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 latitudephi
isu = 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.
Methods
Name | Description | |
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anglePairToGreatArc(angleA: LongitudeLatitudeNumber, angleB: LongitudeLatitudeNumber, result?: Arc3d): Arc3d | undefined | See radiansPairToGreatArc, which does this computation with positions from angleA and angleB directly as radians |
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clone(): Ellipsoid | return a clone with same coordinates | |
cloneTransformed(transform: Transform): Ellipsoid | undefined | return a cloned and transformed ellipsoid. | |
constantLatitudeArc(longitudeSweep: AngleSweep, latitude: Angle, result?: Arc3d): Arc3d | undefined | Return an arc (circular or elliptical) at constant longitude | |
constantLongitudeArc(longitude: Angle, latitudeSweep: AngleSweep, result?: Arc3d): Arc3d | undefined | Return an arc (circular or elliptical) at constant longitude | |
createPlaneSection(plane: Plane3dByOriginAndUnitNormal): Arc3d | undefined | Construct an arc for the section cut of a plane with the ellipsoid. | |
createSectionArcPointPointVectorInPlane(pointAnglesA: LongitudeLatitudeNumber, pointAnglesB: LongitudeLatitudeNumber, inPlaneVector: Vector3d, result?: Arc3d): Arc3d | undefined | Construct an arc which start at pointA (defined by its angle position) ends at pointB (defined by its angle position) * contains the 3rd vector as an in-plane point. |
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intersectRay(ray: Ray3d, rayFractions: number[] | undefined, xyz: Point3d[] | undefined, thetaPhiRadians: Point2d[] | undefined): number | Compute intersections with a ray. | |
isAlmostEqual(other: Ellipsoid): boolean | test equality of the 4 points | |
otherEllipsoidAnglesToThisEllipsoidAngles(otherEllipsoid: Ellipsoid | undefined, otherAngles: LongitudeLatitudeNumber, result?: LongitudeLatitudeNumber): LongitudeLatitudeNumber | undefined | Evaluate the surface normal on other ellipsoid at given anglesIf other is undefined, default to unit sphere. |
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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): LongitudeLatitudeNumber | undefined | Find the closest point of the (patch of the) ellipsoid. | |
radiansPairToEquatorialEllipsoid(thetaARadians: number, phiARadians: number, thetaBRadians: number, phiBRadians: number, result?: Ellipsoid): Ellipsoid | undefined | For a given pair of points on an ellipsoid, construct another ellipsoid touches the same xyz points in space * has transformation modified so that the original two points are on the equator. |
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radiansPairToGreatArc(thetaARadians: number, phiARadians: number, thetaBRadians: number, phiBRadians: number, result?: Arc3d): Arc3d | undefined | For a given pair of points on an ellipsoid, construct an arc (possibly elliptical) which passes through both points is completely within the ellipsoid surface has its centerEvaluate a point on the ellipsoid at angles give in radians. |
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radiansToFrenetFrame(thetaRadians: number, phiRadians: number, result?: Transform): Transform | undefined | 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): Ray3d | undefined | 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 interpolation between. |
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surfaceNormalToAngles(normal: Vector3d, result?: LongitudeLatitudeNumber): LongitudeLatitudeNumber | Find the (unique) extreme point for a given true surface perpendicular vector (outward) | |
surfaceNormalToRadians(normal: Vector3d, result?: Point2d): Point2d | Find the (unique) extreme point for a given true surface perpendicular vector (outward) | Deprecated |
tryTransformInPlace(transform: Transform): boolean | Apply the transform to each point | |
create(matrixOrTransform?: Transform | Matrix3d): Ellipsoid Static | Create with a clone (not capture) with given transform. | |
createCenterMatrixRadii(center: Point3d, axes: 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: Ellipsoid | undefined, thetaRadians: number, phiRadians: number, result?: Ray3d): Ray3d | undefined Static | * if ellipsoid is given, return its surface point and unit normal as a Ray3d. |
Properties
Name | Type | Description | |
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transformRef Accessor ReadOnly | Transform |
Defined in
Last Updated: 08 January, 2020