@ue-too/curve / index / BCurve

クラス: BCurve

定義: 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)

例

Create and evaluate a cubic Bezier curve

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);

コンストラクター

コンストラクター

new BCurve(controlPoints): BCurve

定義: packages/curve/src/b-curve.ts:171

パラメータ

controlPoints

Point[]

戻り値

BCurve

アクセッサー

AABB

署名を取得する

get AABB(): object

定義: packages/curve/src/b-curve.ts:1469

戻り値

object

max

max: Point

min

min: Point

---

fullLength

署名を取得する

get fullLength(): number

定義: packages/curve/src/b-curve.ts:423

戻り値

number

メソッド

advanceAtTWithLength()

advanceAtTWithLength(tVal, length): AdvanceAtTWithLengthRes

定義: packages/curve/src/b-curve.ts:1218

パラメータ

tVal

number

length

number

戻り値

AdvanceAtTWithLengthRes

---

advanceByDistance()

advanceByDistance(startT, distance): AdvanceAtTWithLengthRes

定義: packages/curve/src/b-curve.ts:1306

パラメータ

startT

number

distance

number

戻り値

AdvanceAtTWithLengthRes

---

compute()

compute(tVal): Point

定義: packages/curve/src/b-curve.ts:327

パラメータ

tVal

number

戻り値

Point

---

curvature()

curvature(tVal): number

定義: packages/curve/src/b-curve.ts:937

パラメータ

tVal

number

戻り値

number

---

derivative()

derivative(tVal): Point

定義: packages/curve/src/b-curve.ts:459

パラメータ

tVal

number

戻り値

Point

---

derivativeByPercentage()

derivativeByPercentage(percentage): Point

定義: packages/curve/src/b-curve.ts:236

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

パラメータ

percentage

number

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

戻り値

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.

例

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

定義: packages/curve/src/b-curve.ts:463

パラメータ

tVal

number

戻り値

Point

---

determinant3by3()

determinant3by3(matrix): number

定義: packages/curve/src/b-curve.ts:924

パラメータ

matrix

number[][]

戻り値

number

---

findArcs()

findArcs(errorThreshold): object[]

定義: packages/curve/src/b-curve.ts:737

パラメータ

errorThreshold

number

戻り値

object[]

---

findArcStartingAt()

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

定義: packages/curve/src/b-curve.ts:772

パラメータ

errorThreshold

number

low

number

戻り値

{ 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

定義: packages/curve/src/b-curve.ts:1415

パラメータ

x

number

y

number

LUT

object[]

circleRadius

number

distanceEpsilon

number = 5

pd2?

number

pd1?

number

戻り値

number

---

fitArc()

fitArc(startPoint, endPoint, midPoint): object

定義: packages/curve/src/b-curve.ts:851

パラメータ

startPoint

Point

endPoint

Point

midPoint

Point

戻り値

object

center?

optional center: Point

endPoint?

optional endPoint: Point

exists

exists: boolean

radius?

optional radius: number

startPoint?

optional startPoint: Point

---

get()

get(tVal): Point

定義: packages/curve/src/b-curve.ts:343

パラメータ

tVal

number

戻り値

Point

---

getArcLengthLUT()

getArcLengthLUT(steps): object

定義: packages/curve/src/b-curve.ts:469

パラメータ

steps

number = 50

戻り値

object

arcLengthLUT

arcLengthLUT: object[]

controlPoints

controlPoints: Point[]

---

getArcs()

getArcs(errorThreshold): object[]

定義: packages/curve/src/b-curve.ts:768

Get a sequence of circular arcs that approximate the curve.

パラメータ

errorThreshold

number

Maximum allowed radial error when fitting an arc.

戻り値

object[]

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

---

getCacheStats()

getCacheStats(): object

定義: packages/curve/src/b-curve.ts:149

Gets cache statistics for performance monitoring

戻り値

object

Object containing cache size and hit rate information

hitRate

hitRate: number

size

size: number

---

getCircleIntersections()

getCircleIntersections(circleCenter, circleRadius): object[]

定義: packages/curve/src/b-curve.ts:1161

パラメータ

circleCenter

Point

circleRadius

number

戻り値

object[]

---

getCoefficientOfTTerms()

getCoefficientOfTTerms(): Point[]

定義: packages/curve/src/b-curve.ts:961

戻り値

Point[]

---

getCoefficientOfTTermsWithControlPoints()

getCoefficientOfTTermsWithControlPoints(controlPoints): Point[]

定義: packages/curve/src/b-curve.ts:971

パラメータ

controlPoints

Point[]

戻り値

Point[]

---

getControlPoints()

getControlPoints(): Point[]

定義: packages/curve/src/b-curve.ts:297

戻り値

Point[]

---

getControlPointsAlignedWithXAxis()

getControlPointsAlignedWithXAxis(): object[]

定義: packages/curve/src/b-curve.ts:1013

戻り値

object[]

---

getCurveIntersections()

getCurveIntersections(curve, deduplicationTolerance?): object[]

定義: packages/curve/src/b-curve.ts:1458

パラメータ

curve

BCurve

deduplicationTolerance?

number

戻り値

object[]

---

getDerivativeCoefficients()

getDerivativeCoefficients(): Point[]

定義: packages/curve/src/b-curve.ts:965

戻り値

Point[]

---

getDerivativeControlPoints()

getDerivativeControlPoints(controlPoints): Point[]

定義: packages/curve/src/b-curve.ts:273

パラメータ

controlPoints

Point[]

戻り値

Point[]

---

getExtrema()

getExtrema(): object

定義: packages/curve/src/b-curve.ts:1032

戻り値

object

x

x: number[]

y

y: number[]

---

getLineIntersections()

getLineIntersections(line): number[]

定義: packages/curve/src/b-curve.ts:1116

パラメータ

line

Line

戻り値

number[]

---

getLUT()

getLUT(steps): Point[]

定義: packages/curve/src/b-curve.ts:390

パラメータ

steps

number = 100

戻り値

Point[]

---

getLUTWithTVal()

getLUTWithTVal(steps?): object[]

定義: packages/curve/src/b-curve.ts:405

パラメータ

steps?

number

戻り値

object[]

---

getPointbyPercentage()

getPointbyPercentage(percentage): Point

定義: packages/curve/src/b-curve.ts:182

パラメータ

percentage

number

戻り値

Point

---

getProjection()

getProjection(point): object

定義: packages/curve/src/b-curve.ts:666

パラメータ

point

Point

戻り値

object

projection

projection: Point = preliminaryProjectionPoint

tVal

tVal: number = preliminaryProjectionTVal

---

getSelfIntersections()

getSelfIntersections(): object[]

定義: packages/curve/src/b-curve.ts:1147

戻り値

object[]

---

lengthAtT()

lengthAtT(tVal): number

定義: packages/curve/src/b-curve.ts:431

パラメータ

tVal

number

戻り値

number

---

normal()

normal(tVal): object

定義: packages/curve/src/b-curve.ts:1491

パラメータ

tVal

number

戻り値

object

direction

direction: Point

tVal

tVal: number

---

preWarmCache()

preWarmCache(steps): void

定義: packages/curve/src/b-curve.ts:160

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

パラメータ

steps

number = 100

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

戻り値

void

---

refineBinary()

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

定義: packages/curve/src/b-curve.ts:1354

パラメータ

curve

BCurve

x

number

y

number

LUT

object[]

i

number

targetDistance

number = 0

epsilon

number = 0.01

戻り値

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

---

secondDerivative()

secondDerivative(tVal): Point

定義: packages/curve/src/b-curve.ts:954

パラメータ

tVal

number

戻り値

Point

---

setControlPointAtIndex()

setControlPointAtIndex(index, newPoint): boolean

定義: packages/curve/src/b-curve.ts:312

パラメータ

index

number

newPoint

Point

戻り値

boolean

---

setControlPoints()

setControlPoints(controlPoints): void

定義: packages/curve/src/b-curve.ts:301

パラメータ

controlPoints

Point[]

戻り値

void

---

split()

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

定義: packages/curve/src/b-curve.ts:507

パラメータ

tVal

number

戻り値

[Point[], Point[]]

---

splitAndTakeMidCurve()

splitAndTakeMidCurve(tVal, tVal2): BCurve

定義: packages/curve/src/b-curve.ts:658

パラメータ

tVal

number

tVal2

number

戻り値

BCurve

---

splitIn3Curves()

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

定義: packages/curve/src/b-curve.ts:638

パラメータ

tVal

number

tVal2

number

戻り値

[BCurve, BCurve, BCurve]

---

splitIn3WithControlPoints()

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

定義: packages/curve/src/b-curve.ts:618

パラメータ

tVal

number

tVal2

number

戻り値

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

---

splitIntoCurves()

splitIntoCurves(tVal): [BCurve, BCurve]

定義: packages/curve/src/b-curve.ts:502

パラメータ

tVal

number

戻り値

[BCurve, BCurve]

---

translateRotateControlPoints()

translateRotateControlPoints(translation, rotationAngle): Point[]

定義: packages/curve/src/b-curve.ts:1102

パラメータ

translation

Point

rotationAngle

number

戻り値

Point[]