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Cartesian3 from "./Cartesian3.js";
import Cartographic from "./Cartographic.js";
import defined from "./defined.js";
import DeveloperError from "./DeveloperError.js";
import Interval from "./Interval.js";
import CesiumMath from "./Math.js";
import Matrix3 from "./Matrix3.js";
import QuadraticRealPolynomial from "./QuadraticRealPolynomial.js";
import QuarticRealPolynomial from "./QuarticRealPolynomial.js";
import Ray from "./Ray.js";
/**
* Functions for computing the intersection between geometries such as rays, planes, triangles, and ellipsoids.
*
* @namespace IntersectionTests
*/
const 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();
}
const origin = ray.origin;
const direction = ray.direction;
const normal = plane.normal;
const 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;
}
const 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);
};
const scratchEdge0 = new Cartesian3();
const scratchEdge1 = new Cartesian3();
const scratchPVec = new Cartesian3();
const scratchTVec = new Cartesian3();
const scratchQVec = new Cartesian3();
/**
* Computes the intersection of a ray and a triangle as a parametric distance along the input ray. The result is negative when the triangle is behind the ray.
*
* Implements {@link https://cadxfem.org/inf/Fast%20MinimumStorage%20RayTriangle%20Intersection.pdf|
* Fast Minimum Storage Ray/Triangle Intersection} by Tomas Moller and Ben Trumbore.
*
* @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 = cullBackFaces ?? false;
const origin = ray.origin;
const direction = ray.direction;
const edge0 = Cartesian3.subtract(p1, p0, scratchEdge0);
const edge1 = Cartesian3.subtract(p2, p0, scratchEdge1);
const p = Cartesian3.cross(direction, edge1, scratchPVec);
const det = Cartesian3.dot(edge0, p);
let tvec;
let q;
let u;
let v;
let 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;
}
const 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.
*
* Implements {@link https://cadxfem.org/inf/Fast%20MinimumStorage%20RayTriangle%20Intersection.pdf|
* Fast Minimum Storage Ray/Triangle Intersection} by Tomas Moller and Ben Trumbore.
*
* @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,
) {
const t = IntersectionTests.rayTriangleParametric(
ray,
p0,
p1,
p2,
cullBackFaces,
);
if (!defined(t) || t < 0.0) {
return undefined;
}
Eif (!defined(result)) {
result = new Cartesian3();
}
Cartesian3.multiplyByScalar(ray.direction, t, result);
return Cartesian3.add(ray.origin, result, result);
};
const 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');
const ray = scratchLineSegmentTriangleRay;
Cartesian3.clone(v0, ray.origin);
Cartesian3.subtract(v1, v0, ray.direction);
Cartesian3.normalize(ray.direction, ray.direction);
const t = IntersectionTests.rayTriangleParametric(
ray,
p0,
p1,
p2,
cullBackFaces,
);
if (!defined(t) || t < 0.0 || t > Cartesian3.distance(v0, v1)) {
return undefined;
}
Eif (!defined(result)) {
result = new Cartesian3();
}
Cartesian3.multiplyByScalar(ray.direction, t, result);
return Cartesian3.add(ray.origin, result, result);
};
function solveQuadratic(a, b, c, result) {
const det = b * b - 4.0 * a * c;
if (det < 0.0) {
return undefined;
} else if (det > 0.0) {
const denom = 1.0 / (2.0 * a);
const disc = Math.sqrt(det);
const root0 = (-b + disc) * denom;
const root1 = (-b - disc) * denom;
Iif (root0 < root1) {
result.root0 = root0;
result.root1 = root1;
} else {
result.root0 = root1;
result.root1 = root0;
}
return result;
}
const root = -b / (2.0 * a);
if (root === 0.0) {
return undefined;
}
result.root0 = result.root1 = root;
return result;
}
const raySphereRoots = {
root0: 0.0,
root1: 0.0,
};
function raySphere(ray, sphere, result) {
if (!defined(result)) {
result = new Interval();
}
const origin = ray.origin;
const direction = ray.direction;
const center = sphere.center;
const radiusSquared = sphere.radius * sphere.radius;
const diff = Cartesian3.subtract(origin, center, scratchPVec);
const a = Cartesian3.dot(direction, direction);
const b = 2.0 * Cartesian3.dot(direction, diff);
const c = Cartesian3.magnitudeSquared(diff) - radiusSquared;
const 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 {Interval} [result] The result onto which to store the result.
* @returns {Interval} The interval containing scalar 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;
};
const 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 {Interval} [result] The result onto which to store the result.
* @returns {Interval} The interval containing scalar points along the ray 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');
const ray = scratchLineSegmentRay;
Cartesian3.clone(p0, ray.origin);
const direction = Cartesian3.subtract(p1, p0, ray.direction);
const 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;
};
const scratchQ = new Cartesian3();
const scratchW = new Cartesian3();
/**
* Computes the intersection points of a ray with an ellipsoid.
*
* @param {Ray} ray The ray.
* @param {Ellipsoid} ellipsoid The ellipsoid.
* @returns {Interval} The interval containing scalar 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');
const inverseRadii = ellipsoid.oneOverRadii;
const q = Cartesian3.multiplyComponents(inverseRadii, ray.origin, scratchQ);
const w = Cartesian3.multiplyComponents(
inverseRadii,
ray.direction,
scratchW,
);
const q2 = Cartesian3.magnitudeSquared(q);
const qw = Cartesian3.dot(q, w);
let 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.
const 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.
const root0 = temp / w2;
const root1 = difference / temp;
Iif (root0 < root1) {
return new Interval(root0, root1);
}
return {
start: root1,
stop: root0,
};
}
// qw2 == product. Repeated roots (2 intersections).
const root = Math.sqrt(difference / w2);
return new Interval(root, 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 new Interval(0.0, temp / w2);
}
// q2 == 1.0. On ellipsoid.
Iif (qw < 0.0) {
// Looking inward.
w2 = Cartesian3.magnitudeSquared(w);
return new Interval(0.0, -qw / w2);
}
// qw >= 0.0. Looking outward or tangent.
return undefined;
};
const scratchRayIntervalX = new Interval();
const scratchRayIntervalY = new Interval();
const scratchRayIntervalZ = new Interval();
/**
* Computes the intersection points of a ray with an axis-aligned bounding box. (axis-aligned in the same space as the ray)
*
* @param {Ray} ray The ray.
* @param {AxisAlignedBoundingBox} box The axis-aligned bounding box.
* @param {Interval | undefined} result The interval containing scalar points along the ray or undefined if there are no intersections.
*/
IntersectionTests.rayAxisAlignedBoundingBox = function (ray, box, result) {
//>>includeStart('debug', pragmas.debug);
Iif (!defined(ray)) {
throw new DeveloperError("ray is required.");
}
Iif (!defined(box)) {
throw new DeveloperError("box is required.");
}
//>>includeEnd('debug');
Iif (!defined(result)) {
result = new Interval();
}
const tx = rayIntervalAlongAABBAxis(
ray.origin.x,
ray.direction.x,
box.minimum.x,
box.maximum.x,
scratchRayIntervalX,
);
const ty = rayIntervalAlongAABBAxis(
ray.origin.y,
ray.direction.y,
box.minimum.y,
box.maximum.y,
scratchRayIntervalY,
);
const tz = rayIntervalAlongAABBAxis(
ray.origin.z,
ray.direction.z,
box.minimum.z,
box.maximum.z,
scratchRayIntervalZ,
);
result.start = tx.start > ty.start ? tx.start : ty.start; //Get Greatest Min
result.stop = tx.stop < ty.stop ? tx.stop : ty.stop; //Get Smallest Max
if (tx.start > ty.stop || ty.start > tx.stop) {
return undefined;
}
if (result.start > tz.stop || tz.start > result.stop) {
return undefined;
}
if (tz.start > result.start) {
result.start = tz.start;
}
if (tz.stop < result.stop) {
result.stop = tz.stop;
}
return result;
};
function rayIntervalAlongAABBAxis(origin, direction, min, max, result) {
result.start = (min - origin) / direction;
result.stop = (max - origin) / direction;
if (result.stop < result.start) {
const tmp = result.stop;
result.stop = result.start;
result.start = tmp;
}
return result;
}
function addWithCancellationCheck(left, right, tolerance) {
const 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;
}
/**
* @private
*/
IntersectionTests.quadraticVectorExpression = function (A, b, c, x, w) {
const xSquared = x * x;
const wSquared = w * w;
const l2 = (A[Matrix3.COLUMN1ROW1] - A[Matrix3.COLUMN2ROW2]) * wSquared;
const l1 =
w *
(x *
addWithCancellationCheck(
A[Matrix3.COLUMN1ROW0],
A[Matrix3.COLUMN0ROW1],
CesiumMath.EPSILON15,
) +
b.y);
const l0 =
A[Matrix3.COLUMN0ROW0] * xSquared +
A[Matrix3.COLUMN2ROW2] * wSquared +
x * b.x +
c;
const r1 =
wSquared *
addWithCancellationCheck(
A[Matrix3.COLUMN2ROW1],
A[Matrix3.COLUMN1ROW2],
CesiumMath.EPSILON15,
);
const r0 =
w *
(x *
addWithCancellationCheck(A[Matrix3.COLUMN2ROW0], A[Matrix3.COLUMN0ROW2]) +
b.z);
let cosines;
const solutions = [];
if (r0 === 0.0 && r1 === 0.0) {
cosines = QuadraticRealPolynomial.computeRealRoots(l2, l1, l0);
if (cosines.length === 0) {
return solutions;
}
const cosine0 = cosines[0];
const 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));
Iif (cosines.length === 2) {
const cosine1 = cosines[1];
const 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;
}
const r0Squared = r0 * r0;
const r1Squared = r1 * r1;
const l2Squared = l2 * l2;
const r0r1 = r0 * r1;
const c4 = l2Squared + r1Squared;
const c3 = 2.0 * (l1 * l2 + r0r1);
const c2 = 2.0 * l0 * l2 + l1 * l1 - r1Squared + r0Squared;
const c1 = 2.0 * (l0 * l1 - r0r1);
const c0 = l0 * l0 - r0Squared;
Iif (c4 === 0.0 && c3 === 0.0 && c2 === 0.0 && c1 === 0.0) {
return solutions;
}
cosines = QuarticRealPolynomial.computeRealRoots(c4, c3, c2, c1, c0);
const length = cosines.length;
Iif (length === 0) {
return solutions;
}
for (let i = 0; i < length; ++i) {
const cosine = cosines[i];
const cosineSquared = cosine * cosine;
const sineSquared = Math.max(1.0 - cosineSquared, 0.0);
const sine = Math.sqrt(sineSquared);
//const left = l2 * cosineSquared + l1 * cosine + l0;
let 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,
);
}
const right = addWithCancellationCheck(
r1 * cosine,
r0,
CesiumMath.EPSILON15,
);
const 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 Iif (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;
};
const firstAxisScratch = new Cartesian3();
const secondAxisScratch = new Cartesian3();
const thirdAxisScratch = new Cartesian3();
const referenceScratch = new Cartesian3();
const bCart = new Cartesian3();
const bScratch = new Matrix3();
const btScratch = new Matrix3();
const diScratch = new Matrix3();
const dScratch = new Matrix3();
const cScratch = new Matrix3();
const tempMatrix = new Matrix3();
const aScratch = new Matrix3();
const sScratch = new Cartesian3();
const closestScratch = new Cartesian3();
const 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');
const position = ray.origin;
const direction = ray.direction;
if (!Cartesian3.equals(position, Cartesian3.ZERO)) {
const normal = ellipsoid.geodeticSurfaceNormal(position, firstAxisScratch);
if (Cartesian3.dot(direction, normal) >= 0.0) {
// The location provided is the closest point in altitude
return position;
}
}
const intersects = defined(this.rayEllipsoid(ray, ellipsoid));
// Compute the scaled direction vector.
const f = ellipsoid.transformPositionToScaledSpace(
direction,
firstAxisScratch,
);
// Constructs a basis from the unit scaled direction vector. Construct its rotation and transpose.
const firstAxis = Cartesian3.normalize(f, f);
const reference = Cartesian3.mostOrthogonalAxis(f, referenceScratch);
const secondAxis = Cartesian3.normalize(
Cartesian3.cross(reference, firstAxis, secondAxisScratch),
secondAxisScratch,
);
const thirdAxis = Cartesian3.normalize(
Cartesian3.cross(firstAxis, secondAxis, thirdAxisScratch),
thirdAxisScratch,
);
const 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;
const B_T = Matrix3.transpose(B, btScratch);
// Get the scaling matrix and its inverse.
const D_I = Matrix3.fromScale(ellipsoid.radii, diScratch);
const D = Matrix3.fromScale(ellipsoid.oneOverRadii, dScratch);
const 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;
const temp = Matrix3.multiply(
Matrix3.multiply(B_T, D, tempMatrix),
C,
tempMatrix,
);
const A = Matrix3.multiply(
Matrix3.multiply(temp, D_I, aScratch),
B,
aScratch,
);
const b = Matrix3.multiplyByVector(temp, position, bCart);
// Solve for the solutions to the expression in standard form:
const solutions = IntersectionTests.quadraticVectorExpression(
A,
Cartesian3.negate(b, firstAxisScratch),
0.0,
0.0,
1.0,
);
let s;
let altitude;
const length = solutions.length;
if (length > 0) {
let closest = Cartesian3.clone(Cartesian3.ZERO, closestScratch);
let maximumValue = Number.NEGATIVE_INFINITY;
for (let i = 0; i < length; ++i) {
s = Matrix3.multiplyByVector(
D_I,
Matrix3.multiplyByVector(B, solutions[i], sScratch),
sScratch,
);
const v = Cartesian3.normalize(
Cartesian3.subtract(s, position, referenceScratch),
referenceScratch,
);
const dotProduct = Cartesian3.dot(v, direction);
if (dotProduct > maximumValue) {
maximumValue = dotProduct;
closest = Cartesian3.clone(s, closest);
}
}
const 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;
};
const 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
* const origin = Cesium.Cartesian3.fromDegrees(-75.59777, 40.03883);
* const normal = ellipsoid.geodeticSurfaceNormal(origin);
* const plane = Cesium.Plane.fromPointNormal(origin, normal);
*
* const p0 = new Cesium.Cartesian3(...);
* const p1 = new Cesium.Cartesian3(...);
*
* // find the intersection of the line segment from p0 to p1 and the tangent plane at origin.
* const 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();
}
const difference = Cartesian3.subtract(
endPoint1,
endPoint0,
lineSegmentPlaneDifference,
);
const normal = plane.normal;
const nDotDiff = Cartesian3.dot(normal, difference);
// check if the segment and plane are parallel
if (Math.abs(nDotDiff) < CesiumMath.EPSILON6) {
return undefined;
}
const nDotP0 = Cartesian3.dot(normal, endPoint0);
const 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
* const origin = Cesium.Cartesian3.fromDegrees(-75.59777, 40.03883);
* const normal = ellipsoid.geodeticSurfaceNormal(origin);
* const plane = Cesium.Plane.fromPointNormal(origin, normal);
*
* const p0 = new Cesium.Cartesian3(...);
* const p1 = new Cesium.Cartesian3(...);
* const p2 = new Cesium.Cartesian3(...);
*
* // convert the triangle composed of points (p0, p1, p2) to three triangles that don't cross the plane
* const 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');
const planeNormal = plane.normal;
const planeD = plane.distance;
const p0Behind = Cartesian3.dot(planeNormal, p0) + planeD < 0.0;
const p1Behind = Cartesian3.dot(planeNormal, p1) + planeD < 0.0;
const p2Behind = Cartesian3.dot(planeNormal, p2) + planeD < 0.0;
// Given these dots products, the calls to lineSegmentPlaneIntersection
// always have defined results.
let numBehind = 0;
numBehind += p0Behind ? 1 : 0;
numBehind += p1Behind ? 1 : 0;
numBehind += p2Behind ? 1 : 0;
let 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 Eif (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 Eif (!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;
};
export default IntersectionTests;
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