = skirtHeight > 0.0;
const isGeographic = options.isGeographic ?? true;
const ellipsoid = options.ellipsoid ?? Ellipsoid.default;
const oneOverGlobeSemimajorAxis = 1.0 / ellipsoid.maximumRadius;
const nativeRectangle = Rectangle.clone(options.nativeRectangle);
const rectangle = Rectangle.clone(options.rectangle);
let geographicWest;
let geographicSouth;
let geographicEast;
let 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;
}
let relativeToCenter = options.relativeToCenter;
const hasRelativeToCenter = defined(relativeToCenter);
relativeToCenter = hasRelativeToCenter ? relativeToCenter : Cartesian3.ZERO;
const includeWebMercatorT = options.includeWebMercatorT ?? false;
const exaggeration = options.exaggeration ?? 1.0;
const exaggerationRelativeHeight = options.exaggerationRelativeHeight ?? 0.0;
const hasExaggeration = exaggeration !== 1.0;
const includeGeodeticSurfaceNormals = hasExaggeration;
const structure = options.structure ?? HeightmapTessellator.DEFAULT_STRUCTURE;
const heightScale =
structure.heightScale ?? HeightmapTessellator.DEFAULT_STRUCTURE.heightScale;
const heightOffset =
structure.heightOffset ??
HeightmapTessellator.DEFAULT_STRUCTURE.heightOffset;
const elementsPerHeight =
structure.elementsPerHeight ??
HeightmapTessellator.DEFAULT_STRUCTURE.elementsPerHeight;
const stride =
structure.stride ?? HeightmapTessellator.DEFAULT_STRUCTURE.stride;
const elementMultiplier =
structure.elementMultiplier ??
HeightmapTessellator.DEFAULT_STRUCTURE.elementMultiplier;
const isBigEndian =
structure.isBigEndian ?? HeightmapTessellator.DEFAULT_STRUCTURE.isBigEndian;
let rectangleWidth = Rectangle.computeWidth(nativeRectangle);
let rectangleHeight = Rectangle.computeHeight(nativeRectangle);
const granularityX = rectangleWidth / (width - 1);
const granularityY = rectangleHeight / (height - 1);
if (!isGeographic) {
rectangleWidth *= oneOverGlobeSemimajorAxis;
rectangleHeight *= oneOverGlobeSemimajorAxis;
}
const radiiSquared = ellipsoid.radiiSquared;
const radiiSquaredX = radiiSquared.x;
const radiiSquaredY = radiiSquared.y;
const radiiSquaredZ = radiiSquared.z;
let minimumHeight = 65536.0;
let maximumHeight = -65536.0;
const fromENU = Transforms.eastNorthUpToFixedFrame(
relativeToCenter,
ellipsoid,
);
const toENU = Matrix4.inverseTransformation(fromENU, matrix4Scratch);
let southMercatorY;
let oneOverMercatorHeight;
if (includeWebMercatorT) {
southMercatorY =
WebMercatorProjection.geodeticLatitudeToMercatorAngle(geographicSouth);
oneOverMercatorHeight =
1.0 /
(WebMercatorProjection.geodeticLatitudeToMercatorAngle(geographicNorth) -
southMercatorY);
}
const minimum = minimumScratch;
minimum.x = Number.POSITIVE_INFINITY;
minimum.y = Number.POSITIVE_INFINITY;
minimum.z = Number.POSITIVE_INFINITY;
const maximum = maximumScratch;
maximum.x = Number.NEGATIVE_INFINITY;
maximum.y = Number.NEGATIVE_INFINITY;
maximum.z = Number.NEGATIVE_INFINITY;
let hMin = Number.POSITIVE_INFINITY;
const gridVertexCount = width * height;
const edgeVertexCount = skirtHeight > 0.0 ? width * 2 + height * 2 : 0;
const vertexCount = gridVertexCount + edgeVertexCount;
const positions = new Array(vertexCount);
const heights = new Array(vertexCount);
const uvs = new Array(vertexCount);
const webMercatorTs = includeWebMercatorT ? new Array(vertexCount) : [];
const geodeticSurfaceNormals = includeGeodeticSurfaceNormals
? new Array(vertexCount)
: [];
let startRow = 0;
let endRow = height;
let startCol = 0;
let endCol = width;
if (hasSkirts) {
--startRow;
++endRow;
--startCol;
++endCol;
}
const skirtOffsetPercentage = 0.00001;
for (let rowIndex = startRow; rowIndex < endRow; ++rowIndex) {
let row = rowIndex;
if (row < 0) {
row = 0;
}
if (row >= height) {
row = height - 1;
}
let latitude = nativeRectangle.north - granularityY * row;
if (!isGeographic) {
latitude =
piOverTwo - 2.0 * atan(exp(-latitude * oneOverGlobeSemimajorAxis));
} else {
latitude = toRadians(latitude);
}
let v = (latitude - geographicSouth) / (geographicNorth - geographicSouth);
v = CesiumMath.clamp(v, 0.0, 1.0);
const isNorthEdge = rowIndex === startRow;
const isSouthEdge = rowIndex === endRow - 1;
if (skirtHeight > 0.0) {
if (isNorthEdge) {
latitude += skirtOffsetPercentage * rectangleHeight;
} else if (isSouthEdge) {
latitude -= skirtOffsetPercentage * rectangleHeight;
}
}
const cosLatitude = cos(latitude);
const nZ = sin(latitude);
const kZ = radiiSquaredZ * nZ;
let webMercatorT;
if (includeWebMercatorT) {
webMercatorT =
(WebMercatorProjection.geodeticLatitudeToMercatorAngle(latitude) -
southMercatorY) *
oneOverMercatorHeight;
}
for (let colIndex = startCol; colIndex < endCol; ++colIndex) {
let col = colIndex;
if (col < 0) {
col = 0;
}
if (col >= width) {
col = width - 1;
}
const terrainOffset = row * (width * stride) + col * stride;
let heightSample;
if (elementsPerHeight === 1) {
heightSample = heightmap[terrainOffset];
} else {
heightSample = 0;
let 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);
let longitude = nativeRectangle.west + granularityX * col;
if (!isGeographic) {
longitude = longitude * oneOverGlobeSemimajorAxis;
} else {
longitude = toRadians(longitude);
}
let u = (longitude - geographicWest) / (geographicEast - geographicWest);
u = CesiumMath.clamp(u, 0.0, 1.0);
let index = row * width + col;
if (skirtHeight > 0.0) {
const isWestEdge = colIndex === startCol;
const isEastEdge = colIndex === endCol - 1;
const isEdge = isNorthEdge || isSouthEdge || isWestEdge || isEastEdge;
const 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 Eif (isNorthEdge) {
// Add after west, south, and east indices. North indices are ordered west to east.
index = gridVertexCount + height + width + height + col;
}
}
}
const nX = cosLatitude * cos(longitude);
const nY = cosLatitude * sin(longitude);
const kX = radiiSquaredX * nX;
const kY = radiiSquaredY * nY;
const gamma = sqrt(kX * nX + kY * nY + kZ * nZ);
const oneOverGamma = 1.0 / gamma;
const rSurfaceX = kX * oneOverGamma;
const rSurfaceY = kY * oneOverGamma;
const rSurfaceZ = kZ * oneOverGamma;
const 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;
}
Iif (includeGeodeticSurfaceNormals) {
geodeticSurfaceNormals[index] =
ellipsoid.geodeticSurfaceNormal(position);
}
}
}
const boundingSphere3D = BoundingSphere.fromPoints(positions);
let orientedBoundingBox;
if (defined(rectangle)) {
orientedBoundingBox = OrientedBoundingBox.fromRectangle(
rectangle,
minimumHeight,
maximumHeight,
ellipsoid,
);
}
let occludeePointInScaledSpace;
if (hasRelativeToCenter) {
const occluder = new EllipsoidalOccluder(ellipsoid);
occludeePointInScaledSpace =
occluder.computeHorizonCullingPointPossiblyUnderEllipsoid(
relativeToCenter,
positions,
minimumHeight,
);
}
const aaBox = new AxisAlignedBoundingBox(minimum, maximum, relativeToCenter);
const encoding = new TerrainEncoding(
relativeToCenter,
aaBox,
hMin,
maximumHeight,
fromENU,
false,
includeWebMercatorT,
includeGeodeticSurfaceNormals,
exaggeration,
exaggerationRelativeHeight,
);
const vertices = new Float32Array(vertexCount * encoding.stride);
let bufferIndex = 0;
for (let 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;
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