# Geometry Helpers *API Collection* ## Topics ### Rounding and Grid - [`GSUnitVector`](/Core/GlyphsCore/GSUnitVector) - [`GSCross`](/Core/GlyphsCore/GSCross) - [`GSRoundHandle`](/Core/GlyphsCore/GSRoundHandle) - [`GSRoundGrid`](/Core/GlyphsCore/GSRoundGrid) - [`GSRoundPoint`](/Core/GlyphsCore/GSRoundPoint) - [`GSRoundPointToDirection`](/Core/GlyphsCore/GSRoundPointToDirection) - [`GSRoundPointToLine`](/Core/GlyphsCore/GSRoundPointToLine) - [`GSRoundPointGrid`](/Core/GlyphsCore/GSRoundPointGrid) - [`GSRoundPointGridSetting`](/Core/GlyphsCore/GSRoundPointGridSetting) - [`GSRoundPointGridSettingMax`](/Core/GlyphsCore/GSRoundPointGridSettingMax) - [`GSRoundSize`](/Core/GlyphsCore/GSRoundSize) - [`GSRoundRectGrid`](/Core/GlyphsCore/GSRoundRectGrid) - [`GSRoundRect`](/Core/GlyphsCore/GSRoundRect) ### Point, Size, and Rect Utilities - [`GSMaxPoint`](/Core/GlyphsCore/GSMaxPoint) - [`GSMinPoint`](/Core/GlyphsCore/GSMinPoint) - [`GSScaleRect`](/Core/GlyphsCore/GSScaleRect) - [`GSScaleRectAroundPoint`](/Core/GlyphsCore/GSScaleRectAroundPoint) - [`GSCenteredRectInRect`](/Core/GlyphsCore/GSCenteredRectInRect) - [`GSValidateRect`](/Core/GlyphsCore/GSValidateRect) - [`GSValidateRange`](/Core/GlyphsCore/GSValidateRange) - [`GSScaleSize`](/Core/GlyphsCore/GSScaleSize) - [`GSScalePoint`](/Core/GlyphsCore/GSScalePoint) - [`GSAddPoints`](/Core/GlyphsCore/GSAddPoints) - [`GSSubtractPoints`](/Core/GlyphsCore/GSSubtractPoints) - [`GSFlipUnitPoint`](/Core/GlyphsCore/GSFlipUnitPoint) - [`GSInterpolatePoints`](/Core/GlyphsCore/GSInterpolatePoints) - [`GSAbsolutePointInRect`](/Core/GlyphsCore/GSAbsolutePointInRect) - [`GSRelativePointInRect`](/Core/GlyphsCore/GSRelativePointInRect) ### Vectors and Distances - [`GSUnitVectorFromTo`](/Core/GlyphsCore/GSUnitVectorFromTo) - [`GSUnitVectorFromAngle`](/Core/GlyphsCore/GSUnitVectorFromAngle) - [`GSNormalVector1`](/Core/GlyphsCore/GSNormalVector1) - [`GSNormalVector2`](/Core/GlyphsCore/GSNormalVector2) - [`GSSkewVectorRelativeToItself`](/Core/GlyphsCore/GSSkewVectorRelativeToItself) - [`GSSquareDistance`](/Core/GlyphsCore/GSSquareDistance) - [`GSDistance`](/Core/GlyphsCore/GSDistance) - [`GSLengthOfVector`](/Core/GlyphsCore/GSLengthOfVector) - [`GSDistanceN`](/Core/GlyphsCore/GSDistanceN) ### Angles and Slopes - [`GSNormalizeAngleRAD`](/Core/GlyphsCore/GSNormalizeAngleRAD) — Returns a value in the interval [0, 2π). - [`GSNormalizeAngleDEG`](/Core/GlyphsCore/GSNormalizeAngleDEG) — Returns a value in the interval [0, 360). - [`GSNormalizeAngleDirection`](/Core/GlyphsCore/GSNormalizeAngleDirection) — Returns a version of the angle that matches the given direction. - [`GSSlope`](/Core/GlyphsCore/GSSlope) ### Rect Geometry - [`GSRectFromTwoPoints`](/Core/GlyphsCore/GSRectFromTwoPoints) - [`GSRectFromFourPoints`](/Core/GlyphsCore/GSRectFromFourPoints) — Returns the bounds of the given four points. - [`GSRectInsetWithEdgeInsets`](/Core/GlyphsCore/GSRectInsetWithEdgeInsets) ### General Geometry - [`GSAngleOfVector`](/Core/GlyphsCore/GSAngleOfVector) - [`GSAngleBetweenVectors`](/Core/GlyphsCore/GSAngleBetweenVectors) - [`GSSlantPointAroundY`](/Core/GlyphsCore/GSSlantPointAroundY) - [`GSCircleSegmentFromPointsAndTangents`](/Core/GlyphsCore/GSCircleSegmentFromPointsAndTangents) - [`GSOffsetLine`](/Core/GlyphsCore/GSOffsetLine) - [`GSDot`](/Core/GlyphsCore/GSDot) - [`GSClamp`](/Core/GlyphsCore/GSClamp) - [`GSAreaOfTriangle`](/Core/GlyphsCore/GSAreaOfTriangle) - [`GSPointIsLeftOfLine`](/Core/GlyphsCore/GSPointIsLeftOfLine) - [`GSLeftRayHitsLine`](/Core/GlyphsCore/GSLeftRayHitsLine) - [`GSLeftRayHitsSegment`](/Core/GlyphsCore/GSLeftRayHitsSegment) - [`GSLeftRayHitsCubic`](/Core/GlyphsCore/GSLeftRayHitsCubic) - [`GSLeftRayHitsQuadraticSpline`](/Core/GlyphsCore/GSLeftRayHitsQuadraticSpline) - [`GSMiddlePointLine`](/Core/GlyphsCore/GSMiddlePointLine) - [`GSMiddlePointCubic`](/Core/GlyphsCore/GSMiddlePointCubic) - [`GSCheckColinearLines`](/Core/GlyphsCore/GSCheckColinearLines) ### Intersections - [`GSIntersectCubicCubicPoints`](/Core/GlyphsCore/GSIntersectCubicCubicPoints) - [`GSIntersectCubicCubicPointsA`](/Core/GlyphsCore/GSIntersectCubicCubicPointsA) - [`GSIntersectCubicCubicUnlimited`](/Core/GlyphsCore/GSIntersectCubicCubicUnlimited) - [`GSIntersectCubicCubicUnlimitedA`](/Core/GlyphsCore/GSIntersectCubicCubicUnlimitedA) - [`GSIntersectCubicLine`](/Core/GlyphsCore/GSIntersectCubicLine) — Finds all intersections between a curve and a line. - [`GSIntersectCubicLineA`](/Core/GlyphsCore/GSIntersectCubicLineA) - [`GSIntersectCubicLineTimes`](/Core/GlyphsCore/GSIntersectCubicLineTimes) - [`GSIntersectCubicLineUnlimited`](/Core/GlyphsCore/GSIntersectCubicLineUnlimited) - [`GSIntersectCubicLineUnlimitedA`](/Core/GlyphsCore/GSIntersectCubicLineUnlimitedA) - [`GSIntersectCubicLineUnlimitedTimes`](/Core/GlyphsCore/GSIntersectCubicLineUnlimitedTimes) - [`GSIntersectQuadraticSplineLine`](/Core/GlyphsCore/GSIntersectQuadraticSplineLine) - [`GSIntersectQuadraticSplineLineA`](/Core/GlyphsCore/GSIntersectQuadraticSplineLineA) - [`GSIntersectQuadraticLineMatchEndA`](/Core/GlyphsCore/GSIntersectQuadraticLineMatchEndA) - [`GSIntersectQuadraticLine`](/Core/GlyphsCore/GSIntersectQuadraticLine) - [`GSIntersectQuadraticQuadraticSpline`](/Core/GlyphsCore/GSIntersectQuadraticQuadraticSpline) - [`GSIntersectQuadraticQuadraticSplineA`](/Core/GlyphsCore/GSIntersectQuadraticQuadraticSplineA) - [`GSIntersectCubicQuadraticSpline`](/Core/GlyphsCore/GSIntersectCubicQuadraticSpline) - [`GSIntersectCubicQuadraticSplineA`](/Core/GlyphsCore/GSIntersectCubicQuadraticSplineA) - [`GSPointOnQuadraticSpline`](/Core/GlyphsCore/GSPointOnQuadraticSpline) - [`GSCollinearLines`](/Core/GlyphsCore/GSCollinearLines) - [`GSIntersectLineLine`](/Core/GlyphsCore/GSIntersectLineLine) - [`GSIntersectLineLineUnlimited`](/Core/GlyphsCore/GSIntersectLineLineUnlimited) - [`GSIntersectRays`](/Core/GlyphsCore/GSIntersectRays) - [`GSIntersectLineWithRect`](/Core/GlyphsCore/GSIntersectLineWithRect) - [`GSClipLineWithRect`](/Core/GlyphsCore/GSClipLineWithRect) - [`GSCircleContainsRect`](/Core/GlyphsCore/GSCircleContainsRect) - [`GSIntersectCircles`](/Core/GlyphsCore/GSIntersectCircles) ### Nearest Points and Distances - [`GSNearestPointOnCubicSegmentBounds`](/Core/GlyphsCore/GSNearestPointOnCubicSegmentBounds) - [`GSNearestPointOnCubicSegment`](/Core/GlyphsCore/GSNearestPointOnCubicSegment) - [`GSNearestPointOnQuarticSegment`](/Core/GlyphsCore/GSNearestPointOnQuarticSegment) - [`GSNearestPointOnQuartic`](/Core/GlyphsCore/GSNearestPointOnQuartic) - [`GSNearestPointOnQuadraticPoints`](/Core/GlyphsCore/GSNearestPointOnQuadraticPoints) - [`GSDistanceOfPointFromCurve`](/Core/GlyphsCore/GSDistanceOfPointFromCurve) - [`GSSquareDistanceOfPointFromCurveSegment`](/Core/GlyphsCore/GSSquareDistanceOfPointFromCurveSegment) - [`GSDistanceOfPointFromLineSegment`](/Core/GlyphsCore/GSDistanceOfPointFromLineSegment) - [`GSDistanceOfPointFromLine`](/Core/GlyphsCore/GSDistanceOfPointFromLine) - [`GSNearestPointOnCubic`](/Core/GlyphsCore/GSNearestPointOnCubic) - [`GSNearestPointOnQuadraticSpline`](/Core/GlyphsCore/GSNearestPointOnQuadraticSpline) - [`GSNearestPointOnLinePoints`](/Core/GlyphsCore/GSNearestPointOnLinePoints) - [`GSNearestPointOnLineUnlimited`](/Core/GlyphsCore/GSNearestPointOnLineUnlimited) - [`GSDividCubicPointsAtDistance`](/Core/GlyphsCore/GSDividCubicPointsAtDistance) ### Curve Parameters and Solvers - [`GSCalcCubicParameters`](/Core/GlyphsCore/GSCalcCubicParameters) - [`GSCalcQuadraticParameters`](/Core/GlyphsCore/GSCalcQuadraticParameters) - [`GSSolveQuadratic`](/Core/GlyphsCore/GSSolveQuadratic) - [`GSSolveCubic`](/Core/GlyphsCore/GSSolveCubic) - [`GSDividLineAtDistance`](/Core/GlyphsCore/GSDividLineAtDistance) - [`GSExtendCurvePoints`](/Core/GlyphsCore/GSExtendCurvePoints) - [`GSFitCurveToOriginPoints`](/Core/GlyphsCore/GSFitCurveToOriginPoints) - [`GSFitCurveToOriginPointsDirection`](/Core/GlyphsCore/GSFitCurveToOriginPointsDirection) - [`GSCurveIsFlat`](/Core/GlyphsCore/GSCurveIsFlat) - [`GSCurveIsFlatError`](/Core/GlyphsCore/GSCurveIsFlatError) ### Curve Subdivision and Conversion - [`GSHalveCubicPoints`](/Core/GlyphsCore/GSHalveCubicPoints) - [`GSHalveCubicSegment`](/Core/GlyphsCore/GSHalveCubicSegment) - [`GSHalveQuadraticPoints`](/Core/GlyphsCore/GSHalveQuadraticPoints) - [`GSHalveQuadraticSegment`](/Core/GlyphsCore/GSHalveQuadraticSegment) - [`GSQuadratic2Cubic`](/Core/GlyphsCore/GSQuadratic2Cubic) - [`GSDividQuadraticPoints`](/Core/GlyphsCore/GSDividQuadraticPoints) - [`GSDividQuadraticSpline`](/Core/GlyphsCore/GSDividQuadraticSpline) - [`GSDividCubicPoints`](/Core/GlyphsCore/GSDividCubicPoints) - [`GSDividCubicPointsTs`](/Core/GlyphsCore/GSDividCubicPointsTs) - [`GSDividCubicSegment`](/Core/GlyphsCore/GSDividCubicSegment) - [`GSDividQuarticSegment`](/Core/GlyphsCore/GSDividQuarticSegment) - [`GSApproximateQuartic`](/Core/GlyphsCore/GSApproximateQuartic) - [`GSQuarticToCubic`](/Core/GlyphsCore/GSQuarticToCubic) — Converts from a quartic curve segment to two cubic curve segments. - [`GSSegmentBetweenPoints`](/Core/GlyphsCore/GSSegmentBetweenPoints) ### Curve Evaluation and Tangents - [`GSPointOnLine`](/Core/GlyphsCore/GSPointOnLine) - [`GSPointOffsetFromLine`](/Core/GlyphsCore/GSPointOffsetFromLine) — Like `GSPointOnLine`, but with the returned point offset by a certain amount onto a parallel line. So, more like the inverse of `GSNearestPointOnLine`. - [`GSPointOffsetAtAngle`](/Core/GlyphsCore/GSPointOffsetAtAngle) — Returns a new point offset by the given distance in the direction of the given angle in radiants. - [`GSPointAtTime`](/Core/GlyphsCore/GSPointAtTime) - [`GSPointOnCubicPoints`](/Core/GlyphsCore/GSPointOnCubicPoints) - [`GSPointOnCubicSegment`](/Core/GlyphsCore/GSPointOnCubicSegment) - [`GSPointOnQuarticPoints`](/Core/GlyphsCore/GSPointOnQuarticPoints) - [`GSPointOnQuarticSegment`](/Core/GlyphsCore/GSPointOnQuarticSegment) - [`GSPointOnQuadraticPoints`](/Core/GlyphsCore/GSPointOnQuadraticPoints) - [`GSTangentOnQuadraticPoints`](/Core/GlyphsCore/GSTangentOnQuadraticPoints) - [`GSTangentOnQuadraticSegment`](/Core/GlyphsCore/GSTangentOnQuadraticSegment) - [`GSTangentOnCubicSegment`](/Core/GlyphsCore/GSTangentOnCubicSegment) - [`GSTangentOnCubicPoints`](/Core/GlyphsCore/GSTangentOnCubicPoints) - [`GSTangentOnQuadraticThroughPoint`](/Core/GlyphsCore/GSTangentOnQuadraticThroughPoint) ### Lengths, Extrema, and Bounds - [`GSLengthOfCubicPoints`](/Core/GlyphsCore/GSLengthOfCubicPoints) - [`GSLengthOfQuadraticSpline`](/Core/GlyphsCore/GSLengthOfQuadraticSpline) - [`GSTForDistanceCubic`](/Core/GlyphsCore/GSTForDistanceCubic) - [`GSTForDistanceQuadraticSpline`](/Core/GlyphsCore/GSTForDistanceQuadraticSpline) - [`GSExtremeTimesOfCubicUnlimited`](/Core/GlyphsCore/GSExtremeTimesOfCubicUnlimited) - [`GSExtremeTimesOfCubic`](/Core/GlyphsCore/GSExtremeTimesOfCubic) - [`GSExtremePointsOfCubic`](/Core/GlyphsCore/GSExtremePointsOfCubic) - [`GSExtremesOfCubic`](/Core/GlyphsCore/GSExtremesOfCubic) - [`GSTangentPointsAtAngel`](/Core/GlyphsCore/GSTangentPointsAtAngel) - [`GSBoundsOfQuadratic`](/Core/GlyphsCore/GSBoundsOfQuadratic) - [`GSBoundsOfQuadraticSpline`](/Core/GlyphsCore/GSBoundsOfQuadraticSpline) - [`GSBoundsOfCubic`](/Core/GlyphsCore/GSBoundsOfCubic) - [`GSBoundingRectOfCubic`](/Core/GlyphsCore/GSBoundingRectOfCubic) - [`GSBoundsOfQuartic`](/Core/GlyphsCore/GSBoundsOfQuartic) - [`GSBoundingRectOfQuadratic`](/Core/GlyphsCore/GSBoundingRectOfQuadratic) - [`GSBoundsOfTransformedRect`](/Core/GlyphsCore/GSBoundsOfTransformedRect) ### Inflections, Curvature, and Normals - [`GSCubicHasInflection`](/Core/GlyphsCore/GSCubicHasInflection) - [`GSComputeInflection`](/Core/GlyphsCore/GSComputeInflection) - [`GSComputeInflectionTimes`](/Core/GlyphsCore/GSComputeInflectionTimes) - [`GSComputeInflectionTimesTolerance`](/Core/GlyphsCore/GSComputeInflectionTimesTolerance) - [`GSTransformComponents`](/Core/GlyphsCore/GSTransformComponents) - [`curvatureMaxima`](/Core/GlyphsCore/curvatureMaxima) - [`GSCurvatureSquaredForT`](/Core/GlyphsCore/GSCurvatureSquaredForT) - [`GSSignedCurvatureForT`](/Core/GlyphsCore/GSSignedCurvatureForT) — Use this function as compared to `curvatureSquaredForT` if you compute the square root of the result anyway or if you need to know the sign of the curvature. - [`GSNormalCubicForT`](/Core/GlyphsCore/GSNormalCubicForT) - [`GSNormalQuadraticForT`](/Core/GlyphsCore/GSNormalQuadraticForT) ### Curve Repair and Combination - [`GSCombineSegments3`](/Core/GlyphsCore/GSCombineSegments3) - [`GSCombineSegments3Fit`](/Core/GlyphsCore/GSCombineSegments3Fit) - [`GSFixDeadCurve`](/Core/GlyphsCore/GSFixDeadCurve) - [`GSNormalizeCubicHandleRatios`](/Core/GlyphsCore/GSNormalizeCubicHandleRatios) - [`GSGetOptimalSplitParameter`](/Core/GlyphsCore/GSGetOptimalSplitParameter) - [`GSShiftPointAlongLine`](/Core/GlyphsCore/GSShiftPointAlongLine) - [`GSFixBounds`](/Core/GlyphsCore/GSFixBounds) ### N-Dimensional Vectors - [`GSMakeNVector`](/Core/GlyphsCore/GSMakeNVector) - [`GSInitNVector`](/Core/GlyphsCore/GSInitNVector) - [`GSDistanceOfPointFromLineN`](/Core/GlyphsCore/GSDistanceOfPointFromLineN) - [`GSMultiplyNVectors`](/Core/GlyphsCore/GSMultiplyNVectors) ### Comparison and Sorting - [`GSSortPointValue`](/Core/GlyphsCore/GSSortPointValue) - [`GSSortPoint`](/Core/GlyphsCore/GSSortPoint) - [`GSSortInteger`](/Core/GlyphsCore/GSSortInteger) - [`GSSortFloat`](/Core/GlyphsCore/GSSortFloat) - [`GSSortFloatLenient`](/Core/GlyphsCore/GSSortFloatLenient) - [`GSComparePoint`](/Core/GlyphsCore/GSComparePoint) - [`GSCompareSize`](/Core/GlyphsCore/GSCompareSize) - [`GSCompareTransformStruct`](/Core/GlyphsCore/GSCompareTransformStruct) - [`GSAffineTransformIsIdentity`](/Core/GlyphsCore/GSAffineTransformIsIdentity) - [`GSCompareRect`](/Core/GlyphsCore/GSCompareRect) - [`GSCompareRange`](/Core/GlyphsCore/GSCompareRange) ### Numeric Conversion and Rotation - [`GSFloatToFraction`](/Core/GlyphsCore/GSFloatToFraction) - [`GSAngleToSlope`](/Core/GlyphsCore/GSAngleToSlope) — convert and angle (CCV from 12 o’clock) to run/rise as stored in the hhea table - [`GSAngleFromString`](/Core/GlyphsCore/GSAngleFromString) — The angle of run/rise. This can be used to write the italic angle so the angle is positive CCV from 12 o’clock - [`GSRotatePointAroundCenter`](/Core/GlyphsCore/GSRotatePointAroundCenter) - [`GSRotatePoint`](/Core/GlyphsCore/GSRotatePoint) ### Ellipse and Rect Proximity - [`GSNearestPointOnEllipse`](/Core/GlyphsCore/GSNearestPointOnEllipse) - [`GSDistanceOfPointFromEllipse`](/Core/GlyphsCore/GSDistanceOfPointFromEllipse) - [`GSNearestPointOnRect`](/Core/GlyphsCore/GSNearestPointOnRect) - [`GSDistanceOfPointFromRect`](/Core/GlyphsCore/GSDistanceOfPointFromRect) ### Clothoids - [`GSMakeClothoid`](/Core/GlyphsCore/GSMakeClothoid) - [`GSMakeClothoidSymmetric`](/Core/GlyphsCore/GSMakeClothoidSymmetric) ### String Conversion - [`GSStringFromPoint`](/Core/GlyphsCore/GSStringFromPoint) - [`GSStringFromRect`](/Core/GlyphsCore/GSStringFromRect) - [`GSStringFromPoint3`](/Core/GlyphsCore/GSStringFromPoint3) - [`GSStringFromTransformStruct`](/Core/GlyphsCore/GSStringFromTransformStruct) - [`GSAffineSolver`](/Core/GlyphsCore/GSAffineSolver) ### Rect Alignment and Handles - [`GSRectWithCenter`](/Core/GlyphsCore/GSRectWithCenter) - [`GSHandleRect`](/Core/GlyphsCore/GSHandleRect) - [`GSMirrorAlignment`](/Core/GlyphsCore/GSMirrorAlignment) - [`GSAlignedPointForBounds`](/Core/GlyphsCore/GSAlignedPointForBounds) - [`GSHandleRectForBounds`](/Core/GlyphsCore/GSHandleRectForBounds) ### Point3 - [`GSMakePoint3`](/Core/GlyphsCore/GSMakePoint3) - [`GSRotatePoint3`](/Core/GlyphsCore/GSRotatePoint3) - [`GSRotatePoint3Center`](/Core/GlyphsCore/GSRotatePoint3Center) - [`GSCalc`](/Core/GlyphsCore/GSCalc) - [`GSPointFromArray`](/Core/GlyphsCore/GSPointFromArray) ### Miscellaneous Math and Transforms - [`GSFindDivisorClosestTo`](/Core/GlyphsCore/GSFindDivisorClosestTo) - [`GSAffineTransformMappingLine2Line`](/Core/GlyphsCore/GSAffineTransformMappingLine2Line) - [`GSColinearLines`](/Core/GlyphsCore/GSColinearLines) - [`GSColinearLinesTolerance`](/Core/GlyphsCore/GSColinearLinesTolerance) - [`GSGreenHarmony`](/Core/GlyphsCore/GSGreenHarmony)