getBase: Get a 3D basis from a normal

In tunelipt/model3d: Funções para manipulação de modelos 3D.

Description

When projecting a 3D object into a plane it is necessary to have a local 2D coordinate system on the plane. This coordinate system is given by 2 orthonormal unit vectors. On the other hand, the plane o projection is usually characterized by its normal so it is useful to get the local 2D coordinate system from this normal. There are infinite solutions to this problem but what this function do is use the normal (which in the local reference system is z) to build "nice" local coordinate system. This function does that by trying to align the local system as closely as possible to (x, y, z) global coordinate system.

Usage

  getBase(bz)

Arguments

bz	A normal to the plane of projection.

Value

Matrix where the columns are the unit vectors of the local coordinate system (x, y and z)

Examples

bz <- c(sqrt(2)/2, sqrt(2,2), 0)
print(getBase(bz))

tunelipt/model3d documentation built on Nov. 5, 2019, 10:59 a.m.