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- {"version":3,"file":"OrientedBoundingBox-8897f474.js","sources":["../../../../Source/Core/OrientedBoundingBox.js"],"sourcesContent":["import BoundingSphere from \"./BoundingSphere.js\";\nimport Cartesian2 from \"./Cartesian2.js\";\nimport Cartesian3 from \"./Cartesian3.js\";\nimport Cartographic from \"./Cartographic.js\";\nimport Check from \"./Check.js\";\nimport defaultValue from \"./defaultValue.js\";\nimport defined from \"./defined.js\";\nimport DeveloperError from \"./DeveloperError.js\";\nimport Ellipsoid from \"./Ellipsoid.js\";\nimport EllipsoidTangentPlane from \"./EllipsoidTangentPlane.js\";\nimport Intersect from \"./Intersect.js\";\nimport Interval from \"./Interval.js\";\nimport CesiumMath from \"./Math.js\";\nimport Matrix3 from \"./Matrix3.js\";\nimport Plane from \"./Plane.js\";\nimport Rectangle from \"./Rectangle.js\";\n\n/**\n * Creates an instance of an OrientedBoundingBox.\n * 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.\n * @alias OrientedBoundingBox\n * @constructor\n *\n * @param {Cartesian3} [center=Cartesian3.ZERO] The center of the box.\n * @param {Matrix3} [halfAxes=Matrix3.ZERO] The three orthogonal half-axes of the bounding box.\n * Equivalently, the transformation matrix, to rotate and scale a 0x0x0\n * cube centered at the origin.\n *\n *\n * @example\n * // Create an OrientedBoundingBox using a transformation matrix, a position where the box will be translated, and a scale.\n * var center = new Cesium.Cartesian3(1.0, 0.0, 0.0);\n * var halfAxes = Cesium.Matrix3.fromScale(new Cesium.Cartesian3(1.0, 3.0, 2.0), new Cesium.Matrix3());\n *\n * var obb = new Cesium.OrientedBoundingBox(center, halfAxes);\n *\n * @see BoundingSphere\n * @see BoundingRectangle\n */\nfunction OrientedBoundingBox(center, halfAxes) {\n /**\n * The center of the box.\n * @type {Cartesian3}\n * @default {@link Cartesian3.ZERO}\n */\n this.center = Cartesian3.clone(defaultValue(center, Cartesian3.ZERO));\n /**\n * The transformation matrix, to rotate the box to the right position.\n * @type {Matrix3}\n * @default {@link Matrix3.ZERO}\n */\n this.halfAxes = Matrix3.clone(defaultValue(halfAxes, Matrix3.ZERO));\n}\n\n/**\n * The number of elements used to pack the object into an array.\n * @type {Number}\n */\nOrientedBoundingBox.packedLength =\n Cartesian3.packedLength + Matrix3.packedLength;\n\n/**\n * Stores the provided instance into the provided array.\n *\n * @param {OrientedBoundingBox} value The value to pack.\n * @param {Number[]} array The array to pack into.\n * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.\n *\n * @returns {Number[]} The array that was packed into\n */\nOrientedBoundingBox.pack = function (value, array, startingIndex) {\n //>>includeStart('debug', pragmas.debug);\n Check.typeOf.object(\"value\", value);\n Check.defined(\"array\", array);\n //>>includeEnd('debug');\n\n startingIndex = defaultValue(startingIndex, 0);\n\n Cartesian3.pack(value.center, array, startingIndex);\n Matrix3.pack(value.halfAxes, array, startingIndex + Cartesian3.packedLength);\n\n return array;\n};\n\n/**\n * Retrieves an instance from a packed array.\n *\n * @param {Number[]} array The packed array.\n * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.\n * @param {OrientedBoundingBox} [result] The object into which to store the result.\n * @returns {OrientedBoundingBox} The modified result parameter or a new OrientedBoundingBox instance if one was not provided.\n */\nOrientedBoundingBox.unpack = function (array, startingIndex, result) {\n //>>includeStart('debug', pragmas.debug);\n Check.defined(\"array\", array);\n //>>includeEnd('debug');\n\n startingIndex = defaultValue(startingIndex, 0);\n\n if (!defined(result)) {\n result = new OrientedBoundingBox();\n }\n\n Cartesian3.unpack(array, startingIndex, result.center);\n Matrix3.unpack(\n array,\n startingIndex + Cartesian3.packedLength,\n result.halfAxes\n );\n return result;\n};\n\nvar scratchCartesian1 = new Cartesian3();\nvar scratchCartesian2 = new Cartesian3();\nvar scratchCartesian3 = new Cartesian3();\nvar scratchCartesian4 = new Cartesian3();\nvar scratchCartesian5 = new Cartesian3();\nvar scratchCartesian6 = new Cartesian3();\nvar scratchCovarianceResult = new Matrix3();\nvar scratchEigenResult = {\n unitary: new Matrix3(),\n diagonal: new Matrix3(),\n};\n\n/**\n * Computes an instance of an OrientedBoundingBox of the given positions.\n * This is an implementation of Stefan Gottschalk's Collision Queries using Oriented Bounding Boxes solution (PHD thesis).\n * Reference: http://gamma.cs.unc.edu/users/gottschalk/main.pdf\n *\n * @param {Cartesian3[]} [positions] List of {@link Cartesian3} points that the bounding box will enclose.\n * @param {OrientedBoundingBox} [result] The object onto which to store the result.\n * @returns {OrientedBoundingBox} The modified result parameter or a new OrientedBoundingBox instance if one was not provided.\n *\n * @example\n * // Compute an object oriented bounding box enclosing two points.\n * var box = Cesium.OrientedBoundingBox.fromPoints([new Cesium.Cartesian3(2, 0, 0), new Cesium.Cartesian3(-2, 0, 0)]);\n */\nOrientedBoundingBox.fromPoints = function (positions, result) {\n if (!defined(result)) {\n result = new OrientedBoundingBox();\n }\n\n if (!defined(positions) || positions.length === 0) {\n result.halfAxes = Matrix3.ZERO;\n result.center = Cartesian3.ZERO;\n return result;\n }\n\n var i;\n var length = positions.length;\n\n var meanPoint = Cartesian3.clone(positions[0], scratchCartesian1);\n for (i = 1; i < length; i++) {\n Cartesian3.add(meanPoint, positions[i], meanPoint);\n }\n var invLength = 1.0 / length;\n Cartesian3.multiplyByScalar(meanPoint, invLength, meanPoint);\n\n var exx = 0.0;\n var exy = 0.0;\n var exz = 0.0;\n var eyy = 0.0;\n var eyz = 0.0;\n var ezz = 0.0;\n var p;\n\n for (i = 0; i < length; i++) {\n p = Cartesian3.subtract(positions[i], meanPoint, scratchCartesian2);\n exx += p.x * p.x;\n exy += p.x * p.y;\n exz += p.x * p.z;\n eyy += p.y * p.y;\n eyz += p.y * p.z;\n ezz += p.z * p.z;\n }\n\n exx *= invLength;\n exy *= invLength;\n exz *= invLength;\n eyy *= invLength;\n eyz *= invLength;\n ezz *= invLength;\n\n var covarianceMatrix = scratchCovarianceResult;\n covarianceMatrix[0] = exx;\n covarianceMatrix[1] = exy;\n covarianceMatrix[2] = exz;\n covarianceMatrix[3] = exy;\n covarianceMatrix[4] = eyy;\n covarianceMatrix[5] = eyz;\n covarianceMatrix[6] = exz;\n covarianceMatrix[7] = eyz;\n covarianceMatrix[8] = ezz;\n\n var eigenDecomposition = Matrix3.computeEigenDecomposition(\n covarianceMatrix,\n scratchEigenResult\n );\n var rotation = Matrix3.clone(eigenDecomposition.unitary, result.halfAxes);\n\n var v1 = Matrix3.getColumn(rotation, 0, scratchCartesian4);\n var v2 = Matrix3.getColumn(rotation, 1, scratchCartesian5);\n var v3 = Matrix3.getColumn(rotation, 2, scratchCartesian6);\n\n var u1 = -Number.MAX_VALUE;\n var u2 = -Number.MAX_VALUE;\n var u3 = -Number.MAX_VALUE;\n var l1 = Number.MAX_VALUE;\n var l2 = Number.MAX_VALUE;\n var l3 = Number.MAX_VALUE;\n\n for (i = 0; i < length; i++) {\n p = positions[i];\n u1 = Math.max(Cartesian3.dot(v1, p), u1);\n u2 = Math.max(Cartesian3.dot(v2, p), u2);\n u3 = Math.max(Cartesian3.dot(v3, p), u3);\n\n l1 = Math.min(Cartesian3.dot(v1, p), l1);\n l2 = Math.min(Cartesian3.dot(v2, p), l2);\n l3 = Math.min(Cartesian3.dot(v3, p), l3);\n }\n\n v1 = Cartesian3.multiplyByScalar(v1, 0.5 * (l1 + u1), v1);\n v2 = Cartesian3.multiplyByScalar(v2, 0.5 * (l2 + u2), v2);\n v3 = Cartesian3.multiplyByScalar(v3, 0.5 * (l3 + u3), v3);\n\n var center = Cartesian3.add(v1, v2, result.center);\n Cartesian3.add(center, v3, center);\n\n var scale = scratchCartesian3;\n scale.x = u1 - l1;\n scale.y = u2 - l2;\n scale.z = u3 - l3;\n Cartesian3.multiplyByScalar(scale, 0.5, scale);\n Matrix3.multiplyByScale(result.halfAxes, scale, result.halfAxes);\n\n return result;\n};\n\nvar scratchOffset = new Cartesian3();\nvar scratchScale = new Cartesian3();\nfunction fromPlaneExtents(\n planeOrigin,\n planeXAxis,\n planeYAxis,\n planeZAxis,\n minimumX,\n maximumX,\n minimumY,\n maximumY,\n minimumZ,\n maximumZ,\n result\n) {\n //>>includeStart('debug', pragmas.debug);\n if (\n !defined(minimumX) ||\n !defined(maximumX) ||\n !defined(minimumY) ||\n !defined(maximumY) ||\n !defined(minimumZ) ||\n !defined(maximumZ)\n ) {\n throw new DeveloperError(\n \"all extents (minimum/maximum X/Y/Z) are required.\"\n );\n }\n //>>includeEnd('debug');\n\n if (!defined(result)) {\n result = new OrientedBoundingBox();\n }\n\n var halfAxes = result.halfAxes;\n Matrix3.setColumn(halfAxes, 0, planeXAxis, halfAxes);\n Matrix3.setColumn(halfAxes, 1, planeYAxis, halfAxes);\n Matrix3.setColumn(halfAxes, 2, planeZAxis, halfAxes);\n\n var centerOffset = scratchOffset;\n centerOffset.x = (minimumX + maximumX) / 2.0;\n centerOffset.y = (minimumY + maximumY) / 2.0;\n centerOffset.z = (minimumZ + maximumZ) / 2.0;\n\n var scale = scratchScale;\n scale.x = (maximumX - minimumX) / 2.0;\n scale.y = (maximumY - minimumY) / 2.0;\n scale.z = (maximumZ - minimumZ) / 2.0;\n\n var center = result.center;\n centerOffset = Matrix3.multiplyByVector(halfAxes, centerOffset, centerOffset);\n Cartesian3.add(planeOrigin, centerOffset, center);\n Matrix3.multiplyByScale(halfAxes, scale, halfAxes);\n\n return result;\n}\n\nvar scratchRectangleCenterCartographic = new Cartographic();\nvar scratchRectangleCenter = new Cartesian3();\nvar scratchPerimeterCartographicNC = new Cartographic();\nvar scratchPerimeterCartographicNW = new Cartographic();\nvar scratchPerimeterCartographicCW = new Cartographic();\nvar scratchPerimeterCartographicSW = new Cartographic();\nvar scratchPerimeterCartographicSC = new Cartographic();\nvar scratchPerimeterCartesianNC = new Cartesian3();\nvar scratchPerimeterCartesianNW = new Cartesian3();\nvar scratchPerimeterCartesianCW = new Cartesian3();\nvar scratchPerimeterCartesianSW = new Cartesian3();\nvar scratchPerimeterCartesianSC = new Cartesian3();\nvar scratchPerimeterProjectedNC = new Cartesian2();\nvar scratchPerimeterProjectedNW = new Cartesian2();\nvar scratchPerimeterProjectedCW = new Cartesian2();\nvar scratchPerimeterProjectedSW = new Cartesian2();\nvar scratchPerimeterProjectedSC = new Cartesian2();\n\nvar scratchPlaneOrigin = new Cartesian3();\nvar scratchPlaneNormal = new Cartesian3();\nvar scratchPlaneXAxis = new Cartesian3();\nvar scratchHorizonCartesian = new Cartesian3();\nvar scratchHorizonProjected = new Cartesian2();\nvar scratchMaxY = new Cartesian3();\nvar scratchMinY = new Cartesian3();\nvar scratchZ = new Cartesian3();\nvar scratchPlane = new Plane(Cartesian3.UNIT_X, 0.0);\n\n/**\n * Computes an OrientedBoundingBox that bounds a {@link Rectangle} on the surface of an {@link Ellipsoid}.\n * There are no guarantees about the orientation of the bounding box.\n *\n * @param {Rectangle} rectangle The cartographic rectangle on the surface of the ellipsoid.\n * @param {Number} [minimumHeight=0.0] The minimum height (elevation) within the tile.\n * @param {Number} [maximumHeight=0.0] The maximum height (elevation) within the tile.\n * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid on which the rectangle is defined.\n * @param {OrientedBoundingBox} [result] The object onto which to store the result.\n * @returns {OrientedBoundingBox} The modified result parameter or a new OrientedBoundingBox instance if none was provided.\n *\n * @exception {DeveloperError} rectangle.width must be between 0 and pi.\n * @exception {DeveloperError} rectangle.height must be between 0 and pi.\n * @exception {DeveloperError} ellipsoid must be an ellipsoid of revolution (<code>radii.x == radii.y</code>)\n */\nOrientedBoundingBox.fromRectangle = function (\n rectangle,\n minimumHeight,\n maximumHeight,\n ellipsoid,\n result\n) {\n //>>includeStart('debug', pragmas.debug);\n if (!defined(rectangle)) {\n throw new DeveloperError(\"rectangle is required\");\n }\n if (rectangle.width < 0.0 || rectangle.width > CesiumMath.TWO_PI) {\n throw new DeveloperError(\"Rectangle width must be between 0 and 2*pi\");\n }\n if (rectangle.height < 0.0 || rectangle.height > CesiumMath.PI) {\n throw new DeveloperError(\"Rectangle height must be between 0 and pi\");\n }\n if (\n defined(ellipsoid) &&\n !CesiumMath.equalsEpsilon(\n ellipsoid.radii.x,\n ellipsoid.radii.y,\n CesiumMath.EPSILON15\n )\n ) {\n throw new DeveloperError(\n \"Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y)\"\n );\n }\n //>>includeEnd('debug');\n\n minimumHeight = defaultValue(minimumHeight, 0.0);\n maximumHeight = defaultValue(maximumHeight, 0.0);\n ellipsoid = defaultValue(ellipsoid, Ellipsoid.WGS84);\n\n var minX, maxX, minY, maxY, minZ, maxZ, plane;\n\n if (rectangle.width <= CesiumMath.PI) {\n // The bounding box will be aligned with the tangent plane at the center of the rectangle.\n var tangentPointCartographic = Rectangle.center(\n rectangle,\n scratchRectangleCenterCartographic\n );\n var tangentPoint = ellipsoid.cartographicToCartesian(\n tangentPointCartographic,\n scratchRectangleCenter\n );\n var tangentPlane = new EllipsoidTangentPlane(tangentPoint, ellipsoid);\n plane = tangentPlane.plane;\n\n // If the rectangle spans the equator, CW is instead aligned with the equator (because it sticks out the farthest at the equator).\n var lonCenter = tangentPointCartographic.longitude;\n var latCenter =\n rectangle.south < 0.0 && rectangle.north > 0.0\n ? 0.0\n : tangentPointCartographic.latitude;\n\n // Compute XY extents using the rectangle at maximum height\n var perimeterCartographicNC = Cartographic.fromRadians(\n lonCenter,\n rectangle.north,\n maximumHeight,\n scratchPerimeterCartographicNC\n );\n var perimeterCartographicNW = Cartographic.fromRadians(\n rectangle.west,\n rectangle.north,\n maximumHeight,\n scratchPerimeterCartographicNW\n );\n var perimeterCartographicCW = Cartographic.fromRadians(\n rectangle.west,\n latCenter,\n maximumHeight,\n scratchPerimeterCartographicCW\n );\n var perimeterCartographicSW = Cartographic.fromRadians(\n rectangle.west,\n rectangle.south,\n maximumHeight,\n scratchPerimeterCartographicSW\n );\n var perimeterCartographicSC = Cartographic.fromRadians(\n lonCenter,\n rectangle.south,\n maximumHeight,\n scratchPerimeterCartographicSC\n );\n\n var perimeterCartesianNC = ellipsoid.cartographicToCartesian(\n perimeterCartographicNC,\n scratchPerimeterCartesianNC\n );\n var perimeterCartesianNW = ellipsoid.cartographicToCartesian(\n perimeterCartographicNW,\n scratchPerimeterCartesianNW\n );\n var perimeterCartesianCW = ellipsoid.cartographicToCartesian(\n perimeterCartographicCW,\n scratchPerimeterCartesianCW\n );\n var perimeterCartesianSW = ellipsoid.cartographicToCartesian(\n perimeterCartographicSW,\n scratchPerimeterCartesianSW\n );\n var perimeterCartesianSC = ellipsoid.cartographicToCartesian(\n perimeterCartographicSC,\n scratchPerimeterCartesianSC\n );\n\n var perimeterProjectedNC = tangentPlane.projectPointToNearestOnPlane(\n perimeterCartesianNC,\n scratchPerimeterProjectedNC\n );\n var perimeterProjectedNW = tangentPlane.projectPointToNearestOnPlane(\n perimeterCartesianNW,\n scratchPerimeterProjectedNW\n );\n var perimeterProjectedCW = tangentPlane.projectPointToNearestOnPlane(\n perimeterCartesianCW,\n scratchPerimeterProjectedCW\n );\n var perimeterProjectedSW = tangentPlane.projectPointToNearestOnPlane(\n perimeterCartesianSW,\n scratchPerimeterProjectedSW\n );\n var perimeterProjectedSC = tangentPlane.projectPointToNearestOnPlane(\n perimeterCartesianSC,\n scratchPerimeterProjectedSC\n );\n\n minX = Math.min(\n perimeterProjectedNW.x,\n perimeterProjectedCW.x,\n perimeterProjectedSW.x\n );\n maxX = -minX; // symmetrical\n\n maxY = Math.max(perimeterProjectedNW.y, perimeterProjectedNC.y);\n minY = Math.min(perimeterProjectedSW.y, perimeterProjectedSC.y);\n\n // Compute minimum Z using the rectangle at minimum height, since it will be deeper than the maximum height\n perimeterCartographicNW.height = perimeterCartographicSW.height = minimumHeight;\n perimeterCartesianNW = ellipsoid.cartographicToCartesian(\n perimeterCartographicNW,\n scratchPerimeterCartesianNW\n );\n perimeterCartesianSW = ellipsoid.cartographicToCartesian(\n perimeterCartographicSW,\n scratchPerimeterCartesianSW\n );\n\n minZ = Math.min(\n Plane.getPointDistance(plane, perimeterCartesianNW),\n Plane.getPointDistance(plane, perimeterCartesianSW)\n );\n maxZ = maximumHeight; // Since the tangent plane touches the surface at height = 0, this is okay\n\n return fromPlaneExtents(\n tangentPlane.origin,\n tangentPlane.xAxis,\n tangentPlane.yAxis,\n tangentPlane.zAxis,\n minX,\n maxX,\n minY,\n maxY,\n minZ,\n maxZ,\n result\n );\n }\n\n // Handle the case where rectangle width is greater than PI (wraps around more than half the ellipsoid).\n var fullyAboveEquator = rectangle.south > 0.0;\n var fullyBelowEquator = rectangle.north < 0.0;\n var latitudeNearestToEquator = fullyAboveEquator\n ? rectangle.south\n : fullyBelowEquator\n ? rectangle.north\n : 0.0;\n var centerLongitude = Rectangle.center(\n rectangle,\n scratchRectangleCenterCartographic\n ).longitude;\n\n // 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.\n // This results in a better fit than the obb approach for smaller rectangles, which orients with the rectangle's center normal.\n var planeOrigin = Cartesian3.fromRadians(\n centerLongitude,\n latitudeNearestToEquator,\n maximumHeight,\n ellipsoid,\n scratchPlaneOrigin\n );\n planeOrigin.z = 0.0; // center the plane on the equator to simpify plane normal calculation\n var isPole =\n Math.abs(planeOrigin.x) < CesiumMath.EPSILON10 &&\n Math.abs(planeOrigin.y) < CesiumMath.EPSILON10;\n var planeNormal = !isPole\n ? Cartesian3.normalize(planeOrigin, scratchPlaneNormal)\n : Cartesian3.UNIT_X;\n var planeYAxis = Cartesian3.UNIT_Z;\n var planeXAxis = Cartesian3.cross(planeNormal, planeYAxis, scratchPlaneXAxis);\n plane = Plane.fromPointNormal(planeOrigin, planeNormal, scratchPlane);\n\n // Get the horizon point relative to the center. This will be the farthest extent in the plane's X dimension.\n var horizonCartesian = Cartesian3.fromRadians(\n centerLongitude + CesiumMath.PI_OVER_TWO,\n latitudeNearestToEquator,\n maximumHeight,\n ellipsoid,\n scratchHorizonCartesian\n );\n maxX = Cartesian3.dot(\n Plane.projectPointOntoPlane(\n plane,\n horizonCartesian,\n scratchHorizonProjected\n ),\n planeXAxis\n );\n minX = -maxX; // symmetrical\n\n // Get the min and max Y, using the height that will give the largest extent\n maxY = Cartesian3.fromRadians(\n 0.0,\n rectangle.north,\n fullyBelowEquator ? minimumHeight : maximumHeight,\n ellipsoid,\n scratchMaxY\n ).z;\n minY = Cartesian3.fromRadians(\n 0.0,\n rectangle.south,\n fullyAboveEquator ? minimumHeight : maximumHeight,\n ellipsoid,\n scratchMinY\n ).z;\n\n var farZ = Cartesian3.fromRadians(\n rectangle.east,\n latitudeNearestToEquator,\n maximumHeight,\n ellipsoid,\n scratchZ\n );\n minZ = Plane.getPointDistance(plane, farZ);\n maxZ = 0.0; // plane origin starts at maxZ already\n\n // min and max are local to the plane axes\n return fromPlaneExtents(\n planeOrigin,\n planeXAxis,\n planeYAxis,\n planeNormal,\n minX,\n maxX,\n minY,\n maxY,\n minZ,\n maxZ,\n result\n );\n};\n\n/**\n * Duplicates a OrientedBoundingBox instance.\n *\n * @param {OrientedBoundingBox} box The bounding box to duplicate.\n * @param {OrientedBoundingBox} [result] The object onto which to store the result.\n * @returns {OrientedBoundingBox} The modified result parameter or a new OrientedBoundingBox instance if none was provided. (Returns undefined if box is undefined)\n */\nOrientedBoundingBox.clone = function (box, result) {\n if (!defined(box)) {\n return undefined;\n }\n\n if (!defined(result)) {\n return new OrientedBoundingBox(box.center, box.halfAxes);\n }\n\n Cartesian3.clone(box.center, result.center);\n Matrix3.clone(box.halfAxes, result.halfAxes);\n\n return result;\n};\n\n/**\n * Determines which side of a plane the oriented bounding box is located.\n *\n * @param {OrientedBoundingBox} box The oriented bounding box to test.\n * @param {Plane} plane The plane to test against.\n * @returns {Intersect} {@link Intersect.INSIDE} if the entire box is on the side of the plane\n * the normal is pointing, {@link Intersect.OUTSIDE} if the entire box is\n * on the opposite side, and {@link Intersect.INTERSECTING} if the box\n * intersects the plane.\n */\nOrientedBoundingBox.intersectPlane = function (box, plane) {\n //>>includeStart('debug', pragmas.debug);\n if (!defined(box)) {\n throw new DeveloperError(\"box is required.\");\n }\n\n if (!defined(plane)) {\n throw new DeveloperError(\"plane is required.\");\n }\n //>>includeEnd('debug');\n\n var center = box.center;\n var normal = plane.normal;\n var halfAxes = box.halfAxes;\n var normalX = normal.x,\n normalY = normal.y,\n normalZ = normal.z;\n // plane is used as if it is its normal; the first three components are assumed to be normalized\n var radEffective =\n Math.abs(\n normalX * halfAxes[Matrix3.COLUMN0ROW0] +\n normalY * halfAxes[Matrix3.COLUMN0ROW1] +\n normalZ * halfAxes[Matrix3.COLUMN0ROW2]\n ) +\n Math.abs(\n normalX * halfAxes[Matrix3.COLUMN1ROW0] +\n normalY * halfAxes[Matrix3.COLUMN1ROW1] +\n normalZ * halfAxes[Matrix3.COLUMN1ROW2]\n ) +\n Math.abs(\n normalX * halfAxes[Matrix3.COLUMN2ROW0] +\n normalY * halfAxes[Matrix3.COLUMN2ROW1] +\n normalZ * halfAxes[Matrix3.COLUMN2ROW2]\n );\n var distanceToPlane = Cartesian3.dot(normal, center) + plane.distance;\n\n if (distanceToPlane <= -radEffective) {\n // The entire box is on the negative side of the plane normal\n return Intersect.OUTSIDE;\n } else if (distanceToPlane >= radEffective) {\n // The entire box is on the positive side of the plane normal\n return Intersect.INSIDE;\n }\n return Intersect.INTERSECTING;\n};\n\nvar scratchCartesianU = new Cartesian3();\nvar scratchCartesianV = new Cartesian3();\nvar scratchCartesianW = new Cartesian3();\nvar scratchPPrime = new Cartesian3();\n\n/**\n * Computes the estimated distance squared from the closest point on a bounding box to a point.\n *\n * @param {OrientedBoundingBox} box The box.\n * @param {Cartesian3} cartesian The point\n * @returns {Number} The estimated distance squared from the bounding sphere to the point.\n *\n * @example\n * // Sort bounding boxes from back to front\n * boxes.sort(function(a, b) {\n * return Cesium.OrientedBoundingBox.distanceSquaredTo(b, camera.positionWC) - Cesium.OrientedBoundingBox.distanceSquaredTo(a, camera.positionWC);\n * });\n */\nOrientedBoundingBox.distanceSquaredTo = function (box, cartesian) {\n // See Geometric Tools for Computer Graphics 10.4.2\n\n //>>includeStart('debug', pragmas.debug);\n if (!defined(box)) {\n throw new DeveloperError(\"box is required.\");\n }\n if (!defined(cartesian)) {\n throw new DeveloperError(\"cartesian is required.\");\n }\n //>>includeEnd('debug');\n\n var offset = Cartesian3.subtract(cartesian, box.center, scratchOffset);\n\n var halfAxes = box.halfAxes;\n var u = Matrix3.getColumn(halfAxes, 0, scratchCartesianU);\n var v = Matrix3.getColumn(halfAxes, 1, scratchCartesianV);\n var w = Matrix3.getColumn(halfAxes, 2, scratchCartesianW);\n\n var uHalf = Cartesian3.magnitude(u);\n var vHalf = Cartesian3.magnitude(v);\n var wHalf = Cartesian3.magnitude(w);\n\n Cartesian3.normalize(u, u);\n Cartesian3.normalize(v, v);\n Cartesian3.normalize(w, w);\n\n var pPrime = scratchPPrime;\n pPrime.x = Cartesian3.dot(offset, u);\n pPrime.y = Cartesian3.dot(offset, v);\n pPrime.z = Cartesian3.dot(offset, w);\n\n var distanceSquared = 0.0;\n var d;\n\n if (pPrime.x < -uHalf) {\n d = pPrime.x + uHalf;\n distanceSquared += d * d;\n } else if (pPrime.x > uHalf) {\n d = pPrime.x - uHalf;\n distanceSquared += d * d;\n }\n\n if (pPrime.y < -vHalf) {\n d = pPrime.y + vHalf;\n distanceSquared += d * d;\n } else if (pPrime.y > vHalf) {\n d = pPrime.y - vHalf;\n distanceSquared += d * d;\n }\n\n if (pPrime.z < -wHalf) {\n d = pPrime.z + wHalf;\n distanceSquared += d * d;\n } else if (pPrime.z > wHalf) {\n d = pPrime.z - wHalf;\n distanceSquared += d * d;\n }\n\n return distanceSquared;\n};\n\nvar scratchCorner = new Cartesian3();\nvar scratchToCenter = new Cartesian3();\n\n/**\n * The distances calculated by the vector from the center of the bounding box to position projected onto direction.\n * <br>\n * If you imagine the infinite number of planes with normal direction, this computes the smallest distance to the\n * closest and farthest planes from position that intersect the bounding box.\n *\n * @param {OrientedBoundingBox} box The bounding box to calculate the distance to.\n * @param {Cartesian3} position The position to calculate the distance from.\n * @param {Cartesian3} direction The direction from position.\n * @param {Interval} [result] A Interval to store the nearest and farthest distances.\n * @returns {Interval} The nearest and farthest distances on the bounding box from position in direction.\n */\nOrientedBoundingBox.computePlaneDistances = function (\n box,\n position,\n direction,\n result\n) {\n //>>includeStart('debug', pragmas.debug);\n if (!defined(box)) {\n throw new DeveloperError(\"box is required.\");\n }\n\n if (!defined(position)) {\n throw new DeveloperError(\"position is required.\");\n }\n\n if (!defined(direction)) {\n throw new DeveloperError(\"direction is required.\");\n }\n //>>includeEnd('debug');\n\n if (!defined(result)) {\n result = new Interval();\n }\n\n var minDist = Number.POSITIVE_INFINITY;\n var maxDist = Number.NEGATIVE_INFINITY;\n\n var center = box.center;\n var halfAxes = box.halfAxes;\n\n var u = Matrix3.getColumn(halfAxes, 0, scratchCartesianU);\n var v = Matrix3.getColumn(halfAxes, 1, scratchCartesianV);\n var w = Matrix3.getColumn(halfAxes, 2, scratchCartesianW);\n\n // project first corner\n var corner = Cartesian3.add(u, v, scratchCorner);\n Cartesian3.add(corner, w, corner);\n Cartesian3.add(corner, center, corner);\n\n var toCenter = Cartesian3.subtract(corner, position, scratchToCenter);\n var mag = Cartesian3.dot(direction, toCenter);\n\n minDist = Math.min(mag, minDist);\n maxDist = Math.max(mag, maxDist);\n\n // project second corner\n Cartesian3.add(center, u, corner);\n Cartesian3.add(corner, v, corner);\n Cartesian3.subtract(corner, w, corner);\n\n Cartesian3.subtract(corner, position, toCenter);\n mag = Cartesian3.dot(direction, toCenter);\n\n minDist = Math.min(mag, minDist);\n maxDist = Math.max(mag, maxDist);\n\n // project third corner\n Cartesian3.add(center, u, corner);\n Cartesian3.subtract(corner, v, corner);\n Cartesian3.add(corner, w, corner);\n\n Cartesian3.subtract(corner, position, toCenter);\n mag = Cartesian3.dot(direction, toCenter);\n\n minDist = Math.min(mag, minDist);\n maxDist = Math.max(mag, maxDist);\n\n // project fourth corner\n Cartesian3.add(center, u, corner);\n Cartesian3.subtract(corner, v, corner);\n Cartesian3.subtract(corner, w, corner);\n\n Cartesian3.subtract(corner, position, toCenter);\n mag = Cartesian3.dot(direction, toCenter);\n\n minDist = Math.min(mag, minDist);\n maxDist = Math.max(mag, maxDist);\n\n // project fifth corner\n Cartesian3.subtract(center, u, corner);\n Cartesian3.add(corner, v, corner);\n Cartesian3.add(corner, w, corner);\n\n Cartesian3.subtract(corner, position, toCenter);\n mag = Cartesian3.dot(direction, toCenter);\n\n minDist = Math.min(mag, minDist);\n maxDist = Math.max(mag, maxDist);\n\n // project sixth corner\n Cartesian3.subtract(center, u, corner);\n Cartesian3.add(corner, v, corner);\n Cartesian3.subtract(corner, w, corner);\n\n Cartesian3.subtract(corner, position, toCenter);\n mag = Cartesian3.dot(direction, toCenter);\n\n minDist = Math.min(mag, minDist);\n maxDist = Math.max(mag, maxDist);\n\n // project seventh corner\n Cartesian3.subtract(center, u, corner);\n Cartesian3.subtract(corner, v, corner);\n Cartesian3.add(corner, w, corner);\n\n Cartesian3.subtract(corner, position, toCenter);\n mag = Cartesian3.dot(direction, toCenter);\n\n minDist = Math.min(mag, minDist);\n maxDist = Math.max(mag, maxDist);\n\n // project eighth corner\n Cartesian3.subtract(center, u, corner);\n Cartesian3.subtract(corner, v, corner);\n Cartesian3.subtract(corner, w, corner);\n\n Cartesian3.subtract(corner, position, toCenter);\n mag = Cartesian3.dot(direction, toCenter);\n\n minDist = Math.min(mag, minDist);\n maxDist = Math.max(mag, maxDist);\n\n result.start = minDist;\n result.stop = maxDist;\n return result;\n};\n\nvar scratchBoundingSphere = new BoundingSphere();\n\n/**\n * Determines whether or not a bounding box is hidden from view by the occluder.\n *\n * @param {OrientedBoundingBox} box The bounding box surrounding the occludee object.\n * @param {Occluder} occluder The occluder.\n * @returns {Boolean} <code>true</code> if the box is not visible; otherwise <code>false</code>.\n */\nOrientedBoundingBox.isOccluded = function (box, occluder) {\n //>>includeStart('debug', pragmas.debug);\n if (!defined(box)) {\n throw new DeveloperError(\"box is required.\");\n }\n if (!defined(occluder)) {\n throw new DeveloperError(\"occluder is required.\");\n }\n //>>includeEnd('debug');\n\n var sphere = BoundingSphere.fromOrientedBoundingBox(\n box,\n scratchBoundingSphere\n );\n\n return !occluder.isBoundingSphereVisible(sphere);\n};\n\n/**\n * Determines which side of a plane the oriented bounding box is located.\n *\n * @param {Plane} plane The plane to test against.\n * @returns {Intersect} {@link Intersect.INSIDE} if the entire box is on the side of the plane\n * the normal is pointing, {@link Intersect.OUTSIDE} if the entire box is\n * on the opposite side, and {@link Intersect.INTERSECTING} if the box\n * intersects the plane.\n */\nOrientedBoundingBox.prototype.intersectPlane = function (plane) {\n return OrientedBoundingBox.intersectPlane(this, plane);\n};\n\n/**\n * Computes the estimated distance squared from the closest point on a bounding box to a point.\n *\n * @param {Cartesian3} cartesian The point\n * @returns {Number} The estimated distance squared from the bounding sphere to the point.\n *\n * @example\n * // Sort bounding boxes from back to front\n * boxes.sort(function(a, b) {\n * return b.distanceSquaredTo(camera.positionWC) - a.distanceSquaredTo(camera.positionWC);\n * });\n */\nOrientedBoundingBox.prototype.distanceSquaredTo = function (cartesian) {\n return OrientedBoundingBox.distanceSquaredTo(this, cartesian);\n};\n\n/**\n * The distances calculated by the vector from the center of the bounding box to position projected onto direction.\n * <br>\n * If you imagine the infinite number of planes with normal direction, this computes the smallest distance to the\n * closest and farthest planes from position that intersect the bounding box.\n *\n * @param {Cartesian3} position The position to calculate the distance from.\n * @param {Cartesian3} direction The direction from position.\n * @param {Interval} [result] A Interval to store the nearest and farthest distances.\n * @returns {Interval} The nearest and farthest distances on the bounding box from position in direction.\n */\nOrientedBoundingBox.prototype.computePlaneDistances = function (\n position,\n direction,\n result\n) {\n return OrientedBoundingBox.computePlaneDistances(\n this,\n position,\n direction,\n result\n );\n};\n\n/**\n * Determines whether or not a bounding box is hidden from view by the occluder.\n *\n * @param {Occluder} occluder The occluder.\n * @returns {Boolean} <code>true</code> if the sphere is not visible; otherwise <code>false</code>.\n */\nOrientedBoundingBox.prototype.isOccluded = function (occluder) {\n return OrientedBoundingBox.isOccluded(this, occluder);\n};\n\n/**\n * Compares the provided OrientedBoundingBox componentwise and returns\n * <code>true</code> if they are equal, <code>false</code> otherwise.\n *\n * @param {OrientedBoundingBox} left The first OrientedBoundingBox.\n * @param {OrientedBoundingBox} right The second OrientedBoundingBox.\n * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.\n */\nOrientedBoundingBox.equals = function (left, right) {\n return (\n left === right ||\n (defined(left) &&\n defined(right) &&\n Cartesian3.equals(left.center, right.center) &&\n Matrix3.equals(left.halfAxes, right.halfAxes))\n );\n};\n\n/**\n * Duplicates this OrientedBoundingBox instance.\n *\n * @param {OrientedBoundingBox} [result] The object onto which to store the result.\n * @returns {OrientedBoundingBox} The 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