Document — Math, Bounds, OSD & Conversions

This page covers the math solvers, bounding-box types, quaternion/timer utilities, point classification, curve/surface conversion helpers, and OSD utilities found in lines 4959–6350 of Document.swift. For the core document lifecycle, shape tools, and XCAF I/O see the main Document page.

Topics

gp_Quaternion · OSD_Timer · Bnd_OBB · Bnd_Range · BRepClass3d Point Classification · TDataXtd_Constraint · OSD_MemInfo · ShapeFix_EdgeProjAux · Geom2dAPI_Interpolate · Geom2dAPI_PointsToBSpline · TDataXtd_PatternStd · BRepAlgo_FaceRestrictor · math_Matrix · math_Gauss · math_SVD · math_DirectPolynomialRoots · math_Jacobi · Convert_CircleToBSplineCurve · Convert_SphereToBSplineSurface · Convert Conic Curves to BSpline · Convert Elementary Surfaces to BSpline · math_Householder · math_Crout · ShapeFix_IntersectionTool · XCAFDoc_AssemblyItemRef · BRepAlgo_Image · OSD_Path · BRepClass_FClassifier · Bnd_BoundSortBox · TNaming_Naming · Precision Constants · IntAna Analytic Intersections · OSD_Chronometer · OSD_Process · Draft_Modification · Convert_CompBezierCurvesToBSplineCurve · Geom_OffsetSurface Extensions

gp_Quaternion

Wraps gp_Quaternion — OCCT’s unit-quaternion for representing 3D rotations. Obtain one via init(x:y:z:w:), fromAxisAngle, or fromVectors.

`Quaternion.init(x:y:z:w:)`

Create a quaternion from its four components.

public convenience init(x: Double = 0, y: Double = 0, z: Double = 0, w: Double = 1)

Parameters: x, y, z — vector part; w — scalar part. Defaults to the identity quaternion (0, 0, 0, 1).
OCCT: gp_Quaternion(x, y, z, w) (via OCCTQuaternionCreate).

Example:

let identity = Quaternion()
let q = Quaternion(x: 0, y: 0, z: 0.7071, w: 0.7071)

`Quaternion.fromAxisAngle(axis:angle:)`

Create a quaternion from an axis-angle rotation.

public static func fromAxisAngle(axis: SIMD3<Double>, angle: Double) -> Quaternion

Parameters: axis — rotation axis (need not be normalized); angle — rotation angle in radians.
OCCT: gp_Quaternion::SetVectorAndAngle (via OCCTQuaternionCreateFromAxisAngle).

Example:

let q = Quaternion.fromAxisAngle(axis: SIMD3(0, 0, 1), angle: .pi / 4)

`Quaternion.fromVectors(from:to:)`

Create a quaternion representing the shortest-arc rotation from one vector to another.

public static func fromVectors(from: SIMD3<Double>, to: SIMD3<Double>) -> Quaternion

Parameters: from — source direction; to — target direction.
OCCT: gp_Quaternion::SetRotation (via OCCTQuaternionCreateFromVectors).

Example:

let q = Quaternion.fromVectors(from: SIMD3(1, 0, 0), to: SIMD3(0, 1, 0))

`components`

The four quaternion components (x, y, z, w).

public var components: (x: Double, y: Double, z: Double, w: Double) { get }

OCCT: gp_Quaternion::X/Y/Z/W (via OCCTQuaternionGetComponents).

Example:

let c = q.components
print(c.w)  // scalar part

`setEulerAngles(order:alpha:beta:gamma:)`

Set the quaternion from Euler angles.

public func setEulerAngles(order: Int32, alpha: Double, beta: Double, gamma: Double)

Parameters: order — Euler convention index (0 = Intrinsic_XYZ, see gp_EulerSequence); alpha, beta, gamma — angles in radians.
OCCT: gp_Quaternion::SetEulerAngles (via OCCTQuaternionSetEulerAngles).

Example:

q.setEulerAngles(order: 0, alpha: 0.1, beta: 0.2, gamma: 0.3)

`getEulerAngles(order:)`

Get the Euler angle decomposition of this quaternion.

public func getEulerAngles(order: Int32) -> (alpha: Double, beta: Double, gamma: Double)

Parameters: order — Euler convention index (same encoding as setEulerAngles).
Returns: Tuple of three angles in radians.
OCCT: gp_Quaternion::GetEulerAngles (via OCCTQuaternionGetEulerAngles).

Example:

let (a, b, g) = q.getEulerAngles(order: 0)

`matrix`

The 3×3 rotation matrix represented by this quaternion, in row-major order (9 elements).

public var matrix: [Double] { get }

Returns: A 9-element [Double] where matrix[row*3 + col] is M[row][col].
OCCT: gp_Quaternion::GetVectorPart / matrix conversion (via OCCTQuaternionGetMatrix).

Example:

let m = q.matrix
// m[0] m[1] m[2]
// m[3] m[4] m[5]
// m[6] m[7] m[8]

`rotate(_:)`

Rotate a 3D vector by this quaternion.

public func rotate(_ vector: SIMD3<Double>) -> SIMD3<Double>

Parameters: vector — the vector to rotate.
Returns: The rotated vector.
OCCT: gp_Quaternion::Multiply with gp_Vec (via OCCTQuaternionMultiplyVec).
Example:
```
let rotated = q.rotate(SIMD3(1, 0, 0))
```

`multiplied(by:)`

Hamilton product of two quaternions.

public func multiplied(by other: Quaternion) -> Quaternion

Parameters: other — the right-hand quaternion.
Returns: A new Quaternion representing the composed rotation.
OCCT: gp_Quaternion::Multiplied (via OCCTQuaternionMultiply).
Example:
```
let composed = q1.multiplied(by: q2)
```

`axisAngle`

Axis-angle representation of this quaternion.

public var axisAngle: (axis: SIMD3<Double>, angle: Double) { get }

Returns: Tuple of the rotation axis and angle in radians.
OCCT: gp_Quaternion::GetVectorAndAngle (via OCCTQuaternionGetVectorAndAngle).
Example:
```
let (axis, angle) = q.axisAngle
```

`rotationAngle`

The rotation angle encoded in this quaternion.

public var rotationAngle: Double { get }

Returns: Angle in radians.
OCCT: gp_Quaternion::GetRotationAngle (via OCCTQuaternionGetRotationAngle).

Example:

print(q.rotationAngle)  // e.g. 0.7853...

`normalize()`

Normalize this quaternion to unit length in-place.

public func normalize()

OCCT: gp_Quaternion::Normalize (via OCCTQuaternionNormalize).
Example:
```
q.normalize()
```

OSD_Timer

Wraps OSD_Timer — a high-resolution wall-clock timer suitable for profiling.

`Timer.init()`

Create a new timer (initially stopped, elapsed = 0).

public init()

OCCT: OSD_Timer() (via OCCTTimerCreate).
Example:
```
let t = Timer()
```

`start()`

Start (or resume) the timer.

public func start()

OCCT: OSD_Timer::Start (via OCCTTimerStart).
Example:
```
t.start()
```

`stop()`

Stop the timer, preserving elapsed time.

public func stop()

OCCT: OSD_Timer::Stop (via OCCTTimerStop).
Example:
```
t.stop()
```

`reset()`

Reset elapsed time to zero.

public func reset()

OCCT: OSD_Timer::Reset (via OCCTTimerReset).
Example:
```
t.reset()
```

`elapsedTime`

Elapsed wall-clock time in seconds.

public var elapsedTime: Double { get }

OCCT: OSD_Timer::ElapsedTime (via OCCTTimerElapsedTime).

Example:

t.start()
// ... work ...
t.stop()
print(t.elapsedTime)

`Timer.wallClockTime`

Current wall-clock time in seconds (static, absolute).

public static var wallClockTime: Double { get }

OCCT: OSD_Timer::GetWallClockTime (via OCCTTimerGetWallClockTime).
Example:
```
let now = Timer.wallClockTime
```

Bnd_OBB

Wraps Bnd_OBB — an oriented bounding box in 3D space defined by center, local axes, and half-sizes.

`OBB.init(center:xDir:yDir:zDir:hx:hy:hz:)`

Create an OBB from explicit center, local axes, and half-extents.

public init(center: SIMD3<Double>, xDir: SIMD3<Double>, yDir: SIMD3<Double>, zDir: SIMD3<Double>,
            hx: Double, hy: Double, hz: Double)

Parameters: center — center point; xDir/yDir/zDir — local orthonormal axes; hx/hy/hz — half-sizes along each axis.
OCCT: Bnd_OBB(center, xDir, yDir, zDir, hx, hy, hz) (via OCCTOBBCreate).

Example:

let obb = OBB(center: SIMD3(0, 0, 0),
              xDir: SIMD3(1, 0, 0), yDir: SIMD3(0, 1, 0), zDir: SIMD3(0, 0, 1),
              hx: 1, hy: 2, hz: 0.5)

`OBB.fromShape(_:)`

Compute the tightest OBB enclosing a shape.

public static func fromShape(_ shape: Shape) -> OBB?

Parameters: shape — the source shape.
Returns: The OBB, or nil if the shape has no computable bounds.
OCCT: BRepBndLib::AddOBB (via OCCTOBBCreateFromShape).

Example:

if let obb = OBB.fromShape(myBox) {
    print(obb.halfSizes)
}

`isVoid`

Whether the OBB is empty (unset).

public var isVoid: Bool { get }

OCCT: Bnd_OBB::IsVoid (via OCCTOBBIsVoid).

`center`

Center of the OBB in world space.

public var center: SIMD3<Double> { get }

OCCT: Bnd_OBB::Center (via OCCTOBBGetCenter).

`halfSizes`

Half-extents along the OBB’s local X, Y, Z axes.

public var halfSizes: SIMD3<Double> { get }

OCCT: Bnd_OBB::XHSize / YHSize / ZHSize (via OCCTOBBGetHalfSizes).

Example:

let volume = obb.halfSizes.x * obb.halfSizes.y * obb.halfSizes.z * 8

`isOut(point:)`

Check if a point lies outside the OBB.

public func isOut(point: SIMD3<Double>) -> Bool

Parameters: point — the 3D point to test.
Returns: true if the point is strictly outside.
OCCT: Bnd_OBB::IsOut(gp_Pnt) (via OCCTOBBIsOutPoint).

Example:

if !obb.isOut(point: SIMD3(0, 0, 0)) { /* center is inside */ }

`isOut(_:)` (OBB overload)

Check if another OBB has no overlap with this one.

public func isOut(_ other: OBB) -> Bool

Parameters: other — OBB to test.
Returns: true if the two OBBs are disjoint.
OCCT: Bnd_OBB::IsOut(Bnd_OBB) (via OCCTOBBIsOutOBB).

`enlarge(by:)`

Expand all half-extents by a gap value.

public func enlarge(by gap: Double)

Parameters: gap — expansion amount on each side.
OCCT: Bnd_OBB::Enlarge (via OCCTOBBEnlarge).

`squareExtent`

Squared length of the OBB diagonal.

public var squareExtent: Double { get }

OCCT: Bnd_OBB::SquareExtent (via OCCTOBBSquareExtent).

Bnd_Range

Wraps Bnd_Range — a 1D interval [min, max] that also carries a “void” (empty) state.

`Range.init(min:max:)`

Create a range with explicit bounds.

public init(min: Double, max: Double)

OCCT: Bnd_Range(min, max) (via OCCTRangeCreate).
Example:
```
let r = Range(min: 0.0, max: 10.0)
```

`Range.init()` (void)

Create a void (empty) range.

public init()

OCCT: Bnd_Range() (via OCCTRangeCreateVoid).

`isVoid`

Whether the range is empty.

public var isVoid: Bool { get }

OCCT: Bnd_Range::IsVoid (via OCCTRangeIsVoid).

`bounds`

Lower and upper bounds of the range.

public var bounds: (first: Double, last: Double)? { get }

Returns: nil if the range is void.
OCCT: Bnd_Range::GetBounds (via OCCTRangeGetBounds).

Example:

if let b = r.bounds {
    print(b.first, b.last)
}

`delta`

Length of the range (max − min).

public var delta: Double { get }

OCCT: Bnd_Range::Delta (via OCCTRangeDelta).

`contains(_:)`

Test whether a value falls within the range.

public func contains(_ value: Double) -> Bool

OCCT: Bnd_Range::IsIntersected / point test (via OCCTRangeContains).

`add(_:)` (value)

Extend the range to include a scalar value.

public func add(_ value: Double)

OCCT: Bnd_Range::Add(Standard_Real) (via OCCTRangeAddValue).

`add(_:)` (Range)

Extend the range to include another range.

public func add(_ other: Range)

OCCT: Bnd_Range::Add(Bnd_Range) (via OCCTRangeAddRange).

`common(_:)`

Intersect this range with another (retain overlap only).

public func common(_ other: Range)

OCCT: Bnd_Range::Common (via OCCTRangeCommon).

`enlarge(by:)`

Expand both boundaries outward by delta.

public func enlarge(by delta: Double)

OCCT: Bnd_Range::Enlarge (via OCCTRangeEnlarge).

`trimFrom(_:)`

Raise the lower boundary to at least lower.

public func trimFrom(_ lower: Double)

OCCT: Bnd_Range::TrimFrom (via OCCTRangeTrimFrom).

`trimTo(_:)`

Lower the upper boundary to at most upper.

public func trimTo(_ upper: Double)

OCCT: Bnd_Range::TrimTo (via OCCTRangeTrimTo).

BRepClass3d Point Classification

Extension on Shape wrapping BRepClass3d_SolidClassifier.

`Shape.PointState`

Classification of a 3D point relative to a solid.

public enum PointState: Int32 {
    case inside = 0
    case outside = 1
    case on = 2
    case unknown = 3
}

`classifyPoint(_:tolerance:)`

Classify a 3D point relative to this solid shape.

public func classifyPoint(_ point: SIMD3<Double>, tolerance: Double = 1e-6) -> PointState

Parameters: point — 3D point; tolerance — classification tolerance.
Returns: .inside, .outside, .on, or .unknown.
OCCT: BRepClass3d_SolidClassifier::Perform (via OCCTShapeClassifyPoint).

Example:

let box = Shape.box(dx: 10, dy: 10, dz: 10)!
let state = box.classifyPoint(SIMD3(5, 5, 5))
// state == .inside

TDataXtd_Constraint

Extension on Document wrapping TDataXtd_Constraint — dimensional and geometric constraints stored as OCAF attributes.

`Document.ConstraintType`

Constraint kind enumeration matching TDataXtd_ConstraintEnum.

public enum ConstraintType: Int32 {
    case radius = 0, diameter, minorRadius, majorRadius
    case tangent, parallel, perpendicular, concentric
    case coincident, distance, angle, equalRadius
    case symmetry, midPoint, equalDistance, fix
    case rigid, from
}

`setConstraint(labelId:)`

Attach a TDataXtd_Constraint attribute to a label.

@discardableResult
public func setConstraint(labelId: Int64) -> Bool

Parameters: labelId — target label identifier.
Returns: true on success.
OCCT: TDataXtd_Constraint::Set (via OCCTDocumentSetConstraint).
Example:
```
doc.setConstraint(labelId: labelId)
```

`constraintSetType(labelId:type:)`

Set the constraint type on an existing constraint attribute.

@discardableResult
public func constraintSetType(labelId: Int64, type: ConstraintType) -> Bool

OCCT: TDataXtd_Constraint::SetType (via OCCTDocumentConstraintSetType).

`constraintGetType(labelId:)`

Retrieve the constraint type.

public func constraintGetType(labelId: Int64) -> ConstraintType?

Returns: nil if no constraint attribute exists on the label.
OCCT: TDataXtd_Constraint::GetType (via OCCTDocumentConstraintGetType).

`constraintNbGeometries(labelId:)`

Number of geometry references attached to this constraint.

public func constraintNbGeometries(labelId: Int64) -> Int

OCCT: TDataXtd_Constraint::NbGeometries (via OCCTDocumentConstraintNbGeometries).

`constraintIsPlanar(labelId:)`

Whether the constraint is a planar (2D) constraint.

public func constraintIsPlanar(labelId: Int64) -> Bool

OCCT: TDataXtd_Constraint::IsPlanar (via OCCTDocumentConstraintIsPlanar).

`constraintIsDimension(labelId:)`

Whether the constraint carries a dimensional value.

public func constraintIsDimension(labelId: Int64) -> Bool

OCCT: TDataXtd_Constraint::IsDimension (via OCCTDocumentConstraintIsDimension).

`constraintSetVerified(labelId:verified:)`

Set the verified flag on a constraint.

@discardableResult
public func constraintSetVerified(labelId: Int64, verified: Bool) -> Bool

OCCT: TDataXtd_Constraint::Verified (via OCCTDocumentConstraintSetVerified).

`constraintGetVerified(labelId:)`

Get the verified flag of a constraint.

public func constraintGetVerified(labelId: Int64) -> Bool

OCCT: TDataXtd_Constraint::Verified accessor (via OCCTDocumentConstraintGetVerified).

`constraintClearGeometries(labelId:)`

Remove all geometry references from a constraint attribute.

@discardableResult
public func constraintClearGeometries(labelId: Int64) -> Bool

OCCT: TDataXtd_Constraint geometry list clear (via OCCTDocumentConstraintClearGeometries).

OSD_MemInfo

Namespace wrapping OSD_MemInfo — process memory statistics.

`MemInfo.heapUsage`

Heap allocated bytes for the current process.

public static var heapUsage: Int64 { get }

OCCT: OSD_MemInfo::Value(OSD_MemInfo_Heap) (via OCCTMemInfoHeapUsage).

`MemInfo.workingSet`

Working set (resident memory) in bytes.

public static var workingSet: Int64 { get }

OCCT: OSD_MemInfo::Value(OSD_MemInfo_WSet) (via OCCTMemInfoWorkingSet).

`MemInfo.heapUsageMiB`

Heap usage as a precise Double in mebibytes.

public static var heapUsageMiB: Double { get }

OCCT: OSD_MemInfo::ValueMiB(OSD_MemInfo_Heap) (via OCCTMemInfoHeapUsageMiB).

`MemInfo.infoString`

Full formatted memory report string from OCCT.

public static var infoString: String? { get }

Returns: A multi-line string with all tracked counters, or nil on error.
OCCT: OSD_MemInfo::ToString (via OCCTMemInfoString).

Example:

if let info = MemInfo.infoString {
    print(info)
}

ShapeFix_EdgeProjAux

Extension on Shape wrapping ShapeFix_EdgeProjAux — projects edge endpoints back onto the 2D pcurve on a face.

`edgeProjAux(faceIndex:edgeIndex:precision:)`

Project edge endpoints onto a face’s 2D parameter space.

public func edgeProjAux(faceIndex: Int, edgeIndex: Int, precision: Double = 1e-6) -> (first: Double, last: Double)?

Parameters: faceIndex — 0-based face index; edgeIndex — 0-based edge index within that face; precision — projection precision.
Returns: (firstParam, lastParam) on the pcurve, or nil if projection fails.
OCCT: ShapeFix_EdgeProjAux::Compute (via OCCTShapeFixEdgeProjAux).

Example:

if let (p1, p2) = shape.edgeProjAux(faceIndex: 0, edgeIndex: 0) {
    print("params:", p1, p2)
}

Geom2dAPI_Interpolate

Extension on Curve2D wrapping Geom2dAPI_Interpolate — exact interpolation through 2D points.

`Curve2D.interpolate2D(points:periodic:tolerance:)`

Interpolate a 2D BSpline curve exactly through the given points.

public static func interpolate2D(points: [(Double, Double)], periodic: Bool = false, tolerance: Double = 1e-6) -> Curve2D?

Parameters: points — ordered (x, y) pairs to pass through; periodic — if true, produce a closed periodic curve; tolerance — interpolation tolerance.
Returns: The interpolated Curve2D, or nil on failure.
OCCT: Geom2dAPI_Interpolate::Perform (via OCCTCurve2DInterpolate2D).

Example:

let pts = [(0.0, 0.0), (1.0, 1.0), (2.0, 0.0)]
if let curve = Curve2D.interpolate2D(points: pts) {
    // curve passes exactly through all three points
}

Geom2dAPI_PointsToBSpline

Extension on Curve2D wrapping Geom2dAPI_PointsToBSpline — least-squares approximation through 2D points.

`Curve2D.approximate2D(points:)`

Approximate a 2D BSpline curve through a set of points (least-squares fit).

public static func approximate2D(points: [(Double, Double)]) -> Curve2D?

Parameters: points — ordered (x, y) pairs to approximate.
Returns: The approximating Curve2D, or nil on failure.
OCCT: Geom2dAPI_PointsToBSpline::Curve (via OCCTCurve2DApproximate2D).
Note: Unlike interpolate2D, the curve does not pass exactly through all points; it minimises squared deviation.

Example:

let pts = [(0.0, 0.0), (0.5, 0.8), (1.0, 0.1), (1.5, 0.9), (2.0, 0.0)]
if let approx = Curve2D.approximate2D(points: pts) {
    // smooth fit curve
}

TDataXtd_PatternStd

Extension on Document wrapping TDataXtd_PatternStd — pattern replication attributes stored in the OCAF document tree.

`Document.PatternSignature`

Pattern type enumeration.

public enum PatternSignature: Int32 {
    case linear = 1
    case circular = 2
    case rectangular = 3
    case radialCircular = 4
    case mirror = 5
}

`setPattern(labelId:)`

Attach a TDataXtd_PatternStd attribute to a label.

@discardableResult
public func setPattern(labelId: Int64) -> Bool

OCCT: TDataXtd_PatternStd::Set (via OCCTDocumentSetPatternStd).

`hasPattern(labelId:)`

Check whether a label carries a pattern attribute.

public func hasPattern(labelId: Int64) -> Bool

OCCT: TDataXtd_PatternStd::Find (via OCCTDocumentHasPattern).

`patternSetSignature(labelId:signature:)`

Set the pattern type.

@discardableResult
public func patternSetSignature(labelId: Int64, signature: PatternSignature) -> Bool

OCCT: TDataXtd_PatternStd::SetSignature (via OCCTDocumentPatternSetSignature).

`patternGetSignature(labelId:)`

Retrieve the pattern type.

public func patternGetSignature(labelId: Int64) -> PatternSignature?

Returns: nil if no pattern attribute exists.
OCCT: TDataXtd_PatternStd::Signature (via OCCTDocumentPatternGetSignature).

`patternNbTrsfs(labelId:)`

Number of transforms (instances) defined by this pattern.

public func patternNbTrsfs(labelId: Int64) -> Int

OCCT: TDataXtd_PatternStd::NbTrsfs (via OCCTDocumentPatternNbTrsfs).

BRepAlgo_FaceRestrictor

Extension on Shape wrapping BRepAlgo_FaceRestrictor — rebuilds a face bounded by its wires.

`faceRestrictAlgo(faceIndex:)`

Restrict a face to its wire boundaries and return the resulting face count.

public func faceRestrictAlgo(faceIndex: Int) -> Int

Parameters: faceIndex — 0-based index of the face to restrict.
Returns: Number of result faces produced by the restrictor.
OCCT: BRepAlgo_FaceRestrictor::Perform / NbFaces (via OCCTShapeFaceRestrictAlgo).

Example:

let n = shape.faceRestrictAlgo(faceIndex: 0)
print("result faces:", n)

math_Matrix

Wraps math_Matrix — a dense general matrix with 1-based row and column indexing.

`MathMatrix.init(rows:cols:initialValue:)`

Create a matrix of given dimensions, all cells initialised to initialValue.

public init(rows: Int, cols: Int, initialValue: Double = 0.0)

OCCT: math_Matrix(rows, cols, initialValue) (via OCCTMathMatrixCreate).
Example:
```
let m = MathMatrix(rows: 3, cols: 3)
```

`rows`, `cols`

Number of rows / columns.

public var rows: Int { get }
public var cols: Int { get }

OCCT: math_Matrix::RowNumber / ColNumber (via OCCTMathMatrixRows / OCCTMathMatrixCols).

`value(row:col:)`

Read the element at (row, col) — 1-based.

public func value(row: Int, col: Int) -> Double

OCCT: math_Matrix::Value (via OCCTMathMatrixGetValue).
Example:
```
let v = m.value(row: 1, col: 1)
```

`setValue(row:col:value:)`

Write the element at (row, col) — 1-based.

public func setValue(row: Int, col: Int, value: Double)

OCCT: math_Matrix::SetValue (via OCCTMathMatrixSetValue).

`determinant`

Determinant of the matrix.

public var determinant: Double { get }

OCCT: math_Matrix::Determinant (via OCCTMathMatrixDeterminant).

`invert()`

Invert the matrix in-place.

@discardableResult
public func invert() -> Bool

Returns: true on success; false if the matrix is singular.
OCCT: math_Matrix::Invert (via OCCTMathMatrixInvert).

`multiply(by:)`

Scale all elements by a scalar in-place.

public func multiply(by scalar: Double)

OCCT: math_Matrix::Multiply(scalar) (via OCCTMathMatrixMultiplyScalar).

`transpose()`

Transpose the matrix in-place.

public func transpose()

OCCT: math_Matrix::Transpose (via OCCTMathMatrixTranspose).

math_Gauss

Namespace wrapping math_Gauss — direct Gaussian elimination for square linear systems.

`MathGauss.solve(matrix:rhs:)`

Solve Ax = b using Gaussian elimination.

public static func solve(matrix: [Double], rhs: [Double]) -> [Double]?

Parameters: matrix — row-major N×N coefficient matrix (N² elements); rhs — right-hand side vector (N elements).
Returns: Solution vector of length N, or nil on failure (singular matrix).
OCCT: math_Gauss::Solve (via OCCTMathGaussSolve).

Example:

// Solve 2x + y = 5, x + 3y = 10
let A = [2.0, 1.0, 1.0, 3.0]
let b = [5.0, 10.0]
if let x = MathGauss.solve(matrix: A, rhs: b) {
    print(x)  // [1.0, 3.0]
}

`MathGauss.determinant(matrix:n:)`

Compute the determinant of an N×N matrix using Gaussian elimination.

public static func determinant(matrix: [Double], n: Int) -> Double

Parameters: matrix — row-major N×N matrix; n — dimension.
OCCT: math_Gauss::Determinant (via OCCTMathGaussDeterminant).

math_SVD

Namespace wrapping math_SVD — Singular Value Decomposition for least-squares problems.

`MathSVD.solve(matrix:rows:cols:rhs:)`

Solve the overdetermined or exactly determined system Ax ≈ b in the least-squares sense.

public static func solve(matrix: [Double], rows: Int, cols: Int, rhs: [Double]) -> [Double]?

Parameters: matrix — row-major M×N matrix; rows — M; cols — N; rhs — right-hand side (length M).
Returns: Solution vector of length N, or nil on failure.
OCCT: math_SVD::Solve (via OCCTMathSVDSolve).

Example:

// Over-determined 3x2 system
let A = [1.0, 0, 0, 1, 1, 1]
let b = [1.0, 2.0, 3.0]
if let x = MathSVD.solve(matrix: A, rows: 3, cols: 2, rhs: b) {
    print(x)
}

math_DirectPolynomialRoots

Namespace wrapping math_DirectPolynomialRoots — closed-form real root finding for polynomials of degree 1–4.

`MathPolynomialRoots.solve(coefficients:)`

Find real roots of a polynomial a·xⁿ + b·xⁿ⁻¹ + … = 0.

public static func solve(coefficients: [Double]) -> [Double]?

Parameters: coefficients — [a, b, c, …] with the leading coefficient first; must have 2–5 elements (degree 1–4).
Returns: Array of real roots (possibly empty), or nil on error.
OCCT: math_DirectPolynomialRoots (via OCCTMathPolynomialRoots).

Example:

// Solve x² - 5x + 6 = 0 → roots 2, 3
if let roots = MathPolynomialRoots.solve(coefficients: [1.0, -5.0, 6.0]) {
    print(roots)  // [2.0, 3.0] (order may vary)
}

math_Jacobi

Namespace wrapping math_Jacobi — Jacobi iterative eigenvalue decomposition for symmetric matrices.

`MathJacobi.eigenvalues(matrix:n:)`

Compute eigenvalues of an N×N symmetric matrix.

public static func eigenvalues(matrix: [Double], n: Int) -> [Double]?

Parameters: matrix — row-major N×N symmetric matrix; n — dimension.
Returns: Eigenvalue array of length N, or nil on failure.
OCCT: math_Jacobi::Values (via OCCTMathJacobiEigenvalues).

Example:

let sym = [2.0, 1.0, 1.0, 2.0]  // 2x2 identity-ish
if let ev = MathJacobi.eigenvalues(matrix: sym, n: 2) {
    print(ev)  // [1.0, 3.0]
}

Convert_CircleToBSplineCurve

Extension on Curve2D wrapping Convert_CircleToBSplineCurve.

`Curve2D.fromCircleArc(centerX:centerY:radius:u1:u2:)`

Convert a 2D circular arc to a BSpline curve.

public static func fromCircleArc(centerX: Double, centerY: Double, radius: Double,
                                  u1: Double, u2: Double) -> Curve2D?

Parameters: centerX, centerY — arc centre; radius — circle radius; u1, u2 — start and end parameter (in radians).
Returns: The BSpline representation, or nil on failure.
OCCT: Convert_CircleToBSplineCurve (via OCCTConvertCircleToBSpline2D).

Example:

// Half-circle
if let arc = Curve2D.fromCircleArc(centerX: 0, centerY: 0, radius: 1.0, u1: 0, u2: .pi) {
    print(arc.degree)
}

Convert_SphereToBSplineSurface

Extension on Surface wrapping Convert_SphereToBSplineSurface.

`Surface.fromSphere(origin:axis:radius:)`

Convert a sphere to a BSpline surface.

public static func fromSphere(origin: SIMD3<Double>, axis: SIMD3<Double>, radius: Double) -> Surface?

Parameters: origin — sphere centre; axis — sphere axis direction; radius — radius.
Returns: The BSpline surface, or nil on failure.
OCCT: Convert_SphereToBSplineSurface (via OCCTConvertSphereToBSplineSurface).

Example:

if let bsp = Surface.fromSphere(origin: .zero, axis: SIMD3(0, 0, 1), radius: 5.0) {
    print(bsp.surfaceKind)  // .bsplineSurface
}

Convert Conic Curves to BSpline

Extensions on Curve2D for exact BSpline representations of 2D conics.

`Curve2D.fromEllipseArc(centerX:centerY:majorRadius:minorRadius:u1:u2:)`

Convert a 2D ellipse arc to a BSpline curve.

public static func fromEllipseArc(centerX: Double, centerY: Double,
                                   majorRadius: Double, minorRadius: Double,
                                   u1: Double, u2: Double) -> Curve2D?

Parameters: centerX, centerY — ellipse centre; majorRadius, minorRadius — semi-axes; u1, u2 — parameter range.
Returns: BSpline curve, or nil on failure.
OCCT: Convert_EllipseToBSplineCurve (via OCCTConvertEllipseToBSpline2D).

Example:

if let e = Curve2D.fromEllipseArc(centerX: 0, centerY: 0,
                                   majorRadius: 3.0, minorRadius: 1.5,
                                   u1: 0, u2: .pi) { }

`Curve2D.fromHyperbolaArc(centerX:centerY:majorRadius:minorRadius:u1:u2:)`

Convert a 2D hyperbola arc to a BSpline curve.

public static func fromHyperbolaArc(centerX: Double, centerY: Double,
                                     majorRadius: Double, minorRadius: Double,
                                     u1: Double, u2: Double) -> Curve2D?

OCCT: Convert_HyperbolaToBSplineCurve (via OCCTConvertHyperbolaToBSpline2D).

`Curve2D.fromParabolaArc(centerX:centerY:focal:u1:u2:)`

Convert a 2D parabola arc to a BSpline curve.

public static func fromParabolaArc(centerX: Double, centerY: Double, focal: Double,
                                    u1: Double, u2: Double) -> Curve2D?

Parameters: focal — focal distance of the parabola.
OCCT: Convert_ParabolaToBSplineCurve (via OCCTConvertParabolaToBSpline2D).

Convert Elementary Surfaces to BSpline

Extensions on Surface for exact BSpline representations of analytic surfaces.

`Surface.fromCylinder(origin:axis:radius:u1:u2:v1:v2:)`

Convert a cylinder patch to a BSpline surface.

public static func fromCylinder(origin: SIMD3<Double>, axis: SIMD3<Double>, radius: Double,
                                 u1: Double, u2: Double, v1: Double, v2: Double) -> Surface?

Parameters: origin, axis — cylinder position and orientation; radius — cylinder radius; u1/u2 — angular range (radians); v1/v2 — axial parameter range.
OCCT: Convert_CylinderToBSplineSurface (via OCCTConvertCylinderToBSplineSurface).

Example:

if let cyl = Surface.fromCylinder(origin: .zero, axis: SIMD3(0, 0, 1),
                                   radius: 2.0, u1: 0, u2: 2 * .pi,
                                   v1: 0, v2: 5.0) { }

`Surface.fromCone(origin:axis:semiAngle:refRadius:u1:u2:v1:v2:)`

Convert a cone patch to a BSpline surface.

public static func fromCone(origin: SIMD3<Double>, axis: SIMD3<Double>,
                             semiAngle: Double, refRadius: Double,
                             u1: Double, u2: Double, v1: Double, v2: Double) -> Surface?

Parameters: semiAngle — half-angle in radians; refRadius — reference radius at the base.
OCCT: Convert_ConeToBSplineSurface (via OCCTConvertConeToBSplineSurface).

`Surface.fromTorus(origin:axis:majorRadius:minorRadius:)`

Convert a full torus to a BSpline surface.

public static func fromTorus(origin: SIMD3<Double>, axis: SIMD3<Double>,
                              majorRadius: Double, minorRadius: Double) -> Surface?

OCCT: Convert_TorusToBSplineSurface (via OCCTConvertTorusToBSplineSurface).

Example:

if let t = Surface.fromTorus(origin: .zero, axis: SIMD3(0, 0, 1),
                              majorRadius: 5.0, minorRadius: 1.5) { }

math_Householder

Namespace wrapping math_Householder — QR decomposition via Householder reflections for overdetermined systems.

`MathHouseholder.solve(matrix:rows:cols:rhs:)`

Solve Ax ≈ b (M ≥ N) using Householder QR.

public static func solve(matrix: [Double], rows: Int, cols: Int, rhs: [Double]) -> [Double]?

Parameters: matrix — row-major M×N matrix; rows — M (must be ≥ cols); cols — N; rhs — right-hand side (length M).
Returns: Solution vector of length N, or nil on failure or under-determined input.
OCCT: math_Householder::Solve (via OCCTMathHouseholderSolve).

Example:

let A = [1.0, 1, 1, 2, 1, 3]  // 3x2
let b = [6.0, 5.0, 7.0]
if let x = MathHouseholder.solve(matrix: A, rows: 3, cols: 2, rhs: b) {
    print(x)
}

math_Crout

Namespace wrapping math_Crout — LDLᵀ Crout decomposition for symmetric positive-definite systems.

`MathCrout.solve(matrix:rhs:)`

Solve symmetric Ax = b using Crout decomposition.

public static func solve(matrix: [Double], rhs: [Double]) -> [Double]?

Parameters: matrix — row-major N×N symmetric matrix; rhs — right-hand side (length N).
Returns: Solution vector of length N, or nil on failure.
OCCT: math_Crout::Solve (via OCCTMathCroutSolve).

Example:

let A = [4.0, 2, 2, 3]  // 2x2 SPD
let b = [8.0, 5.0]
if let x = MathCrout.solve(matrix: A, rhs: b) {
    print(x)  // [1.8571..., 0.4285...]
}

`MathCrout.determinant(matrix:n:)`

Compute the determinant of a symmetric matrix via Crout factorisation.

public static func determinant(matrix: [Double], n: Int) -> Double

OCCT: math_Crout::Determinant (via OCCTMathCroutDeterminant).

ShapeFix_IntersectionTool

Extension on Shape wrapping ShapeFix_IntersectionTool — repairs self-intersecting wires on a face.

`fixIntersectingWires(faceIndex:precision:)`

Fix intersecting wires on a face of this shape.

@discardableResult
public func fixIntersectingWires(faceIndex: Int, precision: Double = 1e-6) -> Bool

Parameters: faceIndex — 0-based face index; precision — fix tolerance.
Returns: true if any fixes were applied.
OCCT: ShapeFix_IntersectionTool::FixSelfIntersectWire (via OCCTShapeFixIntersectingWires).

Example:

shape.fixIntersectingWires(faceIndex: 0)

XCAFDoc_AssemblyItemRef

Extension on Document wrapping XCAFDoc_AssemblyItemRef — a persistent reference to a specific item (and optionally a subshape) within an assembly hierarchy.

`setAssemblyItemRef(labelId:itemPath:)`

Attach an assembly item reference attribute to a label.

@discardableResult
public func setAssemblyItemRef(labelId: Int64, itemPath: String) -> Bool

Parameters: labelId — target label; itemPath — colon-separated label-entry path string.
OCCT: XCAFDoc_AssemblyItemRef::Set (via OCCTDocumentSetAssemblyItemRef).

`assemblyItemRefPath(labelId:)`

Get the assembly item reference path string.

public func assemblyItemRefPath(labelId: Int64) -> String?

Returns: Path string, or nil if no attribute exists.
OCCT: XCAFDoc_AssemblyItemRef::GetPath (via OCCTDocumentGetAssemblyItemRef).

`assemblyItemRefSetSubshape(labelId:index:)`

Set a subshape index on an assembly item reference.

@discardableResult
public func assemblyItemRefSetSubshape(labelId: Int64, index: Int32) -> Bool

OCCT: XCAFDoc_AssemblyItemRef::SetSubshapeIndex (via OCCTDocumentAssemblyItemRefSetSubshape).

`assemblyItemRefGetSubshape(labelId:)`

Get the subshape index, if set.

public func assemblyItemRefGetSubshape(labelId: Int64) -> Int32?

Returns: The subshape index, or nil if not set (raw value < 0).
OCCT: XCAFDoc_AssemblyItemRef::GetSubshapeIndex (via OCCTDocumentAssemblyItemRefGetSubshape).

`assemblyItemRefHasExtra(labelId:)`

Check whether the assembly item reference carries an extra attribute reference.

public func assemblyItemRefHasExtra(labelId: Int64) -> Bool

OCCT: XCAFDoc_AssemblyItemRef::HasExtraRef (via OCCTDocumentAssemblyItemRefHasExtra).

`assemblyItemRefClearExtra(labelId:)`

Remove the extra attribute reference from an assembly item ref.

@discardableResult
public func assemblyItemRefClearExtra(labelId: Int64) -> Bool

OCCT: XCAFDoc_AssemblyItemRef::RemoveExtraRef (via OCCTDocumentAssemblyItemRefClearExtra).

`assemblyItemRefIsOrphan(labelId:)`

Whether the assembly item reference points to a label that no longer exists.

public func assemblyItemRefIsOrphan(labelId: Int64) -> Bool

OCCT: XCAFDoc_AssemblyItemRef::IsOrphan (via OCCTDocumentAssemblyItemRefIsOrphan).

BRepAlgo_Image

Wraps BRepAlgo_Image — a bidirectional mapping that tracks how shapes evolve through Boolean or healing operations (shape history).

`ShapeImage.init()`

Create an empty shape image map.

public init()

OCCT: BRepAlgo_Image() (via OCCTBRepAlgoImageCreate).

`setRoot(_:)`

Record the root (input) shape of the mapping.

public func setRoot(_ shape: Shape)

OCCT: BRepAlgo_Image::SetRoot (via OCCTBRepAlgoImageSetRoot).

`bind(old:new:)`

Record that old was replaced by new.

public func bind(old: Shape, new: Shape)

OCCT: BRepAlgo_Image::Bind (via OCCTBRepAlgoImageBind).

`hasImage(_:)`

Check if a shape has a recorded replacement image.

public func hasImage(_ shape: Shape) -> Bool

OCCT: BRepAlgo_Image::HasImage (via OCCTBRepAlgoImageHasImage).

`isImage(_:)`

Check if a shape is itself a recorded image of some root shape.

public func isImage(_ shape: Shape) -> Bool

OCCT: BRepAlgo_Image::IsImage (via OCCTBRepAlgoImageIsImage).

`clear()`

Clear all recorded mappings.

public func clear()

OCCT: BRepAlgo_Image::Clear (via OCCTBRepAlgoImageClear).

OSD_Path

Namespace wrapping OSD_Path — platform-independent file path parsing.

`OSDPath.name(_:)`

Extract the filename (without extension) from a path string.

public static func name(_ path: String) -> String?

OCCT: OSD_Path::Name (via OCCTOSDPathName).

Example:

OSDPath.name("/tmp/part.stp")  // "part"

`OSDPath.fileExtension(_:)`

Extract the file extension (with leading dot) from a path string.

public static func fileExtension(_ path: String) -> String?

OCCT: OSD_Path::Extension (via OCCTOSDPathExtension).

Example:

OSDPath.fileExtension("/tmp/part.stp")  // ".stp"

`OSDPath.trek(_:)`

Extract the directory trek portion of a path.

public static func trek(_ path: String) -> String?

OCCT: OSD_Path::Trek (via OCCTOSDPathTrek).

`OSDPath.systemName(_:)`

Get the system-formatted (OS-native) path string.

public static func systemName(_ path: String) -> String?

OCCT: OSD_Path::SystemName (via OCCTOSDPathSystemName).

`OSDPath.folderAndFile(_:)`

Split a path into its folder and filename components.

public static func folderAndFile(_ path: String) -> (folder: String, file: String)?

Returns: Tuple of folder and filename strings, or nil if splitting fails.
OCCT: OSD_Path trek/name split (via OCCTOSDPathFolderAndFile).

Example:

if let (folder, file) = OSDPath.folderAndFile("/tmp/parts/bolt.stp") {
    print(folder, file)
}

`OSDPath.isValid(_:)`

Whether the path string is syntactically valid.

public static func isValid(_ path: String) -> Bool

OCCT: OSD_Path::IsValid (via OCCTOSDPathIsValid).

`OSDPath.isUnixPath(_:)`

Whether the path uses Unix conventions.

public static func isUnixPath(_ path: String) -> Bool

OCCT: OSD_Path system type check (via OCCTOSDPathIsUnixPath).

`OSDPath.isRelative(_:)`

Whether the path is relative (does not start at the filesystem root).

public static func isRelative(_ path: String) -> Bool

OCCT: OSD_Path::IsRelative (via OCCTOSDPathIsRelative).

`OSDPath.isAbsolute(_:)`

Whether the path is absolute.

public static func isAbsolute(_ path: String) -> Bool

OCCT: OSD_Path::IsAbsolute (via OCCTOSDPathIsAbsolute).

BRepClass_FClassifier

Extension on Shape providing 2D face-parameter-space classification and loop building.

`classifyPoint2D(faceIndex:u:v:tolerance:)`

Classify a UV parameter-space point on a face.

public func classifyPoint2D(faceIndex: Int, u: Double, v: Double, tolerance: Double = 1e-6) -> PointState

Parameters: faceIndex — 0-based face index; u, v — UV parameters on the face; tolerance — classification tolerance.
Returns: .inside, .outside, .on, or .unknown (same PointState enum as classifyPoint).
OCCT: BRepClass_FClassifier::Perform (via OCCTShapeClassifyPoint2D).

Example:

let state = shape.classifyPoint2D(faceIndex: 0, u: 0.5, v: 0.5)

`buildLoops(faceIndex:)`

Build edge loops (wires) from the free edges on a face.

public func buildLoops(faceIndex: Int) -> Int

Parameters: faceIndex — 0-based face index.
Returns: Number of loops built, or -1 on error.
OCCT: BRepAlgo_Loop (via OCCTShapeBuildLoops).

`faceDomainEdgeCount(faceIndex:)`

Count the boundary edges of a face using BRepGProp_Domain.

public func faceDomainEdgeCount(faceIndex: Int) -> Int

OCCT: BRepGProp_Domain::NbEdges (via OCCTShapeFaceDomainEdgeCount).

Bnd_BoundSortBox

Wraps Bnd_BoundSortBox — a spatial index for fast AABB-vs-AABB intersection queries.

`BoundSortBox.init(boxes:)`

Create a sort box from an array of axis-aligned bounding boxes.

public init(boxes: [[Double]])

Parameters: boxes — each element is [xmin, ymin, zmin, xmax, ymax, zmax].
OCCT: Bnd_BoundSortBox::Initialize (via OCCTBoundSortBoxCreate).

Example:

let bsb = BoundSortBox(boxes: [
    [0, 0, 0, 1, 1, 1],
    [2, 2, 2, 3, 3, 3],
])

`compare(xmin:ymin:zmin:xmax:ymax:zmax:)`

Find the 0-based indices of stored boxes that intersect a query box.

public func compare(xmin: Double, ymin: Double, zmin: Double,
                    xmax: Double, ymax: Double, zmax: Double) -> [Int]

Returns: Array of 0-based indices into the array supplied at construction.
OCCT: Bnd_BoundSortBox::Compare (via OCCTBoundSortBoxCompare).

Example:

let hits = bsb.compare(xmin: 0.5, ymin: 0.5, zmin: 0.5,
                        xmax: 1.5, ymax: 1.5, zmax: 1.5)
// hits == [0]

TNaming_Naming

Extension on Document wrapping TNaming_Naming — persistent topological naming that survives shape modifications.

`insertNaming(labelId:)`

Insert a TNaming_Naming attribute on a label.

@discardableResult
public func insertNaming(labelId: Int64) -> Bool

OCCT: TNaming_Naming::Insert (via OCCTDocumentInsertNaming).
Example:
```
doc.insertNaming(labelId: shapeLabel)
```

`namingIsDefined(labelId:)`

Check whether a naming attribute is defined and valid on a label.

public func namingIsDefined(labelId: Int64) -> Bool

OCCT: TNaming_Naming::IsDefined (via OCCTDocumentNamingIsDefined).

Precision Constants

Namespace exposing OCCT’s global precision tolerances from Precision.hxx.

`OCCTPrecision.confusion`

General positional/distance confusion tolerance (1×10⁻⁷ by default).

public static var confusion: Double { get }

OCCT: Precision::Confusion() (via OCCTPrecisionConfusion).

`OCCTPrecision.angular`

Angular direction comparison tolerance (1×10⁻¹² by default).

public static var angular: Double { get }

OCCT: Precision::Angular() (via OCCTPrecisionAngular).

`OCCTPrecision.intersection`

Tolerance used by intersection algorithms.

public static var intersection: Double { get }

OCCT: Precision::Intersection() (via OCCTPrecisionIntersection).

`OCCTPrecision.approximation`

Tolerance used by approximation algorithms.

public static var approximation: Double { get }

OCCT: Precision::Approximation() (via OCCTPrecisionApproximation).

`OCCTPrecision.infinite`

Sentinel value representing “infinite” (2×10¹⁰⁰).

public static var infinite: Double { get }

OCCT: Precision::Infinite() (via OCCTPrecisionInfinite).

`OCCTPrecision.pConfusion`

Parametric-space confusion tolerance (scaled by curve-space bounds).

public static var pConfusion: Double { get }

OCCT: Precision::PConfusion() (via OCCTPrecisionPConfusion).

`OCCTPrecision.isInfinite(_:)`

Test whether a value should be treated as infinite.

public static func isInfinite(_ value: Double) -> Bool

OCCT: Precision::IsInfinite (via OCCTPrecisionIsInfinite).

Example:

OCCTPrecision.isInfinite(1e200)  // true
OCCTPrecision.isInfinite(10.0)   // false

IntAna Analytic Intersections

Namespace of static methods wrapping OCCT’s IntAna package — closed-form intersections between lines, planes, spheres, and tori.

`IntAna.ConicQuadResult`

Result of a line-with-quadric intersection.

public struct ConicQuadResult {
    public let points: [SIMD3<Double>]
    public let params: [Double]
    public let isParallel: Bool
}

points — intersection points in 3D; params — corresponding parameters on the line; isParallel — the line is parallel to the quadric surface.

`IntAna.linePlane(lineOrigin:lineDir:planeOrigin:planeNormal:)`

Intersect a parametric line with a plane.

public static func linePlane(lineOrigin: SIMD3<Double>, lineDir: SIMD3<Double>,
                              planeOrigin: SIMD3<Double>, planeNormal: SIMD3<Double>) -> ConicQuadResult

Returns: Up to 1 intersection point; isParallel is true when the line lies in or is parallel to the plane.
OCCT: IntAna_IntConicQuad (via OCCTIntAnaLineQuad).

Example:

let r = IntAna.linePlane(lineOrigin: SIMD3(0, 0, 5), lineDir: SIMD3(0, 0, -1),
                          planeOrigin: .zero, planeNormal: SIMD3(0, 0, 1))
// r.points[0] ≈ (0, 0, 0)

`IntAna.lineSphere(lineOrigin:lineDir:sphereCenter:sphereAxis:radius:)`

Intersect a parametric line with a sphere.

public static func lineSphere(lineOrigin: SIMD3<Double>, lineDir: SIMD3<Double>,
                               sphereCenter: SIMD3<Double>, sphereAxis: SIMD3<Double>,
                               radius: Double) -> ConicQuadResult

Returns: Up to 2 intersection points.
OCCT: IntAna_IntConicQuad with sphere quadric (via OCCTIntAnaLineSphere).

`IntAna.QuadQuadResult`

Result of a quadric-quadric intersection.

public struct QuadQuadResult {
    public let count: Int
    public let lines: [(origin: SIMD3<Double>, direction: SIMD3<Double>)]
    public let points: [SIMD3<Double>]
}

`IntAna.planePlane(p1Origin:p1Normal:p2Origin:p2Normal:)`

Intersect two planes — result is typically a line.

public static func planePlane(p1Origin: SIMD3<Double>, p1Normal: SIMD3<Double>,
                               p2Origin: SIMD3<Double>, p2Normal: SIMD3<Double>) -> QuadQuadResult

OCCT: IntAna_QuadQuadGeo plane-plane (via OCCTIntAnaPlanePlane).

Example:

let r = IntAna.planePlane(p1Origin: .zero, p1Normal: SIMD3(0, 0, 1),
                           p2Origin: .zero, p2Normal: SIMD3(0, 1, 0))
// r.lines[0] is the X-axis intersection line

`IntAna.planeSphere(planeOrigin:planeNormal:sphereCenter:sphereAxis:radius:)`

Intersect a plane with a sphere — result is typically a circle.

public static func planeSphere(planeOrigin: SIMD3<Double>, planeNormal: SIMD3<Double>,
                                sphereCenter: SIMD3<Double>, sphereAxis: SIMD3<Double>,
                                radius: Double) -> QuadQuadResult

OCCT: IntAna_QuadQuadGeo plane-sphere (via OCCTIntAnaPlaneSphere).

`IntAna.threePlanes(p1Origin:p1Normal:p2Origin:p2Normal:p3Origin:p3Normal:)`

Compute the unique intersection point of three planes.

public static func threePlanes(p1Origin: SIMD3<Double>, p1Normal: SIMD3<Double>,
                                p2Origin: SIMD3<Double>, p2Normal: SIMD3<Double>,
                                p3Origin: SIMD3<Double>, p3Normal: SIMD3<Double>) -> SIMD3<Double>?

Returns: The point, or nil if the planes are not in general position.
OCCT: IntAna_Int3Pln (via OCCTIntAna3Planes).

`IntAna.lineTorus(lineOrigin:lineDir:torusCenter:torusAxis:majorRadius:minorRadius:)`

Intersect a parametric line with a torus (up to 4 points).

public static func lineTorus(lineOrigin: SIMD3<Double>, lineDir: SIMD3<Double>,
                              torusCenter: SIMD3<Double>, torusAxis: SIMD3<Double>,
                              majorRadius: Double, minorRadius: Double) -> [SIMD3<Double>]

Returns: Array of 0–4 intersection points.
OCCT: IntAna_IntLinTorus (via OCCTIntAnaLineTorus).

OSD_Chronometer

Namespace wrapping OSD_Chronometer — per-process and per-thread CPU time measurement.

`CPUTime.processCPU()`

Get total process CPU time split into user and system seconds.

public static func processCPU() -> (user: Double, system: Double)

OCCT: OSD_Chronometer::GetProcessCPU (via OCCTGetProcessCPU).
Example:
```
let (user, sys) = CPUTime.processCPU()
```

`CPUTime.threadCPU()`

Get current thread CPU time split into user and system seconds.

public static func threadCPU() -> (user: Double, system: Double)

OCCT: OSD_Chronometer::GetThreadCPU (via OCCTGetThreadCPU).

OSD_Process

Namespace wrapping OSD_Process — process identification and path utilities.

`ProcessInfo.processId`

Current process identifier.

public static var processId: Int { get }

OCCT: OSD_Process::ProcessId (via OCCTProcessId).

`ProcessInfo.userName`

public static var userName: String? { get }

OCCT: OSD_Process::UserName (via OCCTProcessUserName).

`ProcessInfo.executablePath`

Full path to the running executable.

public static var executablePath: String? { get }

OCCT: OSD_Process::ExecutablePath (via OCCTProcessExecutablePath).

`ProcessInfo.executableFolder`

Folder containing the running executable.

public static var executableFolder: String? { get }

OCCT: OSD_Process::ExecutableFolder (via OCCTProcessExecutableFolder).

Draft_Modification

Extension on Shape wrapping Draft_Modification — applies a draft angle to a face, tapering it toward a neutral plane.

`draftModification(faceIndex:direction:angle:neutralPlaneOrigin:neutralPlaneNormal:)`

Apply a draft angle modification to a face of this shape.

public func draftModification(faceIndex: Int, direction: SIMD3<Double>, angle: Double,
                               neutralPlaneOrigin: SIMD3<Double>,
                               neutralPlaneNormal: SIMD3<Double>) -> Shape?

Parameters: faceIndex — 0-based index of the face to draft; direction — pull direction for demoulding; angle — draft angle in radians; neutralPlaneOrigin / neutralPlaneNormal — the plane that stays fixed during drafting.
Returns: The modified shape, or nil on failure (incompatible geometry).
OCCT: Draft_Modification::Add / Perform (via OCCTShapeDraftModification).

Example:

if let drafted = shape.draftModification(faceIndex: 0,
                                          direction: SIMD3(0, 0, 1),
                                          angle: 0.05,
                                          neutralPlaneOrigin: .zero,
                                          neutralPlaneNormal: SIMD3(0, 0, 1)) {
    // drafted face tapers at 0.05 rad ≈ 2.86°
}

Convert_CompBezierCurvesToBSplineCurve

Structures and namespace for converting multi-segment Bezier curves to a single BSpline curve.

`BezierToBSplineResult`

Result of a 3D composite Bezier → BSpline conversion.

public struct BezierToBSplineResult {
    public let degree: Int
    public let poles: [SIMD3<Double>]
    public let knots: [Double]
    public let multiplicities: [Int]
}

`BezierToBSpline2dResult`

Result of a 2D composite Bezier → BSpline conversion.

public struct BezierToBSpline2dResult {
    public let degree: Int
    public let poles: [SIMD2<Double>]
    public let knots: [Double]
    public let multiplicities: [Int]
}

`CompBezierConverter.toBSpline(segments:)`

Convert a sequence of connected 3D Bezier segments to a single BSpline curve.

public static func toBSpline(segments: [[SIMD3<Double>]]) -> BezierToBSplineResult?

Parameters: segments — each element is the ordered control points of one Bezier segment; all segments must have the same number of control points.
Returns: The merged BSpline data, or nil on failure.
OCCT: Convert_CompBezierCurvesToBSplineCurve (via OCCTConvertCompBezierToBSpline).

Example:

let seg1: [SIMD3<Double>] = [SIMD3(0,0,0), SIMD3(1,1,0), SIMD3(2,0,0)]
let seg2: [SIMD3<Double>] = [SIMD3(2,0,0), SIMD3(3,-1,0), SIMD3(4,0,0)]
if let result = CompBezierConverter.toBSpline(segments: [seg1, seg2]) {
    print("degree:", result.degree, "poles:", result.poles.count)
}

`CompBezierConverter.toBSpline2d(segments:)`

Convert a sequence of connected 2D Bezier segments to a single BSpline curve.

public static func toBSpline2d(segments: [[SIMD2<Double>]]) -> BezierToBSpline2dResult?

Parameters: segments — each element is the ordered 2D control points of one Bezier segment; all segments must have the same number of control points.
Returns: The merged 2D BSpline data, or nil on failure.
OCCT: Convert_CompPolynomialToPoles / Convert_CompBezierCurves2dToBSplineCurve2d (via OCCTConvertCompBezier2dToBSpline2d).

Geom_OffsetSurface Extensions

Extensions on Surface for querying and modifying offset surface parameters.

`offsetValue`

The offset distance of this surface (only meaningful for offset surfaces).

public var offsetValue: Double { get }

Returns: Offset distance; returns 0 for non-offset surfaces.
OCCT: Geom_OffsetSurface::Offset (via OCCTSurfaceOffsetValue).

Example:

if surface.isOffsetSurface {
    print("offset:", surface.offsetValue)
}

`setOffsetValue(_:)`

Change the offset distance of an offset surface.

public func setOffsetValue(_ value: Double)

Note: No-op on non-offset surfaces.
OCCT: Geom_OffsetSurface::SetOffsetValue (via OCCTSurfaceSetOffsetValue).
Example:
```
surface.setOffsetValue(2.0)
```

`offsetBasis`

The underlying basis surface of an offset surface.

public var offsetBasis: Surface? { get }

Returns: The basis Surface, or nil if this surface is not an offset surface.
OCCT: Geom_OffsetSurface::BasisSurface (via OCCTSurfaceOffsetBasis).

Example:

if let basis = surface.offsetBasis {
    print("basis kind:", basis.surfaceKind)
}

Document — Math, Bounds, OSD & Conversions

Topics

gp_Quaternion

Quaternion.init(x:y:z:w:)

Quaternion.fromAxisAngle(axis:angle:)

Quaternion.fromVectors(from:to:)

components

setEulerAngles(order:alpha:beta:gamma:)

getEulerAngles(order:)

matrix

rotate(_:)

multiplied(by:)

axisAngle

rotationAngle

normalize()

OSD_Timer

Timer.init()

start()

stop()

reset()

elapsedTime

Timer.wallClockTime

Bnd_OBB

OBB.init(center:xDir:yDir:zDir:hx:hy:hz:)

OBB.fromShape(_:)

isVoid

center

halfSizes

isOut(point:)

isOut(_:) (OBB overload)

enlarge(by:)

squareExtent

Bnd_Range

Range.init(min:max:)

Range.init() (void)

isVoid

bounds

delta

contains(_:)

add(_:) (value)

add(_:) (Range)

common(_:)

enlarge(by:)

trimFrom(_:)

trimTo(_:)

BRepClass3d Point Classification

Shape.PointState

classifyPoint(_:tolerance:)

TDataXtd_Constraint

Document.ConstraintType

setConstraint(labelId:)

constraintSetType(labelId:type:)

constraintGetType(labelId:)

constraintNbGeometries(labelId:)

constraintIsPlanar(labelId:)

constraintIsDimension(labelId:)

constraintSetVerified(labelId:verified:)

constraintGetVerified(labelId:)

constraintClearGeometries(labelId:)

OSD_MemInfo

MemInfo.heapUsage

MemInfo.workingSet

MemInfo.heapUsageMiB

MemInfo.infoString

ShapeFix_EdgeProjAux

edgeProjAux(faceIndex:edgeIndex:precision:)

Geom2dAPI_Interpolate

Curve2D.interpolate2D(points:periodic:tolerance:)

Geom2dAPI_PointsToBSpline

Curve2D.approximate2D(points:)

TDataXtd_PatternStd

Document.PatternSignature

setPattern(labelId:)

hasPattern(labelId:)

patternSetSignature(labelId:signature:)

patternGetSignature(labelId:)

patternNbTrsfs(labelId:)

BRepAlgo_FaceRestrictor

faceRestrictAlgo(faceIndex:)

math_Matrix

`Quaternion.init(x:y:z:w:)`

`Quaternion.fromAxisAngle(axis:angle:)`

`Quaternion.fromVectors(from:to:)`

`components`

`setEulerAngles(order:alpha:beta:gamma:)`

`getEulerAngles(order:)`

`matrix`

`rotate(_:)`

`multiplied(by:)`

`axisAngle`

`rotationAngle`

`normalize()`

`Timer.init()`

`start()`

`stop()`

`reset()`

`elapsedTime`

`Timer.wallClockTime`

`OBB.init(center:xDir:yDir:zDir:hx:hy:hz:)`

`OBB.fromShape(_:)`

`isVoid`

`center`

`halfSizes`

`isOut(point:)`

`isOut(_:)` (OBB overload)

`enlarge(by:)`

`squareExtent`

`Range.init(min:max:)`

`Range.init()` (void)

`isVoid`

`bounds`

`delta`

`contains(_:)`

`add(_:)` (value)

`add(_:)` (Range)

`common(_:)`

`enlarge(by:)`

`trimFrom(_:)`

`trimTo(_:)`

`Shape.PointState`

`classifyPoint(_:tolerance:)`

`Document.ConstraintType`

`setConstraint(labelId:)`

`constraintSetType(labelId:type:)`

`constraintGetType(labelId:)`

`constraintNbGeometries(labelId:)`

`constraintIsPlanar(labelId:)`

`constraintIsDimension(labelId:)`

`constraintSetVerified(labelId:verified:)`

`constraintGetVerified(labelId:)`

`constraintClearGeometries(labelId:)`

`MemInfo.heapUsage`

`MemInfo.workingSet`

`MemInfo.heapUsageMiB`

`MemInfo.infoString`

`edgeProjAux(faceIndex:edgeIndex:precision:)`

`Curve2D.interpolate2D(points:periodic:tolerance:)`

`Curve2D.approximate2D(points:)`

`Document.PatternSignature`

`setPattern(labelId:)`

`hasPattern(labelId:)`

`patternSetSignature(labelId:signature:)`

`patternGetSignature(labelId:)`

`patternNbTrsfs(labelId:)`

`faceRestrictAlgo(faceIndex:)`

`MathMatrix.init(rows:cols:initialValue:)`

`rows`, `cols`

`value(row:col:)`

`setValue(row:col:value:)`

`determinant`

`invert()`

`multiply(by:)`

`transpose()`

`MathGauss.solve(matrix:rhs:)`

`MathGauss.determinant(matrix:n:)`

`MathSVD.solve(matrix:rows:cols:rhs:)`

`MathPolynomialRoots.solve(coefficients:)`

`MathJacobi.eigenvalues(matrix:n:)`

`Curve2D.fromCircleArc(centerX:centerY:radius:u1:u2:)`

`Surface.fromSphere(origin:axis:radius:)`