The horizon line is one of the fundamental geometrical structures of perspective, but the term is often used for several different things that should be carefully distinguished.
In its principal geometrical meaning, the geometrical horizon line is the vanishing line of the horizontal ground plane and of all planes parallel to it. It contains the vanishing points belonging to horizontal spatial directions and, in a conventional upright perspective construction, corresponds to the represented observer’s eye level.
In less technical usage, horizon line may also refer to the visible boundary where land, sea or another extended surface appears to meet the sky. This visible or optical horizon may approximately coincide with the geometrical horizon line under particular conditions, but the two concepts are not identical.
The distinction is essential. A perspective scene can possess a geometrical horizon even when no sky, sea or distant landscape boundary is visible. Conversely, a visible skyline, mountain ridge or terrestrial horizon may occur somewhere other than the geometrical horizon line.
The Fundamental Geometrical Definition
A plane contains many possible line-directions. Every direction within that plane has a corresponding vanishing point. Collectively, those vanishing points form the vanishing line of the plane.
The ordinary geometrical horizon line is therefore the special vanishing line associated with the horizontal plane. All horizontal directional systems that possess a depth component relative to the projection arrangement have vanishing points lying upon this line.
This means that the horizon line should not be understood simply as a horizontal construction mark placed across a perspective drawing. It represents a much deeper geometrical relationship between the observer, horizontal spatial directions, the station point and the picture plane.
Horizon Plane and Horizon Line
The Horizon Plane, also described in related contexts as the horizontal sight plane or sensible-horizon plane, is the horizontal reference plane passing through the observer’s eye-point and perpendicular to the local vertical.
The horizon line is not this plane itself. In a conventional perspective arrangement, it is the line formed where the Horizon Plane intersects the picture plane.
The distinction can therefore be stated simply:
- Horizon Plane: a horizontal plane passing through the eye-point.
- Horizon Line: the trace or intersection of that plane with the picture plane in the conventional arrangement.
The Horizon Plane and horizon line should not be treated as the cause of the convergence of horizontal line systems. Rather, the horizon line is the common locus upon which the vanishing points belonging to horizontal directions are represented.
The Horizon Line as a Vanishing Line
The geometrical horizon line is a line of vanishing points. It contains potentially many different vanishing points, each corresponding to a different horizontal direction.
For example, one horizontal line system may extend directly away from the observer and possess a central vanishing point. Another horizontal system may recede towards the left, another towards the right, and others may occupy intermediate directions. Their vanishing points differ, but because all of these directions lie within the same horizontal plane, their vanishing points lie upon the same horizon line.
The horizon line is therefore not itself a vanishing point. It is the vanishing line containing the potential vanishing points of horizontal directions.
The Horizon Line as a Vanishing Trace
The geometrical horizon line can also be understood as the vanishing trace of the system of horizontal planes.
All mutually parallel horizontal planes share the same projective vanishing line. A ground plane, a horizontal ceiling plane and any other plane parallel to them therefore belong to the same directional plane system and share the same vanishing trace.
The physical planes do not literally meet upon this line. The horizon represents their common projective structure at infinity.
Horizon Line and Eye Level
In the conventional upright and level perspective arrangement, the geometrical horizon line corresponds to the observer’s eye level.
This occurs because the horizontal plane passing through the eye is parallel to the horizontal ground plane. Its intersection with the upright picture plane establishes the geometrical horizon line.
Raising the observer raises this horizon relative to objects in the represented scene; lowering the observer lowers it. Consequently, whether an observer is standing, sitting, close to the floor or at a high viewpoint, the geometrical horizon continues to correspond to that observer’s eye level in the normal level-view arrangement.
However, eye level is not universally synonymous with every kind of horizon. The visible terrestrial horizon, skyline, astronomical horizon and various optical or local horizons are distinct concepts.
The PRC Master Classification of Horizon Types
The Dictionary of Perspective organises horizon terminology into seven broad groups comprising 41 standard, extended, refined or source-dependent concepts:
- Standard or established terms: Astronomical Horizon; Eye Level; Geometrical Horizon; Geometrical Horizon Line; Horizon Line; Sensible Horizon; Skyline; Terrestrial Horizon; Vanishing Line of a Plane; Vertical Vanishing Point; Visible or Apparent Horizon.
- Circular and observer-distance types: Circular Horizon Types A, B and C; Apparently Infinite Horizon Line; Local Horizon Types A, B and C; Medium-Distance Horizon; Non-Infinite Horizon; Osculating-Sphere Horizon Line.
- Primary horizon-line types: Actual Primary Horizon Line; Artificial Primary Horizon Line; Geometrical Primary Horizon Line.
- Secondary and plane-oriented types: Secondary or Auxiliary Horizon Line, physical/optical and geometrical types; Tilted Horizon Line; Transverse or Vertical Horizon Line, physical/optical and geometrical types.
- Optical and geometrical vanishing concepts: Geometrical Vanishing Limit; Optical Horizon Line; Optical Vanishing Limit; Multiple Horizon Lines; Horizon-Line Isocephaly.
- Represented and conceptual terms: Artificial or Constructed Horizon; Horizon — Dual Reality; Mechanical Horizon; Represented Horizon.
- Ambiguous or source-dependent terms: True Horizon; Geographical Horizon; Right Horizon.
These terms do not all refer to the same geometrical entity. The classification is intended precisely to prevent physical, optical, astronomical, represented and projective meanings of horizon from being conflated.
Geometrical Horizon Line
The geometrical horizon line, also called the perspective horizon line or horizontal vanishing line, is the vanishing line of horizontal planes in a perspective projection.
It contains the vanishing points of all horizontal spatial directions that are not parallel to the picture plane. Directions parallel to the picture plane have their vanishing points at infinity and consequently do not produce finite convergence points within the ordinary rectilinear picture.
In an upright construction the geometrical horizon normally appears horizontal. Pitching the viewing direction can move its image position upwards or downwards, while rolling the viewing system or picture plane can make the horizon appear sloping within the image.
The geometrical horizon is a projective structure representing horizontal directions at infinity. It is therefore conceptually different from a physical land–sky or sea–sky boundary at a measurable distance.
Apparently Infinite Horizon Line
The Apparently Infinite Horizon Line describes the geometrical horizon as the projective limit of an indefinitely extended horizontal plane.
Horizontal parallel directions appear to approach corresponding points upon this horizon as depth increases. The horizon nevertheless represents projective infinity, rather than a physical line located at some measurable distance from the observer.
This makes it fundamentally different from an ordinary terrestrial horizon, which is physically finite because of the curvature of the Earth, terrain, occlusion and other environmental conditions.
Optical or Visible Horizon Line
The Optical Horizon Line, also called the visible, apparent, natural or physical horizon in appropriate contexts, is the directly observed or optically imaged boundary where an extended terrestrial surface appears to meet the sky.
Unlike the geometrical horizon line, it is a physical and optical feature. It may be curved, irregular, interrupted or completely hidden. Its apparent form can be affected by terrain, observer height, atmospheric refraction, optical characteristics and imaging conditions.
Over a level, unobstructed sea and under ordinary viewing conditions, the optical horizon may appear close to the geometrical horizon line. On land, hills, trees, buildings and other structures commonly prevent such coincidence.
The two must therefore be identified separately whenever precision matters:
- Geometrical Horizon Line: projective vanishing line of horizontal planes.
- Optical Horizon Line: visible or imaged physical boundary within the observed scene.
Optical Horizon and Optical Vanishing Limit
The optical horizon should also be distinguished from the Optical Vanishing Limit.
An optical horizon is an observable scene boundary. An optical vanishing limit is the distance, region or threshold at which a particular object, line, pattern or detail becomes too small, faint, blurred or low in contrast to remain distinguishable.
The optical vanishing limit therefore depends upon the visual or imaging system and upon the information being viewed. It is not necessarily located upon the visible horizon.
Visible Horizon, Skyline and Horizon Line
A skyline is the visible outline of land, mountains, buildings, trees or other objects against the sky. A skyline may look like a horizon, but it need not be either the visible terrestrial horizon or the geometrical horizon line.
A mountain ridge, for example, may form a strong boundary against the sky while lying much nearer than the distant terrestrial horizon. Likewise, an urban skyline may conceal the true outdoor horizon entirely.
The presence of a strong visible boundary should therefore never by itself be taken as evidence that the geometrical horizon lies there.
Actual and Represented Horizons
The Dictionary distinguishes between actual and represented horizons.
An actual horizon is observed within physical or optical space. A represented horizon is depicted or established within a drawing, painting, photograph, film, diagram, model, instrument display or computer-generated image.
A represented horizon may perform either of two quite different functions:
- it may depict the visible physical boundary between land, water and sky; or
- it may represent the geometrical vanishing line used to organise the perspective construction.
These functions may coincide within a particular image, but they should not be assumed to do so.
Primary Horizon Lines
The Dictionary distinguishes three principal meanings of Primary or Principal Horizon Line:
- Actual Primary Horizon Line: the principal visible horizon directly observed in a physical scene.
- Artificial Primary Horizon Line: the principal visible or geometrical horizon represented within an image.
- Geometrical Primary Horizon Line: the principal vanishing line of the horizontal ground plane and all planes parallel to it.
The third meaning corresponds to the standard geometrical horizon used in linear perspective. It contains the central or principal vanishing point in one-point perspective and the principal left and right horizontal vanishing points in two-point perspective.
Horizon Line in One-Point Perspective
In conventional one-point perspective, the principal receding horizontal line system extends directly away from the observer and converges towards a central vanishing point.
Because that principal line system is horizontal, its vanishing point lies upon the geometrical horizon line. In the familiar level arrangement, this central point also lies at the observer’s represented eye level.
This is a special configuration in which several normally distinct perspective relationships coincide. It should not lead to the assumption that the horizon line itself causes the receding lines to converge. The horizon simply contains the vanishing point belonging to that horizontal direction.
Nor should one-point perspective lead to the belief that a horizon possesses only one vanishing point. The geometrical horizon contains the potential vanishing points of all horizontal directions, even though the construction may emphasise only one principal point.
Horizon Line in Two-Point Perspective
In two-point perspective, two principal horizontal directional systems recede in different directions. Each possesses its own vanishing point.
Because both systems remain horizontal in object space, both vanishing points lie upon the same geometrical horizon line.
The left and right vanishing points may move along the horizon as the object or viewing relationship changes. The horizon does not move simply because an object rotates upon a level horizontal plane; instead, the corresponding directional vanishing points change their positions upon it.
Horizon Line in Three-Point Perspective
Three-point perspective introduces a third principal vanishing direction, commonly corresponding to vertical lines that have acquired a depth component relative to the projection arrangement.
The two principal horizontal vanishing points continue to belong to the horizontal geometrical horizon line. The third, vertical vanishing point does not ordinarily belong to that horizon.
This distinction is important because introducing vertical convergence does not transform the ordinary horizontal horizon into a vertical horizon. Horizontal and vertical directional systems possess different vanishing structures.
Distance Points on the Horizon Line
The geometrical horizon also contains specialised construction points such as distance points.
In a conventional measured perspective construction, left and right distance points are the vanishing points of horizontal directions oriented at 45 degrees to the picture plane. They are positioned upon the horizon line and can be used for constructing measured recession and perspective grids.
The presence of such points further demonstrates that the horizon line is not defined by one single vanishing point. It is a directional line capable of containing many horizontal vanishing points.
Secondary and Auxiliary Horizon Lines
The Dictionary identifies Secondary or Auxiliary Horizon Lines in both physical/optical and geometrical senses.
In the physical or optical sense, a subsidiary apparent boundary may arise from an inclined surface, reflection, local visual field or other secondary spatial relationship.
In the geometrical sense, the expression has sometimes been applied to the vanishing line of an inclined, declined or oblique plane. All directions lying within that plane have vanishing points upon its own vanishing line.
However, because horizon line is conventionally reserved for the vanishing line of the horizontal plane, the more precise preferred expression is generally Vanishing Line of an Inclined Plane.
Inclined Horizon Line
The expression Inclined Horizon Line may be encountered for the vanishing line belonging to an inclined spatial plane.
Such a plane contains many line-directions. Their vanishing points lie upon a common inclined vanishing line, just as horizontal directions lie upon the ordinary horizontal horizon.
For precision, however, this should generally be described as the vanishing line of the inclined plane rather than as another ordinary horizon line.
Tilted or Rolled Horizon Line
A Tilted Horizon Line can describe a horizon that appears sloping because the camera, observer, picture plane or completed image has been rolled relative to the local vertical.
This must be distinguished from the vanishing line of an inclined object plane. A rolled geometrical horizon and an inclined-plane vanishing line are two different geometrical situations even though both may appear as diagonal lines within an image.
The terminology is therefore important:
- Rolled or Tilted Horizon: the ordinary horizon appears sloping because the viewing or image system is rolled.
- Vanishing Line of an Inclined Plane: the vanishing line belonging to a genuinely inclined spatial plane.
Transverse or Vertical Horizon Line
The Dictionary also records Transverse or Vertical Horizon Line as an extended classification with physical/optical and geometrical meanings.
In a physical or optical sense, it can refer to a vertically or transversely oriented apparent boundary or visual limit.
In geometrical perspective, it can refer to the vanishing line of a vertical plane. Depending upon the relationship of that plane to the picture plane, its vanishing line may itself appear vertical, oblique or, in a limiting configuration, lie at infinity.
Again, the more precise terminology is normally Vanishing Line of a Vertical Plane. A vertical vanishing line should not be confused with a vertical vanishing point, which belongs to one particular set of mutually parallel vertical lines.
Multiple Horizon Lines and Vanishing Lines
A complex perspective scene may contain numerous planes of different orientations. Each plane orientation has a corresponding vanishing line.
Consequently, an image can contain several apparent horizon-like or vanishing lines, particularly where there are inclined planes, separate perspective systems, reflections, multiple viewpoints or other complex spatial arrangements.
The term Multiple Horizon Lines can describe this broader situation, but technically only the vanishing line of the horizontal plane is normally called the ordinary horizon line. The others are more precisely the vanishing lines or traces of their respective planes.
Local Horizon
The Dictionary extends horizon terminology to several Local Horizon concepts.
A Local Horizon Type A can be understood as the trace of the observer’s horizontal eye plane upon nearby enclosing surfaces. Inside a room, for example, an imaginary horizontal eye-level line could be continued around the walls.
The corresponding graphical or represented line provides the same local eye-plane reference within a drawing or perspective construction.
A further extended use describes a nearby edge, frame, wall or other object that limits part of the visual field as a local visual or occlusion boundary.
These local horizons should not be confused with the distant outdoor visible horizon. They describe observer-relative boundaries or eye-plane references operating within a nearer spatial environment.
Medium-Distance Horizon
A Medium-Distance Horizon is a visible boundary formed at an intermediate distance by a ridge, hill, mountain, inclined road or other raised terrain.
It may visually separate foreground terrain from the sky and therefore resemble a distant horizon. Geometrically, however, it is normally a skyline or occlusion boundary rather than the projective horizon of the horizontal plane.
This distinction helps explain why the most visually obvious “horizon” in a landscape image does not necessarily identify the true geometrical horizon line of the perspective system.
Non-Infinite Horizons
A Non-Infinite Horizon is a physical, optical or apparent boundary located at a finite observer-relative distance rather than at the projective infinity represented by the geometrical horizon line.
Examples include the visible terrestrial horizon, a terrain ridge, a local visual boundary or the apparent limb of a curved surface.
A drawn geometrical horizon line is physically finite because it appears on a finite sheet, canvas or screen. Nevertheless, what it represents geometrically remains a projective line at infinity. The physical length of the drawn mark should not therefore be confused with the spatial meaning of the horizon represented.
Circular Horizon
The familiar straight horizon line of a flat perspective image represents only a limited section or projection of a much broader directional relationship.
The Dictionary distinguishes three Circular Horizon types:
- Circular Horizon Type A — Earth-Curvature-Influenced Horizon: the terrestrial horizon as affected by the spherical curvature of the Earth.
- Circular Horizon Type B — Complete 360-Degree Horizon: the complete horizon circle surrounding an observer in horizontal directions.
- Circular Horizon Type C — Osculating-Sphere Horizon: a horizon or limb produced where sight lines are tangent to a sphere or locally approximating spherical surface.
A short portion of the terrestrial horizon usually appears approximately straight from a low viewpoint because the Earth is extremely large relative to the observer. Its curvature becomes more evident as the field of view and observer height increase.
Osculating-Sphere Horizon Line
The Osculating-Sphere Horizon Line describes an apparent curved or circular horizon produced where the observer’s sight lines become tangent to a spherical or locally approximated spherical surface.
The concept may be applied to the terrestrial horizon when the Earth is represented by a spherical approximation, to the Earth’s limb from high altitude or space, or to another spherical body or model.
It belongs to a curved-surface horizon geometry and should not be confused with the straight geometrical horizon line conventionally drawn across a flat perspective picture plane.
Sensible Horizon
The Sensible Horizon is the horizontal plane passing through the observer’s eye and perpendicular to the local vertical.
It is therefore a plane rather than the visible boundary between Earth and sky. In perspective terminology it is closely related to the horizontal sight plane or Horizon Plane.
For an observer above the Earth’s curved surface, the visible terrestrial or sea horizon normally lies somewhat below the sensible horizontal. The two concepts consequently should not be treated as identical.
Astronomical Horizon
The Astronomical Horizon, also called the celestial or rational horizon, is a great-circle reference upon the celestial sphere whose plane passes through the centre of the Earth.
It is an astronomical geometrical reference rather than the visible outdoor boundary formed by land, sea or other obstructions.
Its inclusion in the broader horizon classification demonstrates why the unqualified word horizon can be ambiguous across perspective, optics, astronomy and spatial observation.
Geometrical Horizon
The expression Geometrical Horizon itself has more than one established use.
In navigation or geodesy it can refer to a calculated terrestrial horizon determined from the form of the Earth and the observer’s position. In perspective, it may instead refer to the Geometrical Horizon Line, the projective vanishing line of horizontal planes.
These two meanings should be distinguished by context rather than assumed to be identical.
Terrestrial Horizon
Terrestrial Horizon is a broad expression for a horizon associated with the Earth’s surface.
Depending upon context, it may refer to the directly visible land–sky or sea–sky boundary, the complete horizon circle surrounding an observer, or a geometrically calculated terrestrial horizon.
Where precision is required, the more specific terms Visible Horizon, Circular Horizon or Geometrical Horizon should therefore be used.
The Problem with “True Horizon”
The expression True Horizon is potentially ambiguous because it has historically been used for several different concepts.
Depending upon the source, it may refer to an unobstructed visible horizon, a calculated geometrical terrestrial horizon or an astronomical horizon.
The PRC therefore recommends using a more precise expression wherever possible: Visible Horizon, Geometrical Horizon, Sensible Horizon or Astronomical Horizon, according to the intended meaning.
Geographical and Right Horizon
Geographical Horizon is another potentially ambiguous expression. It has been used for several terrestrial or location-dependent horizon concepts and should normally be replaced by a more specific term.
Right Horizon is a historical or specialised expression whose exact meaning depends upon the source in which it occurs. It should therefore not be used as a principal modern term without a precise definition.
Artificial, Constructed and Represented Horizons
An Artificial or Constructed Horizon is deliberately established within an image, model or other representational system.
In a perspective drawing it may serve as the geometrical vanishing line governing horizontal directional systems. In a painting or photograph it may instead depict the visible outdoor horizon. In some images it performs both functions simultaneously.
The broader term Represented Horizon encompasses visible or geometrical horizons appearing in drawings, paintings, photographs, film frames, diagrams, computer-generated imagery and similar forms of representation.
Mechanical Horizon
A Mechanical Horizon is an instrument-generated or displayed horizon reference, such as a horizon indicated by an artificial-horizon or attitude-reference instrument.
It need not be a directly visible physical horizon. Instead, it provides an artificial reference corresponding to the orientation of the viewing or instrument system relative to a defined horizontal frame.
The Dual Reality of a Represented Horizon
A represented horizon can possess what the Dictionary describes as a dual reality.
Within the virtual or represented spatial world, the geometrical horizon functions as the vanishing line towards which horizontal spatial directions extend.
At the same time, in physical picture space, the horizon is simply an actual line, mark, tonal boundary or row of pixels upon the surface of a drawing, painting, photograph, screen or other image.
The same visible feature therefore operates simultaneously within two spaces: the physical surface of the image and the represented spatial reality perceived within it.
Horizon-Line Isocephaly
Horizon-Line Isocephaly concerns the relationship between figures of equal physical height and the observer’s horizon within a perspective representation.
If figures of equal height stand upon the same level ground plane, corresponding points on those figures follow common perspective recession relationships.
Their eyes lie upon the observer’s geometrical horizon only when their eyes are physically at the same height as the observer’s eyes. The tops of their heads do not automatically coincide with the horizon; they normally follow a separate receding line above it.
Movement of the Horizon Line
The apparent position of the geometrical horizon depends upon the relationship between the observer, viewing direction, local horizontal and projection surface.
Changing the observer’s height alters where the horizon passes relative to objects in the scene. Changing the pitch of the viewing system can move the horizon upwards or downwards within the image. Rolling the viewing system or picture can cause the horizon to appear sloping.
These changes should be distinguished from changes in individual vanishing points caused by rotating particular objects or line systems. A horizontal object may rotate while its vanishing points move along the same horizon line.
Horizon Lines in Wide-Field and Spherical Perspective
The familiar straight horizon line belongs especially to a limited flat picture-plane representation. A complete spatial field is not restricted to one short straight segment in front of the observer.
When a much wider field is represented through cylindrical, curvilinear, panoramic or spherical methods, horizontal directional relationships can extend around the observer and may be represented as curves, circles or other transformed structures according to the projection employed.
The straight planar horizon should therefore be understood as one representation of a broader horizontal directional structure rather than as the complete form of the horizon under every possible perspective method.
Common Horizon-Line Misconceptions
Several common assumptions should therefore be avoided:
- The horizon line is not necessarily the visible boundary between land and sky.
- The horizon line is not a single vanishing point; it contains potentially many horizontal vanishing points.
- The horizon line does not itself cause parallel lines to converge.
- Not every vanishing point lies upon the ordinary horizon line; only vanishing points belonging to horizontal directions do so.
- Not every line that resembles a horizon is the geometrical ground-plane horizon.
- A sloping horizon caused by camera roll is not the same thing as the vanishing line of an inclined plane.
- A vertical vanishing point is not a vertical horizon line.
- Eye level coincides with the geometrical horizon only under the relevant conventional geometrical relationship; it is not synonymous with every physical, visible or astronomical horizon.
- A skyline, ridge or building outline is not necessarily the true geometrical horizon.
- The physical visible horizon is finite, while the geometrical perspective horizon represents horizontal directions at projective infinity.
Why the Horizon Line Matters
The horizon line is fundamental to perspective because it connects the observer’s horizontal spatial reference with the directional organisation of the perspective image.
It provides the common geometrical line containing the vanishing points of horizontal directions, establishes the principal horizontal vanishing structure of one- and two-point perspective, relates to eye level in the conventional upright arrangement, and provides a basis for understanding vanishing lines belonging to other planes.
At the same time, the wider PRC classification demonstrates that horizon is not one single concept. There are geometrical, optical, visible, terrestrial, sensible, astronomical, circular, local, primary, secondary, artificial, represented, mechanical and other horizon forms, each referring to a different physical, visual, projective or representational relationship.
Understanding these distinctions provides a foundation for understanding the Horizon Plane, station point, picture plane, eye level, vanishing point, vanishing line, vanishing trace, directional line vanishing, directional plane vanishing, optical vanishing, one-point perspective, two-point perspective, three-point perspective, curvilinear perspective and spherical perspective.