Vector math operations

Usage

vector_length(x)

vector_norm(x)

# S3 method for class 'Vec3'
crossprod(x, y = NULL, ...)

# S3 method for class 'Line'
crossprod(x, y = NULL, ...)

# S3 method for class 'Ray'
crossprod(x, y = NULL, ...)

# S3 method for class 'Plane'
crossprod(x, y = NULL, ...)

dotprod(x, y)

rotate(x, rotaxis, rotangle)

# S3 method for class 'spherical'
rotate(x, rotaxis, rotangle)

angle(x, y)

# S3 method for class 'spherical'
angle(x, y)

project(x, y)

# S3 method for class 'spherical'
project(x, y)

reject(x, y)

# Default S3 method
reject(x, y)

transform_linear(x, A, norm = FALSE)

Arguments

x, y: objects of class "Vec3", "Line", "Ray", or "Plane", where the rows are the observations and the columns are the coordinates.
...: arguments passed to function call
rotaxis: Axis of rotation given as object of class "Vec3", "Line", "Ray", or "Plane".
rotangle: Angle of rotation in radians for "Vec3" objects and in degrees for "Line", "Ray" and "Plane" objects.
A: numeric 3x3 matrix. Transformation matrix.
norm: logical. If TRUE, the transformed vectors are normalized to unit length.

Value

objects of same class as x, i.e. one of "Vec3", "Line", "Ray" or "Plane". vector_length() and %*% return a real number. angle() returns a numeric angle (in degrees, unless x is class "Vec3").

Details

vector_length(): the length of a vector: $||x|| = \sqrt{x_1^2 + x_2^2 + x_3^2}$
vector_norm(): the normalized vector: $\hat{x} = \frac{x}{||x||}$
crossprod(): the cross-product of two vectors, i.e. the vector perpendicular to the 2 vectors. If y = NULL is taken to be the sam,e vector as x: $$x \times y = (x_2 y_3 - x_3 y_2, x_3 y_1 - x_1 y_3, x_1 y_2 - x_2 y_1)$$
dotprod(): the dot product of two vectors: $x \cdot y = x_1 y_1 + x_2 y_2 + x_3 y_3$
angle(): angle between two vectors: $\theta = \arccos{\frac{x \cdot y}{||x|| \, ||y||}}$
project(): projection of one vector onto the other (changes the vector length of second vector, unless their are unit vectors): $$proj_y(x) = \frac{x \cdot y}{||y||^2} y$$
transform_linear(): Linear transformation of a vector by a 3x3 matrix: $x' = A x$

Examples

vec1 <- Vec3(1, 0, 0)
vec2 <- Vec3(0, 0, 1)

vector_length(vec1) # length of a vector
#> [1] 1
crossprod(vec1, vec2) # cross product
#> Vector (Vec3) object (n = 1):
#>  x  y  z 
#>  0 -1  0 
dotprod(vec1, vec2) # dot product
#> [1] 0
rotate(vec1, vec2, pi / 2) # rotation
#> Vector (Vec3) object (n = 1):
#>            x            y            z 
#> 2.220446e-16 1.000000e+00 0.000000e+00 
angle(vec1, vec2) # angle between vectors
#> [1] 1.570796
project(vec1, vec2) # projection of a vector
#> Vector (Vec3) object (n = 1):
#> x y z 
#> 0 0 0 
transform_linear(vec1, matrix(runif(9), 3, 3)) # linear transformation
#> Vector (Vec3) object (n = 1):
#>         x         y         z 
#> 0.1714069 0.1418151 0.1022888