API Reference > geometry-core > CartesianGeometry > Ellipsoid

Ellipsoid Class

  • An Ellipsoid is a (complete) unit sphere with an arbitrary (possibly skewed) Transform to 3d.
  • The (unit) sphere parameterization with respect to longitude theta and latitude phi is
    • u = cos(theta) * cos (phi)
    • v = sin(theta) * cos(phi)
    • w = sin(phi)
  • The sphere (u,v,w) multiply the x,y,z columns of the Ellipsoid transform.

Implements

Methods

Name Description
anglePairToGreatArc(angleA: LongitudeLatitudeNumber, angleB: LongitudeLatitudeNumber, result?: Arc3d): undefined | Arc3d See radiansPairToGreatArc, which does this computation with positions from angleA and angleB directly as radians  
announceClippedArcIntervals(arc: Arc3d, announce?: AnnounceNumberNumberCurvePrimitive): boolean Announce "in" portions of a line segment.  
announceClippedSegmentIntervals(f0: number, f1: number, pointA: Point3d, pointB: Point3d, announce?: AnnounceNumberNumber): boolean Announce "in" portions of a line segment.  
clone(): Ellipsoid return a clone with same coordinates  
cloneTransformed(transform: Transform): undefined | Ellipsoid return a cloned and transformed ellipsoid.  
constantLatitudeArc(longitudeSweep: AngleSweep, latitude: Angle, result?: Arc3d): undefined | Arc3d Return an arc (circular or elliptical) at constant longitude  
constantLongitudeArc(longitude: Angle, latitudeSweep: AngleSweep, result?: Arc3d): undefined | Arc3d Return an arc (circular or elliptical) at constant longitude  
createPlaneSection(plane: Plane3dByOriginAndUnitNormal): undefined | Arc3d Construct an arc for the section cut of a plane with the ellipsoid.  
createSectionArcPointPointVectorInPlane(pointAnglesA: LongitudeLatitudeNumber, pointAnglesB: LongitudeLatitudeNumber, inPlaneVector: Vector3d, result?: Arc3d): undefined | Arc3d Construct an arc which  
intersectRay(ray: Ray3d, rayFractions: undefined | number[], xyz: undefined | Point3d[], thetaPhiRadians: undefined | LongitudeLatitudeNumber[]): number Compute intersections with a ray.  
isAlmostEqual(other: Ellipsoid): boolean test equality of the 4 points  
isPointOnOrInside(point: Point3d): boolean Implement the isPointInOnOrOutside test fom the interface  
localToWorld(localPoint: Readonly<WritableXYAndZ>, result?: Point3d): Point3d * Convert a point within the underlying mapped sphere space to world coordinates.  
otherEllipsoidAnglesToThisEllipsoidAngles(otherEllipsoid: undefined | Ellipsoid, otherAngles: LongitudeLatitudeNumber, result?: LongitudeLatitudeNumber): undefined | LongitudeLatitudeNumber * Evaluate the surface normal on other ellipsoid at given angles  
patchRangeStartEndRadians(theta0Radians: number, theta1Radians: number, phi0Radians: number, phi1Radians: number, result?: Range3d): Range3d Return the range of a uv-aligned patch of the sphere.  
projectPointToSurface(spacePoint: Point3d): undefined | LongitudeLatitudeNumber Find the closest point of the (patch of the) ellipsoid.  
radiansPairToEquatorialEllipsoid(thetaARadians: number, phiARadians: number, thetaBRadians: number, phiBRadians: number, result?: Ellipsoid): undefined | Ellipsoid * For a given pair of points on an ellipsoid, construct another ellipsoid  
radiansPairToGreatArc(thetaARadians: number, phiARadians: number, thetaBRadians: number, phiBRadians: number, result?: Arc3d): undefined | Arc3d * For a given pair of points on an ellipsoid, construct an arc (possibly elliptical) which  
radiansToFrenetFrame(thetaRadians: number, phiRadians: number, result?: Transform): undefined | Transform Evaluate a point and rigid local coordinate frame the ellipsoid at angles give in radians.  
radiansToPoint(thetaRadians: number, phiRadians: number, result?: Point3d): Point3d Evaluate a point on the ellipsoid at angles give in radians.  
radiansToPointAnd2Derivatives(thetaRadians: number, phiRadians: number, point: Point3d, d1Theta: Vector3d, d1Phi: Vector3d, d2ThetaTheta: Vector3d, d2PhiPhi: Vector3d, d2ThetaPhi: Vector3d): void Evaluate a point and derivatives wrt to theta, phi, thetaTheta, phiPhi, and thetaPhi.  
radiansToPointAndDerivatives(thetaRadians: number, phiRadians: number, applyCosPhiFactor: boolean = true, result?: Plane3dByOriginAndVectors): Plane3dByOriginAndVectors Evaluate a point and derivatives with respect to angle on the ellipsoid at angles give in radians.  
radiansToUnitNormalRay(thetaRadians: number, phiRadians: number, result?: Ray3d): undefined | Ray3d Evaluate a point and unit normal at given angles.  
sectionArcWithIntermediateNormal(angleA: LongitudeLatitudeNumber, intermediateNormalFraction: number, angleB: LongitudeLatitudeNumber): Arc3d * create a section arc with and end at positions A and B, and in plane with the normal at a fractional  
silhouetteArc(eyePoint: Point4d): undefined | Arc3d Find the silhouette of the ellipsoid as viewed from a homogeneous eyepoint.  
surfaceNormalToAngles(normal: Vector3d, result?: LongitudeLatitudeNumber): LongitudeLatitudeNumber Find the (unique) extreme point for a given true surface perpendicular vector (outward)  
tryTransformInPlace(transform: Transform): boolean Apply the transform to each point  
worldToLocal(worldPoint: Readonly<WritableXYAndZ>, result?: Point3d): undefined | Point3d * Convert a world point to point within the underlying mapped sphere space.  
create(matrixOrTransform?: Transform | Matrix3d): Ellipsoid Static Create with a clone (not capture) with given transform.  
createCenterMatrixRadii(center: Point3d, axes: undefined | Matrix3d, radiusX: number, radiusY: number, radiusZ: number): Ellipsoid Static Create a transform with given center and directions, applying the radii as multipliers for the respective columns of the axes.  
radiansToUnitNormalRay(ellipsoid: undefined | Ellipsoid, thetaRadians: number, phiRadians: number, result?: Ray3d): undefined | Ray3d Static * if ellipsoid is given, return its surface point and unit normal as a Ray3d.  

Properties

Name Type Description
transformRef Accessor ReadOnly Transform Return a (REFERENCE TO) the transform from world space to the mapped sphere space.  

Defined in

Last Updated: 12 June, 2024