/*global define*/
define([
'./Cartesian3',
'./Cartographic',
'./defaultValue',
'./defined',
'./DeveloperError',
'./Math',
'./Matrix3',
'./QuadraticRealPolynomial',
'./QuarticRealPolynomial',
'./Ray'
], function(
Cartesian3,
Cartographic,
defaultValue,
defined,
DeveloperError,
CesiumMath,
Matrix3,
QuadraticRealPolynomial,
QuarticRealPolynomial,
Ray) {
'use strict';
/**
* Functions for computing the intersection between geometries such as rays, planes, triangles, and ellipsoids.
*
* @exports IntersectionTests
*/
var IntersectionTests = {};
/**
* Computes the intersection of a ray and a plane.
*
* @param {Ray} ray The ray.
* @param {Plane} plane The plane.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The intersection point or undefined if there is no intersections.
*/
IntersectionTests.rayPlane = function(ray, plane, result) {
//>>includeStart('debug', pragmas.debug);
if (!defined(ray)) {
throw new DeveloperError('ray is required.');
}
if (!defined(plane)) {
throw new DeveloperError('plane is required.');
}
//>>includeEnd('debug');
if (!defined(result)) {
result = new Cartesian3();
}
var origin = ray.origin;
var direction = ray.direction;
var normal = plane.normal;
var denominator = Cartesian3.dot(normal, direction);
if (Math.abs(denominator) < CesiumMath.EPSILON15) {
// Ray is parallel to plane. The ray may be in the polygon's plane.
return undefined;
}
var t = (-plane.distance - Cartesian3.dot(normal, origin)) / denominator;
if (t < 0) {
return undefined;
}
result = Cartesian3.multiplyByScalar(direction, t, result);
return Cartesian3.add(origin, result, result);
};
var scratchEdge0 = new Cartesian3();
var scratchEdge1 = new Cartesian3();
var scratchPVec = new Cartesian3();
var scratchTVec = new Cartesian3();
var scratchQVec = new Cartesian3();
/**
* Computes the intersection of a ray and a triangle as a parametric distance along the input ray.
* @memberof IntersectionTests
*
* @param {Ray} ray The ray.
* @param {Cartesian3} p0 The first vertex of the triangle.
* @param {Cartesian3} p1 The second vertex of the triangle.
* @param {Cartesian3} p2 The third vertex of the triangle.
* @param {Boolean} [cullBackFaces=false] If <code>true</code>, will only compute an intersection with the front face of the triangle
* and return undefined for intersections with the back face.
* @returns {Number} The intersection as a parametric distance along the ray, or undefined if there is no intersection.
*/
IntersectionTests.rayTriangleParametric = function(ray, p0, p1, p2, cullBackFaces) {
//>>includeStart('debug', pragmas.debug);
if (!defined(ray)) {
throw new DeveloperError('ray is required.');
}
if (!defined(p0)) {
throw new DeveloperError('p0 is required.');
}
if (!defined(p1)) {
throw new DeveloperError('p1 is required.');
}
if (!defined(p2)) {
throw new DeveloperError('p2 is required.');
}
//>>includeEnd('debug');
cullBackFaces = defaultValue(cullBackFaces, false);
var origin = ray.origin;
var direction = ray.direction;
var edge0 = Cartesian3.subtract(p1, p0, scratchEdge0);
var edge1 = Cartesian3.subtract(p2, p0, scratchEdge1);
var p = Cartesian3.cross(direction, edge1, scratchPVec);
var det = Cartesian3.dot(edge0, p);
var tvec;
var q;
var u;
var v;
var t;
if (cullBackFaces) {
if (det < CesiumMath.EPSILON6) {
return undefined;
}
tvec = Cartesian3.subtract(origin, p0, scratchTVec);
u = Cartesian3.dot(tvec, p);
if (u < 0.0 || u > det) {
return undefined;
}
q = Cartesian3.cross(tvec, edge0, scratchQVec);
v = Cartesian3.dot(direction, q);
if (v < 0.0 || u + v > det) {
return undefined;
}
t = Cartesian3.dot(edge1, q) / det;
} else {
if (Math.abs(det) < CesiumMath.EPSILON6) {
return undefined;
}
var invDet = 1.0 / det;
tvec = Cartesian3.subtract(origin, p0, scratchTVec);
u = Cartesian3.dot(tvec, p) * invDet;
if (u < 0.0 || u > 1.0) {
return undefined;
}
q = Cartesian3.cross(tvec, edge0, scratchQVec);
v = Cartesian3.dot(direction, q) * invDet;
if (v < 0.0 || u + v > 1.0) {
return undefined;
}
t = Cartesian3.dot(edge1, q) * invDet;
}
return t;
};
/**
* Computes the intersection of a ray and a triangle as a Cartesian3 coordinate.
* @memberof IntersectionTests
*
* @param {Ray} ray The ray.
* @param {Cartesian3} p0 The first vertex of the triangle.
* @param {Cartesian3} p1 The second vertex of the triangle.
* @param {Cartesian3} p2 The third vertex of the triangle.
* @param {Boolean} [cullBackFaces=false] If <code>true</code>, will only compute an intersection with the front face of the triangle
* and return undefined for intersections with the back face.
* @param {Cartesian3} [result] The <code>Cartesian3</code> onto which to store the result.
* @returns {Cartesian3} The intersection point or undefined if there is no intersections.
*/
IntersectionTests.rayTriangle = function(ray, p0, p1, p2, cullBackFaces, result) {
var t = IntersectionTests.rayTriangleParametric(ray, p0, p1, p2, cullBackFaces);
if (!defined(t) || t < 0.0) {
return undefined;
}
if (!defined(result)) {
result = new Cartesian3();
}
Cartesian3.multiplyByScalar(ray.direction, t, result);
return Cartesian3.add(ray.origin, result, result);
};
var scratchLineSegmentTriangleRay = new Ray();
/**
* Computes the intersection of a line segment and a triangle.
* @memberof IntersectionTests
*
* @param {Cartesian3} v0 The an end point of the line segment.
* @param {Cartesian3} v1 The other end point of the line segment.
* @param {Cartesian3} p0 The first vertex of the triangle.
* @param {Cartesian3} p1 The second vertex of the triangle.
* @param {Cartesian3} p2 The third vertex of the triangle.
* @param {Boolean} [cullBackFaces=false] If <code>true</code>, will only compute an intersection with the front face of the triangle
* and return undefined for intersections with the back face.
* @param {Cartesian3} [result] The <code>Cartesian3</code> onto which to store the result.
* @returns {Cartesian3} The intersection point or undefined if there is no intersections.
*/
IntersectionTests.lineSegmentTriangle = function(v0, v1, p0, p1, p2, cullBackFaces, result) {
//>>includeStart('debug', pragmas.debug);
if (!defined(v0)) {
throw new DeveloperError('v0 is required.');
}
if (!defined(v1)) {
throw new DeveloperError('v1 is required.');
}
if (!defined(p0)) {
throw new DeveloperError('p0 is required.');
}
if (!defined(p1)) {
throw new DeveloperError('p1 is required.');
}
if (!defined(p2)) {
throw new DeveloperError('p2 is required.');
}
//>>includeEnd('debug');
var ray = scratchLineSegmentTriangleRay;
Cartesian3.clone(v0, ray.origin);
Cartesian3.subtract(v1, v0, ray.direction);
Cartesian3.normalize(ray.direction, ray.direction);
var t = IntersectionTests.rayTriangleParametric(ray, p0, p1, p2, cullBackFaces);
if (!defined(t) || t < 0.0 || t > Cartesian3.distance(v0, v1)) {
return undefined;
}
if (!defined(result)) {
result = new Cartesian3();
}
Cartesian3.multiplyByScalar(ray.direction, t, result);
return Cartesian3.add(ray.origin, result, result);
};
function solveQuadratic(a, b, c, result) {
var det = b * b - 4.0 * a * c;
if (det < 0.0) {
return undefined;
} else if (det > 0.0) {
var denom = 1.0 / (2.0 * a);
var disc = Math.sqrt(det);
var root0 = (-b + disc) * denom;
var root1 = (-b - disc) * denom;
if (root0 < root1) {
result.root0 = root0;
result.root1 = root1;
} else {
result.root0 = root1;
result.root1 = root0;
}
return result;
}
var root = -b / (2.0 * a);
if (root === 0.0) {
return undefined;
}
result.root0 = result.root1 = root;
return result;
}
var raySphereRoots = {
root0 : 0.0,
root1 : 0.0
};
function raySphere(ray, sphere, result) {
if (!defined(result)) {
result = {};
}
var origin = ray.origin;
var direction = ray.direction;
var center = sphere.center;
var radiusSquared = sphere.radius * sphere.radius;
var diff = Cartesian3.subtract(origin, center, scratchPVec);
var a = Cartesian3.dot(direction, direction);
var b = 2.0 * Cartesian3.dot(direction, diff);
var c = Cartesian3.magnitudeSquared(diff) - radiusSquared;
var roots = solveQuadratic(a, b, c, raySphereRoots);
if (!defined(roots)) {
return undefined;
}
result.start = roots.root0;
result.stop = roots.root1;
return result;
}
/**
* Computes the intersection points of a ray with a sphere.
* @memberof IntersectionTests
*
* @param {Ray} ray The ray.
* @param {BoundingSphere} sphere The sphere.
* @param {Object} [result] The result onto which to store the result.
* @returns {Object} An object with the first (<code>start</code>) and the second (<code>stop</code>) intersection scalars for points along the ray or undefined if there are no intersections.
*/
IntersectionTests.raySphere = function(ray, sphere, result) {
//>>includeStart('debug', pragmas.debug);
if (!defined(ray)) {
throw new DeveloperError('ray is required.');
}
if (!defined(sphere)) {
throw new DeveloperError('sphere is required.');
}
//>>includeEnd('debug');
result = raySphere(ray, sphere, result);
if (!defined(result) || result.stop < 0.0) {
return undefined;
}
result.start = Math.max(result.start, 0.0);
return result;
};
var scratchLineSegmentRay = new Ray();
/**
* Computes the intersection points of a line segment with a sphere.
* @memberof IntersectionTests
*
* @param {Cartesian3} p0 An end point of the line segment.
* @param {Cartesian3} p1 The other end point of the line segment.
* @param {BoundingSphere} sphere The sphere.
* @param {Object} [result] The result onto which to store the result.
* @returns {Object} An object with the first (<code>start</code>) and the second (<code>stop</code>) intersection scalars for points along the line segment or undefined if there are no intersections.
*/
IntersectionTests.lineSegmentSphere = function(p0, p1, sphere, result) {
//>>includeStart('debug', pragmas.debug);
if (!defined(p0)) {
throw new DeveloperError('p0 is required.');
}
if (!defined(p1)) {
throw new DeveloperError('p1 is required.');
}
if (!defined(sphere)) {
throw new DeveloperError('sphere is required.');
}
//>>includeEnd('debug');
var ray = scratchLineSegmentRay;
Cartesian3.clone(p0, ray.origin);
var direction = Cartesian3.subtract(p1, p0, ray.direction);
var maxT = Cartesian3.magnitude(direction);
Cartesian3.normalize(direction, direction);
result = raySphere(ray, sphere, result);
if (!defined(result) || result.stop < 0.0 || result.start > maxT) {
return undefined;
}
result.start = Math.max(result.start, 0.0);
result.stop = Math.min(result.stop, maxT);
return result;
};
var scratchQ = new Cartesian3();
var scratchW = new Cartesian3();
/**
* Computes the intersection points of a ray with an ellipsoid.
*
* @param {Ray} ray The ray.
* @param {Ellipsoid} ellipsoid The ellipsoid.
* @returns {Object} An object with the first (<code>start</code>) and the second (<code>stop</code>) intersection scalars for points along the ray or undefined if there are no intersections.
*/
IntersectionTests.rayEllipsoid = function(ray, ellipsoid) {
//>>includeStart('debug', pragmas.debug);
if (!defined(ray)) {
throw new DeveloperError('ray is required.');
}
if (!defined(ellipsoid)) {
throw new DeveloperError('ellipsoid is required.');
}
//>>includeEnd('debug');
var inverseRadii = ellipsoid.oneOverRadii;
var q = Cartesian3.multiplyComponents(inverseRadii, ray.origin, scratchQ);
var w = Cartesian3.multiplyComponents(inverseRadii, ray.direction, scratchW);
var q2 = Cartesian3.magnitudeSquared(q);
var qw = Cartesian3.dot(q, w);
var difference, w2, product, discriminant, temp;
if (q2 > 1.0) {
// Outside ellipsoid.
if (qw >= 0.0) {
// Looking outward or tangent (0 intersections).
return undefined;
}
// qw < 0.0.
var qw2 = qw * qw;
difference = q2 - 1.0; // Positively valued.
w2 = Cartesian3.magnitudeSquared(w);
product = w2 * difference;
if (qw2 < product) {
// Imaginary roots (0 intersections).
return undefined;
} else if (qw2 > product) {
// Distinct roots (2 intersections).
discriminant = qw * qw - product;
temp = -qw + Math.sqrt(discriminant); // Avoid cancellation.
var root0 = temp / w2;
var root1 = difference / temp;
if (root0 < root1) {
return {
start : root0,
stop : root1
};
}
return {
start : root1,
stop : root0
};
} else {
// qw2 == product. Repeated roots (2 intersections).
var root = Math.sqrt(difference / w2);
return {
start : root,
stop : root
};
}
} else if (q2 < 1.0) {
// Inside ellipsoid (2 intersections).
difference = q2 - 1.0; // Negatively valued.
w2 = Cartesian3.magnitudeSquared(w);
product = w2 * difference; // Negatively valued.
discriminant = qw * qw - product;
temp = -qw + Math.sqrt(discriminant); // Positively valued.
return {
start : 0.0,
stop : temp / w2
};
} else {
// q2 == 1.0. On ellipsoid.
if (qw < 0.0) {
// Looking inward.
w2 = Cartesian3.magnitudeSquared(w);
return {
start : 0.0,
stop : -qw / w2
};
}
// qw >= 0.0. Looking outward or tangent.
return undefined;
}
};
function addWithCancellationCheck(left, right, tolerance) {
var difference = left + right;
if ((CesiumMath.sign(left) !== CesiumMath.sign(right)) &&
Math.abs(difference / Math.max(Math.abs(left), Math.abs(right))) < tolerance) {
return 0.0;
}
return difference;
}
function quadraticVectorExpression(A, b, c, x, w) {
var xSquared = x * x;
var wSquared = w * w;
var l2 = (A[Matrix3.COLUMN1ROW1] - A[Matrix3.COLUMN2ROW2]) * wSquared;
var l1 = w * (x * addWithCancellationCheck(A[Matrix3.COLUMN1ROW0], A[Matrix3.COLUMN0ROW1], CesiumMath.EPSILON15) + b.y);
var l0 = (A[Matrix3.COLUMN0ROW0] * xSquared + A[Matrix3.COLUMN2ROW2] * wSquared) + x * b.x + c;
var r1 = wSquared * addWithCancellationCheck(A[Matrix3.COLUMN2ROW1], A[Matrix3.COLUMN1ROW2], CesiumMath.EPSILON15);
var r0 = w * (x * addWithCancellationCheck(A[Matrix3.COLUMN2ROW0], A[Matrix3.COLUMN0ROW2]) + b.z);
var cosines;
var solutions = [];
if (r0 === 0.0 && r1 === 0.0) {
cosines = QuadraticRealPolynomial.computeRealRoots(l2, l1, l0);
if (cosines.length === 0) {
return solutions;
}
var cosine0 = cosines[0];
var sine0 = Math.sqrt(Math.max(1.0 - cosine0 * cosine0, 0.0));
solutions.push(new Cartesian3(x, w * cosine0, w * -sine0));
solutions.push(new Cartesian3(x, w * cosine0, w * sine0));
if (cosines.length === 2) {
var cosine1 = cosines[1];
var sine1 = Math.sqrt(Math.max(1.0 - cosine1 * cosine1, 0.0));
solutions.push(new Cartesian3(x, w * cosine1, w * -sine1));
solutions.push(new Cartesian3(x, w * cosine1, w * sine1));
}
return solutions;
}
var r0Squared = r0 * r0;
var r1Squared = r1 * r1;
var l2Squared = l2 * l2;
var r0r1 = r0 * r1;
var c4 = l2Squared + r1Squared;
var c3 = 2.0 * (l1 * l2 + r0r1);
var c2 = 2.0 * l0 * l2 + l1 * l1 - r1Squared + r0Squared;
var c1 = 2.0 * (l0 * l1 - r0r1);
var c0 = l0 * l0 - r0Squared;
if (c4 === 0.0 && c3 === 0.0 && c2 === 0.0 && c1 === 0.0) {
return solutions;
}
cosines = QuarticRealPolynomial.computeRealRoots(c4, c3, c2, c1, c0);
var length = cosines.length;
if (length === 0) {
return solutions;
}
for ( var i = 0; i < length; ++i) {
var cosine = cosines[i];
var cosineSquared = cosine * cosine;
var sineSquared = Math.max(1.0 - cosineSquared, 0.0);
var sine = Math.sqrt(sineSquared);
//var left = l2 * cosineSquared + l1 * cosine + l0;
var left;
if (CesiumMath.sign(l2) === CesiumMath.sign(l0)) {
left = addWithCancellationCheck(l2 * cosineSquared + l0, l1 * cosine, CesiumMath.EPSILON12);
} else if (CesiumMath.sign(l0) === CesiumMath.sign(l1 * cosine)) {
left = addWithCancellationCheck(l2 * cosineSquared, l1 * cosine + l0, CesiumMath.EPSILON12);
} else {
left = addWithCancellationCheck(l2 * cosineSquared + l1 * cosine, l0, CesiumMath.EPSILON12);
}
var right = addWithCancellationCheck(r1 * cosine, r0, CesiumMath.EPSILON15);
var product = left * right;
if (product < 0.0) {
solutions.push(new Cartesian3(x, w * cosine, w * sine));
} else if (product > 0.0) {
solutions.push(new Cartesian3(x, w * cosine, w * -sine));
} else if (sine !== 0.0) {
solutions.push(new Cartesian3(x, w * cosine, w * -sine));
solutions.push(new Cartesian3(x, w * cosine, w * sine));
++i;
} else {
solutions.push(new Cartesian3(x, w * cosine, w * sine));
}
}
return solutions;
}
var firstAxisScratch = new Cartesian3();
var secondAxisScratch = new Cartesian3();
var thirdAxisScratch = new Cartesian3();
var referenceScratch = new Cartesian3();
var bCart = new Cartesian3();
var bScratch = new Matrix3();
var btScratch = new Matrix3();
var diScratch = new Matrix3();
var dScratch = new Matrix3();
var cScratch = new Matrix3();
var tempMatrix = new Matrix3();
var aScratch = new Matrix3();
var sScratch = new Cartesian3();
var closestScratch = new Cartesian3();
var surfPointScratch = new Cartographic();
/**
* Provides the point along the ray which is nearest to the ellipsoid.
*
* @param {Ray} ray The ray.
* @param {Ellipsoid} ellipsoid The ellipsoid.
* @returns {Cartesian3} The nearest planetodetic point on the ray.
*/
IntersectionTests.grazingAltitudeLocation = function(ray, ellipsoid) {
//>>includeStart('debug', pragmas.debug);
if (!defined(ray)) {
throw new DeveloperError('ray is required.');
}
if (!defined(ellipsoid)) {
throw new DeveloperError('ellipsoid is required.');
}
//>>includeEnd('debug');
var position = ray.origin;
var direction = ray.direction;
if (!Cartesian3.equals(position, Cartesian3.ZERO)) {
var normal = ellipsoid.geodeticSurfaceNormal(position, firstAxisScratch);
if (Cartesian3.dot(direction, normal) >= 0.0) { // The location provided is the closest point in altitude
return position;
}
}
var intersects = defined(this.rayEllipsoid(ray, ellipsoid));
// Compute the scaled direction vector.
var f = ellipsoid.transformPositionToScaledSpace(direction, firstAxisScratch);
// Constructs a basis from the unit scaled direction vector. Construct its rotation and transpose.
var firstAxis = Cartesian3.normalize(f, f);
var reference = Cartesian3.mostOrthogonalAxis(f, referenceScratch);
var secondAxis = Cartesian3.normalize(Cartesian3.cross(reference, firstAxis, secondAxisScratch), secondAxisScratch);
var thirdAxis = Cartesian3.normalize(Cartesian3.cross(firstAxis, secondAxis, thirdAxisScratch), thirdAxisScratch);
var B = bScratch;
B[0] = firstAxis.x;
B[1] = firstAxis.y;
B[2] = firstAxis.z;
B[3] = secondAxis.x;
B[4] = secondAxis.y;
B[5] = secondAxis.z;
B[6] = thirdAxis.x;
B[7] = thirdAxis.y;
B[8] = thirdAxis.z;
var B_T = Matrix3.transpose(B, btScratch);
// Get the scaling matrix and its inverse.
var D_I = Matrix3.fromScale(ellipsoid.radii, diScratch);
var D = Matrix3.fromScale(ellipsoid.oneOverRadii, dScratch);
var C = cScratch;
C[0] = 0.0;
C[1] = -direction.z;
C[2] = direction.y;
C[3] = direction.z;
C[4] = 0.0;
C[5] = -direction.x;
C[6] = -direction.y;
C[7] = direction.x;
C[8] = 0.0;
var temp = Matrix3.multiply(Matrix3.multiply(B_T, D, tempMatrix), C, tempMatrix);
var A = Matrix3.multiply(Matrix3.multiply(temp, D_I, aScratch), B, aScratch);
var b = Matrix3.multiplyByVector(temp, position, bCart);
// Solve for the solutions to the expression in standard form:
var solutions = quadraticVectorExpression(A, Cartesian3.negate(b, firstAxisScratch), 0.0, 0.0, 1.0);
var s;
var altitude;
var length = solutions.length;
if (length > 0) {
var closest = Cartesian3.clone(Cartesian3.ZERO, closestScratch);
var maximumValue = Number.NEGATIVE_INFINITY;
for ( var i = 0; i < length; ++i) {
s = Matrix3.multiplyByVector(D_I, Matrix3.multiplyByVector(B, solutions[i], sScratch), sScratch);
var v = Cartesian3.normalize(Cartesian3.subtract(s, position, referenceScratch), referenceScratch);
var dotProduct = Cartesian3.dot(v, direction);
if (dotProduct > maximumValue) {
maximumValue = dotProduct;
closest = Cartesian3.clone(s, closest);
}
}
var surfacePoint = ellipsoid.cartesianToCartographic(closest, surfPointScratch);
maximumValue = CesiumMath.clamp(maximumValue, 0.0, 1.0);
altitude = Cartesian3.magnitude(Cartesian3.subtract(closest, position, referenceScratch)) * Math.sqrt(1.0 - maximumValue * maximumValue);
altitude = intersects ? -altitude : altitude;
surfacePoint.height = altitude;
return ellipsoid.cartographicToCartesian(surfacePoint, new Cartesian3());
}
return undefined;
};
var lineSegmentPlaneDifference = new Cartesian3();
/**
* Computes the intersection of a line segment and a plane.
*
* @param {Cartesian3} endPoint0 An end point of the line segment.
* @param {Cartesian3} endPoint1 The other end point of the line segment.
* @param {Plane} plane The plane.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The intersection point or undefined if there is no intersection.
*
* @example
* var origin = Cesium.Cartesian3.fromDegrees(-75.59777, 40.03883);
* var normal = ellipsoid.geodeticSurfaceNormal(origin);
* var plane = Cesium.Plane.fromPointNormal(origin, normal);
*
* var p0 = new Cesium.Cartesian3(...);
* var p1 = new Cesium.Cartesian3(...);
*
* // find the intersection of the line segment from p0 to p1 and the tangent plane at origin.
* var intersection = Cesium.IntersectionTests.lineSegmentPlane(p0, p1, plane);
*/
IntersectionTests.lineSegmentPlane = function(endPoint0, endPoint1, plane, result) {
//>>includeStart('debug', pragmas.debug);
if (!defined(endPoint0)) {
throw new DeveloperError('endPoint0 is required.');
}
if (!defined(endPoint1)) {
throw new DeveloperError('endPoint1 is required.');
}
if (!defined(plane)) {
throw new DeveloperError('plane is required.');
}
//>>includeEnd('debug');
if (!defined(result)) {
result = new Cartesian3();
}
var difference = Cartesian3.subtract(endPoint1, endPoint0, lineSegmentPlaneDifference);
var normal = plane.normal;
var nDotDiff = Cartesian3.dot(normal, difference);
// check if the segment and plane are parallel
if (Math.abs(nDotDiff) < CesiumMath.EPSILON6) {
return undefined;
}
var nDotP0 = Cartesian3.dot(normal, endPoint0);
var t = -(plane.distance + nDotP0) / nDotDiff;
// intersection only if t is in [0, 1]
if (t < 0.0 || t > 1.0) {
return undefined;
}
// intersection is endPoint0 + t * (endPoint1 - endPoint0)
Cartesian3.multiplyByScalar(difference, t, result);
Cartesian3.add(endPoint0, result, result);
return result;
};
/**
* Computes the intersection of a triangle and a plane
*
* @param {Cartesian3} p0 First point of the triangle
* @param {Cartesian3} p1 Second point of the triangle
* @param {Cartesian3} p2 Third point of the triangle
* @param {Plane} plane Intersection plane
* @returns {Object} An object with properties <code>positions</code> and <code>indices</code>, which are arrays that represent three triangles that do not cross the plane. (Undefined if no intersection exists)
*
* @example
* var origin = Cesium.Cartesian3.fromDegrees(-75.59777, 40.03883);
* var normal = ellipsoid.geodeticSurfaceNormal(origin);
* var plane = Cesium.Plane.fromPointNormal(origin, normal);
*
* var p0 = new Cesium.Cartesian3(...);
* var p1 = new Cesium.Cartesian3(...);
* var p2 = new Cesium.Cartesian3(...);
*
* // convert the triangle composed of points (p0, p1, p2) to three triangles that don't cross the plane
* var triangles = Cesium.IntersectionTests.trianglePlaneIntersection(p0, p1, p2, plane);
*/
IntersectionTests.trianglePlaneIntersection = function(p0, p1, p2, plane) {
//>>includeStart('debug', pragmas.debug);
if ((!defined(p0)) ||
(!defined(p1)) ||
(!defined(p2)) ||
(!defined(plane))) {
throw new DeveloperError('p0, p1, p2, and plane are required.');
}
//>>includeEnd('debug');
var planeNormal = plane.normal;
var planeD = plane.distance;
var p0Behind = (Cartesian3.dot(planeNormal, p0) + planeD) < 0.0;
var p1Behind = (Cartesian3.dot(planeNormal, p1) + planeD) < 0.0;
var p2Behind = (Cartesian3.dot(planeNormal, p2) + planeD) < 0.0;
// Given these dots products, the calls to lineSegmentPlaneIntersection
// always have defined results.
var numBehind = 0;
numBehind += p0Behind ? 1 : 0;
numBehind += p1Behind ? 1 : 0;
numBehind += p2Behind ? 1 : 0;
var u1, u2;
if (numBehind === 1 || numBehind === 2) {
u1 = new Cartesian3();
u2 = new Cartesian3();
}
if (numBehind === 1) {
if (p0Behind) {
IntersectionTests.lineSegmentPlane(p0, p1, plane, u1);
IntersectionTests.lineSegmentPlane(p0, p2, plane, u2);
return {
positions : [p0, p1, p2, u1, u2 ],
indices : [
// Behind
0, 3, 4,
// In front
1, 2, 4,
1, 4, 3
]
};
} else if (p1Behind) {
IntersectionTests.lineSegmentPlane(p1, p2, plane, u1);
IntersectionTests.lineSegmentPlane(p1, p0, plane, u2);
return {
positions : [p0, p1, p2, u1, u2 ],
indices : [
// Behind
1, 3, 4,
// In front
2, 0, 4,
2, 4, 3
]
};
} else if (p2Behind) {
IntersectionTests.lineSegmentPlane(p2, p0, plane, u1);
IntersectionTests.lineSegmentPlane(p2, p1, plane, u2);
return {
positions : [p0, p1, p2, u1, u2 ],
indices : [
// Behind
2, 3, 4,
// In front
0, 1, 4,
0, 4, 3
]
};
}
} else if (numBehind === 2) {
if (!p0Behind) {
IntersectionTests.lineSegmentPlane(p1, p0, plane, u1);
IntersectionTests.lineSegmentPlane(p2, p0, plane, u2);
return {
positions : [p0, p1, p2, u1, u2 ],
indices : [
// Behind
1, 2, 4,
1, 4, 3,
// In front
0, 3, 4
]
};
} else if (!p1Behind) {
IntersectionTests.lineSegmentPlane(p2, p1, plane, u1);
IntersectionTests.lineSegmentPlane(p0, p1, plane, u2);
return {
positions : [p0, p1, p2, u1, u2 ],
indices : [
// Behind
2, 0, 4,
2, 4, 3,
// In front
1, 3, 4
]
};
} else if (!p2Behind) {
IntersectionTests.lineSegmentPlane(p0, p2, plane, u1);
IntersectionTests.lineSegmentPlane(p1, p2, plane, u2);
return {
positions : [p0, p1, p2, u1, u2 ],
indices : [
// Behind
0, 1, 4,
0, 4, 3,
// In front
2, 3, 4
]
};
}
}
// if numBehind is 3, the triangle is completely behind the plane;
// otherwise, it is completely in front (numBehind is 0).
return undefined;
};
return IntersectionTests;
});