Morpho (version 2.2)

crossProduct: calculate the orthogonal complement of a 3D-vector

Description

calculate the orthogonal complement of a 3D-vector

Usage

crossProduct(x, y)
tangentPlane(x)

Arguments

x

vector of length 3.

y

vector of length 3.

Value

• tangentPlane:

  crossProduct: returns a vector of length 3.

• y
  vector orthogonal to x
• z
  vector orthogonal to x and y

Details

calculate the orthogonal complement of a 3D-vector or the 3D-crossproduct, finding an orthogonal vector to a plane in 3D.

Examples

require(rgl)

x <- c(1,0,0)
y <- c(0,1,0)

#example tangentPlane
z <- tangentPlane(x)
#visualize result
lines3d(rbind(0, x), col=2, lwd=2)
## show complement
lines3d(rbind(z$y, 0, z$z), col=3, lwd=2)
# example crossProduct
z <- crossProduct(x, y)
# show x and y
lines3d(rbind(x, 0, y), col=2, lwd=2)
# show z
lines3d(rbind(0, z), col=3, lwd=2)