/** * @license * Cesium - https://github.com/CesiumGS/cesium * Version 1.99 * * Copyright 2011-2022 Cesium Contributors * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. * * Columbus View (Pat. Pend.) * * Portions licensed separately. * See https://github.com/CesiumGS/cesium/blob/main/LICENSE.md for full licensing details. */ define(['exports', './Transforms-ac2d28a9', './Matrix2-f9f1b94b', './Matrix3-ea964448', './Check-40d84a28', './defaultValue-135942ca', './EllipsoidTangentPlane-244dda7a', './Math-efde0c7b', './Plane-93af52b2'], (function (exports, Transforms, Matrix2, Matrix3, Check, defaultValue, EllipsoidTangentPlane, Math$1, Plane) { 'use strict'; /** * Creates an instance of an OrientedBoundingBox. * An OrientedBoundingBox of some object is a closed and convex cuboid. It can provide a tighter bounding volume than {@link BoundingSphere} or {@link AxisAlignedBoundingBox} in many cases. * @alias OrientedBoundingBox * @constructor * * @param {Cartesian3} [center=Cartesian3.ZERO] The center of the box. * @param {Matrix3} [halfAxes=Matrix3.ZERO] The three orthogonal half-axes of the bounding box. * Equivalently, the transformation matrix, to rotate and scale a 0x0x0 * cube centered at the origin. * * * @example * // Create an OrientedBoundingBox using a transformation matrix, a position where the box will be translated, and a scale. * const center = new Cesium.Cartesian3(1.0, 0.0, 0.0); * const halfAxes = Cesium.Matrix3.fromScale(new Cesium.Cartesian3(1.0, 3.0, 2.0), new Cesium.Matrix3()); * * const obb = new Cesium.OrientedBoundingBox(center, halfAxes); * * @see BoundingSphere * @see BoundingRectangle */ function OrientedBoundingBox(center, halfAxes) { /** * The center of the box. * @type {Cartesian3} * @default {@link Cartesian3.ZERO} */ this.center = Matrix3.Cartesian3.clone(defaultValue.defaultValue(center, Matrix3.Cartesian3.ZERO)); /** * The transformation matrix, to rotate the box to the right position. * @type {Matrix3} * @default {@link Matrix3.ZERO} */ this.halfAxes = Matrix3.Matrix3.clone(defaultValue.defaultValue(halfAxes, Matrix3.Matrix3.ZERO)); } /** * The number of elements used to pack the object into an array. * @type {Number} */ OrientedBoundingBox.packedLength = Matrix3.Cartesian3.packedLength + Matrix3.Matrix3.packedLength; /** * Stores the provided instance into the provided array. * * @param {OrientedBoundingBox} value The value to pack. * @param {Number[]} array The array to pack into. * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements. * * @returns {Number[]} The array that was packed into */ OrientedBoundingBox.pack = function (value, array, startingIndex) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("value", value); Check.Check.defined("array", array); //>>includeEnd('debug'); startingIndex = defaultValue.defaultValue(startingIndex, 0); Matrix3.Cartesian3.pack(value.center, array, startingIndex); Matrix3.Matrix3.pack(value.halfAxes, array, startingIndex + Matrix3.Cartesian3.packedLength); return array; }; /** * Retrieves an instance from a packed array. * * @param {Number[]} array The packed array. * @param {Number} [startingIndex=0] The starting index of the element to be unpacked. * @param {OrientedBoundingBox} [result] The object into which to store the result. * @returns {OrientedBoundingBox} The modified result parameter or a new OrientedBoundingBox instance if one was not provided. */ OrientedBoundingBox.unpack = function (array, startingIndex, result) { //>>includeStart('debug', pragmas.debug); Check.Check.defined("array", array); //>>includeEnd('debug'); startingIndex = defaultValue.defaultValue(startingIndex, 0); if (!defaultValue.defined(result)) { result = new OrientedBoundingBox(); } Matrix3.Cartesian3.unpack(array, startingIndex, result.center); Matrix3.Matrix3.unpack( array, startingIndex + Matrix3.Cartesian3.packedLength, result.halfAxes ); return result; }; const scratchCartesian1 = new Matrix3.Cartesian3(); const scratchCartesian2 = new Matrix3.Cartesian3(); const scratchCartesian3 = new Matrix3.Cartesian3(); const scratchCartesian4 = new Matrix3.Cartesian3(); const scratchCartesian5 = new Matrix3.Cartesian3(); const scratchCartesian6 = new Matrix3.Cartesian3(); const scratchCovarianceResult = new Matrix3.Matrix3(); const scratchEigenResult = { unitary: new Matrix3.Matrix3(), diagonal: new Matrix3.Matrix3(), }; /** * Computes an instance of an OrientedBoundingBox of the given positions. * This is an implementation of Stefan Gottschalk's Collision Queries using Oriented Bounding Boxes solution (PHD thesis). * Reference: http://gamma.cs.unc.edu/users/gottschalk/main.pdf * * @param {Cartesian3[]} [positions] List of {@link Cartesian3} points that the bounding box will enclose. * @param {OrientedBoundingBox} [result] The object onto which to store the result. * @returns {OrientedBoundingBox} The modified result parameter or a new OrientedBoundingBox instance if one was not provided. * * @example * // Compute an object oriented bounding box enclosing two points. * const box = Cesium.OrientedBoundingBox.fromPoints([new Cesium.Cartesian3(2, 0, 0), new Cesium.Cartesian3(-2, 0, 0)]); */ OrientedBoundingBox.fromPoints = function (positions, result) { if (!defaultValue.defined(result)) { result = new OrientedBoundingBox(); } if (!defaultValue.defined(positions) || positions.length === 0) { result.halfAxes = Matrix3.Matrix3.ZERO; result.center = Matrix3.Cartesian3.ZERO; return result; } let i; const length = positions.length; const meanPoint = Matrix3.Cartesian3.clone(positions[0], scratchCartesian1); for (i = 1; i < length; i++) { Matrix3.Cartesian3.add(meanPoint, positions[i], meanPoint); } const invLength = 1.0 / length; Matrix3.Cartesian3.multiplyByScalar(meanPoint, invLength, meanPoint); let exx = 0.0; let exy = 0.0; let exz = 0.0; let eyy = 0.0; let eyz = 0.0; let ezz = 0.0; let p; for (i = 0; i < length; i++) { p = Matrix3.Cartesian3.subtract(positions[i], meanPoint, scratchCartesian2); exx += p.x * p.x; exy += p.x * p.y; exz += p.x * p.z; eyy += p.y * p.y; eyz += p.y * p.z; ezz += p.z * p.z; } exx *= invLength; exy *= invLength; exz *= invLength; eyy *= invLength; eyz *= invLength; ezz *= invLength; const covarianceMatrix = scratchCovarianceResult; covarianceMatrix[0] = exx; covarianceMatrix[1] = exy; covarianceMatrix[2] = exz; covarianceMatrix[3] = exy; covarianceMatrix[4] = eyy; covarianceMatrix[5] = eyz; covarianceMatrix[6] = exz; covarianceMatrix[7] = eyz; covarianceMatrix[8] = ezz; const eigenDecomposition = Matrix3.Matrix3.computeEigenDecomposition( covarianceMatrix, scratchEigenResult ); const rotation = Matrix3.Matrix3.clone(eigenDecomposition.unitary, result.halfAxes); let v1 = Matrix3.Matrix3.getColumn(rotation, 0, scratchCartesian4); let v2 = Matrix3.Matrix3.getColumn(rotation, 1, scratchCartesian5); let v3 = Matrix3.Matrix3.getColumn(rotation, 2, scratchCartesian6); let u1 = -Number.MAX_VALUE; let u2 = -Number.MAX_VALUE; let u3 = -Number.MAX_VALUE; let l1 = Number.MAX_VALUE; let l2 = Number.MAX_VALUE; let l3 = Number.MAX_VALUE; for (i = 0; i < length; i++) { p = positions[i]; u1 = Math.max(Matrix3.Cartesian3.dot(v1, p), u1); u2 = Math.max(Matrix3.Cartesian3.dot(v2, p), u2); u3 = Math.max(Matrix3.Cartesian3.dot(v3, p), u3); l1 = Math.min(Matrix3.Cartesian3.dot(v1, p), l1); l2 = Math.min(Matrix3.Cartesian3.dot(v2, p), l2); l3 = Math.min(Matrix3.Cartesian3.dot(v3, p), l3); } v1 = Matrix3.Cartesian3.multiplyByScalar(v1, 0.5 * (l1 + u1), v1); v2 = Matrix3.Cartesian3.multiplyByScalar(v2, 0.5 * (l2 + u2), v2); v3 = Matrix3.Cartesian3.multiplyByScalar(v3, 0.5 * (l3 + u3), v3); const center = Matrix3.Cartesian3.add(v1, v2, result.center); Matrix3.Cartesian3.add(center, v3, center); const scale = scratchCartesian3; scale.x = u1 - l1; scale.y = u2 - l2; scale.z = u3 - l3; Matrix3.Cartesian3.multiplyByScalar(scale, 0.5, scale); Matrix3.Matrix3.multiplyByScale(result.halfAxes, scale, result.halfAxes); return result; }; const scratchOffset = new Matrix3.Cartesian3(); const scratchScale = new Matrix3.Cartesian3(); function fromPlaneExtents( planeOrigin, planeXAxis, planeYAxis, planeZAxis, minimumX, maximumX, minimumY, maximumY, minimumZ, maximumZ, result ) { //>>includeStart('debug', pragmas.debug); if ( !defaultValue.defined(minimumX) || !defaultValue.defined(maximumX) || !defaultValue.defined(minimumY) || !defaultValue.defined(maximumY) || !defaultValue.defined(minimumZ) || !defaultValue.defined(maximumZ) ) { throw new Check.DeveloperError( "all extents (minimum/maximum X/Y/Z) are required." ); } //>>includeEnd('debug'); if (!defaultValue.defined(result)) { result = new OrientedBoundingBox(); } const halfAxes = result.halfAxes; Matrix3.Matrix3.setColumn(halfAxes, 0, planeXAxis, halfAxes); Matrix3.Matrix3.setColumn(halfAxes, 1, planeYAxis, halfAxes); Matrix3.Matrix3.setColumn(halfAxes, 2, planeZAxis, halfAxes); let centerOffset = scratchOffset; centerOffset.x = (minimumX + maximumX) / 2.0; centerOffset.y = (minimumY + maximumY) / 2.0; centerOffset.z = (minimumZ + maximumZ) / 2.0; const scale = scratchScale; scale.x = (maximumX - minimumX) / 2.0; scale.y = (maximumY - minimumY) / 2.0; scale.z = (maximumZ - minimumZ) / 2.0; const center = result.center; centerOffset = Matrix3.Matrix3.multiplyByVector(halfAxes, centerOffset, centerOffset); Matrix3.Cartesian3.add(planeOrigin, centerOffset, center); Matrix3.Matrix3.multiplyByScale(halfAxes, scale, halfAxes); return result; } const scratchRectangleCenterCartographic = new Matrix3.Cartographic(); const scratchRectangleCenter = new Matrix3.Cartesian3(); const scratchPerimeterCartographicNC = new Matrix3.Cartographic(); const scratchPerimeterCartographicNW = new Matrix3.Cartographic(); const scratchPerimeterCartographicCW = new Matrix3.Cartographic(); const scratchPerimeterCartographicSW = new Matrix3.Cartographic(); const scratchPerimeterCartographicSC = new Matrix3.Cartographic(); const scratchPerimeterCartesianNC = new Matrix3.Cartesian3(); const scratchPerimeterCartesianNW = new Matrix3.Cartesian3(); const scratchPerimeterCartesianCW = new Matrix3.Cartesian3(); const scratchPerimeterCartesianSW = new Matrix3.Cartesian3(); const scratchPerimeterCartesianSC = new Matrix3.Cartesian3(); const scratchPerimeterProjectedNC = new Matrix2.Cartesian2(); const scratchPerimeterProjectedNW = new Matrix2.Cartesian2(); const scratchPerimeterProjectedCW = new Matrix2.Cartesian2(); const scratchPerimeterProjectedSW = new Matrix2.Cartesian2(); const scratchPerimeterProjectedSC = new Matrix2.Cartesian2(); const scratchPlaneOrigin = new Matrix3.Cartesian3(); const scratchPlaneNormal = new Matrix3.Cartesian3(); const scratchPlaneXAxis = new Matrix3.Cartesian3(); const scratchHorizonCartesian = new Matrix3.Cartesian3(); const scratchHorizonProjected = new Matrix2.Cartesian2(); const scratchMaxY = new Matrix3.Cartesian3(); const scratchMinY = new Matrix3.Cartesian3(); const scratchZ = new Matrix3.Cartesian3(); const scratchPlane = new Plane.Plane(Matrix3.Cartesian3.UNIT_X, 0.0); /** * Computes an OrientedBoundingBox that bounds a {@link Rectangle} on the surface of an {@link Ellipsoid}. * There are no guarantees about the orientation of the bounding box. * * @param {Rectangle} rectangle The cartographic rectangle on the surface of the ellipsoid. * @param {Number} [minimumHeight=0.0] The minimum height (elevation) within the tile. * @param {Number} [maximumHeight=0.0] The maximum height (elevation) within the tile. * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the rectangle is defined. * @param {OrientedBoundingBox} [result] The object onto which to store the result. * @returns {OrientedBoundingBox} The modified result parameter or a new OrientedBoundingBox instance if none was provided. * * @exception {DeveloperError} rectangle.width must be between 0 and pi. * @exception {DeveloperError} rectangle.height must be between 0 and pi. * @exception {DeveloperError} ellipsoid must be an ellipsoid of revolution (radii.x == radii.y) */ OrientedBoundingBox.fromRectangle = function ( rectangle, minimumHeight, maximumHeight, ellipsoid, result ) { //>>includeStart('debug', pragmas.debug); if (!defaultValue.defined(rectangle)) { throw new Check.DeveloperError("rectangle is required"); } if (rectangle.width < 0.0 || rectangle.width > Math$1.CesiumMath.TWO_PI) { throw new Check.DeveloperError("Rectangle width must be between 0 and 2*pi"); } if (rectangle.height < 0.0 || rectangle.height > Math$1.CesiumMath.PI) { throw new Check.DeveloperError("Rectangle height must be between 0 and pi"); } if ( defaultValue.defined(ellipsoid) && !Math$1.CesiumMath.equalsEpsilon( ellipsoid.radii.x, ellipsoid.radii.y, Math$1.CesiumMath.EPSILON15 ) ) { throw new Check.DeveloperError( "Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y)" ); } //>>includeEnd('debug'); minimumHeight = defaultValue.defaultValue(minimumHeight, 0.0); maximumHeight = defaultValue.defaultValue(maximumHeight, 0.0); ellipsoid = defaultValue.defaultValue(ellipsoid, Matrix3.Ellipsoid.WGS84); let minX, maxX, minY, maxY, minZ, maxZ, plane; if (rectangle.width <= Math$1.CesiumMath.PI) { // The bounding box will be aligned with the tangent plane at the center of the rectangle. const tangentPointCartographic = Matrix2.Rectangle.center( rectangle, scratchRectangleCenterCartographic ); const tangentPoint = ellipsoid.cartographicToCartesian( tangentPointCartographic, scratchRectangleCenter ); const tangentPlane = new EllipsoidTangentPlane.EllipsoidTangentPlane(tangentPoint, ellipsoid); plane = tangentPlane.plane; // If the rectangle spans the equator, CW is instead aligned with the equator (because it sticks out the farthest at the equator). const lonCenter = tangentPointCartographic.longitude; const latCenter = rectangle.south < 0.0 && rectangle.north > 0.0 ? 0.0 : tangentPointCartographic.latitude; // Compute XY extents using the rectangle at maximum height const perimeterCartographicNC = Matrix3.Cartographic.fromRadians( lonCenter, rectangle.north, maximumHeight, scratchPerimeterCartographicNC ); const perimeterCartographicNW = Matrix3.Cartographic.fromRadians( rectangle.west, rectangle.north, maximumHeight, scratchPerimeterCartographicNW ); const perimeterCartographicCW = Matrix3.Cartographic.fromRadians( rectangle.west, latCenter, maximumHeight, scratchPerimeterCartographicCW ); const perimeterCartographicSW = Matrix3.Cartographic.fromRadians( rectangle.west, rectangle.south, maximumHeight, scratchPerimeterCartographicSW ); const perimeterCartographicSC = Matrix3.Cartographic.fromRadians( lonCenter, rectangle.south, maximumHeight, scratchPerimeterCartographicSC ); const perimeterCartesianNC = ellipsoid.cartographicToCartesian( perimeterCartographicNC, scratchPerimeterCartesianNC ); let perimeterCartesianNW = ellipsoid.cartographicToCartesian( perimeterCartographicNW, scratchPerimeterCartesianNW ); const perimeterCartesianCW = ellipsoid.cartographicToCartesian( perimeterCartographicCW, scratchPerimeterCartesianCW ); let perimeterCartesianSW = ellipsoid.cartographicToCartesian( perimeterCartographicSW, scratchPerimeterCartesianSW ); const perimeterCartesianSC = ellipsoid.cartographicToCartesian( perimeterCartographicSC, scratchPerimeterCartesianSC ); const perimeterProjectedNC = tangentPlane.projectPointToNearestOnPlane( perimeterCartesianNC, scratchPerimeterProjectedNC ); const perimeterProjectedNW = tangentPlane.projectPointToNearestOnPlane( perimeterCartesianNW, scratchPerimeterProjectedNW ); const perimeterProjectedCW = tangentPlane.projectPointToNearestOnPlane( perimeterCartesianCW, scratchPerimeterProjectedCW ); const perimeterProjectedSW = tangentPlane.projectPointToNearestOnPlane( perimeterCartesianSW, scratchPerimeterProjectedSW ); const perimeterProjectedSC = tangentPlane.projectPointToNearestOnPlane( perimeterCartesianSC, scratchPerimeterProjectedSC ); minX = Math.min( perimeterProjectedNW.x, perimeterProjectedCW.x, perimeterProjectedSW.x ); maxX = -minX; // symmetrical maxY = Math.max(perimeterProjectedNW.y, perimeterProjectedNC.y); minY = Math.min(perimeterProjectedSW.y, perimeterProjectedSC.y); // Compute minimum Z using the rectangle at minimum height, since it will be deeper than the maximum height perimeterCartographicNW.height = perimeterCartographicSW.height = minimumHeight; perimeterCartesianNW = ellipsoid.cartographicToCartesian( perimeterCartographicNW, scratchPerimeterCartesianNW ); perimeterCartesianSW = ellipsoid.cartographicToCartesian( perimeterCartographicSW, scratchPerimeterCartesianSW ); minZ = Math.min( Plane.Plane.getPointDistance(plane, perimeterCartesianNW), Plane.Plane.getPointDistance(plane, perimeterCartesianSW) ); maxZ = maximumHeight; // Since the tangent plane touches the surface at height = 0, this is okay return fromPlaneExtents( tangentPlane.origin, tangentPlane.xAxis, tangentPlane.yAxis, tangentPlane.zAxis, minX, maxX, minY, maxY, minZ, maxZ, result ); } // Handle the case where rectangle width is greater than PI (wraps around more than half the ellipsoid). const fullyAboveEquator = rectangle.south > 0.0; const fullyBelowEquator = rectangle.north < 0.0; const latitudeNearestToEquator = fullyAboveEquator ? rectangle.south : fullyBelowEquator ? rectangle.north : 0.0; const centerLongitude = Matrix2.Rectangle.center( rectangle, scratchRectangleCenterCartographic ).longitude; // Plane is located at the rectangle's center longitude and the rectangle's latitude that is closest to the equator. It rotates around the Z axis. // This results in a better fit than the obb approach for smaller rectangles, which orients with the rectangle's center normal. const planeOrigin = Matrix3.Cartesian3.fromRadians( centerLongitude, latitudeNearestToEquator, maximumHeight, ellipsoid, scratchPlaneOrigin ); planeOrigin.z = 0.0; // center the plane on the equator to simpify plane normal calculation const isPole = Math.abs(planeOrigin.x) < Math$1.CesiumMath.EPSILON10 && Math.abs(planeOrigin.y) < Math$1.CesiumMath.EPSILON10; const planeNormal = !isPole ? Matrix3.Cartesian3.normalize(planeOrigin, scratchPlaneNormal) : Matrix3.Cartesian3.UNIT_X; const planeYAxis = Matrix3.Cartesian3.UNIT_Z; const planeXAxis = Matrix3.Cartesian3.cross( planeNormal, planeYAxis, scratchPlaneXAxis ); plane = Plane.Plane.fromPointNormal(planeOrigin, planeNormal, scratchPlane); // Get the horizon point relative to the center. This will be the farthest extent in the plane's X dimension. const horizonCartesian = Matrix3.Cartesian3.fromRadians( centerLongitude + Math$1.CesiumMath.PI_OVER_TWO, latitudeNearestToEquator, maximumHeight, ellipsoid, scratchHorizonCartesian ); maxX = Matrix3.Cartesian3.dot( Plane.Plane.projectPointOntoPlane( plane, horizonCartesian, scratchHorizonProjected ), planeXAxis ); minX = -maxX; // symmetrical // Get the min and max Y, using the height that will give the largest extent maxY = Matrix3.Cartesian3.fromRadians( 0.0, rectangle.north, fullyBelowEquator ? minimumHeight : maximumHeight, ellipsoid, scratchMaxY ).z; minY = Matrix3.Cartesian3.fromRadians( 0.0, rectangle.south, fullyAboveEquator ? minimumHeight : maximumHeight, ellipsoid, scratchMinY ).z; const farZ = Matrix3.Cartesian3.fromRadians( rectangle.east, latitudeNearestToEquator, maximumHeight, ellipsoid, scratchZ ); minZ = Plane.Plane.getPointDistance(plane, farZ); maxZ = 0.0; // plane origin starts at maxZ already // min and max are local to the plane axes return fromPlaneExtents( planeOrigin, planeXAxis, planeYAxis, planeNormal, minX, maxX, minY, maxY, minZ, maxZ, result ); }; /** * Computes an OrientedBoundingBox that bounds an affine transformation. * * @param {Matrix4} transformation The affine transformation. * @param {OrientedBoundingBox} [result] The object onto which to store the result. * @returns {OrientedBoundingBox} The modified result parameter or a new OrientedBoundingBox instance if none was provided. */ OrientedBoundingBox.fromTransformation = function (transformation, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("transformation", transformation); //>>includeEnd('debug'); if (!defaultValue.defined(result)) { result = new OrientedBoundingBox(); } result.center = Matrix2.Matrix4.getTranslation(transformation, result.center); result.halfAxes = Matrix2.Matrix4.getMatrix3(transformation, result.halfAxes); result.halfAxes = Matrix3.Matrix3.multiplyByScalar( result.halfAxes, 0.5, result.halfAxes ); return result; }; /** * Duplicates a OrientedBoundingBox instance. * * @param {OrientedBoundingBox} box The bounding box to duplicate. * @param {OrientedBoundingBox} [result] The object onto which to store the result. * @returns {OrientedBoundingBox} The modified result parameter or a new OrientedBoundingBox instance if none was provided. (Returns undefined if box is undefined) */ OrientedBoundingBox.clone = function (box, result) { if (!defaultValue.defined(box)) { return undefined; } if (!defaultValue.defined(result)) { return new OrientedBoundingBox(box.center, box.halfAxes); } Matrix3.Cartesian3.clone(box.center, result.center); Matrix3.Matrix3.clone(box.halfAxes, result.halfAxes); return result; }; /** * Determines which side of a plane the oriented bounding box is located. * * @param {OrientedBoundingBox} box The oriented bounding box to test. * @param {Plane} plane The plane to test against. * @returns {Intersect} {@link Intersect.INSIDE} if the entire box is on the side of the plane * the normal is pointing, {@link Intersect.OUTSIDE} if the entire box is * on the opposite side, and {@link Intersect.INTERSECTING} if the box * intersects the plane. */ OrientedBoundingBox.intersectPlane = function (box, plane) { //>>includeStart('debug', pragmas.debug); if (!defaultValue.defined(box)) { throw new Check.DeveloperError("box is required."); } if (!defaultValue.defined(plane)) { throw new Check.DeveloperError("plane is required."); } //>>includeEnd('debug'); const center = box.center; const normal = plane.normal; const halfAxes = box.halfAxes; const normalX = normal.x, normalY = normal.y, normalZ = normal.z; // plane is used as if it is its normal; the first three components are assumed to be normalized const radEffective = Math.abs( normalX * halfAxes[Matrix3.Matrix3.COLUMN0ROW0] + normalY * halfAxes[Matrix3.Matrix3.COLUMN0ROW1] + normalZ * halfAxes[Matrix3.Matrix3.COLUMN0ROW2] ) + Math.abs( normalX * halfAxes[Matrix3.Matrix3.COLUMN1ROW0] + normalY * halfAxes[Matrix3.Matrix3.COLUMN1ROW1] + normalZ * halfAxes[Matrix3.Matrix3.COLUMN1ROW2] ) + Math.abs( normalX * halfAxes[Matrix3.Matrix3.COLUMN2ROW0] + normalY * halfAxes[Matrix3.Matrix3.COLUMN2ROW1] + normalZ * halfAxes[Matrix3.Matrix3.COLUMN2ROW2] ); const distanceToPlane = Matrix3.Cartesian3.dot(normal, center) + plane.distance; if (distanceToPlane <= -radEffective) { // The entire box is on the negative side of the plane normal return Transforms.Intersect.OUTSIDE; } else if (distanceToPlane >= radEffective) { // The entire box is on the positive side of the plane normal return Transforms.Intersect.INSIDE; } return Transforms.Intersect.INTERSECTING; }; const scratchCartesianU = new Matrix3.Cartesian3(); const scratchCartesianV = new Matrix3.Cartesian3(); const scratchCartesianW = new Matrix3.Cartesian3(); const scratchValidAxis2 = new Matrix3.Cartesian3(); const scratchValidAxis3 = new Matrix3.Cartesian3(); const scratchPPrime = new Matrix3.Cartesian3(); /** * Computes the estimated distance squared from the closest point on a bounding box to a point. * * @param {OrientedBoundingBox} box The box. * @param {Cartesian3} cartesian The point * @returns {Number} The distance squared from the oriented bounding box to the point. Returns 0 if the point is inside the box. * * @example * // Sort bounding boxes from back to front * boxes.sort(function(a, b) { * return Cesium.OrientedBoundingBox.distanceSquaredTo(b, camera.positionWC) - Cesium.OrientedBoundingBox.distanceSquaredTo(a, camera.positionWC); * }); */ OrientedBoundingBox.distanceSquaredTo = function (box, cartesian) { // See Geometric Tools for Computer Graphics 10.4.2 //>>includeStart('debug', pragmas.debug); if (!defaultValue.defined(box)) { throw new Check.DeveloperError("box is required."); } if (!defaultValue.defined(cartesian)) { throw new Check.DeveloperError("cartesian is required."); } //>>includeEnd('debug'); const offset = Matrix3.Cartesian3.subtract(cartesian, box.center, scratchOffset); const halfAxes = box.halfAxes; let u = Matrix3.Matrix3.getColumn(halfAxes, 0, scratchCartesianU); let v = Matrix3.Matrix3.getColumn(halfAxes, 1, scratchCartesianV); let w = Matrix3.Matrix3.getColumn(halfAxes, 2, scratchCartesianW); const uHalf = Matrix3.Cartesian3.magnitude(u); const vHalf = Matrix3.Cartesian3.magnitude(v); const wHalf = Matrix3.Cartesian3.magnitude(w); let uValid = true; let vValid = true; let wValid = true; if (uHalf > 0) { Matrix3.Cartesian3.divideByScalar(u, uHalf, u); } else { uValid = false; } if (vHalf > 0) { Matrix3.Cartesian3.divideByScalar(v, vHalf, v); } else { vValid = false; } if (wHalf > 0) { Matrix3.Cartesian3.divideByScalar(w, wHalf, w); } else { wValid = false; } const numberOfDegenerateAxes = !uValid + !vValid + !wValid; let validAxis1; let validAxis2; let validAxis3; if (numberOfDegenerateAxes === 1) { let degenerateAxis = u; validAxis1 = v; validAxis2 = w; if (!vValid) { degenerateAxis = v; validAxis1 = u; } else if (!wValid) { degenerateAxis = w; validAxis2 = u; } validAxis3 = Matrix3.Cartesian3.cross(validAxis1, validAxis2, scratchValidAxis3); if (degenerateAxis === u) { u = validAxis3; } else if (degenerateAxis === v) { v = validAxis3; } else if (degenerateAxis === w) { w = validAxis3; } } else if (numberOfDegenerateAxes === 2) { validAxis1 = u; if (vValid) { validAxis1 = v; } else if (wValid) { validAxis1 = w; } let crossVector = Matrix3.Cartesian3.UNIT_Y; if (crossVector.equalsEpsilon(validAxis1, Math$1.CesiumMath.EPSILON3)) { crossVector = Matrix3.Cartesian3.UNIT_X; } validAxis2 = Matrix3.Cartesian3.cross(validAxis1, crossVector, scratchValidAxis2); Matrix3.Cartesian3.normalize(validAxis2, validAxis2); validAxis3 = Matrix3.Cartesian3.cross(validAxis1, validAxis2, scratchValidAxis3); Matrix3.Cartesian3.normalize(validAxis3, validAxis3); if (validAxis1 === u) { v = validAxis2; w = validAxis3; } else if (validAxis1 === v) { w = validAxis2; u = validAxis3; } else if (validAxis1 === w) { u = validAxis2; v = validAxis3; } } else if (numberOfDegenerateAxes === 3) { u = Matrix3.Cartesian3.UNIT_X; v = Matrix3.Cartesian3.UNIT_Y; w = Matrix3.Cartesian3.UNIT_Z; } const pPrime = scratchPPrime; pPrime.x = Matrix3.Cartesian3.dot(offset, u); pPrime.y = Matrix3.Cartesian3.dot(offset, v); pPrime.z = Matrix3.Cartesian3.dot(offset, w); let distanceSquared = 0.0; let d; if (pPrime.x < -uHalf) { d = pPrime.x + uHalf; distanceSquared += d * d; } else if (pPrime.x > uHalf) { d = pPrime.x - uHalf; distanceSquared += d * d; } if (pPrime.y < -vHalf) { d = pPrime.y + vHalf; distanceSquared += d * d; } else if (pPrime.y > vHalf) { d = pPrime.y - vHalf; distanceSquared += d * d; } if (pPrime.z < -wHalf) { d = pPrime.z + wHalf; distanceSquared += d * d; } else if (pPrime.z > wHalf) { d = pPrime.z - wHalf; distanceSquared += d * d; } return distanceSquared; }; const scratchCorner = new Matrix3.Cartesian3(); const scratchToCenter = new Matrix3.Cartesian3(); /** * The distances calculated by the vector from the center of the bounding box to position projected onto direction. *
* If you imagine the infinite number of planes with normal direction, this computes the smallest distance to the * closest and farthest planes from position that intersect the bounding box. * * @param {OrientedBoundingBox} box The bounding box to calculate the distance to. * @param {Cartesian3} position The position to calculate the distance from. * @param {Cartesian3} direction The direction from position. * @param {Interval} [result] A Interval to store the nearest and farthest distances. * @returns {Interval} The nearest and farthest distances on the bounding box from position in direction. */ OrientedBoundingBox.computePlaneDistances = function ( box, position, direction, result ) { //>>includeStart('debug', pragmas.debug); if (!defaultValue.defined(box)) { throw new Check.DeveloperError("box is required."); } if (!defaultValue.defined(position)) { throw new Check.DeveloperError("position is required."); } if (!defaultValue.defined(direction)) { throw new Check.DeveloperError("direction is required."); } //>>includeEnd('debug'); if (!defaultValue.defined(result)) { result = new Transforms.Interval(); } let minDist = Number.POSITIVE_INFINITY; let maxDist = Number.NEGATIVE_INFINITY; const center = box.center; const halfAxes = box.halfAxes; const u = Matrix3.Matrix3.getColumn(halfAxes, 0, scratchCartesianU); const v = Matrix3.Matrix3.getColumn(halfAxes, 1, scratchCartesianV); const w = Matrix3.Matrix3.getColumn(halfAxes, 2, scratchCartesianW); // project first corner const corner = Matrix3.Cartesian3.add(u, v, scratchCorner); Matrix3.Cartesian3.add(corner, w, corner); Matrix3.Cartesian3.add(corner, center, corner); const toCenter = Matrix3.Cartesian3.subtract(corner, position, scratchToCenter); let mag = Matrix3.Cartesian3.dot(direction, toCenter); minDist = Math.min(mag, minDist); maxDist = Math.max(mag, maxDist); // project second corner Matrix3.Cartesian3.add(center, u, corner); Matrix3.Cartesian3.add(corner, v, corner); Matrix3.Cartesian3.subtract(corner, w, corner); Matrix3.Cartesian3.subtract(corner, position, toCenter); mag = Matrix3.Cartesian3.dot(direction, toCenter); minDist = Math.min(mag, minDist); maxDist = Math.max(mag, maxDist); // project third corner Matrix3.Cartesian3.add(center, u, corner); Matrix3.Cartesian3.subtract(corner, v, corner); Matrix3.Cartesian3.add(corner, w, corner); Matrix3.Cartesian3.subtract(corner, position, toCenter); mag = Matrix3.Cartesian3.dot(direction, toCenter); minDist = Math.min(mag, minDist); maxDist = Math.max(mag, maxDist); // project fourth corner Matrix3.Cartesian3.add(center, u, corner); Matrix3.Cartesian3.subtract(corner, v, corner); Matrix3.Cartesian3.subtract(corner, w, corner); Matrix3.Cartesian3.subtract(corner, position, toCenter); mag = Matrix3.Cartesian3.dot(direction, toCenter); minDist = Math.min(mag, minDist); maxDist = Math.max(mag, maxDist); // project fifth corner Matrix3.Cartesian3.subtract(center, u, corner); Matrix3.Cartesian3.add(corner, v, corner); Matrix3.Cartesian3.add(corner, w, corner); Matrix3.Cartesian3.subtract(corner, position, toCenter); mag = Matrix3.Cartesian3.dot(direction, toCenter); minDist = Math.min(mag, minDist); maxDist = Math.max(mag, maxDist); // project sixth corner Matrix3.Cartesian3.subtract(center, u, corner); Matrix3.Cartesian3.add(corner, v, corner); Matrix3.Cartesian3.subtract(corner, w, corner); Matrix3.Cartesian3.subtract(corner, position, toCenter); mag = Matrix3.Cartesian3.dot(direction, toCenter); minDist = Math.min(mag, minDist); maxDist = Math.max(mag, maxDist); // project seventh corner Matrix3.Cartesian3.subtract(center, u, corner); Matrix3.Cartesian3.subtract(corner, v, corner); Matrix3.Cartesian3.add(corner, w, corner); Matrix3.Cartesian3.subtract(corner, position, toCenter); mag = Matrix3.Cartesian3.dot(direction, toCenter); minDist = Math.min(mag, minDist); maxDist = Math.max(mag, maxDist); // project eighth corner Matrix3.Cartesian3.subtract(center, u, corner); Matrix3.Cartesian3.subtract(corner, v, corner); Matrix3.Cartesian3.subtract(corner, w, corner); Matrix3.Cartesian3.subtract(corner, position, toCenter); mag = Matrix3.Cartesian3.dot(direction, toCenter); minDist = Math.min(mag, minDist); maxDist = Math.max(mag, maxDist); result.start = minDist; result.stop = maxDist; return result; }; const scratchXAxis = new Matrix3.Cartesian3(); const scratchYAxis = new Matrix3.Cartesian3(); const scratchZAxis = new Matrix3.Cartesian3(); /** * Computes the eight corners of an oriented bounding box. The corners are ordered by (-X, -Y, -Z), (-X, -Y, +Z), (-X, +Y, -Z), (-X, +Y, +Z), (+X, -Y, -Z), (+X, -Y, +Z), (+X, +Y, -Z), (+X, +Y, +Z). * * @param {OrientedBoundingBox} box The oriented bounding box. * @param {Cartesian3[]} [result] An array of eight {@link Cartesian3} instances onto which to store the corners. * @returns {Cartesian3[]} The modified result parameter or a new array if none was provided. */ OrientedBoundingBox.computeCorners = function (box, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("box", box); //>>includeEnd('debug'); if (!defaultValue.defined(result)) { result = [ new Matrix3.Cartesian3(), new Matrix3.Cartesian3(), new Matrix3.Cartesian3(), new Matrix3.Cartesian3(), new Matrix3.Cartesian3(), new Matrix3.Cartesian3(), new Matrix3.Cartesian3(), new Matrix3.Cartesian3(), ]; } const center = box.center; const halfAxes = box.halfAxes; const xAxis = Matrix3.Matrix3.getColumn(halfAxes, 0, scratchXAxis); const yAxis = Matrix3.Matrix3.getColumn(halfAxes, 1, scratchYAxis); const zAxis = Matrix3.Matrix3.getColumn(halfAxes, 2, scratchZAxis); Matrix3.Cartesian3.clone(center, result[0]); Matrix3.Cartesian3.subtract(result[0], xAxis, result[0]); Matrix3.Cartesian3.subtract(result[0], yAxis, result[0]); Matrix3.Cartesian3.subtract(result[0], zAxis, result[0]); Matrix3.Cartesian3.clone(center, result[1]); Matrix3.Cartesian3.subtract(result[1], xAxis, result[1]); Matrix3.Cartesian3.subtract(result[1], yAxis, result[1]); Matrix3.Cartesian3.add(result[1], zAxis, result[1]); Matrix3.Cartesian3.clone(center, result[2]); Matrix3.Cartesian3.subtract(result[2], xAxis, result[2]); Matrix3.Cartesian3.add(result[2], yAxis, result[2]); Matrix3.Cartesian3.subtract(result[2], zAxis, result[2]); Matrix3.Cartesian3.clone(center, result[3]); Matrix3.Cartesian3.subtract(result[3], xAxis, result[3]); Matrix3.Cartesian3.add(result[3], yAxis, result[3]); Matrix3.Cartesian3.add(result[3], zAxis, result[3]); Matrix3.Cartesian3.clone(center, result[4]); Matrix3.Cartesian3.add(result[4], xAxis, result[4]); Matrix3.Cartesian3.subtract(result[4], yAxis, result[4]); Matrix3.Cartesian3.subtract(result[4], zAxis, result[4]); Matrix3.Cartesian3.clone(center, result[5]); Matrix3.Cartesian3.add(result[5], xAxis, result[5]); Matrix3.Cartesian3.subtract(result[5], yAxis, result[5]); Matrix3.Cartesian3.add(result[5], zAxis, result[5]); Matrix3.Cartesian3.clone(center, result[6]); Matrix3.Cartesian3.add(result[6], xAxis, result[6]); Matrix3.Cartesian3.add(result[6], yAxis, result[6]); Matrix3.Cartesian3.subtract(result[6], zAxis, result[6]); Matrix3.Cartesian3.clone(center, result[7]); Matrix3.Cartesian3.add(result[7], xAxis, result[7]); Matrix3.Cartesian3.add(result[7], yAxis, result[7]); Matrix3.Cartesian3.add(result[7], zAxis, result[7]); return result; }; const scratchRotationScale = new Matrix3.Matrix3(); /** * Computes a transformation matrix from an oriented bounding box. * * @param {OrientedBoundingBox} box The oriented bounding box. * @param {Matrix4} result The object onto which to store the result. * @returns {Matrix4} The modified result parameter or a new {@link Matrix4} instance if none was provided. */ OrientedBoundingBox.computeTransformation = function (box, result) { //>>includeStart('debug', pragmas.debug); Check.Check.typeOf.object("box", box); //>>includeEnd('debug'); if (!defaultValue.defined(result)) { result = new Matrix2.Matrix4(); } const translation = box.center; const rotationScale = Matrix3.Matrix3.multiplyByUniformScale( box.halfAxes, 2.0, scratchRotationScale ); return Matrix2.Matrix4.fromRotationTranslation(rotationScale, translation, result); }; const scratchBoundingSphere = new Transforms.BoundingSphere(); /** * Determines whether or not a bounding box is hidden from view by the occluder. * * @param {OrientedBoundingBox} box The bounding box surrounding the occludee object. * @param {Occluder} occluder The occluder. * @returns {Boolean} true if the box is not visible; otherwise false. */ OrientedBoundingBox.isOccluded = function (box, occluder) { //>>includeStart('debug', pragmas.debug); if (!defaultValue.defined(box)) { throw new Check.DeveloperError("box is required."); } if (!defaultValue.defined(occluder)) { throw new Check.DeveloperError("occluder is required."); } //>>includeEnd('debug'); const sphere = Transforms.BoundingSphere.fromOrientedBoundingBox( box, scratchBoundingSphere ); return !occluder.isBoundingSphereVisible(sphere); }; /** * Determines which side of a plane the oriented bounding box is located. * * @param {Plane} plane The plane to test against. * @returns {Intersect} {@link Intersect.INSIDE} if the entire box is on the side of the plane * the normal is pointing, {@link Intersect.OUTSIDE} if the entire box is * on the opposite side, and {@link Intersect.INTERSECTING} if the box * intersects the plane. */ OrientedBoundingBox.prototype.intersectPlane = function (plane) { return OrientedBoundingBox.intersectPlane(this, plane); }; /** * Computes the estimated distance squared from the closest point on a bounding box to a point. * * @param {Cartesian3} cartesian The point * @returns {Number} The estimated distance squared from the bounding sphere to the point. * * @example * // Sort bounding boxes from back to front * boxes.sort(function(a, b) { * return b.distanceSquaredTo(camera.positionWC) - a.distanceSquaredTo(camera.positionWC); * }); */ OrientedBoundingBox.prototype.distanceSquaredTo = function (cartesian) { return OrientedBoundingBox.distanceSquaredTo(this, cartesian); }; /** * The distances calculated by the vector from the center of the bounding box to position projected onto direction. *
* If you imagine the infinite number of planes with normal direction, this computes the smallest distance to the * closest and farthest planes from position that intersect the bounding box. * * @param {Cartesian3} position The position to calculate the distance from. * @param {Cartesian3} direction The direction from position. * @param {Interval} [result] A Interval to store the nearest and farthest distances. * @returns {Interval} The nearest and farthest distances on the bounding box from position in direction. */ OrientedBoundingBox.prototype.computePlaneDistances = function ( position, direction, result ) { return OrientedBoundingBox.computePlaneDistances( this, position, direction, result ); }; /** * Computes the eight corners of an oriented bounding box. The corners are ordered by (-X, -Y, -Z), (-X, -Y, +Z), (-X, +Y, -Z), (-X, +Y, +Z), (+X, -Y, -Z), (+X, -Y, +Z), (+X, +Y, -Z), (+X, +Y, +Z). * * @param {Cartesian3[]} [result] An array of eight {@link Cartesian3} instances onto which to store the corners. * @returns {Cartesian3[]} The modified result parameter or a new array if none was provided. */ OrientedBoundingBox.prototype.computeCorners = function (result) { return OrientedBoundingBox.computeCorners(this, result); }; /** * Computes a transformation matrix from an oriented bounding box. * * @param {Matrix4} result The object onto which to store the result. * @returns {Matrix4} The modified result parameter or a new {@link Matrix4} instance if none was provided. */ OrientedBoundingBox.prototype.computeTransformation = function (result) { return OrientedBoundingBox.computeTransformation(this, result); }; /** * Determines whether or not a bounding box is hidden from view by the occluder. * * @param {Occluder} occluder The occluder. * @returns {Boolean} true if the sphere is not visible; otherwise false. */ OrientedBoundingBox.prototype.isOccluded = function (occluder) { return OrientedBoundingBox.isOccluded(this, occluder); }; /** * Compares the provided OrientedBoundingBox componentwise and returns * true if they are equal, false otherwise. * * @param {OrientedBoundingBox} left The first OrientedBoundingBox. * @param {OrientedBoundingBox} right The second OrientedBoundingBox. * @returns {Boolean} true if left and right are equal, false otherwise. */ OrientedBoundingBox.equals = function (left, right) { return ( left === right || (defaultValue.defined(left) && defaultValue.defined(right) && Matrix3.Cartesian3.equals(left.center, right.center) && Matrix3.Matrix3.equals(left.halfAxes, right.halfAxes)) ); }; /** * Duplicates this OrientedBoundingBox instance. * * @param {OrientedBoundingBox} [result] The object onto which to store the result. * @returns {OrientedBoundingBox} The modified result parameter or a new OrientedBoundingBox instance if one was not provided. */ OrientedBoundingBox.prototype.clone = function (result) { return OrientedBoundingBox.clone(this, result); }; /** * Compares this OrientedBoundingBox against the provided OrientedBoundingBox componentwise and returns * true if they are equal, false otherwise. * * @param {OrientedBoundingBox} [right] The right hand side OrientedBoundingBox. * @returns {Boolean} true if they are equal, false otherwise. */ OrientedBoundingBox.prototype.equals = function (right) { return OrientedBoundingBox.equals(this, right); }; exports.OrientedBoundingBox = OrientedBoundingBox; }));