Class G20

constructor

• new G20(x?, y?, a?, b?): G20

• Parameters

  • x: number = 0
  • y: number = 0
  • a: number = 0
  • b: number = 0

  Returns G20

Readonlychange$

Static Readonlyex

Static Readonlyey

Static ReadonlyI

Static Readonlyone

Static Readonlyzero

a

• get a(): number

• Returns number

• set a(a): void

• Parameters

  • a: number

  Returns void

b

• get b(): number

• Returns number

• set b(b): void

• Parameters

  • b: number

  Returns void

x

• get x(): number

• Returns number

• set x(x): void

• Parameters

  • x: number

  Returns void

y

• get y(): number

• Returns number

• set y(y): void

• Parameters

  • y: number

  Returns void

__add__

• __add__(rhs): G20

• Parameters

  • rhs: number | G20

  Returns G20

__bang__

• __bang__(): G20

• Returns G20

__div__

• __div__(rhs): G20

• Parameters

  • rhs: number | G20

  Returns G20

__eq__

• __eq__(rhs): boolean

• Parameters

  • rhs: number | G20

  Returns boolean

__lshift__

• __lshift__(rhs): G20

• Parameters

  • rhs: number | G20

  Returns G20

__mul__

• __mul__(rhs): G20

• Parameters

  • rhs: number | G20

  Returns G20

__ne__

• __ne__(rhs): boolean

• Parameters

  • rhs: number | G20

  Returns boolean

__neg__

• __neg__(): G20

• Returns G20

__pos__

• __pos__(): G20

• Returns G20

__radd__

• __radd__(lhs): G20

• Parameters

  • lhs: number | G20

  Returns G20

__rdiv__

• __rdiv__(lhs): G20

• Parameters

  • lhs: number | G20

  Returns G20

__rlshift__

• __rlshift__(lhs): G20

• Parameters

  • lhs: number | G20

  Returns G20

__rmul__

• __rmul__(lhs): G20

• Parameters

  • lhs: number | G20

  Returns G20

__rrshift__

• __rrshift__(lhs): G20

• Parameters

  • lhs: number | G20

  Returns G20

__rshift__

• __rshift__(rhs): G20

• Parameters

  • rhs: number | G20

  Returns G20

__rsub__

• __rsub__(lhs): G20

• Parameters

  • lhs: number | G20

  Returns G20

__rvbar__

• __rvbar__(lhs): G20

• Parameters

  • lhs: number | G20

  Returns G20

__rwedge__

• __rwedge__(lhs): G20

• Parameters

  • lhs: number | G20

  Returns G20

__sub__

• __sub__(rhs): G20

• Parameters

  • rhs: number | G20

  Returns G20

__tilde__

• __tilde__(): G20

• Returns G20

__vbar__

• __vbar__(rhs): G20

• Parameters

  • rhs: number | G20

  Returns G20

__wedge__

• __wedge__(rhs): G20

• Parameters

  • rhs: number | G20

  Returns G20

add

• add(rhs): G20

• Parameters

  • rhs: G20

  Returns G20

add2

• add2(a, b): G20

• Parameters

  • a: Readonly<G20>
  • b: Readonly<G20>

  Returns G20

addPseudo

• addPseudo(β): G20

• Parameters

  • β: number

  Returns G20

addScalar

• addScalar(a, α?): G20

• Adds a multiple of a scalar to this multivector.

  Parameters

  • a: number

    The scalar value to be added to this multivector.
  • α: number = 1

    The fraction of (a * uom) to be added. Default is 1.

  Returns G20

  this + (a * uom) * α

clear

• clear(): this

• A convenience function for set(0, 0, 0, 0). Requires this multivector to be mutable.

  Returns this

clone

• clone(): G20

• Returns G20

conj

• conj(): G20

• Returns G20

copy

• copy(mv): this

• A convenience function for set(mv.x, mv.y, mv.a, mv.b). Requires this multivector to be mutable.

  Parameters

  • mv: Readonly<G20>

  Returns this

copySpinor

• copySpinor(spinor): this

• A convenience function for set(0, 0, spinor.a, spinor.b). Requires this multivector to be mutable.

  Parameters

  • spinor: Readonly<Spinor>

  Returns this

copyVector

• copyVector(vector): this

• A convenience function for set(vector.x, vector.y, 0, 0). Requires this multivector to be mutable.

  Parameters

  • vector: Readonly<Vector>

  Returns this

distanceTo

• distanceTo(v): number

• Parameters

  • v: G20

  Returns number

distanceToSquared

• distanceToSquared(v): number

• Parameters

  • v: G20

  Returns number

div

• div(rhs): G20

• Parameters

  • rhs: G20

    The multivector dividend.

  Returns G20

  this / m;

dot

• dot(v): number

• Parameters

  • v: G20

  Returns number

equals

• equals(v, eps?): boolean

• Parameters

  • v: G20
  • Optionaleps: number

  Returns boolean

exp

• exp(): G20

• Returns G20

ext

• ext(m): G20

• Parameters

  • m: G20

  Returns G20

  this ^ m

inv

• inv(): G20

• Computes the right inverse of this multivector. inv(X) satisfies X * inv(X) = 1.

  Returns G20

  inverse(this)

isLocked

• isLocked(): boolean

• Determines whether this multivector is locked. If the multivector is in the unlocked state then it is mutable. If the multivector is in the locked state then it is immutable.

  Returns boolean

isMutable

• isMutable(): boolean

• Returns boolean

isZero

• isZero(eps?): boolean

• Determines whether this multivector is exactly 0 (zero).

  Parameters

  • Optionaleps: number

  Returns boolean

lco

• lco(rhs): G20

• Parameters

  • rhs: G20

  Returns G20

lerp

• lerp(v, t): G20

• Parameters

  • v: G20
  • t: number

  Returns G20

lock

• lock(): number

• Locks this multivector (preventing any further mutation), and returns a token that may be used to unlock it.

  Returns number

magnitude

• magnitude(): number

• Returns number

mul

• mul(rhs): G20

• Parameters

  • rhs: G20

  Returns G20

  this * m

neg

• neg(): G20

• Returns G20

normalize

• normalize(): G20

• Returns G20

quaditude

• quaditude(): number

• Returns number

rco

• rco(m): G20

• Parameters

  • m: G20

  Returns G20

reflect

• reflect(n): G20

• If this is mutable, then sets this multivector to its reflection in the plane orthogonal to vector n. The result is mutable. If this is immutable (locked), a copy of this is made, which is then reflected. The result is immutable (locked).

  i.e. The result is mutable (unlocked) iff this is mutable (unlocked).

  Mathematically,

  this ⟼ - n * this * n

  Geometrically,

  Reflects this multivector in the plane orthogonal to the unit vector, n. This implementation does assume that n is a vector, but does not assume that it is normalized to unity.

  If n is not a unit vector then the result is scaled by n squared. The scalar component gets an extra minus sign. The pseudoscalar component does not change sign. The units of measure are carried through but in most cases n SHOULD be dimensionless.

  Parameters

  • n: Readonly<Vector>

    The unit vector that defines the reflection plane.

  Returns G20

rev

• rev(): G20

• reverse has a ++-- structure on the grades. The scalar component, a, will not change. The vector components, x and y, will not change. The bivector component, b, will change sign.

  Returns G20

rotate

• rotate(radians): G20

• Parameters

  • radians: number

  Returns G20

rotorFromAngle

• rotorFromAngle(θ): G20

• Sets this multivector to a rotor that rotates through angle θ in the oriented plane defined by I.

  Parameters

  • θ: number

    The rotation angle in radians when the rotor is applied on both sides as R * M * ~R

  Returns G20

rotorFromDirections

• rotorFromDirections(a, b): G20

• Computes a rotor, R, from two unit vectors, where R = (|b||a| + b * a) / sqrt(2 * |b||a|(|b||a| + b << a))

  The result is independent of the magnitudes of a and b.

  Parameters

  • a: Readonly<Vector>

    The starting vector
  • b: Readonly<Vector>

    The ending vector

  Returns G20

  The rotor representing a rotation from a to b.

rotorFromVectorToVector

• rotorFromVectorToVector(a, b): G20

• R = sqrt(|b|/|a|) * (|b||a| + b * a) / sqrt(2 * |b||a|(|b||a| + b << a))

  The result is depends on the magnitudes of a and b.

  Parameters

  • a: Readonly<Vector>
  • b: Readonly<Vector>

  Returns G20

scale

• scale(α): G20

• Parameters

  • α: number

  Returns G20

scp

• scp(m): G20

• Parameters

  • m: G20

  Returns G20

  this | m

set

• set(x, y, a?, b?): this

• Sets the coordinates of this multivector. Requires this multivector to be mutable.

  Parameters

  • x: number

    The coordinate along the x-axis.
  • y: number

    The coordinate along the y-axis.
  • a: number = 0

    The scalar coordinate.
  • b: number = 0

    The bivector coordinate.

  Returns this

sub

• sub(rhs): G20

• Parameters

  • rhs: G20

  Returns G20

subScalar

• subScalar(a, α?): G20

• Subtracts a multiple of a scalar from this multivector.

  Parameters

  • a: number

    The scalar value to be subtracted from this multivector.
  • α: number = 1

    The fraction of (a * uom) to be subtracted. Default is 1.

  Returns G20

  this - (a * uom) * α

toString

• toString(): string

• Returns string

unlock

• unlock(token): this

• Unlocks this multivector (allowing mutation), using a token that was obtained from a preceding lock method call.

  Parameters

  • token: number

  Returns this

versor

• versor(a, b): G20

• this ⟼ a * b

  Sets this Geometric2 to the geometric product a * b of the vector arguments.

  Parameters

  • a: Vector
  • b: Vector

  Returns G20

Staticadd

• add(v1, v2): G20

• Parameters

  • v1: Readonly<G20>
  • v2: Readonly<G20>

  Returns G20

StaticangleBetween

• angleBetween(v1, v2): number

• Parameters

  • v1: Readonly<Vector>
  • v2: Readonly<Vector>

  Returns number

Staticbivector

• bivector(b): G20

• Parameters

  • b: number

  Returns G20

Staticcopy

• copy(mv): G20

• Parameters

  • mv: Readonly<G20>

  Returns G20

StaticdistanceBetween

• distanceBetween(v1, v2): number

• Parameters

  • v1: Readonly<Vector>
  • v2: Readonly<Vector>

  Returns number

StaticdistanceBetweenSquared

• distanceBetweenSquared(v1, v2): number

• Parameters

  • v1: Readonly<Vector>
  • v2: Readonly<Vector>

  Returns number

StaticfromBivector

• fromBivector(B): G20

• Parameters

  • B: Readonly<Bivector>

  Returns G20

StaticfromScalar

• fromScalar(alpha): G20

• Parameters

  • alpha: Readonly<Scalar>

  Returns G20

StaticfromSpinor

• fromSpinor(R): G20

• Parameters

  • R: Readonly<Spinor>

  Returns G20

StaticfromVector

• fromVector(v): G20

• Parameters

  • v: Readonly<Vector>

  Returns G20

StaticratioBetween

• ratioBetween(v1, v2): number

• Parameters

  • v1: Readonly<G20>
  • v2: Readonly<G20>

  Returns number

StaticrotorFromDirections

• rotorFromDirections(a, b): G20

• Parameters

  • a: Vector
  • b: Vector

  Returns G20

StaticrotorFromVectorToVector

• rotorFromVectorToVector(a, b): G20

• Parameters

  • a: Vector
  • b: Vector

  Returns G20

Staticscalar

• scalar(a): G20

• Parameters

  • a: number

  Returns G20

Staticspinor

• spinor(a, b): G20

• Parameters

  • a: number
  • b: number

  Returns G20

Staticsub

• sub(v1, v2): G20

• Parameters

  • v1: G20
  • v2: G20

  Returns G20

Staticsubtract

• subtract(v1, v2): G20

• Parameters

  • v1: G20
  • v2: G20

  Returns G20

Staticvector

• vector(x, y): G20

• Parameters

  • x: number
  • y: number

  Returns G20