Arc3d Class

Circular or elliptic arc.

• The angle to point equation is:
  • X = center + cos(theta) * vector0 + sin(theta) * vector90
• When the two vectors are perpendicular and have equal length, it is a true circle.
• Non-perpendicular vectors are always elliptic.
• Vectors of unequal length are always elliptic.
• To create an ellipse in the common "major and minor axis" form of an ellipse:
  • vector0 is the vector from the center to the major axis extreme.
  • vector90 is the vector from the center to the minor axis extreme.
  • Note that constructing these vectors to the extreme points makes them perpendicular.
• The method toScaledMatrix3d() can be called to convert the unrestricted vector0, vector90 to perpendicular form.
• The unrestricted form is much easier to work with for common calculations: stroking, projection to 2d, intersection with plane.

Extends

• CurvePrimitive

Implements

• BeJSONFunctions

Methods

Name	Description
allPerpendicularAngles(spacePoint: Point3d, _extend: booleantrue, endpoints: booleanfalse): number[]	Return all radian angles where the ellipse tangent is perpendicular to the vector to a spacePoint.
angleToPointAndDerivative(theta: Angle, result?: Ray3d): Ray3d	Evaluate the point and derivative with respect to the angle (in radians)
announceClipIntervals(clipper: Clipper, announce?: AnnounceNumberNumberCurvePrimitive): boolean	Find intervals of this CurvePrimitive that are interior to a clipper
appendPlaneIntersectionPoints(plane: PlaneAltitudeEvaluator, result: CurveLocationDetail[]): number	Compute intersections with a plane.
areaToChordXY(fraction0: number, fraction1: number): number	Return the (signed!) area between (a fractional portion of) the arc and the chord between those points
circularRadius(): undefined | number	If the arc is circular, return its radius.
circularRadiusXY(): undefined | number	Return radius if the vector0 and vector90 are of equal length and perpendicular.
clone(): Arc3d	Return a clone of this arc.
cloneAtZ(z?: number): Arc3d	Return a clone of this arc, projected to given z value.
cloneInRotatedBasis(theta: Angle): Arc3d	Return an arc whose basis vectors are rotated by given angle within the current basis space.
clonePartialCurve(fractionA: number, fractionB: number): Arc3d	Return (if possible) an arc which is a portion of this curve.
cloneTransformed(transform: Transform): Arc3d	Return a clone of the arc, with transform applied
closestPoint(spacePoint: Point3d, extend: VariantCurveExtendParameter, result?: CurveLocationDetail): CurveLocationDetail	Return details of the closest point on the arc, optionally extending to full ellipse.
computeStrokeCountForOptions(options?: StrokeOptions): number	Return the stroke count required for given options.
constructCircularArcChainApproximation(options?: EllipticalArcApproximationOptions): undefined | Arc3d | CurveChain	Construct a circular arc chain approximation to the instance elliptical arc.
constructOffsetXY(offsetDistanceOrOptions: number | OffsetOptions): undefined | CurvePrimitive | CurvePrimitive[]	Construct an offset of the instance curve as viewed in the xy-plane (ignoring z).
curveLength(): number	If this is a circular arc, return the simple length derived from radius and sweep.
curveLengthBetweenFractions(fraction0: number, fraction1: number): number	* If this is a circular arc, return the simple length derived from radius and sweep.
dispatchToGeometryHandler(handler: GeometryHandler): any	Second step of double dispatch: call handler.handleArc3d(this)
emitStrokableParts(handler: IStrokeHandler, options?: StrokeOptions): void	Emit strokes to caller-supplied handler
emitStrokes(dest: LineString3d, options?: StrokeOptions): void	Emit strokes to caller-supplied linestring
endPoint(result?: Point3d): Point3d	Return the end point of the arc.
extendRange(range: Range3d, transform?: Transform): void	Extend a range to include the range of the arc.
extendRangeInSweep(range: Range3d, sweep: AngleSweep, transform?: Transform): void	Extend a range to include the range of the arc, using specified range in place of the arc range.
fractionAndRadialFractionToPoint(arcFraction: number, radialFraction: number, result?: Point3d): Point3d	Convert fractional arc and radial positions to xyz coordinates
fractionToPoint(fraction: number, result?: Point3d): Point3d	Convert a fractional position to xyz coordinates
fractionToPointAnd2Derivatives(fraction: number, result?: Plane3dByOriginAndVectors): Plane3dByOriginAndVectors	Construct a plane with
fractionToPointAndDerivative(fraction: number, result?: Ray3d): Ray3d	Convert a fractional position to xyz coordinates and derivative with respect to fraction.
getFractionToDistanceScale(): undefined | number	The arc has simple proportional arc length if and only if it is a circular arc.
isAlmostEqual(otherGeometry: GeometryQuery): boolean	Test if this arc is almost equal to another GeometryQuery object
isInPlane(plane: Plane3dByOriginAndUnitNormal): boolean	Return true if the ellipse center and basis vectors are in the plane
isSameGeometryClass(other: GeometryQuery): boolean	Test if this and other are both instances of Arc3d.
matrixClone(): Matrix3d	Read property for (clone of) matrix of vector0, vector90, unit normal
maxVectorLength(): number	Return the larger of the two defining vectors.
moveSignedDistanceFromFraction(startFraction: number, signedDistance: number, allowExtension: "false", result?: CurveLocationDetail): CurveLocationDetail	* See extended comments on CurvePrimitive.moveSignedDistanceFromFraction
otherArcAsLocalVectors(other: Arc3d): undefined | ArcVectors	Compute the center and vectors of another arc as local coordinates within this arc's frame.
projectedParameterRange(ray: Vector3d | Ray3d, lowHigh?: Range1d): undefined | Range1d	Project instance geometry (via dispatch) onto the given ray, and return the extreme fractional parameters of projection.
quickEccentricity(): number	Return a quick estimate of the eccentricity of the ellipse.
quickLength(): number	Return an approximate (but easy to compute) arc length.
radiansToPoint(radians: number, result?: Point3d): Point3d	Evaluate the point with respect to the angle (in radians)
radiansToPointAndDerivative(radians: number, result?: Ray3d): Ray3d	Evaluate the point and derivative with respect to the angle (in radians)
radiansToRotatedBasis(radians: number, result?: Plane3dByOriginAndVectors): Plane3dByOriginAndVectors	Return a parametric plane with
rangeBetweenFractions(fraction0: number, fraction1: number, transform?: Transform): Range3d	Returns a (high accuracy) range of the curve between fractional positions
reverseInPlace(): void	Reverse the sweep of the arc.
scaleAboutCenterInPlace(scaleFactor: number): void	Scale the vector0 and vector90 vectors by scaleFactor
set(center: Point3d, matrix: Matrix3d, sweep: AngleSweep): void	Redefine the arc with (clones of) given data.
setFrom(other: Arc3d): void	Copy center, matrix, and sweep from other Arc3d
setFromJSON(json?: any): void	Set this arc from a json object with these values:
setRefs(center: Point3d, matrix: Matrix3d, sweep: AngleSweep): void	Redefine the arc with (captured references to) given data.
setVector0Vector90(vector0: Vector3d, vector90: Vector3d): void	Replace the arc's 0 and 90 degree vectors.
startPoint(result?: Point3d): Point3d	Return the start point of the arc.
toJSON(): any	Convert to a JSON object.
toScaledMatrix3d(): { axes: Matrix3d, center: Point3d, r0: number, r90: number, sweep: AngleSweep }	Return the arc definition with rigid matrix form with axis radii
toTransformedPoint4d(matrix: Matrix4d): { center: Point4d, sweep: AngleSweep, vector0: Point4d, vector90: Point4d }	Return the arc definition with center, two vectors, and angle sweep, transformed to 4d points.
toTransformedVectors(transform?: Transform): { center: Point3d, sweep: AngleSweep, vector0: Vector3d, vector90: Vector3d }	Return the arc definition with center, two vectors, and angle sweep, optionally transformed.
toVectors(): ArcVectors	Return the arc definition with center, two vectors, and angle sweep;
tryTransformInPlace(transform: Transform): boolean	Apply a transform to the arc basis vectors.
create(center: Point3d, vector0: Vector3d, vector90: Vector3d, sweep?: AngleSweep, result?: Arc3d): Arc3d Static	Create an arc by center with vectors to points at 0 and 90 degrees in parameter space.
createCenterNormalRadius(center: Point3d, normal: Vector3d, radius: number, result?: Arc3d): Arc3d Static	Create a (full circular) arc from center, normal and radius
createCircularStartEndRadius(start: Point3d, end: Point3d, radius: number, helper: Point3d | Vector3d): undefined | Arc3d Static	Create a circular arc defined by start and end points and radius.
createCircularStartMiddleEnd(pointA: Readonly<WritableXYAndZ>, pointB: Readonly<WritableXYAndZ>, pointC: Readonly<WritableXYAndZ>, result?: Arc3d): LineString3d | Arc3d Static	Create a circular arc defined by start point, any intermediate point, and end point.
createCircularStartTangentEnd(start: Point3d, tangentAtStart: Vector3d, end: Point3d, result?: Arc3d): LineSegment3d | Arc3d Static	Create a circular arc defined by start point, tangent at start point, and end point.
createFilletArc(point0: Point3d, point1: Point3d, point2: Point3d, radius: number): ArcBlendData Static	Determine an arc "at a point of inflection" of a point sequence.
createRefs(center: Point3d, matrix: Matrix3d, sweep: AngleSweep, result?: Arc3d): Arc3d Static	Create an arc, capturing references to center, matrix and sweep.
createScaledXYColumns(center: Point3d, matrix: Matrix3d, radius0: number, radius90: number, sweep?: AngleSweep, result?: Arc3d): Arc3d Static	Create an arc from center, x column to be scaled, and y column to be scaled.
createStartMiddleEnd(point0: Readonly<WritableXYAndZ>, point1: Readonly<WritableXYAndZ>, point2: Readonly<WritableXYAndZ>, sweep?: AngleSweep, result?: Arc3d): undefined | Arc3d Static	Create an elliptical arc from three points on the ellipse: two points on an axis and one in between.
createUnitCircle(): Arc3d Static	Create a new arc which is a unit circle in the xy-plane centered at the origin.
createXY(center: Point3d, radius: number, sweep: AngleSweep...): Arc3d Static	Create a new arc which is parallel to the xy plane, with given center and radius and optional angle sweep.
createXYEllipse(center: Point3d, radiusA: number, radiusB: number, sweep: AngleSweep...): Arc3d Static	Create a new arc which is parallel to the xy plane, with given center and x,y radii, and optional angle sweep
createXYZXYZXYZ(cx: number, cy: number, cz: number, ux: number, uy: number, uz: number, vx: number, vy: number, vz: number, sweep?: AngleSweep, result?: Arc3d): Arc3d Static	Create an arc by center (cx,cy,xz) with vectors (ux,uy,uz) and (vx,vy,vz) to points at 0 and 90 degrees in

Inherited methods

Name	Inherited from	Description
addMappedStrokesToLineString3D(map: StrokeCountMap, linestring: LineString3d): number	CurvePrimitive	Evaluate strokes at fractions indicated in a StrokeCountMap.
collectCurvePrimitives(collectorArray?: CurvePrimitive[], smallestPossiblePrimitives: booleanfalse, explodeLinestrings: booleanfalse): CurvePrimitive[]	CurvePrimitive	Return an array containing only the curve primitives.
collectCurvePrimitivesGo(collectorArray: CurvePrimitive[], _smallestPossiblePrimitives: boolean, _explodeLinestrings: booleanfalse): void	CurvePrimitive	Return an array containing only the curve primitives.
computeAndAttachRecursiveStrokeCounts(options?: StrokeOptions, parentMap?: StrokeCountMap): void	CurvePrimitive	Attach StrokeCountMap structure to this primitive (and recursively to any children)
curveLengthWithFixedIntervalCountQuadrature(fraction0: number, fraction1: number, numInterval: number, numGauss: number5): number	CurvePrimitive	Run an integration (with a default Gaussian quadrature) with a fixed fractional step
fractionAndDistanceToPointOnTangent(fraction: number, distance: number): Point3d	CurvePrimitive	Construct a point extrapolated along tangent at fraction.
fractionToCurvature(fraction: number): undefined | number	CurvePrimitive	Returns the (absolute) curvature magnitude.
fractionToFrenetFrame(fraction: number, result?: Transform): undefined | Transform	CurvePrimitive	Construct a frenet frame:
fractionToPointAndUnitTangent(fraction: number, result?: Ray3d): Ray3d	CurvePrimitive	Returns a ray whose origin is the curve point and direction is the unit tangent.
fractionToSignedXYRadiusOfCurvature(fraction: number): number	CurvePrimitive	Construct signed distance from a point on the planar curve to its center of curvature (in xy only).
moveSignedDistanceFromFractionGeneric(startFraction: number, signedDistance: number, allowExtension: boolean, result?: CurveLocationDetail): CurveLocationDetail Protected	CurvePrimitive	Generic algorithm to search for point at signed distance from a fractional startPoint.
range(transform?: Transform, result?: Range3d): Range3d	CurvePrimitive	Return the range of the entire GeometryQuery tree.
rangeBetweenFractionsByClone(fraction0: number, fraction1: number, transform?: Transform): Range3d	CurvePrimitive	Returns a (high accuracy) range of the curve between fractional positions
rangeBetweenFractionsByCount(fraction0: number, fraction1: number, count: number, transform?: Transform, extrapolationFactor: number0.0): Range3d	CurvePrimitive	Returns an approximate range based on a fixed number of evaluations
tryTranslateInPlace(dx: number, dy: number0.0, dz: number0.0): boolean	CurvePrimitive	Try to move the geometry by dx,dy,dz.
areAlmostEqual(a: GeometryQuery, b: GeometryQuery): boolean Static	CurvePrimitive	Apply instance method isAlmostEqual if both are defined.
installStrokeCountMap(curve: CurvePrimitive, curveMap: StrokeCountMap, parentMap?: StrokeCountMap): void Static	CurvePrimitive	Final install step to save curveMap in curve.

Properties

Name	Type	Description
center Accessor ReadOnly	Point3d	Read property for (clone of) center
curvePrimitiveType Readonly	"arc"	String name for schema properties
isCircular Accessor ReadOnly	boolean	Return true if the vector0 and vector90 are of equal length and perpendicular.
isExtensibleFractionSpace Accessor ReadOnly	boolean	An Arc3d extends along its complete elliptic arc
matrixRef Accessor ReadOnly	Matrix3d	Read property for (reference to) matrix of vector0, vector90, unit normal
perpendicularVector Accessor ReadOnly	Vector3d	Read property for (clone of) plane normal, with arbitrary length.
quadratureGuassCount Static Readonly	"5"	Gauss point quadrature count for evaluating curve length.
quadratureIntervalAngleDegrees Static Readonly	"10"	In quadrature for arc length, use this interval (divided by quickEccentricity)
sweep Accessor	AngleSweep	Sweep of the angle.
vector0 Accessor ReadOnly	Vector3d	Read property for (clone of) vector0
vector90 Accessor ReadOnly	Vector3d	Read property for (clone of) vector90

Inherited properties

Name	Type	Inherited from	Description
children Accessor ReadOnly	undefined | GeometryQuery[]	CurvePrimitive	Return GeometryQuery children for recursive queries. * leaf classes do not need to implement.
geometryCategory Readonly	"curvePrimitive"	CurvePrimitive	String name for schema properties
parent	any | undefined	CurvePrimitive	Data attached by various algorithms (e.g.
strokeData	StrokeCountMap | undefined	CurvePrimitive	Data attached during stroking for facets.

Defined in

• curve/Arc3d.ts Line 225