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 the constructing the 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 | |
|---|---|---|
| constructor(): Arc3d Protected | ||
| allPerpendicularAngles(spacePoint: Point3d, _extend: boolean = true, _endpoints: boolean = false): number[] | Return all angles (in radians) 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. | |
| circularRadius(): number | undefined | If the arc is circular, return its radius. | |
| 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): CurvePrimitive | undefined | Return (if possible) an arc which is a portion of this curve. | |
| cloneTransformed(transform: Transform): CurvePrimitive | 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. | |
| 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 tof the arc. | |
| extendRange(range: Range3d, transform?: Transform): void | Extend a range to include the range of the arc. | |
| 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 origin at the fractional position along the arc x axis is the first derivative, i.e. |
|
| fractionToPointAndDerivative(fraction: number, result?: Ray3d): Ray3d | Convert a fractional position to xyz coordinates and derivative with respect to fraction. | |
| getFractionToDistanceScale(): number | undefined | 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. | |
| 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.moveSignedDistanceFromFractionA zero length line generates CurveSearchStatus.error* Nonzero length line generates CurveSearchStatus.success or CurveSearchStatus.stoppedAtBoundary |
|
| otherArcAsLocalVectors(other: Arc3d): ArcVectors | undefined | Compute the center and vectors of another arc as local coordinates within this arc's frame. | |
| quickEccentricity(): number | Return a quick estimate of the eccentricity of the ellipse. | |
| quickLength(): number | Return an approximate (but easy to compute) arc length. | |
| 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 origin at arc center vectorU from center to arc at angle (in radians) * vectorV from center to arc at 90 degrees past the angle. |
|
| 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 | undefined): 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: center center point vector0 vector from center to 0 degree point in parameter space (commonly but not always the major axis vector) * vector90 vector from center to 90 degree point in parameter space (commonly but not always the minor axis vector) |
|
| 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 tof the arc. | |
| toJSON(): any | Convert to a JSON object. | |
| toScaledMatrix3d(): object | Return the arc definition with rigid matrix form with axis radii. | |
| toTransformedPoint4d(matrix: Matrix4d): object | Return the arc definition with center, two vectors, and angle sweep, transformed to 4d points. | |
| toTransformedVectors(transform?: Transform): object | 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 | Creat 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 | |
| createCircularStartMiddleEnd(pointA: XYAndZ, pointB: XYAndZ, pointC: XYAndZ, result?: Arc3d): Arc3d | LineString3d | undefined Static | Create a circular arc defined by start point, any intermediate 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. | |
| createUnitCircle(): Arc3d Static | Create a new arc which is a unit circle centered at the origin. | |
| createXY(center: Point3d, radius: number, sweep: AngleSweep = AngleSweep.create360()): 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 = AngleSweep.create360()): 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 parameter space. |
Inherited methods
| Name | Inherited from | Description |
|---|---|---|
| addMappedStrokesToLineString3D(map: StrokeCountMap, linestring: LineString3d): number | CurvePrimitive | * evaluate strokes at fractions indicated in a StrokeCountMap. |
| computeAndAttachRecursiveStrokeCounts(options?: StrokeOptions, parentMap?: StrokeCountMap): void | CurvePrimitive | attach StrokeCountMap structure to this primitive (and recursively to any children) * Base class implementation (here) gets the simple count from computeStrokeCountForOptions and attaches it. |
| curveLengthWithFixedIntervalCountQuadrature(fraction0: number, fraction1: number, numInterval: number, numGauss: number = 5): number | CurvePrimitive | Run an integration (with a default gaussian quadrature) with a fixed fractional step This is typically called by specific curve type implementations of curveLengthBetweenFractions. |
| fractionAndDistanceToPointOnTangent(fraction: number, distance: number): Point3d | CurvePrimitive | Construct a point extrapolated along tangent at fraction. |
| fractionToFrenetFrame(fraction: number, result?: Transform): Transform | undefined | CurvePrimitive | Construct a frenet frame: origin at the point on the curve x axis is unit vector along the curve (tangent) * y axis is perpendicular and in the plane of the osculating circle. |
| fractionToPointAndUnitTangent(fraction: number, result?: Ray3d): Ray3d | CurvePrimitive | Returns a ray whose origin is the curve point and direction is the unit tangent. |
| 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 | GeometryQuery | return the range of the entire (tree) GeometryQuery |
| tryTranslateInPlace(dx: number, dy: number = 0, dz: number = 0): boolean | GeometryQuery | try to move the geometry by dx,dy,dz |
| 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 | "arc" = "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 | |
| matrix Accessor ReadOnly | Matrix3d | read property for (clone of!) matrix of vector0, vector90, unit normal | |
| 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 | 5 | Gauss point quadrature count for evaluating curve length. | |
| quadratureIntervalAngleDegrees Static | 10 | In quadrature for arc length, use this interval (divided by quickEccentricity) | |
| sweep Accessor | AngleSweep | property getter for the angle sweep | |
| 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 | GeometryQuery[] | undefined | GeometryQuery | return GeometryQuery children for recursive queries. * leaf classes do not need to implement. |
| geometryCategory | "curvePrimitive" = "curvePrimitive" | CurvePrimitive | String name for schema properties |
| strokeData | undefined | StrokeCountMap | CurvePrimitive | data attached during stroking for facets. |
Defined in
Last Updated: 08 January, 2020