Crate hypercurve 

Curve primitives built on the hyper geometry stack.

This crate starts with a line/circular-arc core using hyperreal::Real coordinates and the hyperlimit predicate policy model. The core topology follows the robust-computation principle of deciding predicates before branching; see Shewchuk, “Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates” (Discrete & Computational Geometry 18(3), 305-363, 1997).

Structs

Aabb2

An axis-aligned bounding box for two-dimensional curve geometry.

ArcArcIntersectionPoint

One point in an arc-arc intersection result.

Bezier2Facts

Structural facts for polynomial Bezier curves.

BezierAlgebraicCoordinateImage

One exact coordinate image of a Bezier expression at an algebraic parameter.

BezierAlgebraicEndpointImage2

Exact point and tangent images for one algebraic split endpoint.

BezierAlgebraicParameter2

Algebraic Bezier parameter represented by a polynomial and isolating interval.

BezierAlgebraicPointImage2

Exact algebraic image of a Bezier point.

BezierAlgebraicRationalCoordinateImage

One exact rational-function coordinate image at an algebraic parameter.

BezierAlgebraicSameTangentOrderReport

Report for a certified algebraic same-tangent higher-order predicate.

BezierAlgebraicScalarSignReport

Sign construction report for a cross, dot, or norm-squared scalar.

BezierAlgebraicTangentImage2

Exact algebraic image of a Bezier derivative vector.

BezierAlgebraicTangentOrderReport

Report for a certified algebraic tangent-order predicate.

BezierAlgebraicTangentVector2

A represented algebraic tangent vector with exact coordinate evidence.

BezierAlgebraicTangentVectorReport

Extraction report for a represented tangent vector.

BezierArcLengthParameterRegion2

Certified parameter region for an inverse arc-length query.

BezierAreaMomentPrefixSums2

Exact prefix sums of Bezier area and first-moment boundary contributions.

BezierAreaMoments2

Exact Green’s-theorem area and first-moment boundary contributions.

BezierAreaPrefixSums2

Exact prefix sums of Bezier signed-area boundary contributions.

BezierArrangementChain2

One endpoint-connected traversal chain through retained Bezier fragments.

BezierArrangementFragment2

One retained Bezier arrangement fragment with source provenance.

BezierArrangementGraph2

Branch-free retained Bezier arrangement graph.

BezierArrangementTraversal2

Traversal result for a branch-free retained Bezier arrangement graph.

BezierBoundaryLoop2

A closed native Bezier/conic boundary loop.

BezierCurveIntersectionPoint

Certified geometric intersection point between two Bezier segments.

BezierCurveIntersectionRegion

Pair of parameter spans that covers one possible curve/curve intersection region.

BezierFitCertificate

Certificate attached to a zero-error Bezier primitive fit.

BezierFlatteningCertificate

Certificate attached to a flattened Bezier polyline.

BezierFlatteningOptions

Options for certified Bezier-to-polyline flattening.

BezierGraphContact

Certified contact on a shared-axis monotone Bezier graph relation.

BezierLengthBounds2

Exact lower and upper bounds for a Bezier segment’s arc length.

BezierLineContact

Certified represented root of a Bezier/supporting-line predicate.

BezierMonotoneSpan

Closed parameter span on which a Bezier has no certified interior extremum.

BezierOffsetPreflight2

Exact source analysis retained before a staged Bezier offset candidate is built.

BezierParameterInterval

Closed isolating interval for a Bezier parameter root.

BezierParameterPolynomial

Power-basis polynomial used to define an algebraic Bezier parameter.

BezierRegion2

A retained higher-order region with native Bezier/conic boundary loops.

BezierRetainedBoundaryLoop2

A closed retained Bezier/conic boundary loop.

BezierRetainedCurveEnvelope2

Exact curve-interior envelope for retained Bezier/conic carriers.

BezierRetainedCurvedNestingRoleReport2

Exact nesting-derived role assignment for native retained curved loops.

BezierRetainedEndpointEnvelope2

Exact endpoint envelope for a retained Bezier region or loop.

BezierRetainedFragmentSource2

Arrangement provenance for one retained boundary fragment.

BezierRetainedLineOverlapSplit2

Exact split evidence for a positive-dimensional line-image overlap.

BezierRetainedLineRegionRoleReport2

Exact role assignment for retained line-image Bezier boundary loops.

BezierRetainedLinearOverlapSplit2

Exact Bezier-parameter split evidence for a linearly parameterized overlap.

BezierRetainedLinearOverlapSplitGraph2

Graph refined at all certified linearly-parameterized overlap endpoints.

BezierRetainedLinearOverlapTraversal2

Traversal through a graph whose certified linear overlaps were refined.

BezierRetainedOverlap2

One certified overlap pair in a retained Bezier arrangement graph.

BezierRetainedOverlapRefinedFragment2

One fragment in a graph refined by certified linear-overlap split points.

BezierRetainedOverlapReport2

Exact overlap report for materialized retained Bezier arrangement fragments.

BezierRetainedOverlapTraversal2

Retained traversal after consuming certified duplicate materialized overlaps.

BezierRetainedRegion2

A higher-order retained region built from accepted native/algebraic carriers.

BezierRetainedResolvedLinearOverlap2

One resolved overlap span after exact linear-overlap graph refinement.

BezierRetainedSignedAreaRoleReport2

Exact orientation-derived role assignment for native retained Bezier loops.

BezierSplitMaterialization2

Ordered split result for one Bezier segment.

BooleanBoundaryChain

One endpoint-connected directed boundary chain.

BooleanBoundaryChainSet

Endpoint-connected boundary chains.

BooleanBoundaryFragmentSet

Boundary fragments selected by a boolean operation.

BooleanBoundaryLoop

One closed boolean result boundary loop.

BooleanBoundaryLoopSet

Closed boolean boundary loops before material/hole role assignment.

BooleanFragmentClassification

Boolean classification for one source fragment.

BooleanFragmentSelection

Boolean classification for all fragments in a region-pair fragment set.

BulgeVertex2

A point plus the bulge for the outgoing segment.

CertifiedBezierLineFit2

A zero-error line fit recovered from a certified flattened Bezier polyline.

CertifiedBezierLineImage2

A Bezier or conic segment certified to trace exactly one endpoint line segment.

CertifiedBezierLineImageOffset2

Exact offset of a certified Bezier/conic line image.

CertifiedBezierLineOffset2

Exact offset of a certified zero-error line fit.

CertifiedBezierPointFit2

A zero-error point fit recovered from a certified flattened Bezier polyline.

CertifiedBezierPointImage2

A Bezier or conic segment certified to be one exact affine point.

CertifiedBezierPolyline2

A polyline produced by certified Bezier flattening.

CircularArc2

A finite circular arc segment.

CircularArc2Facts

Structural facts for a CircularArc2.

Contour2

A closed sequence of connected native segments.

ContourFragment

One source-contour fragment between adjacent split markers.

ContourFragmentSet

Ordered fragments from a split contour.

ContourIntersectionSet

A normalized set of contour-pair topology events.

ContourOverlapIntersection

A finite overlap event between two contours.

ContourPointIntersection

A point event between two contours.

ContourSplitMap

Per-segment split parameters for a contour.

ContourSplitMarkers

Point-bearing split markers grouped by source contour segment.

ContourUncertainIntersection

An uncertain segment-pair relation.

CubicBezier2

A polynomial cubic Bezier segment with four exact control points.

CurvePolicy

Operation-level policy for curve algorithms.

CurveString2

An ordered sequence of connected native segments.

CurveStringFacts

Structural facts for a curve string or contour segment list.

CurveStringIntersection

One segment-pair event between two curve strings.

DirectedBooleanFragment

A selected fragment with geometry already oriented for result traversal.

EndpointTangent2

Exact first-derivative information at a Bezier endpoint.

FiniteContourImport2

Result of importing a finite closed line ring.

FiniteCurveStringImport2

Result of importing a finite open line string.

FinitePolyline2

Finite f64 polyline emitted from a native curve object.

FiniteProjectionOptions

Options for projecting native curves to finite f64 polylines.

FiniteRegionProfile2

A finite material ring and the finite hole rings owned by it.

FiniteRegionProjection2

Finite f64 projection of a region with material and hole roles retained.

LineArcIntersectionPoint

One point in a line-arc intersection result.

LineSeg2

A finite line segment.

LineSeg2Facts

Structural facts for a LineSeg2.

ParamRange

Parameter range on a segment.

PlanarPcurveImageEqualityReport2

Evidence report for one planar pcurve image-equality predicate.

Point2

A two-dimensional point.

Point2Facts

Structural facts for a Point2.

PolylineReconstructionOptions

Controls reconstruction of line and circular-arc segments from sampled polyline points.

PolynomialBSplineBezierExtraction2

Exact Bezier extraction report for one polynomial B-spline.

PolynomialBSplineCurve2

Exact polynomial B-spline curve in the plane.

PredicatePolicy

Runtime policy for predicate escalation.

PreparedCircularArc2

Prepared sweep and circle classifier for a fixed CircularArc2.

PreparedContourView2

A borrowed contour with cached contour and segment bounding boxes.

PreparedCurveStringView2

A borrowed curve string with cached segment and whole-string bounding boxes.

PreparedLineSeg2

Prepared point-line classifier for a fixed LineSeg2.

PreparedRegionView2

A borrowed region view with cached contour and region bounding boxes.

PreparedRetainedPlanarFace2

Prepared retained planar face for repeated support-surface and UV queries.

QuadraticBezier2

A polynomial quadratic Bezier segment with three exact control points.

Rational

Ratio of two integers

RationalBSplineBezierExtraction2

Exact rational Bezier extraction report for a retained NURBS curve.

RationalBSplineCurve2

Exact rational B-spline/NURBS curve in the plane.

RationalBSplineNativeTopologyReport2

Native-topology audit report for a retained rational B-spline extraction.

RationalBezierAlgebraicPointImage2

Exact algebraic image of a rational quadratic Bezier affine point.

RationalBezierAlgebraicTangentImage2

Exact algebraic image of a rational quadratic Bezier derivative vector.

RationalBezierSpan2

One exact rational Bezier span extracted from a retained NURBS curve.

RationalBezierSpanTopologyReport2

Native-topology audit report for one retained rational Bezier span.

RationalQuadraticBSplineBezierExtraction2

Exact rational Bezier extraction report for one quadratic NURBS curve.

RationalQuadraticBSplineCurve2

Exact quadratic NURBS curve in the plane.

RationalQuadraticBezier2

A rational quadratic Bezier segment with exact control points and weights.

RationalQuadraticBezier2Facts

Structural facts for rational quadratic Bezier/conic segments.

Real

(More) Real numbers

Region2

An owned planar region with explicit material and hole contour bins.

RegionContourFragments

Fragments for one keyed contour in a region-pair query.

RegionContourIntersection

Intersections between two keyed contours from a region-pair query.

RegionContourKey

Identifies one contour inside a region-pair query.

RegionContourProfile

A material contour and the hole contours owned by it.

RegionFacts

Structural facts for a region prepared from material and hole contours.

RegionFragmentSet

Fragment inventory for both regions in a region-pair query.

RegionIntersectionSet

Normalized contour-pair intersections between two regions.

RegionView2

Borrowed view over material and hole contours.

RetainedBSplineSpanFactReport2

Span-local fact report for one B-spline/NURBS extraction.

RetainedBSplineSpanFacts2

Span-local facts produced from B-spline/NURBS Bezier extraction.

RetainedCurveCacheSummary2

Prepared-cache shape summary for a retained curve.

RetainedCurveIdentity2

Stable source identity for a retained curve.

RetainedCurveProfile2

Retained curve profile combining identity, domain, trim, endpoints, and cache facts.

RetainedEndpointEvidence2

Exact endpoint evidence at the active retained domain boundaries.

RetainedImportRecord2

Retained audit record for one imported finite curve carrier.

RetainedParameterDomain1

Exact one-dimensional parameter domain.

RetainedPlanarFace2

Retained planar face assembled from material and hole pcurve trim loops.

RetainedPlanarFaceEdgeUseReport2

Evidence report for a retained planar pcurve edge-use query.

RetainedPlanarFacePointReport2

Evidence report for an exact UV point-in-face query.

RetainedPlanarPcurve2

Open retained pcurve on a planar support surface.

RetainedPlanarSurfaceIdentity2

Opaque identity of a retained planar support surface.

RetainedPlanarTrimLoop2

Closed retained trim-loop pcurve on a planar support surface.

RetainedSourceTolerance2

Absolute/relative tolerance carried from an import source.

RetainedSpanWeightDomainReport2

Nonzero-weight evidence for a retained rational span.

RetainedTrimInterval1

Exact trim interval on a retained curve domain.

Segment2Facts

Structural facts for a native Segment2.

SegmentKindCounts

Counts of native segment families in a prepared object.

SegmentSplitMarker

A local split marker with both ordering parameter and geometric point.

SegmentSplitPoint

A local split parameter on one contour segment.

Similarity2

A 2D affine transform whose linear part is a nonsingular similarity.

SymbolicDependencyMask

Opaque bit mask of symbolic dependencies visible in a Real.

Tolerance

Optional absolute/relative tolerance metadata for edge-preview operations.

Enums

ArcArcIntersection

Intersection between two circular arcs.

Axis2

Coordinate axis used by Bezier monotonicity and bounds predicates.

BezierAlgebraicImageStatus

Status for a Bezier algebraic point or tangent image.

BezierAlgebraicSameTangentOrderStatus

Status for comparing two same-direction algebraic tangent branches with second-order local evidence.

BezierAlgebraicTangentOrderStatus

Status for algebraic tangent-order comparison.

BezierAlgebraicTangentVectorStatus

Status for extracting represented tangent coordinates from an image.

BezierCurveRelation

Coarse certified relation between two polynomial Bezier segments.

BezierCuspClassification

Certified cusp status visible to this exact predicate slice.

BezierDegree

Polynomial Bezier curve degree.

BezierEndpoint

An endpoint of a parametric Bezier segment.

BezierEndpointPointImage2

Exact point image retained at an algebraic split endpoint.

BezierEndpointTangentImage2

Exact tangent image retained at an algebraic split endpoint.

BezierFitBoundKind

Proof status for a Bezier fitting error bound.

BezierFitErrorMetric

Error metric used by a zero-error primitive fit.

BezierInflectionClassification

Certified inflection status for a polynomial Bezier segment.

BezierLineContactKind

Certified contact kind for a represented Bezier/supporting-line root.

BezierLineContactRelation

Supporting-line relation with represented root contact classification.

BezierLineFitRelation

Result of attempting a zero-error line fit.

BezierLineImageFitRelation

Result of attempting to fit the Bezier/conic object itself to a line.

BezierLineRelation

Certified relation between a Bezier segment and an infinite supporting line.

BezierMonotoneGraphContactOrder

Certified order of two Bezier graph curves with represented contact kinds.

BezierMonotoneGraphOrder

Certified order of two Bezier graph curves over one shared monotone axis.

BezierOffsetCandidate2

Result of a staged Bezier/conic offset attempt.

BezierOffsetRisk

Exact source-curve hazard that must be resolved before a Bezier offset is treated as a topology product.

BezierParameter2

Exact Bezier parameter carrier.

BezierPointFitRelation

Result of attempting a zero-error point fit.

BezierPointImageFitRelation

Result of attempting to fit the Bezier/conic object to one point.

BezierRetainedEnvelopeSourceKind

Source class of one retained envelope witness.

BezierRetainedLineOverlapExtent2

Certified extent class for a retained line-image overlap.

BezierRetainedOverlapOrientation2

Orientation of two refined fragments that carry the same overlap image.

BezierRetainedOverlapRelation2

Exact positive-dimensional overlap relation between two arrangement fragments.

BezierRetainedRegionLoopRole

Material/hole role assigned to one retained Bezier boundary loop.

BezierSplitFragment2

One fragment between adjacent split boundaries.

BezierSubcurve2

A native Bezier subcurve produced by exact split materialization.

BezierTangentTurnOrdering2

Certified turn ordering for two candidate tangents around a base tangent.

BooleanFragmentAction

How a classified source fragment participates in a boolean result.

BooleanOp

Boolean operation requested between two regions.

CircleCircleRelation

Relation between two full circles supporting circular arcs.

Classification

Result of a classification step.

ContourIntersection

One normalized contour-pair topology event.

ContourOperand

Which side of a contour-pair event to inspect.

ContourPointLocation

Point location relative to a closed contour.

CurveError

Errors returned by curve constructors and early topology scaffolding.

FillRule

Fill rule used when classifying contour interiors.

IntersectionKind

Local intersection kind.

LineArcIntersection

Intersection between a line segment and a circular arc.

LineArcOrder

Operand order for a line-arc segment intersection.

LineCircleRelation

Relation between an oriented supporting line and a full circle.

LineLineIntersection

Intersection between two line segments.

LineSide

Side of an oriented line.

NumericMode

Runtime numeric mode for whole curve operations.

OffsetCap

Endpoint cap style for checked open curve-string outlines.

PlanarPcurveImageRelation2

Exact image relation between two retained planar pcurves.

PreparedSegment2

Prepared exact-predicate handle for a native segment.

RationalQuadraticConicKind

Coarse conic family represented by a rational quadratic Bezier segment.

RealSign

Exact sign knowledge exposed by structural inspection.

RegionContourRole

Semantic role of a contour inside a region.

RegionPointLocation

Point location relative to a planar region.

RegionSide

Which region side a contour key belongs to.

RetainedCurveFamily2

Curve family carried by retained curve metadata.

RetainedCurvePeriodicity1

Periodicity evidence for a retained curve.

RetainedImportFormat2

Source family for a lossy retained curve import record.

RetainedImportTopology2

Source topology for a lossy retained curve import record.

RetainedPlanarFaceEdgeUseRelation2

Exact edge-use agreement between a retained planar pcurve and face trims.

RetainedPlanarFacePointLocation2

Point classification result for a retained planar face.

RetainedPlanarTrimLoopRole2

Role of the retained trim loop that owns a matched pcurve edge-use.

RetainedSpanAxisMonotonicity

Certified or retained monotonicity evidence for one extracted spline span.

RetainedTopologyStatus

Topology-readiness status for a retained curve or span.

RetainedTrimDirection

Direction of a trim interval relative to its parameter domain.

Segment2

A native line or circular-arc segment.

SegmentIntersection

Intersection between two native segments.

SegmentKind

Segment primitive family.

UncertaintyReason

Reason an operation could not decide a topology branch.

ZeroStatus

Whether structural inspection can prove zero or nonzero status.

Functions

compare_algebraic_same_tangent_second_order

Compares same-direction algebraic tangent branches by second-order evidence.

compare_algebraic_same_tangent_third_order

Compares same-direction algebraic tangent branches by third-order evidence.

compare_algebraic_tangent_turn_from_base

Compares two candidate tangent turns from a base tangent.

finite_polyline_vertex_centroid

Returns the arithmetic centroid of finite polyline vertices.

finite_ring_signed_area

Returns the finite signed shoelace area of projected ring vertices.

triangulate_finite_rings

Triangulates a finite material ring with owned finite hole rings.

try_finite_polyline_vertex_centroid

Returns the checked arithmetic centroid of finite polyline vertices.

try_finite_ring_signed_area

Returns the checked finite signed shoelace area of projected ring vertices.

Type Aliases

CurveResult

Result alias used by hypercurve.

FiniteTriangle2

A finite triangle emitted from a projected region profile.