import BoundingSphere from "./BoundingSphere.js";
import Cartesian3 from "./Cartesian3.js";
import Check from "./Check.js";
import defaultValue from "./defaultValue.js";
import defined from "./defined.js";
import Ellipsoid from "./Ellipsoid.js";
import Rectangle from "./Rectangle.js";
/**
* Determine whether or not other objects are visible or hidden behind the visible horizon defined by
* an {@link Ellipsoid} and a camera position. The ellipsoid is assumed to be located at the
* origin of the coordinate system. This class uses the algorithm described in the
* {@link https://cesium.com/blog/2013/04/25/Horizon-culling/|Horizon Culling} blog post.
*
* @alias EllipsoidalOccluder
*
* @param {Ellipsoid} ellipsoid The ellipsoid to use as an occluder.
* @param {Cartesian3} [cameraPosition] The coordinate of the viewer/camera. If this parameter is not
* specified, {@link EllipsoidalOccluder#cameraPosition} must be called before
* testing visibility.
*
* @constructor
*
* @example
* // Construct an ellipsoidal occluder with radii 1.0, 1.1, and 0.9.
* var cameraPosition = new Cesium.Cartesian3(5.0, 6.0, 7.0);
* var occluderEllipsoid = new Cesium.Ellipsoid(1.0, 1.1, 0.9);
* var occluder = new Cesium.EllipsoidalOccluder(occluderEllipsoid, cameraPosition);
*
* @private
*/
function EllipsoidalOccluder(ellipsoid, cameraPosition) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("ellipsoid", ellipsoid);
//>>includeEnd('debug');
this._ellipsoid = ellipsoid;
this._cameraPosition = new Cartesian3();
this._cameraPositionInScaledSpace = new Cartesian3();
this._distanceToLimbInScaledSpaceSquared = 0.0;
// cameraPosition fills in the above values
if (defined(cameraPosition)) {
this.cameraPosition = cameraPosition;
}
}
Object.defineProperties(EllipsoidalOccluder.prototype, {
/**
* Gets the occluding ellipsoid.
* @memberof EllipsoidalOccluder.prototype
* @type {Ellipsoid}
*/
ellipsoid: {
get: function () {
return this._ellipsoid;
},
},
/**
* Gets or sets the position of the camera.
* @memberof EllipsoidalOccluder.prototype
* @type {Cartesian3}
*/
cameraPosition: {
get: function () {
return this._cameraPosition;
},
set: function (cameraPosition) {
// See https://cesium.com/blog/2013/04/25/Horizon-culling/
var ellipsoid = this._ellipsoid;
var cv = ellipsoid.transformPositionToScaledSpace(
cameraPosition,
this._cameraPositionInScaledSpace
);
var vhMagnitudeSquared = Cartesian3.magnitudeSquared(cv) - 1.0;
Cartesian3.clone(cameraPosition, this._cameraPosition);
this._cameraPositionInScaledSpace = cv;
this._distanceToLimbInScaledSpaceSquared = vhMagnitudeSquared;
},
},
});
var scratchCartesian = new Cartesian3();
/**
* Determines whether or not a point, the <code>occludee</code>, is hidden from view by the occluder.
*
* @param {Cartesian3} occludee The point to test for visibility.
* @returns {Boolean} <code>true</code> if the occludee is visible; otherwise <code>false</code>.
*
* @example
* var cameraPosition = new Cesium.Cartesian3(0, 0, 2.5);
* var ellipsoid = new Cesium.Ellipsoid(1.0, 1.1, 0.9);
* var occluder = new Cesium.EllipsoidalOccluder(ellipsoid, cameraPosition);
* var point = new Cesium.Cartesian3(0, -3, -3);
* occluder.isPointVisible(point); //returns true
*/
EllipsoidalOccluder.prototype.isPointVisible = function (occludee) {
var ellipsoid = this._ellipsoid;
var occludeeScaledSpacePosition = ellipsoid.transformPositionToScaledSpace(
occludee,
scratchCartesian
);
return isScaledSpacePointVisible(
occludeeScaledSpacePosition,
this._cameraPositionInScaledSpace,
this._distanceToLimbInScaledSpaceSquared
);
};
/**
* Determines whether or not a point expressed in the ellipsoid scaled space, is hidden from view by the
* occluder. To transform a Cartesian X, Y, Z position in the coordinate system aligned with the ellipsoid
* into the scaled space, call {@link Ellipsoid#transformPositionToScaledSpace}.
*
* @param {Cartesian3} occludeeScaledSpacePosition The point to test for visibility, represented in the scaled space.
* @returns {Boolean} <code>true</code> if the occludee is visible; otherwise <code>false</code>.
*
* @example
* var cameraPosition = new Cesium.Cartesian3(0, 0, 2.5);
* var ellipsoid = new Cesium.Ellipsoid(1.0, 1.1, 0.9);
* var occluder = new Cesium.EllipsoidalOccluder(ellipsoid, cameraPosition);
* var point = new Cesium.Cartesian3(0, -3, -3);
* var scaledSpacePoint = ellipsoid.transformPositionToScaledSpace(point);
* occluder.isScaledSpacePointVisible(scaledSpacePoint); //returns true
*/
EllipsoidalOccluder.prototype.isScaledSpacePointVisible = function (
occludeeScaledSpacePosition
) {
return isScaledSpacePointVisible(
occludeeScaledSpacePosition,
this._cameraPositionInScaledSpace,
this._distanceToLimbInScaledSpaceSquared
);
};
var scratchCameraPositionInScaledSpaceShrunk = new Cartesian3();
/**
* Similar to {@link EllipsoidalOccluder#isScaledSpacePointVisible} except tests against an
* ellipsoid that has been shrunk by the minimum height when the minimum height is below
* the ellipsoid. This is intended to be used with points generated by
* {@link EllipsoidalOccluder#computeHorizonCullingPointPossiblyUnderEllipsoid} or
* {@link EllipsoidalOccluder#computeHorizonCullingPointFromVerticesPossiblyUnderEllipsoid}.
*
* @param {Cartesian3} occludeeScaledSpacePosition The point to test for visibility, represented in the scaled space of the possibly-shrunk ellipsoid.
* @returns {Boolean} <code>true</code> if the occludee is visible; otherwise <code>false</code>.
*/
EllipsoidalOccluder.prototype.isScaledSpacePointVisiblePossiblyUnderEllipsoid = function (
occludeeScaledSpacePosition,
minimumHeight
) {
var ellipsoid = this._ellipsoid;
var vhMagnitudeSquared;
var cv;
if (
defined(minimumHeight) &&
minimumHeight < 0.0 &&
ellipsoid.minimumRadius > -minimumHeight
) {
// This code is similar to the cameraPosition setter, but unrolled for performance because it will be called a lot.
cv = scratchCameraPositionInScaledSpaceShrunk;
cv.x = this._cameraPosition.x / (ellipsoid.radii.x + minimumHeight);
cv.y = this._cameraPosition.y / (ellipsoid.radii.y + minimumHeight);
cv.z = this._cameraPosition.z / (ellipsoid.radii.z + minimumHeight);
vhMagnitudeSquared = cv.x * cv.x + cv.y * cv.y + cv.z * cv.z - 1.0;
} else {
cv = this._cameraPositionInScaledSpace;
vhMagnitudeSquared = this._distanceToLimbInScaledSpaceSquared;
}
return isScaledSpacePointVisible(
occludeeScaledSpacePosition,
cv,
vhMagnitudeSquared
);
};
/**
* Computes a point that can be used for horizon culling from a list of positions. If the point is below
* the horizon, all of the positions are guaranteed to be below the horizon as well. The returned point
* is expressed in the ellipsoid-scaled space and is suitable for use with
* {@link EllipsoidalOccluder#isScaledSpacePointVisible}.
*
* @param {Cartesian3} directionToPoint The direction that the computed point will lie along.
* A reasonable direction to use is the direction from the center of the ellipsoid to
* the center of the bounding sphere computed from the positions. The direction need not
* be normalized.
* @param {Cartesian3[]} positions The positions from which to compute the horizon culling point. The positions
* must be expressed in a reference frame centered at the ellipsoid and aligned with the
* ellipsoid's axes.
* @param {Cartesian3} [result] The instance on which to store the result instead of allocating a new instance.
* @returns {Cartesian3} The computed horizon culling point, expressed in the ellipsoid-scaled space.
*/
EllipsoidalOccluder.prototype.computeHorizonCullingPoint = function (
directionToPoint,
positions,
result
) {
return computeHorizonCullingPointFromPositions(
this._ellipsoid,
directionToPoint,
positions,
result
);
};
var scratchEllipsoidShrunk = Ellipsoid.clone(Ellipsoid.UNIT_SPHERE);
/**
* Similar to {@link EllipsoidalOccluder#computeHorizonCullingPoint} except computes the culling
* point relative to an ellipsoid that has been shrunk by the minimum height when the minimum height is below
* the ellipsoid. The returned point is expressed in the possibly-shrunk ellipsoid-scaled space and is suitable
* for use with {@link EllipsoidalOccluder#isScaledSpacePointVisiblePossiblyUnderEllipsoid}.
*
* @param {Cartesian3} directionToPoint The direction that the computed point will lie along.
* A reasonable direction to use is the direction from the center of the ellipsoid to
* the center of the bounding sphere computed from the positions. The direction need not
* be normalized.
* @param {Cartesian3[]} positions The positions from which to compute the horizon culling point. The positions
* must be expressed in a reference frame centered at the ellipsoid and aligned with the
* ellipsoid's axes.
* @param {Number} [minimumHeight] The minimum height of all positions. If this value is undefined, all positions are assumed to be above the ellipsoid.
* @param {Cartesian3} [result] The instance on which to store the result instead of allocating a new instance.
* @returns {Cartesian3} The computed horizon culling point, expressed in the possibly-shrunk ellipsoid-scaled space.
*/
EllipsoidalOccluder.prototype.computeHorizonCullingPointPossiblyUnderEllipsoid = function (
directionToPoint,
positions,
minimumHeight,
result
) {
var possiblyShrunkEllipsoid = getPossiblyShrunkEllipsoid(
this._ellipsoid,
minimumHeight,
scratchEllipsoidShrunk
);
return computeHorizonCullingPointFromPositions(
possiblyShrunkEllipsoid,
directionToPoint,
positions,
result
);
};
/**
* Computes a point that can be used for horizon culling from a list of positions. If the point is below
* the horizon, all of the positions are guaranteed to be below the horizon as well. The returned point
* is expressed in the ellipsoid-scaled space and is suitable for use with
* {@link EllipsoidalOccluder#isScaledSpacePointVisible}.
*
* @param {Cartesian3} directionToPoint The direction that the computed point will lie along.
* A reasonable direction to use is the direction from the center of the ellipsoid to
* the center of the bounding sphere computed from the positions. The direction need not
* be normalized.
* @param {Number[]} vertices The vertices from which to compute the horizon culling point. The positions
* must be expressed in a reference frame centered at the ellipsoid and aligned with the
* ellipsoid's axes.
* @param {Number} [stride=3]
* @param {Cartesian3} [center=Cartesian3.ZERO]
* @param {Cartesian3} [result] The instance on which to store the result instead of allocating a new instance.
* @returns {Cartesian3} The computed horizon culling point, expressed in the ellipsoid-scaled space.
*/
EllipsoidalOccluder.prototype.computeHorizonCullingPointFromVertices = function (
directionToPoint,
vertices,
stride,
center,
result
) {
return computeHorizonCullingPointFromVertices(
this._ellipsoid,
directionToPoint,
vertices,
stride,
center,
result
);
};
/**
* Similar to {@link EllipsoidalOccluder#computeHorizonCullingPointFromVertices} except computes the culling
* point relative to an ellipsoid that has been shrunk by the minimum height when the minimum height is below
* the ellipsoid. The returned point is expressed in the possibly-shrunk ellipsoid-scaled space and is suitable
* for use with {@link EllipsoidalOccluder#isScaledSpacePointVisiblePossiblyUnderEllipsoid}.
*
* @param {Cartesian3} directionToPoint The direction that the computed point will lie along.
* A reasonable direction to use is the direction from the center of the ellipsoid to
* the center of the bounding sphere computed from the positions. The direction need not
* be normalized.
* @param {Number[]} vertices The vertices from which to compute the horizon culling point. The positions
* must be expressed in a reference frame centered at the ellipsoid and aligned with the
* ellipsoid's axes.
* @param {Number} [stride=3]
* @param {Cartesian3} [center=Cartesian3.ZERO]
* @param {Number} [minimumHeight] The minimum height of all vertices. If this value is undefined, all vertices are assumed to be above the ellipsoid.
* @param {Cartesian3} [result] The instance on which to store the result instead of allocating a new instance.
* @returns {Cartesian3} The computed horizon culling point, expressed in the possibly-shrunk ellipsoid-scaled space.
*/
EllipsoidalOccluder.prototype.computeHorizonCullingPointFromVerticesPossiblyUnderEllipsoid = function (
directionToPoint,
vertices,
stride,
center,
minimumHeight,
result
) {
var possiblyShrunkEllipsoid = getPossiblyShrunkEllipsoid(
this._ellipsoid,
minimumHeight,
scratchEllipsoidShrunk
);
return computeHorizonCullingPointFromVertices(
possiblyShrunkEllipsoid,
directionToPoint,
vertices,
stride,
center,
result
);
};
var subsampleScratch = [];
/**
* Computes a point that can be used for horizon culling of a rectangle. If the point is below
* the horizon, the ellipsoid-conforming rectangle is guaranteed to be below the horizon as well.
* The returned point is expressed in the ellipsoid-scaled space and is suitable for use with
* {@link EllipsoidalOccluder#isScaledSpacePointVisible}.
*
* @param {Rectangle} rectangle The rectangle for which to compute the horizon culling point.
* @param {Ellipsoid} ellipsoid The ellipsoid on which the rectangle is defined. This may be different from
* the ellipsoid used by this instance for occlusion testing.
* @param {Cartesian3} [result] The instance on which to store the result instead of allocating a new instance.
* @returns {Cartesian3} The computed horizon culling point, expressed in the ellipsoid-scaled space.
*/
EllipsoidalOccluder.prototype.computeHorizonCullingPointFromRectangle = function (
rectangle,
ellipsoid,
result
) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("rectangle", rectangle);
//>>includeEnd('debug');
var positions = Rectangle.subsample(
rectangle,
ellipsoid,
0.0,
subsampleScratch
);
var bs = BoundingSphere.fromPoints(positions);
// If the bounding sphere center is too close to the center of the occluder, it doesn't make
// sense to try to horizon cull it.
if (Cartesian3.magnitude(bs.center) < 0.1 * ellipsoid.minimumRadius) {
return undefined;
}
return this.computeHorizonCullingPoint(bs.center, positions, result);
};
var scratchEllipsoidShrunkRadii = new Cartesian3();
function getPossiblyShrunkEllipsoid(ellipsoid, minimumHeight, result) {
if (
defined(minimumHeight) &&
minimumHeight < 0.0 &&
ellipsoid.minimumRadius > -minimumHeight
) {
var ellipsoidShrunkRadii = Cartesian3.fromElements(
ellipsoid.radii.x + minimumHeight,
ellipsoid.radii.y + minimumHeight,
ellipsoid.radii.z + minimumHeight,
scratchEllipsoidShrunkRadii
);
ellipsoid = Ellipsoid.fromCartesian3(ellipsoidShrunkRadii, result);
}
return ellipsoid;
}
function computeHorizonCullingPointFromPositions(
ellipsoid,
directionToPoint,
positions,
result
) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("directionToPoint", directionToPoint);
Check.defined("positions", positions);
//>>includeEnd('debug');
if (!defined(result)) {
result = new Cartesian3();
}
var scaledSpaceDirectionToPoint = computeScaledSpaceDirectionToPoint(
ellipsoid,
directionToPoint
);
var resultMagnitude = 0.0;
for (var i = 0, len = positions.length; i < len; ++i) {
var position = positions[i];
var candidateMagnitude = computeMagnitude(
ellipsoid,
position,
scaledSpaceDirectionToPoint
);
if (candidateMagnitude < 0.0) {
// all points should face the same direction, but this one doesn't, so return undefined
return undefined;
}
resultMagnitude = Math.max(resultMagnitude, candidateMagnitude);
}
return magnitudeToPoint(scaledSpaceDirectionToPoint, resultMagnitude, result);
}
var positionScratch = new Cartesian3();
function computeHorizonCullingPointFromVertices(
ellipsoid,
directionToPoint,
vertices,
stride,
center,
result
) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("directionToPoint", directionToPoint);
Check.defined("vertices", vertices);
Check.typeOf.number("stride", stride);
//>>includeEnd('debug');
if (!defined(result)) {
result = new Cartesian3();
}
stride = defaultValue(stride, 3);
center = defaultValue(center, Cartesian3.ZERO);
var scaledSpaceDirectionToPoint = computeScaledSpaceDirectionToPoint(
ellipsoid,
directionToPoint
);
var resultMagnitude = 0.0;
for (var i = 0, len = vertices.length; i < len; i += stride) {
positionScratch.x = vertices[i] + center.x;
positionScratch.y = vertices[i + 1] + center.y;
positionScratch.z = vertices[i + 2] + center.z;
var candidateMagnitude = computeMagnitude(
ellipsoid,
positionScratch,
scaledSpaceDirectionToPoint
);
if (candidateMagnitude < 0.0) {
// all points should face the same direction, but this one doesn't, so return undefined
return undefined;
}
resultMagnitude = Math.max(resultMagnitude, candidateMagnitude);
}
return magnitudeToPoint(scaledSpaceDirectionToPoint, resultMagnitude, result);
}
function isScaledSpacePointVisible(
occludeeScaledSpacePosition,
cameraPositionInScaledSpace,
distanceToLimbInScaledSpaceSquared
) {
// See https://cesium.com/blog/2013/04/25/Horizon-culling/
var cv = cameraPositionInScaledSpace;
var vhMagnitudeSquared = distanceToLimbInScaledSpaceSquared;
var vt = Cartesian3.subtract(
occludeeScaledSpacePosition,
cv,
scratchCartesian
);
var vtDotVc = -Cartesian3.dot(vt, cv);
// If vhMagnitudeSquared < 0 then we are below the surface of the ellipsoid and
// in this case, set the culling plane to be on V.
var isOccluded =
vhMagnitudeSquared < 0
? vtDotVc > 0
: vtDotVc > vhMagnitudeSquared &&
(vtDotVc * vtDotVc) / Cartesian3.magnitudeSquared(vt) >
vhMagnitudeSquared;
return !isOccluded;
}
var scaledSpaceScratch = new Cartesian3();
var directionScratch = new Cartesian3();
function computeMagnitude(ellipsoid, position, scaledSpaceDirectionToPoint) {
var scaledSpacePosition = ellipsoid.transformPositionToScaledSpace(
position,
scaledSpaceScratch
);
var magnitudeSquared = Cartesian3.magnitudeSquared(scaledSpacePosition);
var magnitude = Math.sqrt(magnitudeSquared);
var direction = Cartesian3.divideByScalar(
scaledSpacePosition,
magnitude,
directionScratch
);
// For the purpose of this computation, points below the ellipsoid are consider to be on it instead.
magnitudeSquared = Math.max(1.0, magnitudeSquared);
magnitude = Math.max(1.0, magnitude);
var cosAlpha = Cartesian3.dot(direction, scaledSpaceDirectionToPoint);
var sinAlpha = Cartesian3.magnitude(
Cartesian3.cross(direction, scaledSpaceDirectionToPoint, direction)
);
var cosBeta = 1.0 / magnitude;
var sinBeta = Math.sqrt(magnitudeSquared - 1.0) * cosBeta;
return 1.0 / (cosAlpha * cosBeta - sinAlpha * sinBeta);
}
function magnitudeToPoint(
scaledSpaceDirectionToPoint,
resultMagnitude,
result
) {
// The horizon culling point is undefined if there were no positions from which to compute it,
// the directionToPoint is pointing opposite all of the positions, or if we computed NaN or infinity.
if (
resultMagnitude <= 0.0 ||
resultMagnitude === 1.0 / 0.0 ||
resultMagnitude !== resultMagnitude
) {
return undefined;
}
return Cartesian3.multiplyByScalar(
scaledSpaceDirectionToPoint,
resultMagnitude,
result
);
}
var directionToPointScratch = new Cartesian3();
function computeScaledSpaceDirectionToPoint(ellipsoid, directionToPoint) {
if (Cartesian3.equals(directionToPoint, Cartesian3.ZERO)) {
return directionToPoint;
}
ellipsoid.transformPositionToScaledSpace(
directionToPoint,
directionToPointScratch
);
return Cartesian3.normalize(directionToPointScratch, directionToPointScratch);
}
export default EllipsoidalOccluder;
