r_{1} ∩ r_{2} = X ∈ x, r_{1} ∩ r_{3} = Y ∈ y, r_{2} ∩ r_{3} = Z ∈ z.
In the figure above we can see how to denote (the notation of) the traces. If all three traces are drawn, they are drawn as a solid line only on the part which lies in the I. octant. Other parts, if necessary, are drawn as dashed lines.Animation starts by clicking in the figure above.
horizontal projecting plane
E E ⊥ Π_{1}, E  z e_{1} = E' 
vertical projecting plane
E E ⊥ Π_{2}, E  y e_{2} = E'' 
profile projecting plane
E E ⊥ Π_{3}, E  x e_{3} = E''' 
Σ 
Π_{1}, Σ ⊥ z
Σ ⊥ Π_{2}, Π_{3} Σ  x, y 
Σ 
Π_{2}, Σ ⊥ y
Σ ⊥ Π_{1}, Π_{3} Σ  x, z 
Σ 
Π_{3}, Σ ⊥ x
Σ ⊥ Π_{1}, Π_{2} Σ  y, z 
Trace s_{1} is the line
at infinity of the plane Π_{1}. This type of planes are called horizontal planes. 
Trace s_{2} is the line
at infinity of the plane Π_{2}. This type of planes are called vertical planes. 
Trace s_{3} is the line
at infinity of the plane Π_{3}. This type of planes are called profile planes. 
On these image we highlight the areas where the points of the plane that lie in the 1. octant are projected.
Traces of the symmetry plane. 
Traces of the coincidence plane. 
Traces of any line are points contained in Π_{1}
and Π_{2}. Therefore, if a line lies in a plane then and only then
its horizontal trace lie on the horizontal trace of the plane and its vertical trace
lie on the vertical trace of the plane. And obviously its profile trace lie on the
profile trace of the plane. p ⊂ Ρ <=> P_{1} ∈ r_{1} & P_{2} ∈ r_{2} Construction of the projections of a line in the plane given by its traces. 
Point lies in a plane if and only if the point lies on a line contained in
this plane.
T ∈ Ρ <=> ∃ p ⊂ Ρ & T ∈ p 
Construction is shown in the image on the rightside. Click on the image to start the animation. Describe by words the principle of the construction. 

Construction is shown in the image on the rightside. Click on the image to start the animation. Describe in words the principle of the construction. 

Ρ   Σ =>r_{1}   s_{1} & r_{2}   s_{2}.
Ρ ∩ Σ = P_{1}P_{2}, ifP_{1} = r_{1} ∩ s_{1} & P_{2} = r_{2} ∩ s_{2}.
Parallel planes.  Planes intersect along the line p. 
A construction of the planes from the pencil (p).
a — H principal line  b — V principal line  c — P principal line 
Created by Sonja Gorjanc, translated by Helena Halas and Iva Kodrnja  3DGeomTeh  Developing project of the University of Zagreb