/**
* Cesium - https://github.com/CesiumGS/cesium
*
* Copyright 2011-2020 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/master/LICENSE.md for full licensing details.
*/
define(['exports', './when-8d13db60', './Check-70bec281', './Math-61ede240', './Cartographic-f2a06374', './Cartesian2-16a61632', './BoundingSphere-d018a565', './Plane-aa6c3ce5', './EllipsoidTangentPlane-33ed15f1'], function (exports, when, Check, _Math, Cartographic, Cartesian2, BoundingSphere, Plane, EllipsoidTangentPlane) { '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.
* var center = new Cesium.Cartesian3(1.0, 0.0, 0.0);
* var halfAxes = Cesium.Matrix3.fromScale(new Cesium.Cartesian3(1.0, 3.0, 2.0), new Cesium.Matrix3());
*
* var 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 = Cartographic.Cartesian3.clone(when.defaultValue(center, Cartographic.Cartesian3.ZERO));
/**
* The transformation matrix, to rotate the box to the right position.
* @type {Matrix3}
* @default {@link Matrix3.ZERO}
*/
this.halfAxes = BoundingSphere.Matrix3.clone(when.defaultValue(halfAxes, BoundingSphere.Matrix3.ZERO));
}
/**
* The number of elements used to pack the object into an array.
* @type {Number}
*/
OrientedBoundingBox.packedLength = Cartographic.Cartesian3.packedLength + BoundingSphere.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 = when.defaultValue(startingIndex, 0);
Cartographic.Cartesian3.pack(value.center, array, startingIndex);
BoundingSphere.Matrix3.pack(value.halfAxes, array, startingIndex + Cartographic.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 = when.defaultValue(startingIndex, 0);
if (!when.defined(result)) {
result = new OrientedBoundingBox();
}
Cartographic.Cartesian3.unpack(array, startingIndex, result.center);
BoundingSphere.Matrix3.unpack(array, startingIndex + Cartographic.Cartesian3.packedLength, result.halfAxes);
return result;
};
var scratchCartesian1 = new Cartographic.Cartesian3();
var scratchCartesian2 = new Cartographic.Cartesian3();
var scratchCartesian3 = new Cartographic.Cartesian3();
var scratchCartesian4 = new Cartographic.Cartesian3();
var scratchCartesian5 = new Cartographic.Cartesian3();
var scratchCartesian6 = new Cartographic.Cartesian3();
var scratchCovarianceResult = new BoundingSphere.Matrix3();
var scratchEigenResult = {
unitary : new BoundingSphere.Matrix3(),
diagonal : new BoundingSphere.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.
* var box = Cesium.OrientedBoundingBox.fromPoints([new Cesium.Cartesian3(2, 0, 0), new Cesium.Cartesian3(-2, 0, 0)]);
*/
OrientedBoundingBox.fromPoints = function(positions, result) {
if (!when.defined(result)) {
result = new OrientedBoundingBox();
}
if (!when.defined(positions) || positions.length === 0) {
result.halfAxes = BoundingSphere.Matrix3.ZERO;
result.center = Cartographic.Cartesian3.ZERO;
return result;
}
var i;
var length = positions.length;
var meanPoint = Cartographic.Cartesian3.clone(positions[0], scratchCartesian1);
for (i = 1; i < length; i++) {
Cartographic.Cartesian3.add(meanPoint, positions[i], meanPoint);
}
var invLength = 1.0 / length;
Cartographic.Cartesian3.multiplyByScalar(meanPoint, invLength, meanPoint);
var exx = 0.0;
var exy = 0.0;
var exz = 0.0;
var eyy = 0.0;
var eyz = 0.0;
var ezz = 0.0;
var p;
for (i = 0; i < length; i++) {
p = Cartographic.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;
var 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;
var eigenDecomposition = BoundingSphere.Matrix3.computeEigenDecomposition(covarianceMatrix, scratchEigenResult);
var rotation = BoundingSphere.Matrix3.clone(eigenDecomposition.unitary, result.halfAxes);
var v1 = BoundingSphere.Matrix3.getColumn(rotation, 0, scratchCartesian4);
var v2 = BoundingSphere.Matrix3.getColumn(rotation, 1, scratchCartesian5);
var v3 = BoundingSphere.Matrix3.getColumn(rotation, 2, scratchCartesian6);
var u1 = -Number.MAX_VALUE;
var u2 = -Number.MAX_VALUE;
var u3 = -Number.MAX_VALUE;
var l1 = Number.MAX_VALUE;
var l2 = Number.MAX_VALUE;
var l3 = Number.MAX_VALUE;
for (i = 0; i < length; i++) {
p = positions[i];
u1 = Math.max(Cartographic.Cartesian3.dot(v1, p), u1);
u2 = Math.max(Cartographic.Cartesian3.dot(v2, p), u2);
u3 = Math.max(Cartographic.Cartesian3.dot(v3, p), u3);
l1 = Math.min(Cartographic.Cartesian3.dot(v1, p), l1);
l2 = Math.min(Cartographic.Cartesian3.dot(v2, p), l2);
l3 = Math.min(Cartographic.Cartesian3.dot(v3, p), l3);
}
v1 = Cartographic.Cartesian3.multiplyByScalar(v1, 0.5 * (l1 + u1), v1);
v2 = Cartographic.Cartesian3.multiplyByScalar(v2, 0.5 * (l2 + u2), v2);
v3 = Cartographic.Cartesian3.multiplyByScalar(v3, 0.5 * (l3 + u3), v3);
var center = Cartographic.Cartesian3.add(v1, v2, result.center);
Cartographic.Cartesian3.add(center, v3, center);
var scale = scratchCartesian3;
scale.x = u1 - l1;
scale.y = u2 - l2;
scale.z = u3 - l3;
Cartographic.Cartesian3.multiplyByScalar(scale, 0.5, scale);
BoundingSphere.Matrix3.multiplyByScale(result.halfAxes, scale, result.halfAxes);
return result;
};
var scratchOffset = new Cartographic.Cartesian3();
var scratchScale = new Cartographic.Cartesian3();
function fromPlaneExtents(planeOrigin, planeXAxis, planeYAxis, planeZAxis, minimumX, maximumX, minimumY, maximumY, minimumZ, maximumZ, result) {
//>>includeStart('debug', pragmas.debug);
if (!when.defined(minimumX) ||
!when.defined(maximumX) ||
!when.defined(minimumY) ||
!when.defined(maximumY) ||
!when.defined(minimumZ) ||
!when.defined(maximumZ)) {
throw new Check.DeveloperError('all extents (minimum/maximum X/Y/Z) are required.');
}
//>>includeEnd('debug');
if (!when.defined(result)) {
result = new OrientedBoundingBox();
}
var halfAxes = result.halfAxes;
BoundingSphere.Matrix3.setColumn(halfAxes, 0, planeXAxis, halfAxes);
BoundingSphere.Matrix3.setColumn(halfAxes, 1, planeYAxis, halfAxes);
BoundingSphere.Matrix3.setColumn(halfAxes, 2, planeZAxis, halfAxes);
var centerOffset = scratchOffset;
centerOffset.x = (minimumX + maximumX) / 2.0;
centerOffset.y = (minimumY + maximumY) / 2.0;
centerOffset.z = (minimumZ + maximumZ) / 2.0;
var scale = scratchScale;
scale.x = (maximumX - minimumX) / 2.0;
scale.y = (maximumY - minimumY) / 2.0;
scale.z = (maximumZ - minimumZ) / 2.0;
var center = result.center;
centerOffset = BoundingSphere.Matrix3.multiplyByVector(halfAxes, centerOffset, centerOffset);
Cartographic.Cartesian3.add(planeOrigin, centerOffset, center);
BoundingSphere.Matrix3.multiplyByScale(halfAxes, scale, halfAxes);
return result;
}
var scratchRectangleCenterCartographic = new Cartographic.Cartographic();
var scratchRectangleCenter = new Cartographic.Cartesian3();
var scratchPerimeterCartographicNC = new Cartographic.Cartographic();
var scratchPerimeterCartographicNW = new Cartographic.Cartographic();
var scratchPerimeterCartographicCW = new Cartographic.Cartographic();
var scratchPerimeterCartographicSW = new Cartographic.Cartographic();
var scratchPerimeterCartographicSC = new Cartographic.Cartographic();
var scratchPerimeterCartesianNC = new Cartographic.Cartesian3();
var scratchPerimeterCartesianNW = new Cartographic.Cartesian3();
var scratchPerimeterCartesianCW = new Cartographic.Cartesian3();
var scratchPerimeterCartesianSW = new Cartographic.Cartesian3();
var scratchPerimeterCartesianSC = new Cartographic.Cartesian3();
var scratchPerimeterProjectedNC = new Cartesian2.Cartesian2();
var scratchPerimeterProjectedNW = new Cartesian2.Cartesian2();
var scratchPerimeterProjectedCW = new Cartesian2.Cartesian2();
var scratchPerimeterProjectedSW = new Cartesian2.Cartesian2();
var scratchPerimeterProjectedSC = new Cartesian2.Cartesian2();
var scratchPlaneOrigin = new Cartographic.Cartesian3();
var scratchPlaneNormal = new Cartographic.Cartesian3();
var scratchPlaneXAxis = new Cartographic.Cartesian3();
var scratchHorizonCartesian = new Cartographic.Cartesian3();
var scratchHorizonProjected = new Cartesian2.Cartesian2();
var scratchMaxY = new Cartographic.Cartesian3();
var scratchMinY = new Cartographic.Cartesian3();
var scratchZ = new Cartographic.Cartesian3();
var scratchPlane = new Plane.Plane(Cartographic.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 (<code>radii.x == radii.y</code>)
*/
OrientedBoundingBox.fromRectangle = function(rectangle, minimumHeight, maximumHeight, ellipsoid, result) {
//>>includeStart('debug', pragmas.debug);
if (!when.defined(rectangle)) {
throw new Check.DeveloperError('rectangle is required');
}
if (rectangle.width < 0.0 || rectangle.width > _Math.CesiumMath.TWO_PI) {
throw new Check.DeveloperError('Rectangle width must be between 0 and 2*pi');
}
if (rectangle.height < 0.0 || rectangle.height > _Math.CesiumMath.PI) {
throw new Check.DeveloperError('Rectangle height must be between 0 and pi');
}
if (when.defined(ellipsoid) && !_Math.CesiumMath.equalsEpsilon(ellipsoid.radii.x, ellipsoid.radii.y, _Math.CesiumMath.EPSILON15)) {
throw new Check.DeveloperError('Ellipsoid must be an ellipsoid of revolution (radii.x == radii.y)');
}
//>>includeEnd('debug');
minimumHeight = when.defaultValue(minimumHeight, 0.0);
maximumHeight = when.defaultValue(maximumHeight, 0.0);
ellipsoid = when.defaultValue(ellipsoid, Cartesian2.Ellipsoid.WGS84);
var minX, maxX, minY, maxY, minZ, maxZ, plane;
if (rectangle.width <= _Math.CesiumMath.PI) {
// The bounding box will be aligned with the tangent plane at the center of the rectangle.
var tangentPointCartographic = Cartesian2.Rectangle.center(rectangle, scratchRectangleCenterCartographic);
var tangentPoint = ellipsoid.cartographicToCartesian(tangentPointCartographic, scratchRectangleCenter);
var 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).
var lonCenter = tangentPointCartographic.longitude;
var latCenter = (rectangle.south < 0.0 && rectangle.north > 0.0) ? 0.0 : tangentPointCartographic.latitude;
// Compute XY extents using the rectangle at maximum height
var perimeterCartographicNC = Cartographic.Cartographic.fromRadians(lonCenter, rectangle.north, maximumHeight, scratchPerimeterCartographicNC);
var perimeterCartographicNW = Cartographic.Cartographic.fromRadians(rectangle.west, rectangle.north, maximumHeight, scratchPerimeterCartographicNW);
var perimeterCartographicCW = Cartographic.Cartographic.fromRadians(rectangle.west, latCenter, maximumHeight, scratchPerimeterCartographicCW);
var perimeterCartographicSW = Cartographic.Cartographic.fromRadians(rectangle.west, rectangle.south, maximumHeight, scratchPerimeterCartographicSW);
var perimeterCartographicSC = Cartographic.Cartographic.fromRadians(lonCenter, rectangle.south, maximumHeight, scratchPerimeterCartographicSC);
var perimeterCartesianNC = ellipsoid.cartographicToCartesian(perimeterCartographicNC, scratchPerimeterCartesianNC);
var perimeterCartesianNW = ellipsoid.cartographicToCartesian(perimeterCartographicNW, scratchPerimeterCartesianNW);
var perimeterCartesianCW = ellipsoid.cartographicToCartesian(perimeterCartographicCW, scratchPerimeterCartesianCW);
var perimeterCartesianSW = ellipsoid.cartographicToCartesian(perimeterCartographicSW, scratchPerimeterCartesianSW);
var perimeterCartesianSC = ellipsoid.cartographicToCartesian(perimeterCartographicSC, scratchPerimeterCartesianSC);
var perimeterProjectedNC = tangentPlane.projectPointToNearestOnPlane(perimeterCartesianNC, scratchPerimeterProjectedNC);
var perimeterProjectedNW = tangentPlane.projectPointToNearestOnPlane(perimeterCartesianNW, scratchPerimeterProjectedNW);
var perimeterProjectedCW = tangentPlane.projectPointToNearestOnPlane(perimeterCartesianCW, scratchPerimeterProjectedCW);
var perimeterProjectedSW = tangentPlane.projectPointToNearestOnPlane(perimeterCartesianSW, scratchPerimeterProjectedSW);
var 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).
var fullyAboveEquator = rectangle.south > 0.0;
var fullyBelowEquator = rectangle.north < 0.0;
var latitudeNearestToEquator = fullyAboveEquator ? rectangle.south : (fullyBelowEquator ? rectangle.north : 0.0);
var centerLongitude = Cartesian2.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.
var planeOrigin = Cartographic.Cartesian3.fromRadians(centerLongitude, latitudeNearestToEquator, maximumHeight, ellipsoid, scratchPlaneOrigin);
planeOrigin.z = 0.0; // center the plane on the equator to simpify plane normal calculation
var isPole = Math.abs(planeOrigin.x) < _Math.CesiumMath.EPSILON10 && Math.abs(planeOrigin.y) < _Math.CesiumMath.EPSILON10;
var planeNormal = !isPole ? Cartographic.Cartesian3.normalize(planeOrigin, scratchPlaneNormal) : Cartographic.Cartesian3.UNIT_X;
var planeYAxis = Cartographic.Cartesian3.UNIT_Z;
var planeXAxis = Cartographic.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.
var horizonCartesian = Cartographic.Cartesian3.fromRadians(centerLongitude + _Math.CesiumMath.PI_OVER_TWO, latitudeNearestToEquator, maximumHeight, ellipsoid, scratchHorizonCartesian);
maxX = Cartographic.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 = Cartographic.Cartesian3.fromRadians(0.0, rectangle.north, fullyBelowEquator ? minimumHeight : maximumHeight, ellipsoid, scratchMaxY).z;
minY = Cartographic.Cartesian3.fromRadians(0.0, rectangle.south, fullyAboveEquator ? minimumHeight : maximumHeight, ellipsoid, scratchMinY).z;
var farZ = Cartographic.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);
};
/**
* 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 (!when.defined(box)) {
return undefined;
}
if (!when.defined(result)) {
return new OrientedBoundingBox(box.center, box.halfAxes);
}
Cartographic.Cartesian3.clone(box.center, result.center);
BoundingSphere.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 (!when.defined(box)) {
throw new Check.DeveloperError('box is required.');
}
if (!when.defined(plane)) {
throw new Check.DeveloperError('plane is required.');
}
//>>includeEnd('debug');
var center = box.center;
var normal = plane.normal;
var halfAxes = box.halfAxes;
var 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
var radEffective = Math.abs(normalX * halfAxes[BoundingSphere.Matrix3.COLUMN0ROW0] + normalY * halfAxes[BoundingSphere.Matrix3.COLUMN0ROW1] + normalZ * halfAxes[BoundingSphere.Matrix3.COLUMN0ROW2]) +
Math.abs(normalX * halfAxes[BoundingSphere.Matrix3.COLUMN1ROW0] + normalY * halfAxes[BoundingSphere.Matrix3.COLUMN1ROW1] + normalZ * halfAxes[BoundingSphere.Matrix3.COLUMN1ROW2]) +
Math.abs(normalX * halfAxes[BoundingSphere.Matrix3.COLUMN2ROW0] + normalY * halfAxes[BoundingSphere.Matrix3.COLUMN2ROW1] + normalZ * halfAxes[BoundingSphere.Matrix3.COLUMN2ROW2]);
var distanceToPlane = Cartographic.Cartesian3.dot(normal, center) + plane.distance;
if (distanceToPlane <= -radEffective) {
// The entire box is on the negative side of the plane normal
return BoundingSphere.Intersect.OUTSIDE;
} else if (distanceToPlane >= radEffective) {
// The entire box is on the positive side of the plane normal
return BoundingSphere.Intersect.INSIDE;
}
return BoundingSphere.Intersect.INTERSECTING;
};
var scratchCartesianU = new Cartographic.Cartesian3();
var scratchCartesianV = new Cartographic.Cartesian3();
var scratchCartesianW = new Cartographic.Cartesian3();
var scratchPPrime = new Cartographic.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 estimated distance squared from the bounding sphere to the point.
*
* @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 (!when.defined(box)) {
throw new Check.DeveloperError('box is required.');
}
if (!when.defined(cartesian)) {
throw new Check.DeveloperError('cartesian is required.');
}
//>>includeEnd('debug');
var offset = Cartographic.Cartesian3.subtract(cartesian, box.center, scratchOffset);
var halfAxes = box.halfAxes;
var u = BoundingSphere.Matrix3.getColumn(halfAxes, 0, scratchCartesianU);
var v = BoundingSphere.Matrix3.getColumn(halfAxes, 1, scratchCartesianV);
var w = BoundingSphere.Matrix3.getColumn(halfAxes, 2, scratchCartesianW);
var uHalf = Cartographic.Cartesian3.magnitude(u);
var vHalf = Cartographic.Cartesian3.magnitude(v);
var wHalf = Cartographic.Cartesian3.magnitude(w);
Cartographic.Cartesian3.normalize(u, u);
Cartographic.Cartesian3.normalize(v, v);
Cartographic.Cartesian3.normalize(w, w);
var pPrime = scratchPPrime;
pPrime.x = Cartographic.Cartesian3.dot(offset, u);
pPrime.y = Cartographic.Cartesian3.dot(offset, v);
pPrime.z = Cartographic.Cartesian3.dot(offset, w);
var distanceSquared = 0.0;
var 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;
};
var scratchCorner = new Cartographic.Cartesian3();
var scratchToCenter = new Cartographic.Cartesian3();
/**
* The distances calculated by the vector from the center of the bounding box to position projected onto direction.
* <br>
* 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 (!when.defined(box)) {
throw new Check.DeveloperError('box is required.');
}
if (!when.defined(position)) {
throw new Check.DeveloperError('position is required.');
}
if (!when.defined(direction)) {
throw new Check.DeveloperError('direction is required.');
}
//>>includeEnd('debug');
if (!when.defined(result)) {
result = new BoundingSphere.Interval();
}
var minDist = Number.POSITIVE_INFINITY;
var maxDist = Number.NEGATIVE_INFINITY;
var center = box.center;
var halfAxes = box.halfAxes;
var u = BoundingSphere.Matrix3.getColumn(halfAxes, 0, scratchCartesianU);
var v = BoundingSphere.Matrix3.getColumn(halfAxes, 1, scratchCartesianV);
var w = BoundingSphere.Matrix3.getColumn(halfAxes, 2, scratchCartesianW);
// project first corner
var corner = Cartographic.Cartesian3.add(u, v, scratchCorner);
Cartographic.Cartesian3.add(corner, w, corner);
Cartographic.Cartesian3.add(corner, center, corner);
var toCenter = Cartographic.Cartesian3.subtract(corner, position, scratchToCenter);
var mag = Cartographic.Cartesian3.dot(direction, toCenter);
minDist = Math.min(mag, minDist);
maxDist = Math.max(mag, maxDist);
// project second corner
Cartographic.Cartesian3.add(center, u, corner);
Cartographic.Cartesian3.add(corner, v, corner);
Cartographic.Cartesian3.subtract(corner, w, corner);
Cartographic.Cartesian3.subtract(corner, position, toCenter);
mag = Cartographic.Cartesian3.dot(direction, toCenter);
minDist = Math.min(mag, minDist);
maxDist = Math.max(mag, maxDist);
// project third corner
Cartographic.Cartesian3.add(center, u, corner);
Cartographic.Cartesian3.subtract(corner, v, corner);
Cartographic.Cartesian3.add(corner, w, corner);
Cartographic.Cartesian3.subtract(corner, position, toCenter);
mag = Cartographic.Cartesian3.dot(direction, toCenter);
minDist = Math.min(mag, minDist);
maxDist = Math.max(mag, maxDist);
// project fourth corner
Cartographic.Cartesian3.add(center, u, corner);
Cartographic.Cartesian3.subtract(corner, v, corner);
Cartographic.Cartesian3.subtract(corner, w, corner);
Cartographic.Cartesian3.subtract(corner, position, toCenter);
mag = Cartographic.Cartesian3.dot(direction, toCenter);
minDist = Math.min(mag, minDist);
maxDist = Math.max(mag, maxDist);
// project fifth corner
Cartographic.Cartesian3.subtract(center, u, corner);
Cartographic.Cartesian3.add(corner, v, corner);
Cartographic.Cartesian3.add(corner, w, corner);
Cartographic.Cartesian3.subtract(corner, position, toCenter);
mag = Cartographic.Cartesian3.dot(direction, toCenter);
minDist = Math.min(mag, minDist);
maxDist = Math.max(mag, maxDist);
// project sixth corner
Cartographic.Cartesian3.subtract(center, u, corner);
Cartographic.Cartesian3.add(corner, v, corner);
Cartographic.Cartesian3.subtract(corner, w, corner);
Cartographic.Cartesian3.subtract(corner, position, toCenter);
mag = Cartographic.Cartesian3.dot(direction, toCenter);
minDist = Math.min(mag, minDist);
maxDist = Math.max(mag, maxDist);
// project seventh corner
Cartographic.Cartesian3.subtract(center, u, corner);
Cartographic.Cartesian3.subtract(corner, v, corner);
Cartographic.Cartesian3.add(corner, w, corner);
Cartographic.Cartesian3.subtract(corner, position, toCenter);
mag = Cartographic.Cartesian3.dot(direction, toCenter);
minDist = Math.min(mag, minDist);
maxDist = Math.max(mag, maxDist);
// project eighth corner
Cartographic.Cartesian3.subtract(center, u, corner);
Cartographic.Cartesian3.subtract(corner, v, corner);
Cartographic.Cartesian3.subtract(corner, w, corner);
Cartographic.Cartesian3.subtract(corner, position, toCenter);
mag = Cartographic.Cartesian3.dot(direction, toCenter);
minDist = Math.min(mag, minDist);
maxDist = Math.max(mag, maxDist);
result.start = minDist;
result.stop = maxDist;
return result;
};
var scratchBoundingSphere = new BoundingSphere.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} <code>true</code> if the box is not visible; otherwise <code>false</code>.
*/
OrientedBoundingBox.isOccluded = function(box, occluder) {
//>>includeStart('debug', pragmas.debug);
if (!when.defined(box)) {
throw new Check.DeveloperError('box is required.');
}
if (!when.defined(occluder)) {
throw new Check.DeveloperError('occluder is required.');
}
//>>includeEnd('debug');
var sphere = BoundingSphere.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.
* <br>
* 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);
};
/**
* Determines whether or not a bounding box is hidden from view by the occluder.
*
* @param {Occluder} occluder The occluder.
* @returns {Boolean} <code>true</code> if the sphere is not visible; otherwise <code>false</code>.
*/
OrientedBoundingBox.prototype.isOccluded = function(occluder) {
return OrientedBoundingBox.isOccluded(this, occluder);
};
/**
* Compares the provided OrientedBoundingBox componentwise and returns
* <code>true</code> if they are equal, <code>false</code> otherwise.
*
* @param {OrientedBoundingBox} left The first OrientedBoundingBox.
* @param {OrientedBoundingBox} right The second OrientedBoundingBox.
* @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
*/
OrientedBoundingBox.equals = function(left, right) {
return (left === right) ||
((when.defined(left)) &&
(when.defined(right)) &&
Cartographic.Cartesian3.equals(left.center, right.center) &&
BoundingSphere.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
* <code>true</code> if they are equal, <code>false</code> otherwise.
*
* @param {OrientedBoundingBox} [right] The right hand side OrientedBoundingBox.
* @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
*/
OrientedBoundingBox.prototype.equals = function(right) {
return OrientedBoundingBox.equals(this, right);
};
exports.OrientedBoundingBox = OrientedBoundingBox;
});
