Perspective Object / Scene

A Perspective Object / Scene is the spatial object, group of objects or scene towards which a perspective process, method or system is directed.

Within Perspective Category Theory (PCT), this is more formally identified as the Perspective Target.

The Perspective Object / Scene exists within Object Space or Target Space and provides the spatial subject from which a perspective image, view, measurement, representation, model or other Perspective Product may be formed.

The basic relationship can therefore be expressed as:

Perspective Object / Scene → Perspective Process → Perspective Image, View or Product

Perspective Object / Scene within Perspective Category Theory

Perspective Category Theory distinguishes the object or scene being addressed from the methods, processes and resulting images associated with it.

The Perspective Object / Scene is the target of the perspective operation.

It may subsequently be:

  • viewed;
  • imaged;
  • measured;
  • calculated;
  • projected;
  • represented;
  • transformed;
  • simulated; or
  • modelled.

The Perspective Object / Scene should therefore not be confused with the Perspective Process operating upon it or with the image or representation resulting from that process.

Perspective Target

The Dictionary of Perspective uses the term Perspective Target for the spatial object or scene addressed by a perspective process.

A Perspective Target may consist of:

  • a 1-D object;
  • a 2-D object;
  • a 3-D object; or
  • a 3-D spatial scene.

The target may exist within physical reality, or it may be mathematical, artificial, simulated or imaginary.

The concept therefore applies much more widely than simply to physical objects placed in front of a camera or artist.

Perspective Object and Perspective Scene

A Perspective Object is an individual spatial object or structure addressed by a perspective system.

A Perspective Scene is a broader spatial arrangement containing one or more objects and their surrounding spatial relationships.

For example:

Object: a cube, chair, building, vehicle or human figure.

Scene: a room containing furniture, a street containing buildings and vehicles, or a landscape containing landforms, trees and other objects.

The distinction is useful because perspective may concern the appearance and geometry of an individual object, the organisation of a complete scene, or both simultaneously.

The Object / Scene exists in Object Space

The Perspective Object / Scene normally exists within Object Space, also called Target Space.

Object Space is the physical, artificial, simulated or imagined space containing the object, scene or spatial information to be viewed, measured or represented.

Thus:

Object Space = the spatial domain
Perspective Object / Scene = the target contained within that domain

This distinction is important. The object is not the space itself, although the Dictionary notes that the term Perspective Target can sometimes be used more broadly for either the spatial object/scene or the Target Space towards which the system is directed.

Physical Perspective Objects and Scenes

The most familiar Perspective Targets exist within physical spatial reality.

Examples include:

  • a person;
  • a building;
  • a room;
  • a vehicle;
  • a group of geometrical solids;
  • a landscape;
  • a city street;
  • a microscopic specimen; or
  • an astronomical scene.

Such targets may be observed directly by the eye, imaged by a camera, examined through an instrument, measured mathematically or represented graphically.

The same physical object or scene can therefore participate in many different Perspective Categories and Perspective Processes.

Artificial and Simulated Objects and Scenes

A Perspective Object / Scene need not exist as an ordinary natural spatial arrangement.

Artificial or simulated targets may be deliberately constructed to create particular spatial appearances.

Examples can include:

  • architectural models;
  • stage sets;
  • Forced Perspective environments;
  • Ames Rooms;
  • miniature scenes;
  • physical simulation models; and
  • other deliberately altered spatial arrangements.

In these cases, the physical or modelled target itself may have been designed specifically to produce a selected Perspective Form when viewed or imaged from a particular viewpoint.

Imaginary Perspective Objects and Scenes

A Perspective Target may also be entirely imaginary.

A drawing, painting or computer model may represent an object or scene that has never existed physically.

Examples include:

  • an imagined building;
  • a fictional landscape;
  • a proposed engineering structure;
  • a computer-generated world;
  • an imaginary geometrical construction; or
  • a speculative three-dimensional environment.

The Perspective Object / Scene can still function as the target of a perspective process because it possesses an assumed or modelled spatial organisation that can be viewed, calculated, represented or explored.

Mathematical Perspective Objects and Scenes

A Perspective Target may also be mathematically defined.

A geometrical point, line, plane, solid or mathematically specified spatial arrangement can provide the target for a Perspective Process.

Such objects may possess precisely defined:

  • coordinates;
  • dimensions;
  • positions;
  • orientations;
  • angles;
  • surfaces; and
  • spatial relationships.

The perspective system can then calculate or project these Object-Space properties into corresponding Image-Space relationships.

Size of the Perspective Object / Scene

One important property of a Perspective Target is its absolute spatial size.

The object or scene possesses a size within Object Space independently of the particular perspective image made from it.

Its apparent or measured size in an image may then vary according to factors including:

  • distance;
  • viewpoint;
  • orientation;
  • projection geometry;
  • image scale;
  • magnification; and
  • the particular Perspective Method or System employed.

The physical or modelled size of the target should therefore be distinguished from its apparent size within Image Space.

Form and Shape of the Perspective Object / Scene

The spatial Form or shape of the Perspective Object / Scene is another fundamental target property.

An object may possess a geometrically simple Form, such as a cube or sphere, or a highly complex irregular structure.

The resulting perspective image may preserve some aspects of that Form while changing its apparent:

  • shape;
  • proportion;
  • aspect;
  • visible surface area;
  • outline;
  • foreshortening; or
  • apparent spatial organisation.

The original Form in Object Space and the apparent Form in Image Space must therefore be distinguished carefully.

Structure: Form within Form

The Dictionary identifies structure as another important facet of the Perspective Target.

Structure can be understood as the organisation of Form within Form: the way constituent parts are arranged within the larger object or scene.

A building, for example, may contain:

  • walls;
  • floors;
  • windows;
  • doors;
  • rooms;
  • columns; and
  • other component structures.

A scene may similarly contain many objects arranged in particular spatial relationships.

A Perspective Product can therefore convey information both about the overall target and about the organisation of its constituent parts.

Location

The location of the Perspective Object / Scene within Object Space influences its relationship to the observer, camera, instrument, picture plane or projection system.

An object may be:

  • near or distant;
  • central or lateral;
  • above or below the principal viewing direction;
  • in front of or behind another object; or
  • located at another defined coordinate within the target space.

Changes in location can alter the object’s projected position, apparent scale, occlusion relationships and other perspective properties.

Orientation

The orientation of a Perspective Object is distinct from its position.

An object can remain in the same location while rotating relative to the viewer or image plane.

This can alter:

  • the surfaces that are visible;
  • their apparent shapes;
  • the amount of foreshortening;
  • projected line directions;
  • apparent proportions; and
  • the resulting Perspective Form.

Perspective analysis must therefore consider both where an object is and how it is oriented.

Texture

Texture is another property of a Perspective Object or Scene that may contribute important spatial information.

Surface patterns can reveal:

  • surface orientation;
  • scale;
  • depth;
  • recession;
  • curvature;
  • changes in spatial density; and
  • the organisation of surfaces within a scene.

A regular ground grid, brick wall, tiled floor or repeated surface pattern can make perspective transformations particularly evident.

The texture belongs initially to the target object or scene, while its changing projected appearance forms part of the resulting image.

Lighting and Shadows

The Dictionary also identifies lighting and shadows as important facets of a Perspective Target.

The visible appearance of an object or scene depends partly upon:

  • the location of light sources;
  • the direction of illumination;
  • surface orientation;
  • reflectance;
  • cast shadows;
  • attached shadows; and
  • the surrounding optical environment.

Lighting and shadow therefore contribute to the Perspective Form and to the information available about the target’s three-dimensional structure.

The Viewpoint and the Perspective Object / Scene

A spatial object or scene does not possess only one possible perspective appearance.

Its resulting appearance depends upon the viewpoint from which it is viewed, imaged or represented.

A change in viewpoint can change:

  • apparent size;
  • apparent shape;
  • visible surfaces;
  • occlusion;
  • relative position;
  • line directions;
  • foreshortening; and
  • the overall composition of the scene.

The Perspective Object / Scene therefore remains the target while different viewpoints can produce different perspective views or images of it.

External Aspect of an Object

The Dictionary distinguishes an external aspect of Object Perspective.

This concerns a perspective image or view of a spatial object taken from an external viewpoint and in a particular viewing direction.

The appearance may depend upon:

  • the selected viewpoint;
  • viewing direction;
  • distance;
  • magnification;
  • scale; and
  • the projection system involved.

The same object can therefore generate many different external perspective aspects while retaining the same underlying physical or modelled Form.

Object-Specific Viewpoint

The Dictionary also identifies an internal or object-specific aspect: considering how a surrounding scene would appear from the location or viewpoint associated with a particular object.

This does not imply that an inanimate object literally sees.

Rather, an imaginary viewpoint may be positioned at that object’s location so that spatial relationships can be analysed relative to it.

This kind of object-centred perspective can be useful in mathematical, graphical, physical, engineering and computer-generated spatial analysis.

From Perspective Object / Scene to Perspective Image

The Perspective Object / Scene is transformed through a Perspective Process into a corresponding image, view, measurement or representation.

In general:

Perspective Object / Scene → Perspective System → Perspective Product

For example:

physical scene → camera imaging → photograph

spatial object → graphical construction → perspective drawing

measured scene → mathematical process → spatial model

imagined environment → New Media process → computer-generated image

The resulting Product is related to the target but should not be confused with the target itself.

Object-Space properties and Image-Space appearances

A central problem of perspective is the relationship between the actual properties of the target object or scene and their resulting appearance in Image Space.

For example:

  • parallel Object-Space lines may appear to converge;
  • equal-sized objects may appear unequal because of distance;
  • a rectangular plane may appear trapezoidal;
  • a circular form may appear elliptical;
  • a deep dimension may appear foreshortened;
  • one object may partially conceal another; and
  • three-dimensional depth may be represented on a two-dimensional surface.

These differences arise through the Perspective Process and should not automatically be attributed to changes in the target object itself.

One Object / Scene can produce many Perspective Products

The same Perspective Object / Scene can produce many different images, views, measurements and representations.

It may be:

  • viewed directly;
  • photographed from several viewpoints;
  • represented graphically;
  • measured through instruments;
  • modelled mathematically;
  • scanned digitally;
  • represented through parallel projection; or
  • rendered through central, curvilinear or other projection systems.

The target may remain substantially unchanged while the Perspective Method, viewpoint, Category, Class and resulting Product vary.

This is one reason why the Perspective Object / Scene must be kept conceptually separate from any particular image of it.

The target may be physical or represented

In a longer image chain, the target of a new Perspective Process need not always be an original physical scene.

An existing image or representation may itself become the target of another process.

For example, a photograph may subsequently be:

  • scanned;
  • photographed again;
  • digitally processed;
  • projected;
  • measured; or
  • analysed by a computer-vision system.

In this sense, one system’s Image Space can become another system’s Target Space within a chained perspective process.

Perspective Object / Scene and the Scale–Shape–Size Problem

The distinction between the Perspective Object / Scene and its image is particularly important when considering the relationships between scale, shape and size.

An object’s actual spatial size and Form belong to Object Space.

Its apparent or projected size and shape depend upon the perspective conditions under which it is viewed or imaged.

These include:

  • distance;
  • viewpoint;
  • orientation;
  • foreshortening;
  • projection geometry;
  • scale;
  • resolution; and
  • the method used to define or measure size.

A Perspective Product therefore provides a transformed view of the target rather than an unqualified copy of its spatial properties.

Why Perspective Object / Scene matters

The Perspective Object / Scene identifies what the perspective system is actually directed towards.

Without making this explicit, it becomes easy to confuse:

  • the target with the image;
  • Object Space with Image Space;
  • actual size with apparent size;
  • actual shape with projected shape;
  • physical position with image position;
  • the original spatial structure with its representation; and
  • properties of the target with transformations introduced by the Perspective Process.

Perspective Object / Scene is therefore the spatial object, group of objects or scene that forms the target of a Perspective Process or System, together with relevant properties such as its size, Form, structure, location, orientation, texture, lighting and shadows.

Related Perspective Topics

Object Space →
Image Space →
Perspective Process →
Perspective Product →
Perspective System →
Perspective Category Theory →