Class Spinor3

constructor

• new Spinor3(coords, code): Spinor3

• Initializes the spinor from the specified coordinates. The spinor is not locked. The spinor is not modified.

  Parameters

  • coords: number[]

    [yz, zx, xy, a]
  • code: number

  Returns Spinor3

Static Readonlyone

Static Readonlyzero

a

• get a(): number

• The coordinate corresponding to the 1 basis scalar.

  Returns number
• set a(α): void

• Parameters

  • α: number

  Returns void

length

• get length(): number

• Returns number

maskG3

• get maskG3(): number

• Returns number
• set maskG3(unused): void

• Parameters

  • unused: number

  Returns void

modified

• get modified(): boolean

• Returns boolean

• set modified(modified): void

• Parameters

  • modified: boolean

  Returns void

xy

• get xy(): number

• The coordinate corresponding to the e₁₂ basis bivector.

  Returns number
• set xy(xy): void

• Parameters

  • xy: number

  Returns void

yz

• get yz(): number

• The coordinate corresponding to the e₂₃ basis bivector.

  Returns number
• set yz(yz): void

• Parameters

  • yz: number

  Returns void

zx

• get zx(): number

• The coordinate corresponding to the e₃₁ basis bivector.

  Returns number
• set zx(zx): void

• Parameters

  • zx: number

  Returns void

add

• add(spinor, α?): this

• this ⟼ this + α * spinor

  Parameters

  • spinor: SpinorE3
  • α: number = 1

  Returns this

  this + α * spinor

add2

• add2(a, b): Spinor3

• this ⟼ a + b

  Parameters

  • a: SpinorE3
  • b: SpinorE3

  Returns Spinor3

  a + b

addPseudo

• addPseudo(β): Spinor3

• Intentionally undocumented.

  Parameters

  • β: number

  Returns Spinor3

  this + I * β

addScalar

• addScalar(α): this

• this ⟼ this + α

  Parameters

  • α: number

  Returns this

  this + α

approx

• approx(n): this

• Parameters

  • n: number

  Returns this

arg

• arg(): Spinor3

• arg(A) = grade(log(A), 2)

  Returns Spinor3

  arg(this)

clone

• clone(): Spinor3

• Returns an unlocked (mutable) copy of this.

  Returns Spinor3

conj

• conj(): Spinor3

• The Clifford conjugate. The multiplier for the grade x is (-1) raised to the power x * (x + 1) / 2 The pattern of grades is +--++--+

  Returns Spinor3

  conj(this)

copy

• copy(source): this

• this ⟼ copy(source)

  Parameters

  • source: SpinorE3

  Returns this

  Method

  copy

  Chainable

copyCoordinates

• copyCoordinates(coordinates): Spinor3

• Parameters

  • coordinates: number[]

  Returns Spinor3

copyScalar

• copyScalar(α): Spinor3

• Sets this spinor to the value of the scalar, α.

  Parameters

  • α: number

    The scalar to be copied.

  Returns Spinor3

  Method

  copyScalar

  Chainable

copySpinor

• copySpinor(s): Spinor3

• Intentionally undocumented.

  Parameters

  • s: SpinorE3

  Returns Spinor3

copyVector

• copyVector(vector): Spinor3

• Intentionally undocumented.

  Parameters

  • vector: VectorE3

  Returns Spinor3

div

• div(s): this

• this ⟼ this / s

  Parameters

  • s: SpinorE3

  Returns this

  Method

  div

  Chainable

div2

• div2(a, b): this

• this ⟼ a / b

  Parameters

  • a: SpinorE3
  • b: SpinorE3

  Returns this

  Method

  div2

  Chainable

divByScalar

• divByScalar(α): this

• this ⟼ this / α

  Parameters

  • α: number

  Returns this

  Method

  divByScalar

  Chainable

dual

• dual(v, changeSign): Spinor3

• this ⟼ dual(v) = v <<< inv(I)

  Parameters

  • v: VectorE3

    The vector whose dual will be used to set this spinor.
  • changeSign: boolean

    Changes the sign from the usual convention for a right-handed pseudoscalar.

  Returns Spinor3

  Method

  dual

  Chainable

equals

• equals(other): boolean

• Parameters

  • other: any

  Returns boolean

exp

• exp(): Spinor3

• this ⟼ ethis

  Returns Spinor3

  exp(this)

ext

• ext(rhs): Spinor3

• Parameters

  • rhs: SpinorE3

  Returns Spinor3

ext2

• ext2(a, b): Spinor3

• Parameters

  • a: SpinorE3
  • b: SpinorE3

  Returns Spinor3

getComponent

• getComponent(index): number

• Parameters

  • index: number

  Returns number

grade

• grade(grade): this

• Parameters

  • grade: number

  Returns this

  Method

  grade

  Chainable

inv

• inv(): this

• this ⟼ conj(this) / quad(this)

  Returns this

  Chainable

isLocked

• isLocked(): boolean

• Returns boolean

isOne

• isOne(): boolean

• Returns boolean

isZero

• isZero(): boolean

• Returns boolean

lco

• lco(rhs): Spinor3

• Parameters

  • rhs: SpinorE3

  Returns Spinor3

  Method

  lco

  Chainable

lco2

• lco2(a, b): Spinor3

• Parameters

  • a: SpinorE3
  • b: SpinorE3

  Returns Spinor3

lerp

• lerp(target, α): this

• this ⟼ this + α * (target - this)

  Parameters

  • target: SpinorE3
  • α: number

  Returns this

  Method

  lerp

  Chainable

lerp2

• lerp2(a, b, α): this

• this ⟼ a + α * (b - a)

  Parameters

  • a: SpinorE3
  • b: SpinorE3
  • α: number

  Returns this

  Method

  lerp2

  Chainable

lock

• lock(): number

• Returns number

log

• log(): this

• this ⟼ log(this)

  Returns this

magnitude

• magnitude(): number

• Computes the square root of the squared norm.

  This method does not change this multivector.

  Returns number

magnitudeSansUnits

• magnitudeSansUnits(): number

• Intentionally undocumented.

  Returns number

mul

• mul(rhs): this

• this ⟼ this * rhs

  Parameters

  • rhs: SpinorE3

  Returns this

  Method

  mul

  Chainable

mul2

• mul2(a, b): this

• this ⟼ a * b

  Parameters

  • a: SpinorE3
  • b: SpinorE3

  Returns this

  Method

  mul2

  Chainable

neg

• neg(): this

• Returns this

  Chainable

norm

• norm(): this

• this ⟼ sqrt(this * conj(this))

  Returns this

  Chainable

normalize

• normalize(): this

• this ⟼ this / magnitude(this)

  Returns this

  Chainable

one

• one(): this

• Sets this spinor to the identity element for multiplication, 1.

  Returns this

  Chainable

quad

• quad(): this

• this ⟼ this * conj(this)

  Returns this

  Method

  quad

  Chainable

rco

• rco(rhs): Spinor3

• Parameters

  • rhs: SpinorE3

  Returns Spinor3

rco2

• rco2(a, b): Spinor3

• Parameters

  • a: SpinorE3
  • b: SpinorE3

  Returns Spinor3

reflect

• reflect(n): this

• Sets this Spinor to the value of its reflection in the plane orthogonal to n. The geometric formula for bivector reflection is B' = n * B * n.

  Parameters

  • n: VectorE3

  Returns this

  Method

  reflect

  Chainable

rev

• rev(): this

• this = (w, B) ⟼ (w, -B)

  Returns this

  Chainable

rotate

• rotate(R): this

• this = ⟼ R * this * rev(R)

  Parameters

  • R: SpinorE3

  Returns this

  Method

  rotate

  Chainable

rotorFromDirections

• rotorFromDirections(a, b): this

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

  Parameters

  • a: VectorE3

    The from vector.
  • b: VectorE3

    The to vector.

  Returns this

  The rotor representing a rotation from a to b.

  Method

  rotorFromDirections

  Chainable

rotorFromGeneratorAngle

• rotorFromGeneratorAngle(B, θ): Spinor3

• this = ⟼ exp(- B * θ / 2)

  Parameters

  • B: BivectorE3

    The unit bivector that generates the rotation.
  • θ: number

    The rotation angle in radians.

  Returns Spinor3

rotorFromVectorToVector

• rotorFromVectorToVector(a, b, B): this

• Parameters

  • a: VectorE3
  • b: VectorE3
  • B: BivectorE3

  Returns this

scale

• scale(α): Spinor3

• this ⟼ this * α

  Parameters

  • α: number

  Returns Spinor3

  Method

  scale

  Chainable

scp

• scp(rhs): Spinor3

• Parameters

  • rhs: SpinorE3

  Returns Spinor3

scp2

• scp2(a, b): Spinor3

• Parameters

  • a: SpinorE3
  • b: SpinorE3

  Returns Spinor3

squaredNorm

• squaredNorm(): number

• This method does not change this multivector.

  Returns number

squaredNormSansUnits

• squaredNormSansUnits(): number

• Intentionally undocumented.

  Returns number

stress

• stress(σ): Spinor3

• Parameters

  • σ: VectorE3

  Returns Spinor3

  Method

  stress

  Chainable

sub

• sub(s, α?): this

• this ⟼ this - s * α

  Parameters

  • s: SpinorE3
  • α: number = 1

  Returns this

  Method

  sub

  Chainable

sub2

• sub2(a, b): this

• this ⟼ a - b

  Parameters

  • a: SpinorE3
  • b: SpinorE3

  Returns this

  Method

  sub2

  Chainable

toArray

• toArray(): number[]

• Returns number[]

toExponential

• toExponential(fractionDigits?): string

• Parameters

  • OptionalfractionDigits: number

  Returns string

  Method

  toExponential

toFixed

• toFixed(fractionDigits?): string

• Parameters

  • OptionalfractionDigits: number

  Returns string

  Method

  toFixed

toPrecision

• toPrecision(position?): string

• Parameters

  • Optionalposition: number

  Returns string

  Method

  toPrecision

toString

• toString(radix?): string

• Parameters

  • Optionalradix: number

  Returns string

  A non-normative string representation of the target.

  Method

  toString

unlock

• unlock(token): void

• Parameters

  • token: number

  Returns void

versor

• versor(a, b): this

• this ⟼ a * b

  Sets this Spinor3 to the geometric product, a * b, of the vector arguments.

  Parameters

  • a: VectorE3
  • b: VectorE3

  Returns this

wedge

• wedge(a, b): Spinor3

• this ⟼ a ^ b

  Sets this Spinor3 to the exterior product, a ^ b, of the vector arguments.

  Parameters

  • a: VectorE3
  • b: VectorE3

  Returns Spinor3

  Method

  wedge

  Chainable

zero

• zero(): this

• Sets this spinor to the identity element for addition, 0.

  Returns this

Staticcopy

• copy(spinor): Spinor3

• Parameters

  • spinor: SpinorE3

    The spinor to be copied.

  Returns Spinor3

  A copy of the spinor argument.

Staticdual

• dual(v, changeSign): Spinor3

• Computes dual(V) = v << inv(I).

  Parameters

  • v: VectorE3
  • changeSign: boolean

  Returns Spinor3

StaticfromBivector

• fromBivector(B): Spinor3

• Parameters

  • B: BivectorE3

  Returns Spinor3

StaticisOne

• isOne(spinor): boolean

• Parameters

  • spinor: SpinorE3

  Returns boolean

Staticlerp

• lerp(a, b, α): Spinor3

• Parameters

  • a: SpinorE3
  • b: SpinorE3
  • α: number

  Returns Spinor3

  a + α * (b - a)

Staticrandom

• random(): Spinor3

• Computes a unit spinor with a random direction.

  Returns Spinor3

StaticrotorFromDirections

• rotorFromDirections(a, b): Spinor3

• Computes the rotor that rotates vector a to vector b.

  Parameters

  • a: VectorE3

    The from vector.
  • b: VectorE3

    The to vector.

  Returns Spinor3

Staticspinor

• spinor(yz, zx, xy, a): Spinor3

• Constructs a new Spinor3 from coordinates. The returned spinor is not locked. The returned spinor is not modified.

  Parameters

  • yz: number

    The coordinate corresponding to the e2e3 basis bivector.
  • zx: number

    The coordinate corresponding to the e3e1 basis bivector.
  • xy: number

    The coordinate corresponding to the e1e2 basis bivector.
  • a: number

    The coordinate corresponding to the 1 basis scalar.

  Returns Spinor3

Staticwedge

• wedge(a, b): Spinor3

• Parameters

  • a: VectorE3
  • b: VectorE3

  Returns Spinor3