For a plane there are different ways to define, that can be converted to each other:
Parameter form: Pointform: Plane is defined with the 3 points , . and .
Coordinates form: a x +b y + c z=d
Normal form: with ; d³0
d is the distance to the zeropoint.
has the direction to the zeropoint.
Conversion point form in parameter form
.
Conversion parameter form in point form
; ;
Conversion parameter form in coordinates form
Multiplication with .
=
n1 x + n2 y + n3 z = n1 a1 + n2 a2 + n3 a3
Conversion coordinates form in parameter form
If a 0
; ;
else if b 0
; ;
else if c 0
; ;
else
; ;
, 
. and 
.
with 
; d³0
has the direction to the zeropoint.
.
; 
; 
.
= 
0
; 
; 
; 
; 
; 
; 
; 
; 