Directional Reference Plane is an imaginary geometrical plane in Object Space that passes through the eye-point and is parallel to a particular system of parallel planes.
It provides the reference orientation through which the directional vanishing behaviour of that plane system can be described and analysed. Just as a Directional Reference Line provides the reference direction for a family of parallel lines, a Directional Reference Plane provides the corresponding reference for a family of parallel planes.
Where the Directional Reference Plane intersects the Picture Plane, it forms the corresponding Vanishing Trace.
Basic Definition
A Directional Reference Plane has three fundamental characteristics:
- it passes through the eye-point;
- it is parallel to the object-space plane system being analysed;
- its relationship with the Picture Plane determines the corresponding Vanishing Trace.
The plane is therefore not an arbitrary construction. Its orientation is determined by the orientation of the particular family of parallel planes under consideration.
It is an imaginary geometrical reference, not necessarily a physical plane visible within the scene.
Object Plane and Directional Reference Plane
The object plane and its Directional Reference Plane are parallel but distinct.
The object plane belongs to the spatial object or scene. The Directional Reference Plane passes through the eye-point while retaining the same orientation as the plane system being analysed.
The relationship can be expressed as:
Object-Space Plane System ∥ Directional Reference Plane through Eye-Point
The Directional Reference Plane therefore transfers the orientation of the plane system to the eye-point, where its relationship to the Picture Plane can be used to determine the corresponding perspective vanishing structure.
Directional Reference Plane and Vanishing Trace
The intersection of a Directional Reference Plane with the Picture Plane forms the Vanishing Trace associated with that plane system.
This may be expressed simply as:
Directional Reference Plane ∩ Picture Plane = Vanishing Trace
The Vanishing Trace contains the vanishing points associated with the different line directions lying within the corresponding plane.
The Directional Reference Plane therefore provides the object-space reference geometry, while the Vanishing Trace is its corresponding image-space expression.
Directional Plane Vanishing
Directional Plane Vanishing concerns the apparent convergence of a system of parallel planes towards a common Vanishing Trace.
Each system of parallel planes has a corresponding Directional Reference Plane passing through the eye-point. Its intersection with the Picture Plane establishes the trace towards which the directional structure of those planes converges in perspective.
For example, a set of parallel corridor walls may appear to converge as they recede. The walls themselves remain parallel in Object Space, but their perspective relationship can be analysed through a Directional Reference Plane having the same orientation.
The resulting Vanishing Trace provides the limiting image-space line associated with that plane system.
Plane Vanishing Does Not Replace Line Vanishing
Planes contain lines, and these line directions continue to possess their own vanishing points.
A plane system may therefore possess a Vanishing Trace while individual line systems lying within those planes simultaneously possess corresponding Vanishing Points.
These are related but different geometrical relationships:
- parallel line system → Directional Reference Line → Vanishing Point
- parallel plane system → Directional Reference Plane → Vanishing Trace
The vanishing points of line directions contained within a plane lie upon the Vanishing Trace associated with that plane.
Directional Reference Plane and the Visual Element
The Visual Element of the System provides a general geometrical reference for the spatial system being analysed.
For a family of parallel lines, the Visual Element takes the form of a Directional Reference Line passing through the eye-point and parallel to that line system.
For a family of parallel planes, it takes the form of a Directional Reference Plane passing through the eye-point and parallel to that plane system.
Each differently oriented family of planes can therefore possess its own Directional Reference Plane.
The Visual Element of the System and Directional Reference Line →
Many Directional Reference Planes
There is not one universal Directional Reference Plane for an entire scene.
A spatial scene may contain many differently oriented systems of parallel planes. Each orientation can be represented by its own Directional Reference Plane passing through the same eye-point.
Directional Reference Planes can consequently occur at many orientations around the observer.
For example, a scene might contain:
- horizontal floor planes;
- vertical wall planes;
- inclined roof planes;
- sloping ramps;
- obliquely oriented surfaces.
Each differently oriented plane system possesses its own directional reference relationship and potentially its own Vanishing Trace.
The Horizon Plane as a Directional Reference Plane
The Horizon Plane provides an important special case of the Directional Reference Plane principle.
In the standard level-ground configuration, the Horizon Plane passes horizontally through the eye-point and is parallel to the horizontal Ground Plane.
It therefore acts as the Directional Reference Plane for the horizontal Ground Plane system.
Where this plane intersects the Picture Plane, it produces the familiar horizon line.
Thus:
Horizontal Ground Plane ∥ Horizon Plane through Eye-Point
Horizon Plane ∩ Picture Plane = Horizon Line
The horizon is therefore a special horizontal example of the more general directional-plane principle.
Directional Reference Plane and Aspect Vanishing
The Directional Reference Plane also provides an important reference for understanding Aspect Vanishing.
Directional Plane Vanishing concerns the directional relationship of a system of parallel planes and its Vanishing Trace. Aspect Vanishing concerns the changing visible aspect of a plane as its orientation approaches an edge-on limiting condition.
These effects are related through plane orientation, but they should not be treated as the same phenomenon.
The Directional Reference Plane provides a common reference from which these different plane-related perspective effects can be distinguished.
Directional Reference Plane and Picture Plane
The Directional Reference Plane exists in Object Space, while its trace is expressed on the Picture Plane.
Changing the orientation of the Picture Plane can therefore change the position and orientation of the resulting Vanishing Trace without changing the orientation of the original plane system itself.
This is an important distinction. The reference plane belongs to the directional geometry of the spatial system relative to the eye-point; the resulting trace depends upon where that plane intersects the particular Picture Plane used by the perspective system.
Reference Geometry Is Not Scene Geometry
A Directional Reference Plane should not be mistaken for a physical plane that must actually exist within the scene.
It is a geometrical reference construct established through the eye-point parallel to the spatial plane system being analysed.
The physical planes remain where they are in Object Space. The Directional Reference Plane makes their common orientation explicit relative to the viewpoint and Picture Plane.
This allows their directional perspective relationships to be described without requiring a physical reference plane to pass through the observer.
Why the Directional Reference Plane Matters
The Directional Reference Plane extends the general theory of directional reference from lines to planes.
It explains why differently oriented systems of parallel planes possess different vanishing relationships, why their associated directional vanishing points align upon common traces, and why the horizon represents only one special horizontal example of a much broader geometrical principle.
The concept therefore provides an important connection between Object Space, the eye-point, plane orientation, the Picture Plane, Vanishing Points, Vanishing Lines and Vanishing Traces.