Ground Plane is a principal spatial reference plane used in perspective geometry. In its standard form it is an imaginary or physical horizontal plane in Object Space upon which objects, scenes, grids and other spatial structures may be located or related.
The Ground Plane is especially important in graphical and mathematical perspective because it provides a common spatial reference for analysing distance, position, direction, vanishing, scale and the relationship between the observer, Picture Plane and represented scene.
It is important to distinguish the Ground Plane in Object Space from its perspective image in Image Space. They are related by projection but are not the same plane.
The Ground Plane in Object Space
The Ground Plane belongs principally to Object Space: the physical, artificial, simulated or imagined space containing the objects and spatial information being viewed or represented.
In the conventional level-ground arrangement, the Ground Plane is treated as a horizontal plane extending beneath or through the spatial scene. Objects may stand upon it, lines may run across it, and metric grids may be constructed upon it to analyse depth and spatial recession.
The Ground Plane does not have to correspond literally to visible terrain. It can be an abstract geometrical reference plane used to organise a perspective system.
Ground Plane and Picture Plane
The Picture Plane and Ground Plane serve different geometrical functions.
The Ground Plane belongs to the spatial scene being represented, whereas the Picture Plane is the image or projection surface upon which the perspective representation is formed.
In the traditional linear-perspective arrangement, the Picture Plane is commonly vertical and perpendicular to a level Ground Plane. Their intersection forms the ground line or baseline of the construction.
This is a conventional and particularly useful arrangement, but it should not be mistaken for the only possible perspective configuration.
Ground Plane and Horizon Plane
The Ground Plane and Horizon Plane are distinct planes.
In the standard level-ground configuration they are horizontal and parallel. The Ground Plane lies within the spatial scene, while the Horizon Plane is the horizontal reference plane passing through the eye-point or station point.
The physical separation between the two corresponds to the height of the viewpoint above the Ground Plane and remains constant as the planes extend into space.
This parallel relationship explains why the vanishing line associated with horizontal ground-plane directions occurs at the level of the observer’s horizon in the standard level-view configuration.
The Ground-Plane Horizon
A plane contains infinitely many spatial directions. The vanishing points corresponding to the different parallel directions lying within that plane collectively form its vanishing line.
For a horizontal Ground Plane in the standard level-view arrangement, this vanishing line corresponds to the familiar horizon line.
The horizon should therefore not be understood merely as the visible boundary between land or sea and sky. In geometrical perspective, it is the vanishing line associated with the horizontal ground-plane system.
Ground Plane in Image Space
The projected appearance of the Ground Plane must be distinguished from the original Ground Plane itself.
The Dictionary of Perspective identifies the Perspective Plane (Ground) as the perspective image of the Ground Plane seen in Image Space.
In a standard graphical construction, this represented plane extends from the baseline towards the horizon. As positions on the physical or modelled Ground Plane recede from the Picture Plane, their projected positions approach the ground-plane horizon.
The distinction can therefore be expressed simply as:
Ground Plane in Object Space → projection → Ground Plane in Image Space
Ground-Plane Grids
A Ground Plane is often represented by a metric or rectangular grid. Such a grid provides a convenient way to demonstrate and measure perspective recession.
Equal physical intervals in Object Space do not normally remain equally spaced in the perspective image. As grid divisions recede from the observer, their projected spacing decreases and approaches the plane’s vanishing line.
Ground-plane grids are therefore useful for studying:
- distance and recession;
- scale diminution;
- vanishing points;
- vanishing lines;
- object placement;
- measurement in depth;
- one-, two- and three-point perspective constructions.
Ground Plane in One-Point Perspective
In conventional one-point linear perspective, one principal family of horizontal lines on the Ground Plane recedes directly away from the observer.
These ground-plane orthogonals converge towards the central vanishing point, while directions parallel to the Picture Plane remain parallel within the image.
This familiar arrangement is especially evident in images of roads, railway tracks, corridors, rooms and rectangular floor grids.
It is nevertheless only a special geometrical configuration of the wider relationships possible between Ground Plane, viewpoint, viewing direction and Picture Plane.
Ground Plane in Two-Point Perspective
In two-point perspective, two principal horizontal direction systems within or parallel to the Ground Plane normally recede towards separate vanishing points.
Both vanishing points lie on the Ground Plane’s vanishing line in the standard level-view arrangement.
The Ground Plane therefore supplies a common spatial plane within which differently oriented families of parallel directions can possess different vanishing points while still sharing the same vanishing line.
Two-Point Linear Perspective →
Ground Plane and Station Point
The position of the Station Point relative to the Ground Plane is fundamental to the resulting perspective.
The height of the station point determines the height of the observer above the Ground Plane. Raising or lowering the viewpoint changes how much of the Ground Plane is visible and changes the apparent relationship between objects and the horizon.
Moving the station point horizontally or changing the viewing direction also changes the projected appearance of ground-plane structures even though the Ground Plane itself remains fixed in Object Space.
Ground Plane and Inclined Planes
The Ground Plane is usually defined as the principal level horizontal plane, but spatial scenes can contain many other planes having different orientations.
An inclined, ascending, descending or oblique surface should therefore not automatically be treated as part of the Ground Plane merely because an object stands upon it.
Each differently oriented plane possesses its own directional structure and corresponding vanishing relationships.
This distinction becomes especially important when analysing stairs, ramps, roofs, hills, inclined roads and other non-horizontal surfaces.
Why the Ground Plane Matters
The Ground Plane provides one of the principal geometrical reference structures connecting Object Space, the viewpoint, the Picture Plane and Image Space.
It enables positions and directions within spatial reality to be organised and measured, provides a basis for perspective grids, and establishes the plane whose horizontal directional systems generate the familiar ground-plane horizon in the standard level-view arrangement.
Most importantly, the Ground Plane should not be confused with its image. The original Ground Plane exists in Object Space; its perspective representation is a transformed plane in Image Space.