Curvilinear Perspective is a family of graphical, mathematical and optical perspective systems in which some straight spatial lines are represented by curves, allowing wide, tall, panoramic or hemispherical fields to be organised within a single image.
Unlike conventional rectilinear Linear Perspective, which maps a scene onto one flat picture plane while keeping spatial straight lines straight, Curvilinear Perspective distributes spatial directions through a curved or non-rectilinear image structure.
It can represent:
- a wider field of view than conventional Linear Perspective;
- lateral, vertical and diagonal recession;
- several principal vanishing directions;
- panoramic or hemispherical space;
- peripheral diminution and spatial compression;
- directions above, below and to either side of the observer.
Curvilinear Perspective includes two-, three-, four- and five-point forms, together with cylindrical, azimuthal, stereographic, hyperbolic and other specialist projection systems.
It is closely related to Spherical and Panoramic Perspective, but it should not be treated as identical to either.
INSERT IMAGE 19 — CURVILINEAR PERSPECTIVE
Suggested caption: Curvilinear Perspective organises a wide spatial field through several vanishing directions and curved graphical structures.
What is Curvilinear Perspective?
Curvilinear Perspective describes perspective systems in which the geometry of projection, the shape of the image surface or the transformation applied to the image causes straight spatial lines to appear curved.
A typical curvilinear image may contain:
- a central viewing direction;
- lateral vanishing points to the left and right;
- upper and lower vanishing points;
- curved horizontal or vertical lines;
- compressed peripheral space;
- a circular, elliptical or hemispherical image boundary;
- an extended field of view.
The Dictionary of Perspective defines its principal form as a type of Central Perspective whose completed image has an overall curved structure comparable to a wide-angle or fisheye view. It normally contains between two and five principal vanishing points: a central depth direction, left and right directions and, where required, upper and lower directions.
Curvilinear Perspective is not defined merely by the presence of a curved object. A drawing of a curved road made in otherwise conventional Linear Perspective is not necessarily a curvilinear projection.
The curvature must arise from:
- the projection system;
- the image surface;
- the mapping geometry;
- or the deliberate graphical organisation of the represented field.
Curved objects and curved projection
Two different causes of curvature must be distinguished.
Curvature originating in object space
A line may appear curved because the physical or imagined line itself is curved.
Examples include:
- an arch;
- a circular road;
- a dome;
- a curved wall;
- a cylindrical object.
The representation may still use ordinary rectilinear Linear Perspective.
Curvature originating in the projection system
A physically straight line may be represented as a curve because of the projection or image structure employed.
This occurs in:
- fisheye imaging;
- cylindrical projection;
- spherical projection;
- hemispherical mapping;
- five-point perspective;
- panoramic projection;
- some wide-angle graphical systems.
The Dictionary distinguishes these as object-space-sourced and projection-method-sourced curved lines or vanishing structures.
This distinction prevents the physical geometry of the subject from being confused with the geometry of its representation.
Curvilinear Perspective and Central Perspective
Many forms of Curvilinear Perspective remain types of Central Perspective.
They are central because the represented view is organised in relation to:
- one selected viewpoint;
- one central optical axis or viewing direction;
- one principal projection centre;
- a cone, pyramid or hemispherical field extending from that centre.
Central Perspective does not mean that every line converges towards one central vanishing point. It means that the view is organised around a finite centre of projection or principal viewing direction.
The two main graphical forms of Central Perspective can therefore be understood as:
- Rectilinear Central Perspective — normally called Linear Perspective;
- Curvilinear Central Perspective — using curved image structures to organise a wider field.
Spherical Perspective is different where it represents a genuinely all-direction or multi-directional field around the observer. Such spherical systems should not normally be described as one simple frontal or central view, even though each individual directional view contributing to them may have its own optical axis.
Why use Curvilinear Perspective?
A flat rectilinear picture plane is highly effective for moderate fields of view.
It preserves the straightness of spatial straight lines and provides a coherent, measurable image. However, difficulties become increasingly apparent when a very wide angular field is placed on one flat plane.
Towards the margins:
- image scale per degree of visual angle increases;
- rounded objects may appear stretched;
- human figures and faces may appear elongated;
- repeated forms can become disproportionately wide;
- peripheral space may seem expanded;
- objects can appear skewed when the image is viewed under ordinary conditions.
Curvilinear Perspective redistributes the field differently.
It may reduce some forms of lateral expansion and represent peripheral directions more continuously, but it generally does so by curving some spatial straight lines.
There is therefore a basic representational trade-off:
Rectilinear Perspective preserves straightness but expands marginal scale.
Curvilinear Perspective redistributes angular space but curves some straight lines.
No single flat mapping can simultaneously preserve:
- every spatial straight line as straight;
- uniform angular scale;
- undistorted local shape;
- and an extremely wide field of view.
This relationship is central to the distinction between Linear and Curvilinear Perspective.
The wide-field problem
A normal photograph or Linear Perspective drawing usually represents a comparatively limited part of the surrounding visual field.
Within this restricted area, a flat picture plane works convincingly. The image can preserve straight architectural lines while giving an effective representation of depth.
As the field expands towards 120, 150 or 180 degrees, however, it becomes increasingly difficult to place every direction onto one flat rectilinear image without pronounced marginal expansion.
A wide field includes directions:
- directly ahead;
- far to the left and right;
- above and below;
- approaching positions perpendicular to the central viewing direction.
Curvilinear systems address this problem by treating the field as:
- cylindrical;
- hemispherical;
- spherical;
- radial;
- azimuthal;
- or otherwise curved.
Volume 1 presents five-point Curvilinear Perspective as a hemispherical, multi-directional method capable of representing an approximately 180-degree field, with directional points above, below, left, right and at the centre.
Curvilinear Perspective and human vision
Curvilinear Perspective is frequently associated with human visual experience.
The human visual system differs fundamentally from a conventional flat perspective picture:
- the retina is curved;
- the eyes rotate;
- the head moves;
- attention shifts through successive fixations;
- peripheral directions surround the central field;
- visual experience develops over time;
- the field is not experienced as one permanently fixed flat image.
Straight spatial lines can therefore undergo different angular, retinal and perceptual relationships across a wide field.
However, a curvilinear drawing should not be described simply as a literal picture of the retina. A retinal image is:
- optically formed;
- curved and inverted;
- continuously altered by eye movement;
- interpreted by perceptual processes;
- not directly experienced as a visible hemispherical screen.
Curvilinear Perspective can model important aspects of wide-field angular or visual structure without being identical to retinal physiology or perception.
Volume 1 therefore connects Curvilinear Perspective with wide-field visual projection while recognising that the relationship between curved graphical images, optics and perceived visual space remains complex.
Visual Lateral Distortion
Your theory distinguishes three conjoined aspects of Visual Lateral Distortion.
Type A — angular or curved-retinal mapping
Visual directions are optically mapped through the eye onto a curved retinal surface rather than onto one flat tangent plane.
Type B — increasing egocentric distance
Objects positioned laterally may lie farther from the eye than equivalent objects directly ahead, even where they occupy the same frontal physical plane.
Their angular sizes and separations can therefore change with lateral position.
Type C — changing orientation relative to the line of sight
As an object moves away from the central viewing direction, its surfaces and axes are seen from different angles.
Its aspect, foreshortening and visible proportions can consequently change.
These are not three unrelated events. They are analytically distinguishable components of one optical-geometrical viewing relationship.
Curvilinear Perspective can provide graphical methods for representing some of these lateral and wide-field changes.
Graphical Lateral Distortion
Graphical Lateral Distortion occurs when a wide angular field is centrally projected onto one flat rectilinear picture plane.
Rectilinear mapping preserves spatial straight lines as straight, but planar image scale increases towards the margins.
As a result, peripheral forms may appear:
- enlarged;
- stretched;
- elongated;
- widened;
- asymmetric;
- or skewed.
The effect is particularly noticeable in:
- heads and human figures;
- spheres and rounded objects;
- repeated objects;
- objects close to the camera;
- forms crossing the image boundary.
This is an inherent consequence of exact rectilinear projection and is not necessarily a lens defect.
Viewed monocularly from the geometrically prescribed position and distance, the completed picture reconstructs the original bundle of projection rays. Under ordinary viewing conditions—binocular viewing, an incorrect distance, an off-centre position, eye movements or local fixations—the perceptual compensation may remain incomplete.
Curvilinear, cylindrical and spherical systems redistribute the field and may reduce this edge stretching, but their trade-off is the curvature of some represented straight lines.
Straight lines in Curvilinear Perspective
Curvilinear Perspective does not necessarily curve every line.
Which lines remain straight depends upon:
- the particular projection method;
- the orientation of the line;
- its relationship to the projection centre;
- the geometry of the image surface;
- the way the curved image is flattened or displayed.
In a five-point hemispherical construction, lines passing directly through the centre of vision may remain straight, while lines displaced from the centre bend increasingly.
Depending upon the method:
- verticals may curve;
- horizontals may curve;
- both may curve;
- radial lines may remain straight;
- circular or elliptical arcs may represent sets of spatial parallels.
The presence of curves is therefore systematic rather than decorative.
In an ideal rectilinear projection, a straight spatial line remains straight regardless of field of view. If it appears curved, the cause lies in a non-rectilinear projection, an optical distortion, a curved image surface or the physical curvature of the original line.
Curved vanishing lines
Under rectilinear Linear Perspective, a spatial plane normally possesses a straight vanishing line.
In a Curvilinear Perspective system, the corresponding limiting structure may appear as:
- a circular arc;
- an ellipse;
- a curved horizon;
- a radial boundary;
- a curved vanishing line.
Sets of mutually parallel straight lines in object space may appear to approach a point while following curved image paths.
Their apparent curvature is produced by the projection method rather than by the lines becoming physically curved in space.
Curved vanishing structures help organise:
- lateral recession;
- vertical recession;
- hemispherical space;
- wide-angle grids;
- panoramic fields;
- all-direction representations.
Two-point Curvilinear Perspective
A two-point curvilinear system normally emphasises recession towards two opposing directional points.
These may be:
- left and right;
- above and below;
- front and rear within a cylindrical or panoramic mapping.
Lines approaching these directions may curve across the field.
This form can be useful for:
- broad lateral views;
- cylindrical panoramas;
- extended interiors;
- streets and environments represented across a wide horizontal field.
The image may contain a strong central region while compressing spatial information towards its two lateral limits.
Three-point Curvilinear Perspective
Three-point Curvilinear Perspective introduces another principal direction in addition to the lateral pair.
For example, it may organise:
- left;
- right;
- and a central depth direction.
Alternatively, the third point may represent an upper or lower direction.
As in rectilinear systems, the name identifies the principal organising points rather than the total number of possible spatial vanishing directions.
Curvilinear systems can contain many other local and subsidiary vanishing points corresponding to different sets of spatial parallels.
Four-point Curvilinear Perspective
Four-point perspective commonly represents a very wide lateral and vertical field.
Its four principal directional points may correspond to:
- left;
- right;
- top;
- bottom.
A central viewing direction may remain present as the centre of the image but is not always counted as a separate vanishing point.
Four-point systems can be used to represent:
- wide interiors;
- tall architectural spaces;
- views extending above and below the normal horizon;
- cylindrical or hemispherical fields.
Some four-point systems remain central or frontal because they are organised around one principal optical axis even though several directions are represented simultaneously.
Five-point Curvilinear Perspective
Five-point perspective is the most familiar complete curvilinear drawing system.
It is often described as:
- fisheye perspective;
- hemispherical perspective;
- circular perspective;
- five-point Curvilinear Perspective.
Its principal points are normally:
- centre or forward direction;
- left;
- right;
- above;
- below.
The represented field can approach 180 degrees horizontally and vertically.
A typical construction uses a circular or hemispherical framework. Spatial lines curve between the principal directional limits, and objects become progressively compressed as they approach the edge of the represented hemisphere.
Volume 1 describes the system as a multi-directional view in which the picture plane is conceptually hemispherical rather than one flat rectilinear plane.
INSERT IMAGE 18 — VANISHING POINTS IN ALL DIRECTIONS
Suggested caption: Curvilinear and spherical systems extend vanishing geometry beyond one central point or one straight horizon line.
Azimuthal Curvilinear Perspective
Azimuthal Curvilinear Perspective projects spatial directions onto a plane in relation to one selected centre.
It may represent:
- a hemisphere;
- a full circular field;
- wide-angle directional information;
- map-like or observer-centred space.
Azimuthal methods are used in:
- map projection;
- astronomy;
- hemispherical imaging;
- environmental analysis;
- wide-field graphical representation.
Different azimuthal projections preserve different properties. One may preserve direction from the centre, another distance from the centre, area, local angles or another chosen relationship.
They should therefore be treated as a family of mappings rather than one universal construction.
Cylindrical Curvilinear Perspective
Cylindrical Curvilinear Perspective uses a cylindrical image or projection structure.
It can operate in at least two main ways:
- a wide spatial scene is imaged or projected onto a convex cylindrical surface;
- an image is projected onto the interior of a concave cylindrical screen.
The cylinder is particularly suited to lateral or panoramic extension.
Depending upon the mapping:
- vertical lines may remain straight;
- horizontal directions may curve;
- the horizon may extend around the cylinder;
- lateral space can continue beyond one frontal image.
A cylindrical panorama can represent a complete 360-degree horizontal field while excluding or compressing the extreme upper and lower directions.
The Dictionary therefore connects cylindrical Curvilinear Perspective with panoramic views, wide-angle imaging, curved screens and multi-view systems.
Stereographic Curvilinear Perspective
Stereographic Curvilinear Perspective employs a stereographic mapping between a sphere and a plane.
It can produce a wide-angle or hemispherical image in which many straight spatial lines are represented by circular arcs.
A stereographic projection has the important mathematical property of preserving local angles. It is therefore described as conformal, although it does not preserve scale or area uniformly across the whole image.
In graphical practice, stereographic methods are often associated with:
- five-point perspective;
- circular or fisheye images;
- hemispherical projection;
- maps of spheres;
- wide-field architectural drawings.
The Dictionary identifies stereographic Curvilinear Perspective as a method capable of producing a field approaching 180 degrees while using curved horizontal and vertical structures.
Hyperbolic Curvilinear Perspective
Hyperbolic Curvilinear Perspective uses a curved geometrical structure associated with hyperbolic or negatively curved space.
It can represent an extensive or theoretically unbounded spatial field inside a limited image boundary.
Forms may be related to:
- the Poincaré disc;
- hyperbolic tiling;
- mathematical visualisation;
- recursive or infinitely extending space;
- non-Euclidean graphical systems.
Scale changes rapidly towards the boundary, allowing large amounts of spatial information to be compressed into one finite area.
Hyperbolic Perspective should not be confused with ordinary fisheye projection, although both may produce strongly curved lines and extreme peripheral compression.
Curvilinear and Panoramic Perspective
Curvilinear and Panoramic Perspective overlap, but they are not identical.
Panoramic Perspective is defined principally by its extended field.
Curvilinear Perspective is defined principally by its curved graphical or projection structure.
A panorama may be:
- cylindrical;
- spherical;
- rectilinear and stitched;
- multi-view;
- interactive;
- projected onto a curved screen.
A Curvilinear Perspective image may represent a wide field but does not always form a complete panorama.
A useful distinction is:
Panoramic Perspective concerns how much of the surrounding field is represented.
Curvilinear Perspective concerns how that field is geometrically organised and mapped.
INSERT IMAGE 20 — PANORAMIC PERSPECTIVE
Suggested caption: Panoramic Perspective extends representation laterally, while curvilinear or cylindrical mapping determines how that wide field is organised.
Curvilinear and Spherical Perspective
Curvilinear and Spherical Perspective are closely related, but Spherical Perspective is the broader all-direction concept.
Curvilinear Perspective may represent:
- a wide frontal field;
- a hemisphere;
- a cylindrical region;
- a transformed portion of a sphere.
Spherical Perspective may represent:
- a complete sphere;
- front and rear hemispheres;
- all directions around an observer;
- views above, below, before and behind;
- a Sphere of Vision;
- a sphere of revolution;
- spherical reflection or imaging.
Five-point Curvilinear Perspective commonly represents one hemisphere.
Six-point or other Spherical Perspective systems may add the opposite or rearward direction and represent a complete 360-degree environment.
Curvilinear Perspective should therefore not be used as an automatic synonym for every Spherical Perspective system.
Curvilinear and Linear Perspective
Linear and Curvilinear Perspective offer different solutions to the same basic representational problem.
Linear or Rectilinear Perspective
- normally uses a flat picture plane;
- preserves spatial straight lines as straight;
- provides precise projective measurement;
- works especially well for moderate fields;
- expands planar scale towards wide-field margins.
Curvilinear Perspective
- uses curved or transformed image geometry;
- can represent a much wider field;
- redistributes lateral and peripheral directions;
- may reduce rectilinear edge stretching;
- curves some spatial straight lines;
- often requires more complex construction.
Neither method is universally superior.
Linear Perspective is often preferable for:
- rectilinear architecture;
- technical drawing;
- measurable construction;
- restricted fields of view.
Curvilinear Perspective may be preferable for:
- wide interiors;
- panoramic environments;
- hemispherical views;
- immersive representation;
- spatial fields extending towards the visual periphery.
Curvilinear and Optical Perspective
A Curvilinear Perspective image can be produced by a graphical construction or an optical instrument.
Optical examples include:
- fisheye lenses;
- panoramic mirrors;
- reflecting spheres;
- cylindrical mirrors;
- hemispherical cameras;
- all-sky lenses;
- dome-projection optics.
The form of the image depends upon:
- the geometry of the lens or mirror;
- the mapping function;
- the field of view;
- the receiving sensor or surface;
- later digital transformations.
Curved image lines should not automatically be described as accidental lens distortion.
Some optical systems are deliberately designed to use non-rectilinear projection because it allows them to record a wider angular field.
Conversely, unwanted barrel, pincushion or wave distortion is a departure from a lens’s intended projection. This should be distinguished from an intentionally selected fisheye or curvilinear mapping.
Fisheye Perspective
Fisheye Perspective is an optical or graphical form of extreme wide-angle Curvilinear Perspective.
A fisheye image commonly represents:
- approximately 180 degrees;
- a circular or strongly curved field;
- radial or hemispherical directions;
- pronounced curvature of lines away from the centre;
- compressed peripheral space.
Different fisheye mappings distribute space differently.
They may be:
- equidistant;
- equisolid-angle;
- stereographic;
- orthographic;
- another specialist mapping.
The term fisheye therefore identifies a broad visual and optical family rather than one exact geometry.
A graphical five-point perspective can imitate a fisheye appearance, but a hand-constructed five-point drawing and a particular optical fisheye lens need not follow precisely the same projection formula.
Curvilinear Perspective and Graphical Perspective
Curvilinear Perspective belongs to Graphical Perspective when it is:
- drawn;
- painted;
- diagrammed;
- constructed;
- mapped;
- digitally rendered.
It belongs to Mathematical Perspective where it is generated through:
- geometrical projection;
- coordinate transformation;
- spherical or cylindrical mapping;
- stereographic projection;
- mathematical warping.
It belongs to Optical or Instrument Perspective where it is formed by:
- a lens;
- mirror;
- camera;
- curved display;
- optical projection system.
The finished visible image belongs within Visual Perspective Type 1, while the human retinal and perceptual experience of viewing it belongs within Visual Perspective Type 2.
Curvilinear Perspective may therefore participate in several categories simultaneously.
Curvilinear Perspective and category chaining
A curvilinear image may be produced through a chain such as:
Physical or simulated spatial scene
↓
Curvilinear mathematical mapping
↓
Graphical or optical image formation
↓
Digital processing
↓
Flat or curved display
↓
Optical transmission to the eye
↓
Visual Perspective Type 2
Different stages may introduce different forms of curvature, compression, magnification or transformation.
The final image should therefore not be classified only by how it looks. Its complete process and source should also be identified.
Historical development
Curved spatial representation did not begin with modern fisheye lenses.
Historical precedents include:
- painted domes and vaults;
- panoramic murals;
- cylindrical and circular images;
- maps of the heavens;
- planispheric and cartographic projections;
- reflecting spheres;
- anamorphic and wide-field constructions.
Leonardo da Vinci examined problems connected with lateral viewing, changing visual angles and the representation of wide fields. Later discussions have considered whether some of his observations anticipated aspects of Curvilinear Perspective.
During the nineteenth century, William Herdman and Guido Hauck developed graphical methods involving lateral or curved recession across the picture field.
In the twentieth century, Albert Flocon and André Barre developed systematic accounts of Curvilinear Perspective and five-point construction.
Artists including M.C. Escher explored spherical reflection, curved space and non-standard projection, while Dick Termes developed spherical paintings and Termespheres representing all-direction environments.
Modern photography, computer graphics and virtual reality have made curvilinear, cylindrical and spherical mappings increasingly common.
Curvilinear Perspective in art
Artists use Curvilinear Perspective to:
- represent extensive interiors;
- create panoramic environments;
- emphasise movement;
- intensify spatial immersion;
- show several directions at once;
- bend architecture around the viewer;
- produce expressive or psychological effects;
- question the authority of one flat picture plane.
It can create a stronger sense that the viewer is situated inside a surrounding field rather than looking through a rectangular window.
Curvilinear construction may also be combined with:
- atmospheric colour;
- multiple viewpoints;
- anamorphosis;
- spherical reflection;
- moving or sequential views;
- symbolic spatial organisation.
Curvilinear Perspective in photography and cinema
Curvilinear imaging is used in:
- fisheye photography;
- action cameras;
- security cameras;
- all-sky imaging;
- architectural surveys;
- panoramic photography;
- 360-degree video;
- immersive cinema;
- visual-effects capture.
Digital systems can transform between:
- fisheye images;
- cylindrical panoramas;
- equirectangular images;
- cube maps;
- rectilinear views;
- spherical environments.
Each transformation redistributes scale, direction and shape.
An interactive 360-degree image may store the scene in one mathematical format while displaying only a limited rectilinear or curvilinear view at any one moment.
Curvilinear Perspective in architecture
Architecture contains strong rectilinear structures, making differences between Linear and Curvilinear Perspective particularly visible.
Curvilinear methods can represent:
- very wide interiors;
- domes and vaults;
- atria;
- circular spaces;
- long facades;
- urban panoramas;
- environments surrounding the observer.
They can also help demonstrate how architecture changes in appearance across an extended field rather than from one narrow fixation.
However, curved representations may be less suitable where the principal purpose is exact technical measurement or the preservation of straight architectural edges.
Curvilinear Perspective in science and technology
Curvilinear mappings are used in:
- astronomy;
- cartography;
- meteorology;
- environmental monitoring;
- robotics;
- autonomous vehicles;
- computer vision;
- medical imaging;
- scientific visualisation;
- dome projection;
- virtual and augmented reality.
A robot or autonomous vehicle may combine information from several cameras into a panoramic or spherical environment map.
Astronomers use hemispherical and all-sky projections to represent the celestial sphere.
Virtual-reality systems map complete environments around a moving observer and then generate local views according to head and eye direction.
Strengths of Curvilinear Perspective
Curvilinear Perspective can:
- represent very wide fields;
- include strong lateral and vertical directions;
- compress extensive environments into one image;
- reduce some forms of rectilinear edge stretching;
- suggest a surrounding or immersive field;
- model cylindrical, hemispherical and spherical spaces;
- integrate several vanishing directions;
- connect graphical representation with panoramic and digital media.
It is particularly valuable where one flat rectilinear picture plane is too restrictive.
Limitations of Curvilinear Perspective
Its principal limitations include:
- curvature of spatial straight lines;
- unfamiliar image geometry;
- difficulty of manual construction;
- uneven scale or area;
- strong compression near image boundaries;
- dependence upon the selected mapping;
- difficulty of direct technical measurement;
- possible confusion with lens distortion;
- incomplete correspondence with ordinary perceived visual space.
A Curvilinear Perspective image is not inherently more natural or realistic than a Linear Perspective image.
Its suitability depends upon:
- field of view;
- purpose;
- viewing conditions;
- projection geometry;
- image surface;
- subject matter;
- required spatial properties.
Every projection preserves some relationships while transforming others.
Why Curvilinear Perspective matters
Curvilinear Perspective demonstrates that spatial representation is not confined to one rectangular window or one flat plane.
It provides methods for representing:
- peripheral space;
- wide-angle vision;
- panoramic environments;
- several directional limits;
- cylindrical and hemispherical fields;
- immersive and all-direction media.
It also reveals an important principle:
Perspective is always a transformation between spatial reality, a projection process and an image structure.
Changing the geometry of the image changes which spatial properties are preserved, expanded, compressed or curved.
Curvilinear Perspective therefore provides a vital bridge between:
- Natural and Visual Perspective;
- Graphical and Mathematical Perspective;
- Optical and Instrument Perspective;
- Panoramic and Spherical Perspective;
- photography, cinema and virtual environments.
Curvilinear Perspective in The Art and Science of Perspective
Volume 1, The Past, Present and Future of Visual and Optical Perspective, introduces Curvilinear Perspective within the wider history and theory of graphical, optical and wide-field representation.
Volume 2, Dictionary of Perspective, defines its principal senses and catalogues azimuthal, cylindrical, stereographic, hyperbolic, fisheye, four-point, five-point and related methods.
Volume 3, Natural and Visual Perspective, will examine the wide-field visual relationships to which Curvilinear Perspective is frequently compared.
A later volume, Graphical and Mathematical Perspective, will provide a more detailed account of curvilinear construction, projection geometry and its relationship to Linear and Spherical Perspective.
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