@ue-too/math / index / PointCal

クラス: PointCal

定義: index.ts:89

Utility class for point and vector calculations.

Remarks

PointCal provides static methods for common 2D and 3D mathematical operations used in canvas applications. All methods handle both 2D and 3D coordinates seamlessly.

例

import { PointCal, Point } from '@ue-too/math';

const v1: Point = { x: 1, y: 2 };
const v2: Point = { x: 3, y: 4 };

const sum = PointCal.addVector(v1, v2);
const dot = PointCal.dotProduct(v1, v2);

コンストラクター

コンストラクター

new PointCal(): PointCal

戻り値

PointCal

Angle Utilities

angleFromA2B()

static angleFromA2B(a, b): number

定義: index.ts:439

Calculates the signed angle from vector a to vector b.

パラメータ

a

point

First vector (starting direction)

b

point

Second vector (ending direction)

戻り値

number

The signed angle in radians, range: (-π, π]

Remarks

• Positive angles indicate counter-clockwise rotation from a to b
• Negative angles indicate clockwise rotation from a to b
• Uses atan2 for proper quadrant handling

例

const right = { x: 1, y: 0 };
const up = { x: 0, y: 1 };
const angle = PointCal.angleFromA2B(right, up); // π/2 (90 degrees CCW)

const down = { x: 0, y: -1 };
const angleDown = PointCal.angleFromA2B(right, down); // -π/2 (90 degrees CW)

Geometric Calculations

distanceBetweenPoints()

static distanceBetweenPoints(a, b): number

定義: index.ts:497

Calculates the Euclidean distance between two points.

パラメータ

a

point

First point

b

point

Second point

戻り値

number

The distance between the two points

Remarks

Equivalent to calculating the magnitude of the vector from a to b.

例

const a = { x: 0, y: 0 };
const b = { x: 3, y: 4 };
const distance = PointCal.distanceBetweenPoints(a, b); // 5

---

getLineIntersection()

static getLineIntersection(startPoint, endPoint, startPoint2, endPoint2): object

定義: index.ts:630

Calculates the intersection point of two line segments.

パラメータ

startPoint

Point

Start of first line segment

endPoint

Point

End of first line segment

startPoint2

Point

Start of second line segment

endPoint2

Point

End of second line segment

戻り値

object

Object containing intersection status and details

intersection?

optional intersection: Point

intersects

intersects: boolean

offset?

optional offset: number

Remarks

Returns an object with:

• intersects: Boolean indicating if segments intersect
• intersection: The intersection point (only if intersects is true)
• offset: Parameter t where intersection occurs on first segment (0 to 1)

The segments must actually cross within their bounds (not just their infinite extensions).

Use cases:

• Collision detection between line segments
• Ray casting and visibility checks
• Path intersection detection

例

const line1Start = { x: 0, y: 0 };
const line1End = { x: 10, y: 10 };
const line2Start = { x: 0, y: 10 };
const line2End = { x: 10, y: 0 };

const result = PointCal.getLineIntersection(line1Start, line1End, line2Start, line2End);
// { intersects: true, intersection: { x: 5, y: 5 }, offset: 0.5 }

---

isEqual()

static isEqual(a, b): boolean

定義: index.ts:585

Checks if two points are exactly equal.

パラメータ

a

point

First point

b

point

Second point

戻り値

boolean

True if all coordinates are exactly equal

Remarks

Uses strict equality (===) for comparison. For approximate equality with tolerance, use samePoint instead. Missing z-coordinates are treated as 0.

例

const a = { x: 1, y: 2 };
const b = { x: 1, y: 2 };
PointCal.isEqual(a, b); // true

const c = { x: 1.0000001, y: 2 };
PointCal.isEqual(a, c); // false (use samePoint for tolerance)

---

linearInterpolation()

static linearInterpolation(a, b, t): point

定義: index.ts:549

Performs linear interpolation between two points.

パラメータ

a

point

Starting point (t = 0)

b

point

Ending point (t = 1)

t

number

Interpolation parameter (0 to 1)

戻り値

point

Interpolated point

Remarks

• t = 0 returns point a
• t = 1 returns point b
• t = 0.5 returns the midpoint
• Values outside [0, 1] perform extrapolation

Performance: Suitable for animation loops and real-time interpolation.

例

const a = { x: 0, y: 0 };
const b = { x: 10, y: 20 };
const mid = PointCal.linearInterpolation(a, b, 0.5); // { x: 5, y: 10 }
const quarter = PointCal.linearInterpolation(a, b, 0.25); // { x: 2.5, y: 5 }

---

unitVectorFromA2B()

static unitVectorFromA2B(a, b): Point

定義: index.ts:346

Calculates the unit vector pointing from point a to point b.

パラメータ

a

point

Starting point

b

point

Ending point

戻り値

Point

Unit vector in the direction from a to b

Remarks

Equivalent to calling unitVector(subVector(b, a))

例

const a = { x: 0, y: 0 };
const b = { x: 3, y: 4 };
const direction = PointCal.unitVectorFromA2B(a, b); // { x: 0.6, y: 0.8 }

Transformations

flipYAxis()

static flipYAxis(point): Point

定義: index.ts:519

Flips a point's y-coordinate (mirrors across the x-axis).

パラメータ

point

point

Point to flip

戻り値

Point

Point with negated y-coordinate

Remarks

Useful for converting between coordinate systems where the y-axis direction differs. Common when converting between screen coordinates (y-down) and mathematical coordinates (y-up).

例

const point = { x: 10, y: 20 };
const flipped = PointCal.flipYAxis(point); // { x: 10, y: -20 }

---

rotatePoint()

static rotatePoint(point, angle): Point

定義: index.ts:373

Rotates a point around the origin.

パラメータ

point

point

Point to rotate

angle

number

Rotation angle in radians (counter-clockwise)

戻り値

Point

Rotated point

Remarks

Rotation is performed around the origin (0, 0). Positive angles rotate counter-clockwise, negative angles rotate clockwise. For rotation around a custom anchor, use transformPointWRTAnchor.

Performance: Uses trigonometric functions (sin/cos). For many rotations with the same angle, pre-calculate sin/cos values and apply the transformation manually.

例

const point = { x: 1, y: 0 };
const rotated = PointCal.rotatePoint(point, Math.PI / 2); // { x: 0, y: 1 }

---

transform2NewAxis()

static transform2NewAxis(point, angleFromOriginalAxis2DestAxis): Point

定義: index.ts:400

Transforms a point's coordinates to a new rotated axis system.

パラメータ

point

point

Point in original coordinate system

angleFromOriginalAxis2DestAxis

number

Rotation angle from original to destination axis (radians, CCW positive)

戻り値

Point

Point coordinates in the new axis system

Remarks

This performs an axis rotation transformation, converting coordinates from one reference frame to another rotated by the specified angle.

例

const point = { x: 10, y: 0 };
const angle = Math.PI / 4; // 45 degrees
const transformed = PointCal.transform2NewAxis(point, angle);

---

transformPointWRTAnchor()

static transformPointWRTAnchor(point, anchor, angle): Point

定義: index.ts:468

Rotates a point around a custom anchor point.

パラメータ

point

point

Point to rotate

anchor

point

Anchor point to rotate around

angle

number

Rotation angle in radians (counter-clockwise)

戻り値

Point

Rotated point

Remarks

This is equivalent to:

1. Translate point by -anchor
2. Rotate around origin
3. Translate back by +anchor

例

const point = { x: 10, y: 5 };
const anchor = { x: 5, y: 5 };
const angle = Math.PI / 2; // 90 degrees
const rotated = PointCal.transformPointWRTAnchor(point, anchor, angle);
// Rotates point around anchor (5, 5)

Vector Arithmetic

addVector()

static addVector(a, b): Point

定義: index.ts:115

Adds two vectors together.

パラメータ

a

point

First vector

b

point

Second vector

戻り値

Point

The sum of vectors a and b

Remarks

If either vector lacks a z-coordinate, it's treated as 0. The result will include a z-coordinate if either input has one.

例

const a = { x: 1, y: 2 };
const b = { x: 3, y: 4 };
const sum = PointCal.addVector(a, b); // { x: 4, y: 6 }

// With 3D coordinates
const a3d = { x: 1, y: 2, z: 3 };
const b3d = { x: 4, y: 5, z: 6 };
const sum3d = PointCal.addVector(a3d, b3d); // { x: 5, y: 7, z: 9 }

---

divideVectorByScalar()

static divideVectorByScalar(a, b): Point

定義: index.ts:190

Divides a vector by a scalar value.

パラメータ

a

point

Vector to divide

b

number

Scalar divisor

戻り値

Point

The divided vector, or the original vector if b is 0

Remarks

Division by zero returns the original vector unchanged to prevent NaN values.

例

const v = { x: 10, y: 20 };
const divided = PointCal.divideVectorByScalar(v, 2); // { x: 5, y: 10 }

---

multiplyVectorByScalar()

static multiplyVectorByScalar(a, b): Point

定義: index.ts:167

Multiplies a vector by a scalar value.

パラメータ

a

point

Vector to multiply

b

number

Scalar multiplier

戻り値

Point

The scaled vector

例

const v = { x: 2, y: 3 };
const scaled = PointCal.multiplyVectorByScalar(v, 2.5); // { x: 5, y: 7.5 }

---

subVector()

static subVector(a, b): Point

定義: index.ts:143

Subtracts vector b from vector a.

パラメータ

a

point

Vector to subtract from

b

point

Vector to subtract

戻り値

Point

The difference (a - b)

Remarks

If either vector lacks a z-coordinate, it's treated as 0.

例

const a = { x: 5, y: 7 };
const b = { x: 2, y: 3 };
const diff = PointCal.subVector(a, b); // { x: 3, y: 4 }

Vector Operations

crossProduct()

static crossProduct(a, b): Point

定義: index.ts:315

Calculates the cross product of two vectors.

パラメータ

a

point

First vector

b

point

Second vector

戻り値

Point

The cross product vector perpendicular to both inputs

Remarks

The cross product is perpendicular to both input vectors, following the right-hand rule. For 2D vectors (z undefined), z is treated as 0.

Properties:

• Result is perpendicular to both input vectors
• Magnitude equals area of parallelogram formed by vectors
• Direction follows right-hand rule

例

const a = { x: 1, y: 0, z: 0 };
const b = { x: 0, y: 1, z: 0 };
const cross = PointCal.crossProduct(a, b); // { x: 0, y: 0, z: 1 }

---

dotProduct()

static dotProduct(a, b): number

定義: index.ts:281

Calculates the dot product of two vectors.

パラメータ

a

point

First vector

b

point

Second vector

戻り値

number

The dot product (scalar value)

Remarks

The dot product is: a.x * b.x + a.y * b.y + a.z * b.z

Use cases:

• Determine if vectors are perpendicular (dot = 0)
• Calculate angle between vectors: θ = acos(dot / (|a| * |b|))
• Project one vector onto another

例

const a = { x: 1, y: 0 };
const b = { x: 0, y: 1 };
const dot = PointCal.dotProduct(a, b); // 0 (perpendicular vectors)

const c = { x: 2, y: 3 };
const d = { x: 4, y: 5 };
const dot2 = PointCal.dotProduct(c, d); // 23

---

magnitude()

static magnitude(a): number

定義: index.ts:216

Calculates the magnitude (length) of a vector.

パラメータ

a

point

Vector to measure

戻り値

number

The magnitude of the vector

Remarks

Uses the Euclidean distance formula: √(x² + y² + z²)

例

const v = { x: 3, y: 4 };
const mag = PointCal.magnitude(v); // 5

const v3d = { x: 1, y: 2, z: 2 };
const mag3d = PointCal.magnitude(v3d); // 3

---

unitVector()

static unitVector(a): Point

定義: index.ts:242

Converts a vector to its unit vector (normalized to length 1).

パラメータ

a

point

Vector to normalize

戻り値

Point

Unit vector in the same direction, or zero vector if magnitude is 0

Remarks

A unit vector has magnitude 1 and preserves the original direction. Returns {x: 0, y: 0, z: 0} if the input vector has zero magnitude.

Performance note: This method calls magnitude() twice. For better performance when you need both magnitude and unit vector, calculate magnitude once and divide manually.

例

const v = { x: 3, y: 4 };
const unit = PointCal.unitVector(v); // { x: 0.6, y: 0.8 }