vec
Constructs a 2D vector from vec(x, y), or a 3D vector from vec(x, y, z) -- dispatches on argument count.
x(number) --y(number) --z(number) -- optional -- present makes this a 3D vector
Vectors
add
Adds two vectors of the same dimension (both 2D or both 3D). Also works on complex numbers (complex(3, 4)). Also works on quaternions. Also works on tensors. Also the exact sum of two algebraic numbers.
a(vector) --b(vector) -- same dimension as a
sub
Subtracts b from a, for two vectors of the same dimension. Also works on complex numbers (complex(3, 4)). Also works on quaternions. Also works on tensors.
a(vector) --b(vector) -- same dimension as a
scale
Multiplies a vector by a scalar. Also a number times a quaternion. Also works on tensors.
v(vector) --s(number) -- scale factor
neg
Negates a vector, reversing its direction. Also works on complex numbers (complex(3, 4)). Also works on quaternions. Also works on tensors.
v(vector) --
normalize
Scales a vector to unit length, keeping its direction. Also the unit quaternion q/|q|.
v(vector) --
rotate
Rotates a 2D vector by an angle, in radians. Has no 3D form -- there is no single axis to rotate around. With a quaternion and a 3D vector: the vector rotated by q.
v(vector2) --theta(number) -- angle in radians
dot
The dot product of two vectors of the same dimension. Also the dot product of two quaternions.
a(vector) --b(vector) -- same dimension as a
mag
The magnitude (length) of a vector.
v(vector) --
cross
The cross product of two vectors of the same dimension -- a scalar (the z-component) for two 2D vectors, a vector for two 3D vectors.
a(vector) --b(vector) -- same dimension as a
angle
The angle, in radians, a 2D vector makes with the x-axis. 2D only -- there is no single reference axis in 3D.
v(vector2) --
angleBetween
The angle, in radians, between two vectors of the same dimension.
a(vector) --b(vector) -- same dimension as a
projScalar
The scalar projection of a onto b -- the length of a's component along b.
a(vector) --b(vector) -- same dimension as a
projVector
The vector projection of a onto b -- a's component along b, as a vector.
a(vector) --b(vector) -- same dimension as a
reject
The vector rejection of a from b -- a's component perpendicular to b.
a(vector) --b(vector) -- same dimension as a
scalarTriple
The scalar triple product a . (b x c), for three 3D vectors -- the signed volume of the parallelepiped they span.
a(vector3) --b(vector3) --c(vector3) --
vectorTriple
The vector triple product a x (b x c), for three 3D vectors.
a(vector3) --b(vector3) --c(vector3) --