geo_convert_plane_coord_to_param: Convert plane in coordinate form to parameter from

In wagnius-GmbH/slvwagner: All Stuff that I`m Missing

Convert plane in coordinate form to parameter from

Description

Get parametric function for a plane with the parameter s,t:

\vec x = \vec p + s \cdot \vec u + t \cdot \vec v

The function returns a position vector

\vec p

, and two directions vectors

\vec u, \vec v

. The Vector

\vec p

is also the normal vector (perpendicular to the plane).

Usage

geo_convert_plane_coord_to_param(E, axis = c("x", "y", "z"))

Arguments

E	Plane equation (Ryacas)
axis	character vector indentifiying the axis variables e.g. c("x1","x2","x3")

Details

The coordinate form of the plane is:

a x + b y + c z - d = 0

where

d = \vec p \cdot \vec n

and

\vec n = \begin{pmatrix} a \\ b \\ c \end{pmatrix}

https://de.wikipedia.org/wiki/Ebenengleichung#Normalenform https://en.wikipedia.org/wiki/Euclidean_planes_in_three-dimensional_space

Value

list with matrix containing the Vectors

\vec p, \vec u, \vec v

and

\vec n = \begin{pmatrix} a \\ b \\ c \end{pmatrix},-d

Author(s)

Florian Wagner [e-mail]

Examples

geo_convert_plane_coord_to_param("10*x+15*y+20*z+50")
geo_convert_plane_coord_to_param("-10*x+15*y+20*z+50")
geo_convert_plane_coord_to_param("10*x-15*y+20*z+50")
geo_convert_plane_coord_to_param("10*x+15*y-20*z+50")
geo_convert_plane_coord_to_param("10*x+15*y+20*z-50")
geo_convert_plane_coord_to_param("-10*x-15*y+20*z+50")
geo_convert_plane_coord_to_param("10*x-15*y-20*z+50")
geo_convert_plane_coord_to_param("-10*x+15*y-20*z+50")
geo_convert_plane_coord_to_param("-10*x-15*y+20*z-50")
geo_convert_plane_coord_to_param("10*x-15*y-20*z-50")
geo_convert_plane_coord_to_param("-10*x+15*y-20*z-50")
geo_convert_plane_coord_to_param("10*x+15*y+50")
geo_convert_plane_coord_to_param("10*x+15*z+50")
geo_convert_plane_coord_to_param("10*y+15*z+50")
geo_convert_plane_coord_to_param("10*x+15*y-50")
geo_convert_plane_coord_to_param("10*x+15*z-50")
geo_convert_plane_coord_to_param("10*y+15*z-50")
geo_convert_plane_coord_to_param("-10*x+15*y+50")
geo_convert_plane_coord_to_param("-10*x+15*z+50")
geo_convert_plane_coord_to_param("-10*y+15*z+50")
geo_convert_plane_coord_to_param("10*x-15*y+50")
geo_convert_plane_coord_to_param("10*x-15*z+50")
geo_convert_plane_coord_to_param("10*y-15*z+50")
geo_convert_plane_coord_to_param("-10*z-50")
geo_convert_plane_coord_to_param("-10*y-50")
geo_convert_plane_coord_to_param("-10*x-50")
geo_convert_plane_coord_to_param("-10*z+50")
geo_convert_plane_coord_to_param("-10*y+50")
geo_convert_plane_coord_to_param("-10*x+50")

wagnius-GmbH/slvwagner documentation built on Jan. 19, 2025, 7:10 a.m.