Constructs a mutable instance of Geometric3 from coordinates and an optional unit of measure.
The 8 coordinates are in the order [a, x, y, z, xy, yz, zx, b].
Optional uom: UnitThe optional unit of measure.
Static Readonly IConstructs a basis vector corresponding to the β coordinate.
The returned multivector is locked.
Static Readonly ampereSI base unit of electric current. The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length.
Static Readonly candelaSI base unit of luminous intensity. The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1 / 683 watt per steradian.
Static Readonly coulombSI derived unit of electric charge, quantity of electricity.
Static Readonly e1Constructs a basis vector corresponding to the x coordinate.
The returned multivector is locked.
Static Readonly e2Constructs a basis vector corresponding to the y coordinate.
The returned multivector is locked.
Static Readonly e3Constructs a basis vector corresponding to the z coordinate.
The returned multivector is locked.
Static Readonly jouleSI derived unit of energy, work, quantity of heat.
Static Readonly kelvinSI base unit of thermodynamic temperature. The kelvin, unit of thermodynamic temperature, is the fraction 1 / 273.16 of the thermodynamic temperature of the triple point of water.
Static Readonly kilogramSI base unit of mass. The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.
Static Readonly meterSI base unit of length. The meter is the length of the path travelled by light in vacuum during a time interval of 1 / 299 792 458 of a second.
Static Readonly moleSI base unit of amount of substance.
The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol."
When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.
Static Readonly newtonSI derived unit of force.
Static Readonly oneConstructs a Geometric3 representing the number one. The identity element for multiplication, 1. The returned multivector is locked.
Static Readonly secondSI base unit of time. The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
Static Readonly zeroConstructs a Geometric3 representing the number zero. The identity element for addition, 0. The returned multivector is locked.
The scalar part of this multivector.
The pseudoscalar part of this multivector.
A bitmask describing the grades.
0x0 = zero 0x1 = scalar 0x2 = vector 0x4 = bivector 0x8 = pseudoscalar
The coordinate corresponding to the e1 standard basis vector.
The coordinate corresponding to the e1e2 standard basis bivector.
The coordinate corresponding to the e2 standard basis vector.
The coordinate corresponding to the e2e3 standard basis bivector.
The coordinate corresponding to the e3 standard basis vector.
The coordinate corresponding to the e3e1 standard basis bivector.
Adds a multivector value to this multivector with optional scaling.
The multivector to be added to this multivector.
An optional scale factor that multiplies the multivector argument.
this + M * α
Adds a pseudoscalar value to this multivector.
The pseudoscalar value to be added to this multivector.
Optional uom: UnitThe optional unit of measure.
this + (Iβ * uom)
Adds a scalar value to this multivector.
Optional uom: UnitThe optional unit of measure.
The scalar value to be added to this multivector.
this + (α * uom)
copy(this)
Clifford conjugation
this ⟼ copy(M)
The multivector to be copied.
this ⟼ copy(B)
The bivector to be copied.
Sets this multivector to the value of the scalar, α. The non-scalar components are set to zero.
The scalar to be copied.
The unit of measure.
Copies the spinor argument value into this multivector. The non-spinor components are set to zero.
The spinor to be copied.
Copies the vector argument value into this multivector. The non-vector components are set to zero.
The vector to be copied.
Sets this multivector to the generalized vector cross product with another multivector.
-I * (this ^ m)
this / magnitude(this)
The multivector dividend.
this / m;
this ⟼ this / (a * uom)
The scalar dividend.
Optional uom: UnitThe unit of measure.
dualization: dual(Ak) = Ak << inv(I)
In an n-dimensional Euclidean space, the inverse is the reverse.
this ^ m
Sets this multivector to the result of keeping only the specified grade. This is the grade extraction operation.
the grade to be retained.
grade(this, n)
Computes the inverse of this multivector.
inverse(this)
this << m
Computes the square root of the squared norm.
Returns the geometric product of this multivector with the rhs multivector.
The operand on the right hand side of the * operator.
this * rhs
Optional uom: Unitthis * (α * uom)
this * -1
this >> m
Sets this multivector to its reflection in the plane orthogonal to vector n.
Mathematically,
this ⟼ - n * this * n
Geometrically,
Reflects this multivector in the plane orthogonal to the unit vector, n.
If n is not a unit vector then the result is scaled by n squared.
The unit vector that defines the reflection plane.
reverse(this)
the spinor that rotates this multivector.
R * this * reverse(R)
Sets this multivector to a rotor that rotates through angle θ around the specified axis.
The (unit) vector defining the rotation aspect and orientation.
The rotation angle in radians when the rotor is applied on both sides as R * M * ~R
Sets this multivector to a rotor that rotates through angle θ in the oriented plane defined by B.
The (unit) bivector generating the rotation.
The rotation angle in radians when the rotor is applied on both sides as R * M * ~R
R = (|b||a| + b * a) / sqrt(2 * |b||a|(|b||a| + b << a))
The result is independent of the magnitudes of a and b.
this | m
Currently limited to taking the square root of a positive scalar quantity.
Computes the squared norm of this multivector.
This is an alias for the quaditude method.
this - M * α
Subtracts a multiple of a scalar from this multivector.
The scalar value to be subtracted from this multivector.
Optional uom: UnitThe optional unit of measure.
The fraction of (a * uom) to be subtracted. Default is 1.
this - (a * uom) * α
Static bivectorCreates a grade 2 (bivector) multivector from the specified cartesian coordinates. The bivector returned is in the unlocked (mutable) state.
The coordinate corresponding to the e2e3 basis bivector.
The coordinate corresponding to the e3e1 basis bivector.
The coordinate corresponding to the e1e2 basis bivector.
Optional uom: UnitThe optional unit of measure. Equivalent to 1 if omitted.
Static copyThe multivector to be copied.
Static dualStatic dualStatic dualStatic fromStatic fromStatic fromStatic fromStatic pseudoOptional uom: UnitStatic randomComputes a multivector with random components.
Static rotorComputes the rotor that rotates vector a to vector b.
Static rotorStatic rotorStatic scalarCreates a grade 0 (scalar) multivector with value alpha * uom.
The scalar returned is in the unlocked (mutable) state.
The scaling factor for the unit of measure.
Optional uom: UnitThe optional unit of measure. Equivalent to 1 if omitted.
Static spinorCreates a spinor valued multivector from the specified cartesian coordinates. The spinor returned is in the unlocked (mutable) state.
The scalar coordinate.
The coordinate corresponding to the e2e3 basis bivector.
The coordinate corresponding to the e3e1 basis bivector.
The coordinate corresponding to the e1e2 basis bivector.
Optional uom: UnitThe optional unit of measure. Equivalent to 1 if omitted.
Static vectorCreates a grade 1 (vector) multivector from the specified cartesian coordinates.
The coordinate corresponding to the e1 basis vector.
The coordinate corresponding to the e2 basis vector.
The coordinate corresponding to the e3 basis vector.
Optional uom: UnitThe optional unit of measure. Equivalent to 1 if omitted.
Static wedgeGenerated using TypeDoc
A mutable and lockable multivector in 3D with a Euclidean metric and optional unit of measure.