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;
|
