Viewpoint

A Viewpoint is the spatial position from which an object, scene, image or represented spatial reality is viewed, imaged or constructed.

In graphical and optical perspective it is also commonly called the Station Point, Eye Point, Point of View or Centre of Projection.

The viewpoint establishes the location from which spatial relationships are observed or projected. Changing the viewpoint can therefore change the apparent size, shape, position, overlap and geometrical relationships of objects within the resulting Perspective Image or View.

In simplified form:

Viewpoint + Viewing Direction + Field of View → Perspective View / Image

Viewpoint within Perspective

Perspective represents or reveals spatial reality from a particular positional relationship.

The Viewpoint identifies where the observer, eye, camera, instrument or modelled observer is located relative to the Perspective Object / Scene.

It therefore contributes fundamentally to the Perspective Process because the same object or scene can produce very different appearances when viewed from different spatial positions.

The Viewpoint should be distinguished from:

  • the object or scene being viewed;
  • the Viewing Direction;
  • the Field of View;
  • the Viewing Distance;
  • the Picture Plane; and
  • the resulting Perspective Image or View.

Viewpoint and Station Point

The Dictionary of Perspective treats Station Point as the preferred technical term for the fixed viewing position used in many perspective constructions.

Closely related or synonymous terms include:

  • Eye;
  • Eye Point;
  • Camera Point;
  • Centre of Perspective;
  • Centre of Projection;
  • Observer’s Point;
  • Point of Sight;
  • Point of View;
  • Spectator’s Point;
  • Stand Point;
  • Station Point; and
  • Viewpoint.

These terms generally identify the location from which the relevant perspective relationship is established.

The Viewpoint is a position

A Viewpoint is fundamentally a position in space.

It should not be confused with the direction in which the observer is looking.

An observer may remain at exactly the same Viewpoint while turning the eyes, head, camera or imaging system towards different parts of the surrounding scene.

Conversely, an observer may move to a different Viewpoint while continuing to look in approximately the same direction.

This distinction between position and direction is fundamental to perspective analysis.

Viewpoint and Viewing Direction

Viewpoint and Viewing Direction describe two different properties of a perspective view.

The distinction can be expressed as:

Viewpoint → where the observer or imager is located
Viewing Direction → where the observer or imager is looking

A single Viewpoint can therefore support many different Viewing Directions.

This is particularly obvious when a person stands in one place and looks:

  • straight ahead;
  • to the left or right;
  • upwards;
  • downwards; or
  • around a surrounding panoramic scene.

Keeping these concepts separate avoids treating every change of view as a change of spatial position.

Fixed Viewpoint

Many classical and technical perspective systems employ a fixed Viewpoint.

The observer, eye, camera or constructed Station Point is assumed to remain at one spatial location while the Perspective Image is formed or constructed.

This is characteristic of:

  • classical Linear Perspective;
  • perspective-window constructions;
  • many graphical perspective methods;
  • single-camera photographs; and
  • other single-view imaging systems.

Fixing the Viewpoint allows consistent geometrical relationships to be established between the object, Station Point, projection rays and Image or Picture Plane.

Fixed Viewpoint and Fixed Viewing Direction

Classical graphical perspective normally fixes both the Viewpoint and the Viewing Direction.

This produces a single, systematic perspective view of the object or scene.

In simplified form:

Fixed Viewpoint + Fixed Viewing Direction → Fixed Perspective View

This arrangement is comparable in a basic geometrical sense to a single-lens camera capturing an image from one position and one central direction at a particular moment.

The fixed-view arrangement is extremely useful for constructing and recording Perspective Images, but it should not automatically be treated as equivalent to the continually changing operation of natural human vision.

Real or Constructed Viewpoint

The Dictionary distinguishes a Real or Constructed Viewpoint.

A real Viewpoint is the actual spatial location of an observer, eye, camera or other imaging system.

A constructed Viewpoint is the corresponding geometrical position established within a perspective drawing or construction.

For example, in Linear Perspective the Station Point can be constructed geometrically even when no observer is physically occupying that position during the drawing process.

The constructed Viewpoint represents the position from which the depicted perspective is intended to be understood.

Virtual Viewpoint

A Virtual Viewpoint is a modelled viewpoint used within a digital or simulated perspective system.

It may occur within:

  • Computer-Generated Imagery;
  • Computer-Aided Design;
  • animation;
  • computer games;
  • Virtual Reality;
  • Augmented Reality; or
  • other New Media systems.

The Virtual Viewpoint performs a role comparable to an eye or camera position within the modelled environment.

Unlike a fixed graphical Station Point, however, a Virtual Viewpoint may potentially move or change continuously in real time.

Viewpoint in Linear Perspective

Linear Perspective normally assumes a fixed Viewpoint.

From this Station Point, geometrical projection relationships are established between the spatial object or scene and the Picture Plane.

The Viewpoint therefore helps determine the resulting:

  • projected positions of object points;
  • apparent dimensions;
  • foreshortening;
  • line directions;
  • vanishing relationships; and
  • overall geometrical Form of the image.

The fixed Viewpoint is consequently one of the basic geometrical conditions upon which a conventional Linear Perspective construction depends.

The Perspective Window and the Viewpoint

The classical Perspective Window provides a simple way of understanding a fixed Viewpoint.

A transparent or imaginary plane is positioned between the observer and the spatial scene.

The observer keeps the eye at a fixed location and records where the apparent outlines of the scene intersect the plane.

For an accurate construction, several conditions need to remain fixed:

  • the object or scene;
  • the Eye or Station Point;
  • the Viewing Direction;
  • the Field of View; and
  • the position and orientation of the Perspective Window.

If the observer changes position while the drawing is being constructed, the apparent geometry of the scene also changes.

Viewpoint in Camera Perspective

A camera also forms a Perspective Image from a particular Viewpoint.

For each individual exposure or image frame, the camera records the scene from a particular spatial position and viewing direction.

In this sense, a conventional camera image resembles a perspective-window construction.

The camera location establishes the Viewpoint, while the optical axis establishes a principal Viewing Direction and the lens and image format contribute to the Field of View.

Moving the camera to another location creates a new Viewpoint and therefore a different perspective image of the same scene.

Viewpoint in Natural Vision

Natural human vision is more complex than the fixed-viewpoint model of classical graphical perspective.

The eyes can rotate, the head can turn and the observer can move through the environment.

Consequently, natural visual experience can involve continual changes in:

  • Viewing Direction;
  • point of fixation;
  • Field of View;
  • head orientation;
  • body orientation; and
  • Viewpoint location.

A fixed graphical perspective image therefore represents one selected spatial relationship rather than the complete dynamic operation of natural viewing.

A fixed Viewpoint with changing Viewing Direction

A Viewpoint does not have to move for the observer to explore different parts of a scene.

An observer or imaging system can remain at one fixed spatial location while sampling many Viewing Directions.

This principle underlies:

  • panoramic viewing;
  • 360-degree imagery;
  • circular viewing systems;
  • spherical panoramas; and
  • Sphere-of-Vision representations.

The relationship may be expressed as:

Fixed Viewpoint + Multiple Viewing Directions → Panoramic or Spherical View

This differs fundamentally from moving around an object and observing it from several different Viewpoints.

Moving Viewpoint

A Moving Viewpoint occurs when the observer, camera or virtual imager changes spatial location relative to the object or scene.

Moving around an object reveals different aspects of its Form.

As the Viewpoint changes, the observer may see:

  • different surfaces;
  • different outlines;
  • different overlaps;
  • different apparent proportions;
  • different foreshortening; and
  • different spatial relationships between the object’s parts.

Multiple Viewpoints can therefore provide information that cannot be obtained from one single fixed view.

Viewpoint and the Sphere of Revolution

Moving around an external object while continuing to observe it can be understood through the concept of the Sphere of Revolution.

The observer explores the object from a series of spatially different Viewpoints surrounding it.

This differs from the Sphere of Vision, where the Viewpoint remains fixed and the Viewing Direction changes around the observer.

The distinction can therefore be expressed as:

Sphere of Vision → fixed Viewpoint, changing Viewing Direction
Sphere of Revolution → changing Viewpoint around the object

These two relationships provide fundamentally different kinds of visual information about spatial reality.

Viewpoint and Field of View

The Field of View should also be distinguished from the Viewpoint.

The Viewpoint identifies the position of the observer or imaging system.

The Field of View identifies the total angular extent of the scene that is captured, represented, displayed or visible at a particular time.

Thus:

Viewpoint → position
Viewing Direction → central direction
Field of View → angular extent

Together, these help define the spatial content represented in a Perspective Image or View.

Viewpoint and Viewing Distance

Viewing Distance is the distance between the Viewpoint and the object or image being viewed.

It is therefore not itself the Viewpoint.

Two observers may occupy different Viewpoints at the same distance from an object, while two observers positioned along the same general Viewing Direction may be at different distances.

Viewing Distance can influence:

  • apparent size;
  • angular extent;
  • Field of View requirements;
  • foreshortening relationships; and
  • the experience of a represented image.

Position and distance must therefore be analysed separately.

The correct Viewpoint for a Perspective Image

A perspective image constructed from a specific Station Point possesses an associated viewing position.

In principle, viewing the finished image from approximately the same position and distance used in its construction most closely reproduces the intended geometrical relationship.

If the viewer moves substantially away from this position, the physical picture surface is seen from a different angle or distance.

This introduces an additional optical viewing relationship between the spectator and the already-constructed image.

Human visual perception can often tolerate moderate displacement, but the original construction still possesses its own implied or designed Viewpoint.

The Problem of Viewpoint

The Problem of Viewpoint arises because different Viewpoints produce significantly different images of the same spatial object or scene.

Each Viewpoint therefore supplies useful but incomplete information about three-dimensional Form.

A single view may conceal:

  • rear surfaces;
  • occluded objects;
  • some dimensions;
  • parts of the spatial structure; and
  • alternative aspects of Form.

Consequently, a complete understanding or reconstruction of an object or scene may require several views taken from different Viewpoints.

Single-View and Multi-View Perspective

A Single-View Perspective presents the object or scene from one principal Viewpoint.

A Multi-View Perspective uses or combines information from several Viewpoints.

The distinction can be expressed as:

One Viewpoint → partial aspect of spatial Form
Multiple Viewpoints → several complementary aspects of spatial Form

Multi-view methods can therefore provide additional information for understanding, modelling or reconstructing three-dimensional objects and scenes.

However, integrating several views into one consistent spatial model introduces its own correspondence and reconstruction problems.

Viewpoint and Perspective Transformation

Changing the Viewpoint produces a Perspective Transformation in the resulting image or view.

The physical object may remain unchanged while its projected appearance changes.

Differences can occur in:

  • apparent shape;
  • apparent size;
  • relative position;
  • foreshortening;
  • overlap;
  • visible surface area; and
  • projected geometrical relationships.

The Viewpoint is therefore one of the principal conditions determining how Object-Space Form is transformed into Image-Space Form.

Viewpoint and Object Perspective

Object Perspective can describe the external aspect of an object as seen from a particular Viewpoint and Viewing Direction.

Changing the Viewpoint changes the aspect of the object that becomes available to the observer.

An object can therefore possess many possible Perspective Images or Views without undergoing any physical change itself.

This distinction between object identity and view-dependent appearance is fundamental to perspective.

The binocular Viewpoint problem

Human binocular vision introduces a further complication because the two eyes occupy slightly different spatial positions.

Each eye therefore receives a somewhat different view of the same scene.

The visual system must reconcile these separately angled retinal views into a coherent experienced direction and spatial appearance.

In simplified form:

Left-eye Viewpoint + Right-eye Viewpoint → integrated binocular visual experience

This demonstrates that the apparently simple idea of a single human Viewpoint is, in binocular vision, a useful abstraction from a more complex physiological and perceptual process.

Viewpoint in Virtual Reality and New Media

Digital environments make the Viewpoint an active and potentially continuously variable component of the Perspective System.

A virtual camera or observer may:

  • move through the modelled environment;
  • rotate;
  • look in different directions;
  • change height;
  • approach or retreat from objects; and
  • explore spatial reality from many successive positions.

Virtual Reality can therefore move beyond the fixed Station Point characteristic of a conventional perspective drawing or photograph.

The displayed image may be recalculated continuously according to the changing modelled Viewpoint and Viewing Direction.

Viewpoint is not Perspective

The Viewpoint is a fundamental element or condition of many perspective systems, but it should not itself be confused with the complete Perspective Method, Process or Form.

A full perspective relationship may also depend upon:

  • Viewing Direction;
  • Field of View;
  • Viewing Distance;
  • projection geometry;
  • Picture or Image Surface;
  • Perspective Category;
  • Perspective Method;
  • optical or instrument characteristics; and
  • the spatial properties of the target.

The Viewpoint is therefore one essential component within a larger perspective system.

Why Viewpoint matters

Viewpoint is fundamental because a perspective image or view is always related to some spatial position from which the target is observed, imaged, projected or represented.

Recognising the Viewpoint helps distinguish:

  • position from Viewing Direction;
  • Viewpoint from Field of View;
  • Viewpoint from Viewing Distance;
  • a fixed graphical Station Point from dynamic natural vision;
  • a real Viewpoint from a constructed or virtual Viewpoint;
  • one aspect of an object from the object itself;
  • single-view from multi-view representation; and
  • changes in physical Form from changes produced merely by changing the observer’s position.

Viewpoint is therefore the spatial position of the eye, observer, camera, instrument or modelled viewing system from which a Perspective Object / Scene is viewed, imaged or represented.

Related Perspective Topics

Perspective Image / View →
Perspective Object / Scene →
Perspective Transformation →
Object Space →
Image Space →
Perspective Category Theory →