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import defined from "../Core/defined.js";
import Cartographic from "../Core/Cartographic.js";
import Ellipsoid from "../Core/Ellipsoid.js";
import Intersect from "../Core/Intersect.js";
import Matrix3 from "../Core/Matrix3.js";
import Plane from "../Core/Plane.js";
import CoplanarPolygonOutlineGeometry from "../Core/CoplanarPolygonOutlineGeometry.js";
import BoundingSphere from "../Core/BoundingSphere.js";
import Check from "../Core/Check.js";
import ColorGeometryInstanceAttribute from "../Core/ColorGeometryInstanceAttribute.js";
import GeometryInstance from "../Core/GeometryInstance.js";
import Matrix4 from "../Core/Matrix4.js";
import PerInstanceColorAppearance from "./PerInstanceColorAppearance.js";
import Primitive from "./Primitive.js";
import S2Cell from "../Core/S2Cell.js";
let centerCartographicScratch = new Cartographic();
/**
* A tile bounding volume specified as an S2 cell token with minimum and maximum heights.
* The bounding volume is a k DOP. A k-DOP is the Boolean intersection of extents along k directions.
*
* @alias TileBoundingS2Cell
* @constructor
*
* @param {object} options Object with the following properties:
* @param {string} options.token The token of the S2 cell.
* @param {number} [options.minimumHeight=0.0] The minimum height of the bounding volume.
* @param {number} [options.maximumHeight=0.0] The maximum height of the bounding volume.
* @param {Ellipsoid} [options.ellipsoid=Ellipsoid.WGS84] The ellipsoid.
* @param {boolean} [options.computeBoundingVolumes=true] True to compute the {@link TileBoundingS2Cell#boundingVolume} and
* {@link TileBoundingS2Cell#boundingSphere}. If false, these properties will be undefined.
*
* @private
*/
function TileBoundingS2Cell(options) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("options", options);
Check.typeOf.string("options.token", options.token);
//>>includeEnd('debug');
const s2Cell = S2Cell.fromToken(options.token);
const minimumHeight = options.minimumHeight ?? 0.0;
const maximumHeight = options.maximumHeight ?? 0.0;
const ellipsoid = options.ellipsoid ?? Ellipsoid.WGS84;
this.s2Cell = s2Cell;
this.minimumHeight = minimumHeight;
this.maximumHeight = maximumHeight;
this.ellipsoid = ellipsoid;
const boundingPlanes = computeBoundingPlanes(
s2Cell,
minimumHeight,
maximumHeight,
ellipsoid,
);
this._boundingPlanes = boundingPlanes;
// Pre-compute vertices to speed up the plane intersection test.
const vertices = computeVertices(boundingPlanes);
this._vertices = vertices;
// Pre-compute edge normals to speed up the point-polygon distance check in distanceToCamera.
this._edgeNormals = new Array(6);
this._edgeNormals[0] = computeEdgeNormals(
boundingPlanes[0],
vertices.slice(0, 4),
);
let i;
// Based on the way the edge normals are computed, the edge normals all point away from the "face"
// of the polyhedron they surround, except the plane for the top plane. Therefore, we negate the normals
// for the top plane.
for (i = 0; i < 4; i++) {
this._edgeNormals[0][i] = Cartesian3.negate(
this._edgeNormals[0][i],
this._edgeNormals[0][i],
);
}
this._edgeNormals[1] = computeEdgeNormals(
boundingPlanes[1],
vertices.slice(4, 8),
);
for (i = 0; i < 4; i++) {
// For each plane, iterate through the vertices in CCW order.
this._edgeNormals[2 + i] = computeEdgeNormals(boundingPlanes[2 + i], [
vertices[i % 4],
vertices[(i + 1) % 4],
vertices[4 + ((i + 1) % 4)],
vertices[4 + i],
]);
}
this._planeVertices = [
this._vertices.slice(0, 4),
this._vertices.slice(4, 8),
];
for (i = 0; i < 4; i++) {
this._planeVertices.push([
this._vertices[i % 4],
this._vertices[(i + 1) % 4],
this._vertices[4 + ((i + 1) % 4)],
this._vertices[4 + i],
]);
}
const center = s2Cell.getCenter();
centerCartographicScratch = ellipsoid.cartesianToCartographic(
center,
centerCartographicScratch,
);
centerCartographicScratch.height = (maximumHeight + minimumHeight) / 2;
this.center = ellipsoid.cartographicToCartesian(
centerCartographicScratch,
center,
);
this._boundingSphere = BoundingSphere.fromPoints(vertices);
}
const centerGeodeticNormalScratch = new Cartesian3();
const topCartographicScratch = new Cartographic();
const topScratch = new Cartesian3();
const vertexCartographicScratch = new Cartographic();
const vertexScratch = new Cartesian3();
const vertexGeodeticNormalScratch = new Cartesian3();
const sideNormalScratch = new Cartesian3();
const sideScratch = new Cartesian3();
/**
* Computes bounding planes of the kDOP.
* @private
*/
function computeBoundingPlanes(
s2Cell,
minimumHeight,
maximumHeight,
ellipsoid,
) {
const planes = new Array(6);
const centerPoint = s2Cell.getCenter();
// Compute top plane.
// - Get geodetic surface normal at the center of the S2 cell.
// - Get center point at maximum height of bounding volume.
// - Create top plane from surface normal and top point.
const centerSurfaceNormal = ellipsoid.geodeticSurfaceNormal(
centerPoint,
centerGeodeticNormalScratch,
);
const topCartographic = ellipsoid.cartesianToCartographic(
centerPoint,
topCartographicScratch,
);
topCartographic.height = maximumHeight;
const top = ellipsoid.cartographicToCartesian(topCartographic, topScratch);
const topPlane = Plane.fromPointNormal(top, centerSurfaceNormal);
planes[0] = topPlane;
// Compute bottom plane.
// - Iterate through bottom vertices
// - Get distance from vertex to top plane
// - Find longest distance from vertex to top plane
// - Translate top plane by the distance
let maxDistance = 0;
let i;
const vertices = [];
let vertex, vertexCartographic;
for (i = 0; i < 4; i++) {
vertex = s2Cell.getVertex(i);
vertices[i] = vertex;
vertexCartographic = ellipsoid.cartesianToCartographic(
vertex,
vertexCartographicScratch,
);
vertexCartographic.height = minimumHeight;
const distance = Plane.getPointDistance(
topPlane,
ellipsoid.cartographicToCartesian(vertexCartographic, vertexScratch),
);
if (distance < maxDistance) {
maxDistance = distance;
}
}
const bottomPlane = Plane.clone(topPlane);
// Negate the normal of the bottom plane since we want all normals to point "outwards".
bottomPlane.normal = Cartesian3.negate(
bottomPlane.normal,
bottomPlane.normal,
);
bottomPlane.distance = bottomPlane.distance * -1 + maxDistance;
planes[1] = bottomPlane;
// Compute side planes.
// - Iterate through vertices (in CCW order, by default)
// - Get a vertex and another vertex adjacent to it.
// - Compute geodetic surface normal at one vertex.
// - Compute vector between vertices.
// - Compute normal of side plane. (cross product of top dir and side dir)
for (i = 0; i < 4; i++) {
vertex = vertices[i];
const adjacentVertex = vertices[(i + 1) % 4];
const geodeticNormal = ellipsoid.geodeticSurfaceNormal(
vertex,
vertexGeodeticNormalScratch,
);
const side = Cartesian3.subtract(adjacentVertex, vertex, sideScratch);
let sideNormal = Cartesian3.cross(side, geodeticNormal, sideNormalScratch);
sideNormal = Cartesian3.normalize(sideNormal, sideNormal);
planes[2 + i] = Plane.fromPointNormal(vertex, sideNormal);
}
return planes;
}
let n0Scratch = new Cartesian3();
let n1Scratch = new Cartesian3();
let n2Scratch = new Cartesian3();
let x0Scratch = new Cartesian3();
let x1Scratch = new Cartesian3();
let x2Scratch = new Cartesian3();
const t0Scratch = new Cartesian3();
const t1Scratch = new Cartesian3();
const t2Scratch = new Cartesian3();
let f0Scratch = new Cartesian3();
let f1Scratch = new Cartesian3();
let f2Scratch = new Cartesian3();
let sScratch = new Cartesian3();
const matrixScratch = new Matrix3();
/**
* Computes intersection of 3 planes.
* @private
*/
function computeIntersection(p0, p1, p2) {
n0Scratch = p0.normal;
n1Scratch = p1.normal;
n2Scratch = p2.normal;
x0Scratch = Cartesian3.multiplyByScalar(p0.normal, -p0.distance, x0Scratch);
x1Scratch = Cartesian3.multiplyByScalar(p1.normal, -p1.distance, x1Scratch);
x2Scratch = Cartesian3.multiplyByScalar(p2.normal, -p2.distance, x2Scratch);
f0Scratch = Cartesian3.multiplyByScalar(
Cartesian3.cross(n1Scratch, n2Scratch, t0Scratch),
Cartesian3.dot(x0Scratch, n0Scratch),
f0Scratch,
);
f1Scratch = Cartesian3.multiplyByScalar(
Cartesian3.cross(n2Scratch, n0Scratch, t1Scratch),
Cartesian3.dot(x1Scratch, n1Scratch),
f1Scratch,
);
f2Scratch = Cartesian3.multiplyByScalar(
Cartesian3.cross(n0Scratch, n1Scratch, t2Scratch),
Cartesian3.dot(x2Scratch, n2Scratch),
f2Scratch,
);
matrixScratch[0] = n0Scratch.x;
matrixScratch[1] = n1Scratch.x;
matrixScratch[2] = n2Scratch.x;
matrixScratch[3] = n0Scratch.y;
matrixScratch[4] = n1Scratch.y;
matrixScratch[5] = n2Scratch.y;
matrixScratch[6] = n0Scratch.z;
matrixScratch[7] = n1Scratch.z;
matrixScratch[8] = n2Scratch.z;
const determinant = Matrix3.determinant(matrixScratch);
sScratch = Cartesian3.add(f0Scratch, f1Scratch, sScratch);
sScratch = Cartesian3.add(sScratch, f2Scratch, sScratch);
return new Cartesian3(
sScratch.x / determinant,
sScratch.y / determinant,
sScratch.z / determinant,
);
}
/**
* Compute the vertices of the kDOP.
* @private
*/
function computeVertices(boundingPlanes) {
const vertices = new Array(8);
for (let i = 0; i < 4; i++) {
// Vertices on the top plane.
vertices[i] = computeIntersection(
boundingPlanes[0],
boundingPlanes[2 + ((i + 3) % 4)],
boundingPlanes[2 + (i % 4)],
);
// Vertices on the bottom plane.
vertices[i + 4] = computeIntersection(
boundingPlanes[1],
boundingPlanes[2 + ((i + 3) % 4)],
boundingPlanes[2 + (i % 4)],
);
}
return vertices;
}
let edgeScratch = new Cartesian3();
let edgeNormalScratch = new Cartesian3();
/**
* Compute edge normals on a plane.
* @private
*/
function computeEdgeNormals(plane, vertices) {
const edgeNormals = [];
for (let i = 0; i < 4; i++) {
edgeScratch = Cartesian3.subtract(
vertices[(i + 1) % 4],
vertices[i],
edgeScratch,
);
edgeNormalScratch = Cartesian3.cross(
plane.normal,
edgeScratch,
edgeNormalScratch,
);
edgeNormalScratch = Cartesian3.normalize(
edgeNormalScratch,
edgeNormalScratch,
);
edgeNormals[i] = Cartesian3.clone(edgeNormalScratch);
}
return edgeNormals;
}
Object.defineProperties(TileBoundingS2Cell.prototype, {
/**
* The underlying bounding volume.
*
* @memberof TileBoundingS2Cell.prototype
*
* @type {object}
* @readonly
*/
boundingVolume: {
get: function () {
return this;
},
},
/**
* The underlying bounding sphere.
*
* @memberof TileBoundingS2Cell.prototype
*
* @type {BoundingSphere}
* @readonly
*/
boundingSphere: {
get: function () {
return this._boundingSphere;
},
},
});
const facePointScratch = new Cartesian3();
/**
* The distance to point check for this kDOP involves checking the signed distance of the point to each bounding
* plane. A plane qualifies for a distance check if the point being tested against is in the half-space in the direction
* of the normal i.e. if the signed distance of the point from the plane is greater than 0.
*
* There are 4 possible cases for a point if it is outside the polyhedron:
*
* \ X / X \ / \ / \ /
* ---\---------/--- ---\---------/--- ---X---------/--- ---\---------/---
* \ / \ / \ / \ /
* ---\-----/--- ---\-----/--- ---\-----/--- ---\-----/---
* \ / \ / \ / \ /
* \ /
* \
* / \
* / X \
*
* I II III IV
*
* Case I: There is only one plane selected.
* In this case, we project the point onto the plane and do a point polygon distance check to find the closest point on the polygon.
* The point may lie inside the "face" of the polygon or outside. If it is outside, we need to determine which edges to test against.
*
* Case II: There are two planes selected.
* In this case, the point will lie somewhere on the line created at the intersection of the selected planes or one of the planes.
*
* Case III: There are three planes selected.
* In this case, the point will lie on the vertex, at the intersection of the selected planes.
*
* Case IV: There are more than three planes selected.
* Since we are on an ellipsoid, this will only happen in the bottom plane, which is what we will use for the distance test.
*/
TileBoundingS2Cell.prototype.distanceToCamera = function (frameState) {
//>>includeStart('debug', pragmas.debug);
Check.defined("frameState", frameState);
//>>includeEnd('debug');
const point = frameState.camera.positionWC;
const selectedPlaneIndices = [];
const vertices = [];
let edgeNormals;
if (Plane.getPointDistance(this._boundingPlanes[0], point) > 0) {
selectedPlaneIndices.push(0);
vertices.push(this._planeVertices[0]);
edgeNormals = this._edgeNormals[0];
} else if (Plane.getPointDistance(this._boundingPlanes[1], point) > 0) {
selectedPlaneIndices.push(1);
vertices.push(this._planeVertices[1]);
edgeNormals = this._edgeNormals[1];
}
let i;
let sidePlaneIndex;
for (i = 0; i < 4; i++) {
sidePlaneIndex = 2 + i;
if (
Plane.getPointDistance(this._boundingPlanes[sidePlaneIndex], point) > 0
) {
selectedPlaneIndices.push(sidePlaneIndex);
// Store vertices in CCW order.
vertices.push(this._planeVertices[sidePlaneIndex]);
edgeNormals = this._edgeNormals[sidePlaneIndex];
}
}
// Check if inside all planes.
if (selectedPlaneIndices.length === 0) {
return 0.0;
}
// We use the skip variable when the side plane indices are non-consecutive.
let facePoint;
let selectedPlane;
if (selectedPlaneIndices.length === 1) {
// Handles Case I
selectedPlane = this._boundingPlanes[selectedPlaneIndices[0]];
facePoint = closestPointPolygon(
Plane.projectPointOntoPlane(selectedPlane, point, facePointScratch),
vertices[0],
selectedPlane,
edgeNormals,
);
return Cartesian3.distance(facePoint, point);
} else if (selectedPlaneIndices.length === 2) {
// Handles Case II
// Since we are on the ellipsoid, the dihedral angle between a top plane and a side plane
// will always be acute, so we can do a faster check there.
Iif (selectedPlaneIndices[0] === 0) {
const edge = [
this._vertices[
4 * selectedPlaneIndices[0] + (selectedPlaneIndices[1] - 2)
],
this._vertices[
4 * selectedPlaneIndices[0] + ((selectedPlaneIndices[1] - 2 + 1) % 4)
],
];
facePoint = closestPointLineSegment(point, edge[0], edge[1]);
return Cartesian3.distance(facePoint, point);
}
let minimumDistance = Number.MAX_VALUE;
let distance;
for (i = 0; i < 2; i++) {
selectedPlane = this._boundingPlanes[selectedPlaneIndices[i]];
facePoint = closestPointPolygon(
Plane.projectPointOntoPlane(selectedPlane, point, facePointScratch),
vertices[i],
selectedPlane,
this._edgeNormals[selectedPlaneIndices[i]],
);
distance = Cartesian3.distanceSquared(facePoint, point);
if (distance < minimumDistance) {
minimumDistance = distance;
}
}
return Math.sqrt(minimumDistance);
} else if (selectedPlaneIndices.length > 3) {
// Handles Case IV
facePoint = closestPointPolygon(
Plane.projectPointOntoPlane(
this._boundingPlanes[1],
point,
facePointScratch,
),
this._planeVertices[1],
this._boundingPlanes[1],
this._edgeNormals[1],
);
return Cartesian3.distance(facePoint, point);
}
// Handles Case III
const skip =
selectedPlaneIndices[1] === 2 && selectedPlaneIndices[2] === 5 ? 0 : 1;
// Vertex is on top plane.
Eif (selectedPlaneIndices[0] === 0) {
return Cartesian3.distance(
point,
this._vertices[(selectedPlaneIndices[1] - 2 + skip) % 4],
);
}
// Vertex is on bottom plane.
return Cartesian3.distance(
point,
this._vertices[4 + ((selectedPlaneIndices[1] - 2 + skip) % 4)],
);
};
const dScratch = new Cartesian3();
const pL0Scratch = new Cartesian3();
/**
* Finds point on a line segment closest to a given point.
* @private
*/
function closestPointLineSegment(p, l0, l1) {
const d = Cartesian3.subtract(l1, l0, dScratch);
const pL0 = Cartesian3.subtract(p, l0, pL0Scratch);
let t = Cartesian3.dot(d, pL0);
Iif (t <= 0) {
return l0;
}
const dMag = Cartesian3.dot(d, d);
Iif (t >= dMag) {
return l1;
}
t = t / dMag;
return new Cartesian3(
(1 - t) * l0.x + t * l1.x,
(1 - t) * l0.y + t * l1.y,
(1 - t) * l0.z + t * l1.z,
);
}
const edgePlaneScratch = new Plane(Cartesian3.UNIT_X, 0.0);
/**
* Finds closes point on the polygon, created by the given vertices, from
* a point. The test point and the polygon are all on the same plane.
* @private
*/
function closestPointPolygon(p, vertices, plane, edgeNormals) {
let minDistance = Number.MAX_VALUE;
let distance;
let closestPoint;
let closestPointOnEdge;
for (let i = 0; i < vertices.length; i++) {
const edgePlane = Plane.fromPointNormal(
vertices[i],
edgeNormals[i],
edgePlaneScratch,
);
const edgePlaneDistance = Plane.getPointDistance(edgePlane, p);
// Skip checking against the edge if the point is not in the half-space that the
// edgePlane's normal points towards i.e. if the edgePlane is facing away from the point.
if (edgePlaneDistance < 0) {
continue;
}
closestPointOnEdge = closestPointLineSegment(
p,
vertices[i],
vertices[(i + 1) % 4],
);
distance = Cartesian3.distance(p, closestPointOnEdge);
Eif (distance < minDistance) {
minDistance = distance;
closestPoint = closestPointOnEdge;
}
}
if (!defined(closestPoint)) {
return p;
}
return closestPoint;
}
/**
* Determines which side of a plane this volume is located.
*
* @param {Plane} plane The plane to test against.
* @returns {Intersect} {@link Intersect.INSIDE} if the entire volume is on the side of the plane
* the normal is pointing, {@link Intersect.OUTSIDE} if the entire volume is
* on the opposite side, and {@link Intersect.INTERSECTING} if the volume
* intersects the plane.
*/
TileBoundingS2Cell.prototype.intersectPlane = function (plane) {
//>>includeStart('debug', pragmas.debug);
Check.defined("plane", plane);
//>>includeEnd('debug');
let plusCount = 0;
let negCount = 0;
for (let i = 0; i < this._vertices.length; i++) {
const distanceToPlane =
Cartesian3.dot(plane.normal, this._vertices[i]) + plane.distance;
if (distanceToPlane < 0) {
negCount++;
} else {
plusCount++;
}
}
if (plusCount === this._vertices.length) {
return Intersect.INSIDE;
} else if (negCount === this._vertices.length) {
return Intersect.OUTSIDE;
}
return Intersect.INTERSECTING;
};
/**
* Creates a debug primitive that shows the outline of the tile bounding
* volume.
*
* @param {Color} color The desired color of the primitive's mesh
* @return {Primitive}
*/
TileBoundingS2Cell.prototype.createDebugVolume = function (color) {
//>>includeStart('debug', pragmas.debug);
Check.defined("color", color);
//>>includeEnd('debug');
const modelMatrix = new Matrix4.clone(Matrix4.IDENTITY);
const topPlanePolygon = new CoplanarPolygonOutlineGeometry({
polygonHierarchy: {
positions: this._planeVertices[0],
},
});
const topPlaneGeometry =
CoplanarPolygonOutlineGeometry.createGeometry(topPlanePolygon);
const topPlaneInstance = new GeometryInstance({
geometry: topPlaneGeometry,
id: "outline",
modelMatrix: modelMatrix,
attributes: {
color: ColorGeometryInstanceAttribute.fromColor(color),
},
});
const bottomPlanePolygon = new CoplanarPolygonOutlineGeometry({
polygonHierarchy: {
positions: this._planeVertices[1],
},
});
const bottomPlaneGeometry =
CoplanarPolygonOutlineGeometry.createGeometry(bottomPlanePolygon);
const bottomPlaneInstance = new GeometryInstance({
geometry: bottomPlaneGeometry,
id: "outline",
modelMatrix: modelMatrix,
attributes: {
color: ColorGeometryInstanceAttribute.fromColor(color),
},
});
const sideInstances = [];
for (let i = 0; i < 4; i++) {
const sidePlanePolygon = new CoplanarPolygonOutlineGeometry({
polygonHierarchy: {
positions: this._planeVertices[2 + i],
},
});
const sidePlaneGeometry =
CoplanarPolygonOutlineGeometry.createGeometry(sidePlanePolygon);
sideInstances[i] = new GeometryInstance({
geometry: sidePlaneGeometry,
id: "outline",
modelMatrix: modelMatrix,
attributes: {
color: ColorGeometryInstanceAttribute.fromColor(color),
},
});
}
return new Primitive({
geometryInstances: [
sideInstances[0],
sideInstances[1],
sideInstances[2],
sideInstances[3],
bottomPlaneInstance,
topPlaneInstance,
],
appearance: new PerInstanceColorAppearance({
translucent: false,
flat: true,
}),
asynchronous: false,
});
};
export default TileBoundingS2Cell;
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