Perspective projection is the process by which the spatial position, direction, form or appearance of an object or scene is transferred, mapped or projected into an image, view or representation. Depending upon the system involved, projection may be natural or artificial, optical or geometrical, central or parallel, planar or curved, captured from spatial reality or projected forwards into it.
At its simplest, projection establishes a relationship between object space, one or more projection lines or rays, a projection centre or directional system, and a picture plane, image plane or other projection surface.
The familiar linear-perspective drawing is therefore only one form of perspective projection. The wider field includes natural visual projection, camera and instrument imaging, parallel projection, orthographic and axonometric systems, oblique projection, curvilinear, cylindrical and spherical projection, shadow and light projection, anamorphic systems, computer-generated projection and many specialised mathematical and optical forms.
What Is Projection?
Projection describes a process in which points, lines, surfaces, objects, images or spatial information are transferred from one spatial relationship or representational system into another.
In geometrical perspective, points in object space may be connected to a picture surface by imaginary projection lines. In optical systems, real light rays travel through space, lenses, apertures or other optical components and form an image. In computer graphics, corresponding relationships are calculated mathematically rather than physically traced by light.
Despite these differences, the underlying problem is related: how is spatial information transformed into another spatial or image configuration?
Projection Lines and Projection Rays
Perspective projection can employ several kinds of projection line or ray.
In natural and optical systems, these may be actual light rays. In graphical construction they may be imagined or drawn lines joining spatial points to a station point or picture plane. In mathematical and computer systems they may exist as calculated vectors, rays or transformations within a geometrical model.
The relationship between these projectors is one of the most important ways in which projection systems can be distinguished. They may:
- converge towards or pass through a common finite centre;
- diverge from a common point or source;
- remain mutually parallel; or
- follow more complex curved, transformed or non-standard paths.
The geometry of these rays, together with the orientation and form of the projection surface, determines the resulting image.
The Two Fundamental Directional Classes
The Perspective Research Centre distinguishes two fundamental directional classes of perspective process:
- Viewing or Imaging Class: light, visual information or spatial data passes from an object, scene or existing image towards an eye, camera, sensor, image plane or imaging system.
- Projecting Class: light, images, lines, shadows or spatial information are projected forwards from a source, projector, station point, picture surface or representational system into physical, optical, graphical or simulated space.
This distinction is fundamental because the word projection is often used for both processes. A camera forms a perspective image by receiving light from spatial reality, while a cinema projector projects an existing image forwards onto a screen. Both involve perspective projection, but the direction and function of the process differ.
Captured and Projected Perspective Images
The Dictionary accordingly distinguishes between Captured Perspective Images and Projected Perspective Images.
A captured image belongs principally to the Viewing or Imaging Class. Spatial information travels from the scene towards the imaging system. Human vision, a camera obscura, photographic camera, telescope or microscope can operate in this general direction.
A projected image belongs principally to the Projecting Class. An image, pattern, outline or field of light is sent forwards from a source or projector into another space or onto another surface. Cinema projection, projection mapping and many display systems operate in this direction.
Some modern systems combine or chain both processes. A camera may first capture a spatial scene, a computer may transform the image, and a projector may then project the result back into physical space.
Three Basic Projection Arrangements
The Dictionary identifies three basic optical or geometrical arrangements involving the projection point, spatial object and picture or projection plane.
- Picture plane → projection point → object: an imaging arrangement in which rays from the object pass through the projection point and continue towards an image surface.
- Projection point → object → picture plane: a projecting or shadow arrangement in which rays travel from a source or point, around or past the object, and onto a receiving surface.
- Projection point → picture plane → object: another projecting arrangement in which the projection plane or image field lies between the point and the target spatial object or scene.
These arrangements demonstrate that perspective projection is not restricted to the traditional artist looking through a transparent picture plane. The relative ordering of object, projection point and projection surface can change according to the process involved.
Perspective Projection Modes
The Dictionary of Perspective identifies a number of broad Perspective Projection Modes, including:
- Central Projection;
- Parallel Projection;
- Spherical Projection;
- Anamorphic Projection;
- Line-of-Sight Projection; and
- Non-Standard Projection.
Within these broad modes occur many further types and forms, including linear one-, two-, three- and unlimited-point projection; orthographic, axonometric and oblique projection; cylindrical and curvilinear forms; and numerous optical, graphical, mathematical and digital variants.
Central or Conical Projection
In Central Projection, the projection rays pass through a common finite centre. When points in a spatial scene are related to a single station point or centre of projection, the resulting ray structure forms a cone or pyramid of projection.
This is the basic geometry underlying conventional linear perspective, pinhole imaging and many forms of camera, computer and optical perspective.
The projection centre may represent an eye, camera aperture, optical centre, mathematical point or virtual camera. Spatial points are related to this common centre and mapped onto a picture plane or other image surface.
Central projection differs fundamentally from parallel projection because the projectors do not remain mutually parallel. Their changing angular relationships produce familiar perspective phenomena including diminution with distance and directional convergence.
Central Projection and Central Perspective
Central Projection and Central Perspective should not automatically be treated as exact synonyms.
Central projection is the broad geometrical condition in which rays pass through a common finite centre. The PRC uses Central Perspective more specifically for a unidirectional perspective form organised around a principal viewing direction and unified cone or pyramid of vision.
A projection can therefore be centrally projected in a mathematical sense without necessarily belonging to the narrower unidirectional form classified as Central Perspective.
Likewise, Frontal Perspective is not synonymous with central projection. It describes a particular orientation of the object or scene relative to the viewing direction and picture plane.
Linear or Rectilinear Perspective Projection
Linear Perspective is one of the best-known graphical applications of central projection. A spatial scene is related to a fixed station point and projected onto a flat picture plane.
Straight lines in object space are normally represented as straight lines in the image. Sets of mutually parallel lines with a depth component converge towards corresponding vanishing points, while directions parallel to the picture plane retain a vanishing point at infinity and remain parallel within the conventional rectilinear image.
The standard one-, two- and three-point forms refer to the number and organisation of the principal finite vanishing points selected within the construction. They are particular configurations of central projection rather than entirely separate projection principles.
One-Point Projection
In a conventional one-point linear-perspective projection, one principal set of parallel lines extends in the depth direction and converges towards a central vanishing point.
The remaining principal horizontal and vertical directions are normally parallel to the picture plane and therefore remain parallel in the image.
This is a special geometrical arrangement. It should not be mistaken for the universal form of perspective projection or interpreted as meaning that spatial reality possesses only one possible vanishing direction.
Two-Point Projection
In two-point linear perspective, two principal horizontal sets of parallel lines recede relative to the picture plane. Each possesses its own vanishing point, normally positioned on the horizontal geometrical horizon.
The system retains one station point and one unified projection centre. The expression two-point describes the two principal horizontal vanishing directions, not two viewpoints.
Three-Point Projection
Three-point perspective adds a third principal finite vanishing direction, commonly because vertical lines also recede relative to the projection surface.
The resulting vertical vanishing point may lie above or below the image according to the orientation of the viewing system. The two principal horizontal systems continue to possess their own vanishing points on the corresponding horizontal vanishing line.
Unlimited-Point Projection
Spatial reality is not inherently limited to one, two or three directional systems. Every distinct spatial direction potentially possesses a corresponding geometrical vanishing point.
The concept of unlimited-point perspective therefore recognises a larger directional field in which potentially countless vanishing directions may exist. Conventional one-, two- and three-point systems select only a small number of structurally important directions for practical construction or description.
Parallel Projection
In Parallel Projection, the projectors remain mutually parallel rather than meeting at a finite projection centre.
The viewpoint can therefore be treated geometrically as lying at infinity. The image is not formed from the angular relationships of one finite eye or camera position in the same way as ordinary central projection.
Parallel projection avoids the ordinary diminution of size with distance produced by a finite viewpoint. Parallel object-space directions normally remain parallel in the image rather than converging towards finite vanishing points.
Volume 1 divides parallel projection principally into Orthographic Projection and Oblique Projection.
Orthographic Projection
In Orthographic Projection, the projection lines are perpendicular to the projection or picture plane.
Because the projectors are parallel and perpendicular to the image surface, orthographic projection can preserve dimensions and relationships in ways that make it especially useful for technical, engineering, architectural and scientific representation.
The two broad orthographic forms described in Volume 1 are:
- Primary or Multi-View Projection; and
- Axonometric Projection.
Primary or Multi-View Projection
In Primary or Multi-View Projection, principal object faces or axes are arranged parallel to the projection plane to produce standard orthographic views.
These commonly include:
- plans;
- front elevations;
- side elevations; and
- sections or cutting-plane views.
Several related views can be combined to define the complete three-dimensional geometry of an object without relying upon ordinary optical recession.
First-angle and third-angle projection are two established arrangements used for organising such views in technical drawing.
Axonometric Projection
In Axonometric Projection, an object is rotated relative to the projection plane so that several of its dimensions can be represented simultaneously within one parallel-projection image.
Axonometric projection is subdivided into three principal forms:
- Isometric Projection: the three principal axes possess equal scale or foreshortening.
- Dimetric Projection: two principal axes share one scale while the third differs.
- Trimetric Projection: all three principal axes possess different scales or foreshortenings.
Isometric projection is particularly widely used because its three principal axes are treated uniformly, allowing spatial forms to be represented with a consistent geometrical structure.
Oblique Projection
Oblique Projection is another form of parallel projection, but its projection lines are not perpendicular to the projection plane.
One principal face of the object may be shown directly while depth dimensions recede at a selected oblique angle. Because the depth scale can be chosen independently, oblique systems can deliberately alter the apparent proportions of the represented object.
Important forms include:
- Cavalier Projection;
- Cabinet Projection;
- Military or Plan-Oblique Projection; and
- General Oblique Projection.
These systems are highly useful for diagrams, technical representation, maps and explanatory illustrations, although they do not reproduce the normal finite-viewpoint optical geometry of natural vision.
Cavalier Projection
In Cavalier Projection, one face is commonly represented parallel to the picture surface while receding dimensions are drawn obliquely and normally at full scale.
This can exaggerate the apparent depth of the object, but it provides a simple and easily constructed three-dimensional representation.
Cabinet Projection
Cabinet Projection reduces the scale of the receding dimension, conventionally using a depth reduction such as one-half scale.
The reduction makes the resulting object appear less elongated than in full-depth Cavalier Projection and can provide a visually more balanced representation.
Military or Plan-Oblique Projection
Military Projection, or plan-oblique projection, preserves the horizontal ground plane in true shape while vertical dimensions extend from it.
This makes it useful for representing plans, settlements, landscapes, buildings and other spatial arrangements in which maintaining the geometry of the ground configuration is particularly important.
Perspective Projection versus Parallel Projection
Traditional geometrical terminology sometimes uses perspective projection narrowly to mean central or conical projection, contrasting it with parallel projection.
The wider PRC framework treats perspective more broadly. Parallel projection remains an important form of graphical or mathematical perspective even though it lacks the finite-viewpoint diminution and convergence characteristic of central optical projection.
The fundamental geometrical distinction remains clear:
- Central or conical projection: projection lines relate to a finite centre.
- Parallel projection: projection lines remain parallel and the viewpoint is effectively at infinity.
Spherical Projection
Spherical Projection maps spatial directions or images onto, from or through a spherical surface or spherical directional field.
Unlike an ordinary flat picture plane, a spherical surface can represent a much larger proportion of the directional environment surrounding the observer. This makes spherical forms particularly important for full-field, panoramic, dome, Virtual Reality and other immersive perspective systems.
Spherical perspective is especially useful when the field of view becomes too large to be represented satisfactorily by one conventional flat rectilinear image.
Cylindrical Projection
Cylindrical Projection maps or represents spatial information according to a cylindrical image geometry.
It is particularly associated with panoramas and wide-field representations. A cylindrical perspective may be produced by rotating an imaging system around a common centre, stitching several views, calculating the projection digitally or rendering a scene directly into cylindrical coordinates.
A curved cylindrical display does not automatically mean that the image itself possesses true cylindrical projection geometry. The geometry of the represented image and the geometry of the physical screen must be distinguished.
Curvilinear Projection
Curvilinear Perspective Projection uses non-rectilinear mappings in which lines that would remain straight under conventional linear perspective may appear curved.
Such projection is particularly useful for representing wide fields of view. Fisheye lenses are a familiar optical example: a large angular field is compressed onto a finite flat image surface by a curvilinear mapping.
The resulting curvature should not automatically be dismissed as an error. It may be the intended and geometrically necessary consequence of mapping a large directional field onto a limited image surface.
Flat, Cylindrical and Spherical Image Surfaces
Perspective projection is influenced not only by the projection rays but also by the form of the receiving image surface.
Volume 1 distinguishes three broad image or display geometries:
- Flat or planar image surface;
- Cylindrical image surface; and
- Spherical image surface.
Changing the projection surface changes how the directional field is mapped and can therefore change line curvature, lateral scale, field coverage, vanishing relationships and the overall appearance of represented space.
Anamorphic Projection
Anamorphic Projection deliberately transforms an image so that its apparent shape depends upon a particular viewing position, projection surface or optical transformation.
An image may appear severely stretched or distorted when viewed conventionally but resolve into the intended form from a particular viewpoint or through a corresponding optical device or surface.
Anamorphic methods demonstrate that perspective projection need not always seek a visually ordinary image on the projection surface itself. The system may instead be designed so that a transformed image produces the intended appearance only under specified viewing conditions.
Line-of-Sight Projection
Line-of-Sight Projection organises spatial relationships according to direct viewing or projection directions extending between an observer, instrument or modelled viewpoint and the relevant object, target or image surface.
The line of sight establishes one direction rather than the complete field of view. A perspective system may contain many lines or rays around a central or principal sight direction.
This distinction is important because the line of sight, optical axis, projection centre and directional reference elements can coincide in certain special arrangements without being universally identical concepts.
Non-Standard Projection
Non-Standard Projection encompasses systems that do not conform neatly to the ordinary central, parallel or standard curved-surface arrangements.
Such systems may deliberately distort, combine, split, rotate, warp or otherwise transform spatial information for artistic, technical, analytical or perceptual purposes.
They may include multiple projection centres, different mappings within separate parts of an image, unconventional picture surfaces, transformed viewing directions or combinations of projection principles.
Mixed Projection
Volume 1 also recognises that projection systems can be mixed. Different projection geometries may be combined within one representation, composition or image system.
For example, a single graphical work may combine parallel and central-projection elements, or separate regions may use different spatial mappings.
The resulting image should not automatically be judged according to the rules of only one of its constituent projection systems.
Optical Perspective Projection
In optical perspective projection, light forms, carries or projects an image. The system may be natural, as in vision, or artificial, as in cameras, microscopes, telescopes and projection systems.
The physical behaviour of light adds factors that do not exist in a purely abstract geometrical construction, including refraction, reflection, aperture, focus, optical aberration, image resolution, diffraction, wavelength and illumination.
The geometrical projection structure can nevertheless be analysed separately from these additional optical effects.
Camera Perspective Projection
A camera is one of the most familiar instruments for producing a central optical perspective projection.
Light from points in object space enters the camera through its optical system. Rays from each object point are refracted and brought towards corresponding locations upon the sensor or film, forming a two-dimensional optical image of the spatial scene.
The viewpoint or projection centre determines the principal perspective geometry. Focal length and sensor dimensions influence image scale and field of view, while lens design can introduce or correct additional optical distortions.
The physical image plane of the camera is normally behind the effective optical projection centre. This differs from the conventional graphical perspective arrangement in which an imaginary transparent picture plane is often placed between observer and scene.
Projection in the Human Eye
The eye also forms an optical projection of spatial reality. Light from the external scene enters through the optical system of the eye and forms an image upon the curved retina.
The retinal image surface is therefore not equivalent physically to the flat picture plane normally used in linear-perspective construction. Nevertheless, central projection principles provide an important geometrical model for describing many directional relationships involved in visual imaging.
The curvature and wide field of the visual system are also among the reasons why visual perspective cannot always be reduced without qualification to the geometry of a narrow flat rectilinear picture.
Graphical Perspective Projection
Graphical Perspective Projection replaces or models physical light rays with constructed lines, points, planes and geometrical rules.
The artist or draughtsperson can therefore construct an image without the scene physically projecting light onto the drawing surface. A mathematical or geometrical model reproduces selected relationships associated with spatial or optical projection.
Linear perspective, orthographic projection, axonometry and oblique projection are important graphical examples, although they belong to different geometrical projection families.
Mathematical Perspective Projection
Mathematical Perspective employs geometrical, algebraic or algorithmic relationships to transform spatial coordinates, directions and forms into another representation.
Such projection can model natural optical appearances, create technical drawings, map curved surfaces, produce synthetic camera views or intentionally generate transformations that cannot occur through ordinary unaided vision.
Modern mathematical projection is central to computer graphics, CAD, mapping, astronomy, microscopy, medical imaging, photogrammetry and many other technical fields.
Computer and Virtual Perspective Projection
Computer graphics can model both three-dimensional primary geometry and the resulting two-dimensional secondary geometry of a projected image.
A virtual camera establishes a modelled viewpoint or projection centre. Rays, matrices or equivalent calculations determine how the three-dimensional model is transformed into screen coordinates.
Depending upon the application, the system may employ central perspective, orthographic projection, cylindrical, spherical, fisheye, anamorphic or other mappings.
Virtual Reality and interactive environments extend this principle by recalculating the projection as the viewer moves, allowing the represented perspective to change continuously with the viewpoint.
Primary and Secondary Projection Geometry
Volume 1 distinguishes between primary geometry and secondary geometry.
Primary geometry concerns the three-dimensional arrangement of objects, projection rays, structural lines, the station point and the picture or image surface in spatial reality or its complete geometrical model.
Secondary geometry concerns the resulting relationships between points, lines, planes and shapes within the two-dimensional image or picture surface.
A traditional linear-perspective drawing method can operate largely through secondary geometrical rules, using vanishing points, horizon lines and grids without repeatedly reconstructing the complete three-dimensional ray geometry from which those rules are derived.
Projection and the Picture Plane
The picture plane or projection surface provides the location at which three-dimensional projection relationships become a two-dimensional image in the conventional graphical system.
For a central rectilinear projection, a ray extending between an object-space point and the station point intersects the picture plane at the corresponding projected image point.
Changing the position, orientation or shape of the projection surface can change the resulting image mapping. A planar, cylindrical or spherical surface does not intercept or represent the same directional field in exactly the same way.
Projection and the Station Point
In finite central projection, the station point represents the viewpoint, eye, camera position or centre from which the projection is geometrically organised.
Changing the station point changes the angular relationships between the spatial scene and the image surface and therefore changes the resulting perspective projection.
Parallel projection differs because the viewer is geometrically treated as being at infinity and the projectors remain parallel.
Projection and Vanishing Points
Vanishing points are a consequence of the directional geometry of central or perspectival projection.
A family of mutually parallel spatial lines sharing one direction shares one geometrical vanishing point in image space. This point can be found by passing a line through the station point parallel to that spatial direction and determining where it intersects the picture plane.
When a spatial direction is parallel to the picture plane, the corresponding vanishing point lies at infinity and its projected lines remain parallel in a conventional rectilinear image.
Parallel-projection systems differ because parallel spatial directions ordinarily remain parallel rather than converging towards finite vanishing points.
Projection and Vanishing Lines
A spatial plane contains many possible line-directions. The vanishing points belonging to those different directions collectively form the vanishing line or vanishing trace of the plane.
The ordinary geometrical horizon line is the most familiar example: it is the vanishing line of the horizontal plane.
Inclined, vertical, oblique and other planes possess their own corresponding vanishing lines according to their orientation within the projection system.
Projection and Foreshortening
Projection changes apparent shape according to the angle at which an object, line or surface is presented relative to the viewing and projection arrangement.
This produces aspect or projection foreshortening: dimensions oriented away from a frontal relationship can appear reduced in projected extent.
This should be distinguished from the separate diminution associated with increasing distance from a finite viewpoint. In ordinary central perspective the two effects can operate simultaneously.
Parallel projection can retain aspect foreshortening while eliminating ordinary distance-related perspective diminution.
Projection and Diminution of Size
In finite-viewpoint central projection, the apparent or projected size of comparable objects decreases as their distance from the projection centre increases.
This diminution is one of the fundamental visual characteristics of perspective projection and is closely connected with convergence, recession and depth representation.
Parallel projection does not operate according to the same finite-viewpoint size–distance relationship. Objects at different depths can retain the same represented scale when their dimensions and orientations are otherwise equivalent.
Projection and Field of View
The field of view describes the angular extent of spatial reality represented by a particular perspective image or system.
A relatively narrow field can often be mapped effectively onto a flat rectilinear image. As the represented field becomes wider, however, projection choices become increasingly significant.
Wide-field projection may employ fisheye, cylindrical, spherical, panoramic, multi-camera or other mappings to include directional information that would otherwise lie outside a conventional flat picture.
The form of projection therefore affects not only shape and convergence but also how much of spatial reality can be represented simultaneously.
Shadow Projection
Shadows provide particularly clear physical examples of different projection geometries.
Because the Sun is extremely distant, local solar rays can normally be treated approximately as parallel. A shadow cast by these rays therefore provides an example of parallel projection.
A nearby point-like light source, such as a small lamp, sends rays outwards in diverging directions. The resulting shadow can therefore be analysed as a central or conical projection from the light source towards the receiving surface.
This demonstrates that projection geometry is a physical phenomenon as well as a graphical construction principle.
Projection of Images, Outlines and Light
The Projecting Class is not limited to complete photographic or cinematic images. Perspective projection can involve:
- complete images;
- object outlines or silhouettes;
- shadow forms;
- light beams;
- patterns;
- symbols or graphical information; and
- spatially transformed digital imagery.
The target may be a flat screen, curved surface, physical object, building, atmospheric volume or simulated environment.
Projection Perspective and Display
Projection Perspective in the Projecting Class includes systems that send images or light into physical or represented space.
Examples include conventional cinema projection, immersive displays, projection mapping and other systems in which a projected image is fitted to a particular receiving surface or environment.
The geometry of the projected content, the projector, the receiving surface and the viewer all contribute to the final perceived perspective.
Projection Mapping and Spatial Projection
Projection need not terminate upon a conventional rectangular screen. Images can be projected onto architecture, sculptural objects, floors, walls and irregular three-dimensional surfaces.
The projected image may be geometrically pre-transformed so that it appears correctly proportioned from a selected viewpoint when wrapped across the target surface.
Such systems combine perspective projection, surface geometry and anamorphic correction and demonstrate the increasing integration of graphical, optical and computational perspective.
Gnomonic and Other Specialised Projections
Perspective projection also includes specialised geometrical mappings developed for particular scientific, mathematical or representational purposes.
Gnomonic Projection, for example, projects a spherical surface from the centre of the sphere onto a plane. Great circles on the sphere are thereby mapped as straight lines on the receiving plane.
Other specialised systems include stereographic, coeloscopic, scenographic and related historical or mathematical projection forms. Their geometries differ according to the position of the projection centre, the source surface and the receiving surface.
Map and Cartographic Projection
Cartography provides another major field of projection because the curved surface of the Earth must often be represented upon a flat map.
No single flat projection can reproduce every geometrical property of a sphere without transformation. Different mapping systems therefore preserve or prioritise different relationships of direction, area, distance, shape or scale.
This is another example of the general perspective problem: a spatial reality must be transformed to fit a different representational surface or coordinate system.
Projection Methods
The Dictionary’s broader Perspective Methods — Master Classification demonstrates that the same projection form can often be produced by different operational methods.
Among the principal method families are:
- direct-observation and tracing methods;
- instrument viewing and imaging methods;
- central-projection graphical methods;
- parallel-projection graphical methods;
- ground-grid and recession methods;
- measuring, subdivision and repetition methods; and
- shortcut, modular and freehand methods.
This distinction between projection form and construction method is important. One-point, two-point or three-point perspective describes a geometrical configuration; several different drawing methods can be used to construct that same configuration.
Projection Is Not the Same as Representation
Projection is a process or geometrical relationship. Representation is the broader production of an image, model or equivalent form standing for something else.
A representation may be produced through projection, but not every representation is generated through one simple unified projection system. Some images combine viewpoints, conventions, symbolic elements, diagrams, spatial transformations or separate projection methods.
Understanding the projection involved therefore helps identify how a particular representation relates to its source spatial reality.
Projection Is Not Necessarily Optical
Projection can be optical, but it need not involve actual light.
A graphical construction can model projection using drawn lines. A mathematical projection can transform coordinates through equations. A computer renderer can simulate a camera through numerical operations. An orthographic technical drawing can be produced from geometrical rules rather than from direct optical observation.
These systems remain related because each establishes a defined transformation between spatial or representational structures.
Projection Is Not Necessarily Planar
The phrase picture plane can encourage the assumption that all perspective projection must terminate upon a flat surface.
In fact, images can be formed upon or mapped to flat, cylindrical, spherical and other curved surfaces. The human retina is curved; panoramic and immersive screens may be cylindrical or spherical; digital images can be calculated for almost arbitrary receiving geometries.
The more general term picture surface or projection surface is therefore useful when the receiving geometry is not planar.
Projection and Visual Reality
Perspective projection is not merely an artistic invention. Natural vision and optical imaging already transform spatial reality through direction, distance, angle, projection surface and optical structure.
Graphical perspective models selected aspects of these natural relationships. Parallel and other artificial projections may instead intentionally depart from ordinary visual appearance in order to preserve measurements, improve clarity or achieve another representational purpose.
There is therefore no single projection method suitable for every purpose. Different systems preserve, emphasise, transform or discard different aspects of spatial reality.
Common Misconceptions about Perspective Projection
Several common assumptions should be avoided:
- Perspective projection is not limited to one-point perspective. One-point perspective is only one central-projection configuration.
- Central projection is not identical to Central Perspective. The first is a broad geometrical condition; the second has a more specific meaning within the PRC classification.
- Parallel projection is not the same as finite-viewpoint visual perspective. Its viewpoint is effectively treated as being at infinity.
- Projection does not always require real light. It can be graphical, mathematical or computational.
- Projection need not terminate upon a flat plane. Cylindrical, spherical and other curved surfaces can be used.
- One-, two- and three-point perspective are not complete drawing methods. They describe geometrical configurations that can be constructed using different methods.
- A camera image plane is not physically located like the conventional front picture plane of graphical perspective. Camera rays pass through the optical system and form the physical image behind its effective projection centre.
- Curved lines in a wide-field projection are not necessarily errors. They may be required by the selected projection mapping.
- The number of visible vanishing points does not define the total number of possible spatial directions.
- Projection and representation are related but not synonymous.
Why Perspective Projection Matters
Perspective projection provides one of the fundamental connections between spatial reality, vision, geometry and representation.
It explains how three-dimensional objects and scenes can form two-dimensional images; why directions converge towards vanishing points; why apparent size changes with distance under a finite viewpoint; why parallel projection behaves differently; why picture-plane orientation matters; and why different projection surfaces produce different forms of image geometry.
Its applications extend far beyond perspective drawing. Projection principles underlie vision, photography, cinema, technical drawing, architecture, surveying, cartography, microscopy, telescopy, medical imaging, computer graphics, CAD, computer vision, Virtual and Augmented Reality, projection displays and many other systems for seeing, measuring, modelling and representing spatial reality.
Understanding perspective projection therefore provides a foundation for understanding the station point, picture plane, projection centre, projection lines, Visual Element of the System, vanishing point, vanishing line, horizon line, linear perspective, parallel perspective, orthographic projection, axonometric projection, oblique projection, curvilinear perspective, cylindrical perspective, spherical perspective, optical perspective, graphical perspective and mathematical perspective.