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
Implements
Methods
Name | Description | |
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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) |
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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, distanceTol: numberGeometry.smallMetricDistance, radianTol: numberGeometry.smallAngleRadians): 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 length of the two defining vectors. | |
moveSignedDistanceFromFraction(startFraction: number, signedDistance: number, allowExtension: "false", result?: CurveLocationDetail): CurveLocationDetail | * See extended comments on CurvePrimitive.moveSignedDistanceFromFraction . |
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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 . |
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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. | |
createCircularStartTangentRadius(start: Point3d, tangentAtStart: Vector3d, radius: number, upVector?: Vector3d, sweep?: Angle | AngleSweep): undefined | Arc3d Static | Create a circular arc from start point, tangent at start, radius, optional plane normal, arc sweep. | |
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(start: Readonly<WritableXYAndZ>, middle: Readonly<WritableXYAndZ>, end: 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 |
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addMappedStrokesToLineString3D(map: StrokeCountMap, linestring: LineString3d): number Inherited | CurvePrimitive | Evaluate strokes at fractions indicated in a StrokeCountMap. |
collectCurvePrimitives(collectorArray?: CurvePrimitive[], smallestPossiblePrimitives: booleanfalse, explodeLinestrings: booleanfalse): CurvePrimitive[] Inherited | CurvePrimitive | Return an array containing only the curve primitives. |
collectCurvePrimitivesGo(collectorArray: CurvePrimitive[], _smallestPossiblePrimitives: boolean, _explodeLinestrings: booleanfalse): void Inherited | CurvePrimitive | Return an array containing only the curve primitives. |
computeAndAttachRecursiveStrokeCounts(options?: StrokeOptions, parentMap?: StrokeCountMap): void Inherited | CurvePrimitive | Attach StrokeCountMap structure to this primitive (and recursively to any children) |
curveLengthWithFixedIntervalCountQuadrature(fraction0: number, fraction1: number, numInterval: number, numGauss: number5): number Inherited | CurvePrimitive | Run an integration (with a default Gaussian quadrature) with a fixed fractional step |
fractionAndDistanceToPointOnTangent(fraction: number, distance: number): Point3d Inherited | CurvePrimitive | Construct a point extrapolated along tangent at fraction. |
fractionToCurvature(fraction: number): undefined | number Inherited | CurvePrimitive | Returns the (absolute) curvature magnitude. |
fractionToFrenetFrame(fraction: number, result?: Transform): undefined | Transform Inherited | CurvePrimitive | Construct a frenet frame: |
fractionToPointAndUnitTangent(fraction: number, result?: Ray3d): Ray3d Inherited | CurvePrimitive | Returns a ray whose origin is the curve point and direction is the unit tangent. |
fractionToSignedXYRadiusOfCurvature(fraction: number): number Inherited | 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 Inherited | CurvePrimitive | Generic algorithm to search for point at signed distance from a fractional startPoint. |
range(transform?: Transform, result?: Range3d): Range3d Inherited | CurvePrimitive | Return the range of the entire GeometryQuery tree. |
rangeBetweenFractionsByClone(fraction0: number, fraction1: number, transform?: Transform): Range3d Inherited | 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 Inherited | CurvePrimitive | Returns an approximate range based on a fixed number of evaluations |
tryTranslateInPlace(dx: number, dy: number0.0, dz: number0.0): boolean Inherited | CurvePrimitive | Try to move the geometry by dx,dy,dz. |
areAlmostEqual(a: GeometryQuery, b: GeometryQuery): boolean Static Inherited | CurvePrimitive | Apply instance method isAlmostEqual if both are defined. |
installStrokeCountMap(curve: CurvePrimitive, curveMap: StrokeCountMap, parentMap?: StrokeCountMap): void Static Inherited | CurvePrimitive | Final install step to save curveMap in curve. |
Properties
Name | Type | Description | |
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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 |
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children Accessor Inherited ReadOnly | undefined | GeometryQuery[] | CurvePrimitive | Return GeometryQuery children for recursive queries. * leaf classes do not need to implement. |
geometryCategory Readonly Inherited | "curvePrimitive" | CurvePrimitive | String name for schema properties |
parent Inherited | any | undefined | CurvePrimitive | Data attached by various algorithms (e.g. |
strokeData Inherited | StrokeCountMap | undefined | CurvePrimitive | Data attached during stroking for facets. |
Defined in
- curve/Arc3d.ts Line 224
Last Updated: 17 December, 2024
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