@ue-too/curve / index / BCurve

Class: BCurve

Defined in: packages/curve/src/b-curve.ts:134

Bezier curve class supporting quadratic (3 points) and cubic (4 points) curves.

Remarks

BCurve provides a comprehensive implementation of Bezier curves with:

Curve evaluation at any parameter t (0 to 1)
Arc-length calculation with caching for performance
Curve splitting and subdivision
Geometric queries (projection, intersection, extrema)
Advanced operations (offset, arc fitting, curvature)

Performance Optimizations

Optimized formulas for quadratic and cubic curves
Arc-length caching to avoid recomputation
Lazy computation of lookup tables (LUT)
Gauss-Legendre quadrature for arc-length calculation

Coordinate System

Parameter t ranges from 0 (start) to 1 (end)
Points use {x, y} coordinates
Supports 2D curves (z-coordinate optional but not used)

Example

Create and evaluate a cubic Bezier curve

typescript

const curve = new BCurve([
  { x: 0, y: 0 },     // Start point
  { x: 33, y: 100 },  // Control point 1
  { x: 66, y: 100 },  // Control point 2
  { x: 100, y: 0 }    // End point
]);

// Evaluate at different positions
const start = curve.get(0);    // { x: 0, y: 0 }
const mid = curve.get(0.5);    // Midpoint
const end = curve.get(1);      // { x: 100, y: 0 }

// Get curve length
console.log('Length:', curve.fullLength);

// Get derivative (tangent vector)
const tangent = curve.derivative(0.5);

Constructors

Constructor

new BCurve(controlPoints): BCurve

Defined in: packages/curve/src/b-curve.ts:171

Parameters

controlPoints

Point[]

Returns

BCurve

Accessors

AABB

Get Signature

get AABB(): object

Defined in: packages/curve/src/b-curve.ts:1469

Returns

object

max

max: Point

min

min: Point

fullLength

Get Signature

get fullLength(): number

Defined in: packages/curve/src/b-curve.ts:423

Returns

number

Methods

advanceAtTWithLength()

advanceAtTWithLength(tVal, length): AdvanceAtTWithLengthRes

Defined in: packages/curve/src/b-curve.ts:1218

Parameters

tVal

number

length

number

Returns

AdvanceAtTWithLengthRes

advanceByDistance()

advanceByDistance(startT, distance): AdvanceAtTWithLengthRes

Defined in: packages/curve/src/b-curve.ts:1306

Parameters

startT

number

distance

number

Returns

AdvanceAtTWithLengthRes

compute()

compute(tVal): Point

Defined in: packages/curve/src/b-curve.ts:327

Parameters

tVal

number

Returns

Point

curvature()

curvature(tVal): number

Defined in: packages/curve/src/b-curve.ts:937

Parameters

tVal

number

Returns

number

derivative()

derivative(tVal): Point

Defined in: packages/curve/src/b-curve.ts:459

Parameters

tVal

number

Returns

Point

derivativeByPercentage()

derivativeByPercentage(percentage): Point

Defined in: packages/curve/src/b-curve.ts:236

Gets the derivative (tangent vector) at a given percentage of the curve length.

Parameters

percentage

number

Percentage of the curve length (0 to 1), where 0 is the start and 1 is the end

Returns

Point

The derivative vector at the specified percentage along the curve

Remarks

This method calculates the derivative at a point specified by percentage of arc length, not by the parameter t. This is useful when you want to sample the curve uniformly by distance rather than by parameter value.

Example

typescript

const curve = new BCurve([...]);
const tangent = curve.derivativeByPercentage(0.5); // Derivative at midpoint
const normalized = PointCal.unitVector(tangent); // Normalize for direction

derivativeNormalized()

derivativeNormalized(tVal): Point

Defined in: packages/curve/src/b-curve.ts:463

Parameters

tVal

number

Returns

Point

determinant3by3()

determinant3by3(matrix): number

Defined in: packages/curve/src/b-curve.ts:924

Parameters

matrix

number[][]

Returns

number

findArcs()

findArcs(errorThreshold): object[]

Defined in: packages/curve/src/b-curve.ts:737

Parameters

errorThreshold

number

Returns

object[]

findArcStartingAt()

findArcStartingAt(errorThreshold, low): { arc?: { center: Point; endPoint: Point; endT: number; radius: number; startPoint: Point; startT: number; }; good: boolean; } | null

Defined in: packages/curve/src/b-curve.ts:772

Parameters

errorThreshold

number

low

number

Returns

{ arc?: { center: Point; endPoint: Point; endT: number; radius: number; startPoint: Point; startT: number; }; good: boolean; } | null

findClosest()

findClosest(x, y, LUT, circleRadius, distanceEpsilon, pd2?, pd1?): number

Defined in: packages/curve/src/b-curve.ts:1415

Parameters

x

number

y

number

LUT

object[]

circleRadius

number

distanceEpsilon

number = 5

pd2?

number

pd1?

number

Returns

number

fitArc()

fitArc(startPoint, endPoint, midPoint): object

Defined in: packages/curve/src/b-curve.ts:851

Parameters

Returns

object

center?

optional center: Point

endPoint?

optional endPoint: Point

exists

exists: boolean

radius?

optional radius: number

startPoint?

optional startPoint: Point

get()

get(tVal): Point

Defined in: packages/curve/src/b-curve.ts:343

Parameters

tVal

number

Returns

Point

getArcLengthLUT()

getArcLengthLUT(steps): object

Defined in: packages/curve/src/b-curve.ts:469

Parameters

steps

number = 50

Returns

object

arcLengthLUT

arcLengthLUT: object[]

controlPoints

controlPoints: Point[]

getArcs()

getArcs(errorThreshold): object[]

Defined in: packages/curve/src/b-curve.ts:768

Get a sequence of circular arcs that approximate the curve.

Parameters

errorThreshold

number

Maximum allowed radial error when fitting an arc.

Returns

object[]

A list of arcs that cover the curve from (t=0) to (t=1).

getCacheStats()

getCacheStats(): object

Defined in: packages/curve/src/b-curve.ts:149

Gets cache statistics for performance monitoring

Returns

object

Object containing cache size and hit rate information

hitRate

hitRate: number

size

size: number

getCircleIntersections()

getCircleIntersections(circleCenter, circleRadius): object[]

Defined in: packages/curve/src/b-curve.ts:1161

Parameters

circleCenter

Point

circleRadius

number

Returns

object[]

getCoefficientOfTTerms()

getCoefficientOfTTerms(): Point[]

Defined in: packages/curve/src/b-curve.ts:961

Returns

Point[]

getCoefficientOfTTermsWithControlPoints()

getCoefficientOfTTermsWithControlPoints(controlPoints): Point[]

Defined in: packages/curve/src/b-curve.ts:971

Parameters

controlPoints

Point[]

Returns

Point[]

getControlPoints()

getControlPoints(): Point[]

Defined in: packages/curve/src/b-curve.ts:297

Returns

Point[]

getControlPointsAlignedWithXAxis()

getControlPointsAlignedWithXAxis(): object[]

Defined in: packages/curve/src/b-curve.ts:1013

Returns

object[]

getCurveIntersections()

getCurveIntersections(curve, deduplicationTolerance?): object[]

Defined in: packages/curve/src/b-curve.ts:1458

Parameters

curve

BCurve

deduplicationTolerance?

number

Returns

object[]

getDerivativeCoefficients()

getDerivativeCoefficients(): Point[]

Defined in: packages/curve/src/b-curve.ts:965

Returns

Point[]

getDerivativeControlPoints()

getDerivativeControlPoints(controlPoints): Point[]

Defined in: packages/curve/src/b-curve.ts:273

Parameters

controlPoints

Point[]

Returns

Point[]

getExtrema()

getExtrema(): object

Defined in: packages/curve/src/b-curve.ts:1032

Returns

object

x

x: number[]

y

y: number[]

getLineIntersections()

getLineIntersections(line): number[]

Defined in: packages/curve/src/b-curve.ts:1116

Parameters

line

Line

Returns

number[]

getLUT()

getLUT(steps): Point[]

Defined in: packages/curve/src/b-curve.ts:390

Parameters

steps

number = 100

Returns

Point[]

getLUTWithTVal()

getLUTWithTVal(steps?): object[]

Defined in: packages/curve/src/b-curve.ts:405

Parameters

steps?

number

Returns

object[]

getPointbyPercentage()

getPointbyPercentage(percentage): Point

Defined in: packages/curve/src/b-curve.ts:182

Parameters

percentage

number

Returns

Point

getProjection()

getProjection(point): object

Defined in: packages/curve/src/b-curve.ts:666

Parameters

point

Point

Returns

object

projection

projection: Point = preliminaryProjectionPoint

tVal

tVal: number = preliminaryProjectionTVal

getSelfIntersections()

getSelfIntersections(): object[]

Defined in: packages/curve/src/b-curve.ts:1147

Returns

object[]

lengthAtT()

lengthAtT(tVal): number

Defined in: packages/curve/src/b-curve.ts:431

Parameters

tVal

number

Returns

number

normal()

normal(tVal): object

Defined in: packages/curve/src/b-curve.ts:1491

Parameters

tVal

number

Returns

object

direction

direction: Point

tVal

tVal: number

preWarmCache()

preWarmCache(steps): void

Defined in: packages/curve/src/b-curve.ts:160

Pre-warms the cache with commonly used t values for better performance

Parameters

steps

number = 100

Number of steps to pre-cache (default: 100)

Returns

void

refineBinary()

refineBinary(curve, x, y, LUT, i, targetDistance, epsilon): { distance: number; point: Point; tVal: number; } | undefined

Defined in: packages/curve/src/b-curve.ts:1354

Parameters

curve

BCurve

x

number

y

number

LUT

object[]

i

number

targetDistance

number = 0

epsilon

number = 0.01

Returns

{ distance: number; point: Point; tVal: number; } | undefined

secondDerivative()

secondDerivative(tVal): Point

Defined in: packages/curve/src/b-curve.ts:954

Parameters

tVal

number

Returns

Point

setControlPointAtIndex()

setControlPointAtIndex(index, newPoint): boolean

Defined in: packages/curve/src/b-curve.ts:312

Parameters

index

number

newPoint

Point

Returns

boolean

setControlPoints()

setControlPoints(controlPoints): void

Defined in: packages/curve/src/b-curve.ts:301

Parameters

controlPoints

Point[]

Returns

void

split()

split(tVal): [Point[], Point[]]

Defined in: packages/curve/src/b-curve.ts:507

Parameters

tVal

number

Returns

[Point[], Point[]]

splitAndTakeMidCurve()

splitAndTakeMidCurve(tVal, tVal2): BCurve

Defined in: packages/curve/src/b-curve.ts:658

Parameters

tVal

number

tVal2

number

Returns

BCurve

splitIn3Curves()

splitIn3Curves(tVal, tVal2): [BCurve, BCurve, BCurve]

Defined in: packages/curve/src/b-curve.ts:638

Parameters

tVal

number

tVal2

number

Returns

[BCurve, BCurve, BCurve]

splitIn3WithControlPoints()

splitIn3WithControlPoints(tVal, tVal2): [Point[], Point[], Point[]]

Defined in: packages/curve/src/b-curve.ts:618

Parameters

tVal

number

tVal2

number

Returns

[Point[], Point[], Point[]]

splitIntoCurves()

splitIntoCurves(tVal): [BCurve, BCurve]

Defined in: packages/curve/src/b-curve.ts:502

Parameters

tVal

number

Returns

[BCurve, BCurve]

translateRotateControlPoints()

translateRotateControlPoints(translation, rotationAngle): Point[]

Defined in: packages/curve/src/b-curve.ts:1102

Parameters

translation

Point

rotationAngle

number

Returns

Point[]

Class: BCurve ​

Remarks ​

Performance Optimizations ​

Coordinate System ​

Example ​

Constructors ​

Constructor ​

Parameters ​

controlPoints ​

Returns ​

Accessors ​

AABB ​

Get Signature ​

Returns ​

max ​

min ​

fullLength ​

Get Signature ​

Returns ​

Methods ​

advanceAtTWithLength() ​

Parameters ​

tVal ​

length ​

Returns ​

advanceByDistance() ​

Parameters ​

startT ​

distance ​

Returns ​

compute() ​

Parameters ​

tVal ​

Returns ​

curvature() ​

Parameters ​

tVal ​

Returns ​

derivative() ​

Parameters ​

tVal ​

Returns ​

derivativeByPercentage() ​

Parameters ​

percentage ​

Returns ​

Remarks ​

Example ​

derivativeNormalized() ​

Parameters ​

tVal ​

Returns ​

determinant3by3() ​

Parameters ​

matrix ​

Returns ​

findArcs() ​

Parameters ​

errorThreshold ​

Returns ​

findArcStartingAt() ​

Parameters ​

errorThreshold ​

low ​

Returns ​

findClosest() ​

Parameters ​

x ​

y ​

LUT ​

circleRadius ​

distanceEpsilon ​

pd2? ​

pd1? ​

Returns ​

fitArc() ​

Parameters ​

startPoint ​

endPoint ​

midPoint ​

Class: BCurve

Remarks

Performance Optimizations

Coordinate System

Example

Constructors

Constructor

Parameters

controlPoints

Returns

Accessors

AABB

Get Signature

Returns

max

min

fullLength

Get Signature

Returns

Methods

advanceAtTWithLength()

Parameters

tVal

length

Returns

advanceByDistance()

Parameters

startT

distance

Returns

compute()

Parameters

tVal

Returns

curvature()

Parameters

tVal

Returns

derivative()

Parameters

tVal

Returns

derivativeByPercentage()

Parameters

percentage

Returns

Remarks

Example

derivativeNormalized()

Parameters

tVal

Returns

determinant3by3()

Parameters

matrix

Returns

findArcs()

Parameters

errorThreshold

Returns

findArcStartingAt()

Parameters

errorThreshold

low

Returns

findClosest()

Parameters

x

y

LUT

circleRadius

distanceEpsilon

pd2?

pd1?

Returns

fitArc()

Parameters

startPoint

endPoint

midPoint