Physical Form is the actual physical configuration, structure, shape, outline or volume of a real object or scene in Object Space.
It describes how an object or spatial structure physically exists independently of the particular perspective view, image or representation through which it is observed.
Physical Form must therefore be distinguished from Apparent Form, which is how that physical structure appears through perspective, and from Modelled Form, which is the geometrical approximation used to analyse or represent the relationship between physical reality and appearance.
Physical Form Is Object-Space Form
Physical Form belongs to Object Space: the spatial reality containing the object, scene or structure being viewed, imaged, measured or represented.
A rigid cube, for example, possesses an actual three-dimensional structure in Object Space. Moving the observer around the cube changes its perspective appearance, but does not necessarily change the cube’s Physical Form.
The relationship can therefore be expressed simply as:
Physical Form = actual Object-Space Form
Physical Form and Apparent Form
Physical Form is not Apparent Form.
Apparent Form is the perspective appearance taken by a Physical Form under particular conditions of viewpoint, viewing direction, distance, scale, projection, optics and representation.
The Physical Form itself can remain unchanged while its Apparent Form changes substantially.
For example:
- a rectangular plane may appear foreshortened when viewed obliquely;
- a circular surface may appear elliptical;
- equal physical dimensions at different distances may appear unequal;
- parallel physical directions may appear to converge;
- different parts of an object may become visible or hidden as viewpoint changes.
These are changes in appearance, not necessarily changes in the underlying Physical Form.
Physical Form and Modelled Form
Physical reality is often too complex to analyse directly in complete detail. Perspective geometry therefore employs a Modelled Form: an idealised or assumed geometrical approximation through which Physical Form can be analysed.
A physical object might, for example, be treated geometrically as:
- a point;
- a line;
- a plane;
- a rectangle;
- a cube;
- a sphere;
- a polygon;
- a surface; or
- another defined geometrical structure.
The Modelled Form is not the Physical Form itself. It is the geometrical description through which aspects of that Physical Form are analysed, calculated or represented.
The Three Forms
Perspective analysis distinguishes three related forms of a particular object or scene:
- Physical Form — what spatially exists;
- Modelled Form — the assumed geometrical approximation through which the relationship is analysed;
- Apparent Form — how the spatial Form appears through perspective.
These should not be treated as three unrelated alternatives. They describe different aspects of the same perspective relationship.
For analytical purposes, their relationship can be represented as:
Physical Form + Modelled Form → Apparent Form
This arrow expresses a relationship of dependence and analysis rather than a simple temporal sequence.
Physical Form Does Not Depend on a Particular Viewpoint
Physical Form describes the spatial structure of an object independently of any one particular perspective view.
An observer can:
- move around the object;
- change viewing direction;
- move closer or farther away;
- change Field of View;
- use a different Projection Mode; or
- observe the object through different optical systems.
These changes can produce different Apparent Forms without requiring the Physical Form itself to change.
This distinction is fundamental to perspective because one physical structure can generate many different perspective appearances.
One Physical Form, Many Apparent Forms
A single Physical Form can produce a potentially large range of Apparent Forms.
Consider a cube. Its actual physical structure may remain fixed, but its appearance changes as the observer moves around it. Different faces become visible, apparent edge lengths change, angles alter in the image, and sets of parallel edges acquire different vanishing relationships.
The same principle applies to complex natural and artificial forms.
Perspective therefore does not simply reproduce Physical Form. It produces a viewpoint-dependent appearance of Physical Form.
Apparent Form Does Not Uniquely Reveal Physical Form
The inverse relationship is more difficult.
Although one Physical Form can produce many Apparent Forms, a single Apparent Form can also correspond to more than one possible Physical Form.
Depth, shape, position and scale are therefore not always uniquely recoverable from one perspective image alone.
Additional information may be required, including:
- additional viewpoints;
- known dimensions;
- scale information;
- depth cues;
- object recognition;
- geometrical constraints;
- context; and
- knowledge of the projection or imaging system.
This is one of the central problems in interpreting perspective images.
Physical Form as the Limiting Reality
Within the relationship among Physical, Modelled and Apparent Form, Physical Form provides the underlying spatial reality against which the adequacy of geometrical modelling and apparent correspondence can be considered.
Modelled Form and Apparent Form may approach Physical Form closely under particular conditions, but they should not simply be assumed to coincide with it.
The degree of correspondence depends upon such factors as:
- scale;
- geometrical complexity;
- resolution;
- viewpoint;
- projection conditions;
- optical conditions; and
- the level of approximation used by the perspective system.
Physical Form therefore acts as the limiting reality against which the adequacy of the model and appearance may be assessed.
Physical Form and Scale
Physical Form contains structure at many possible scales.
A building may appear to consist of simple planar walls when viewed from a distance, yet at closer scales those walls contain windows, joints, textures, irregularities and material structures. At still smaller scales, further physical structure becomes significant.
The Physical Form has not necessarily changed; rather, the level at which its structure is being observed or modelled has changed.
This means that any geometrical description of Physical Form necessarily operates at some level of abstraction and scale.
The Scale–Shape–Size Problem
The relationship between Physical Form and geometrical description is central to the Scale–Shape–Size Problem.
A geometrical approximation that adequately represents Physical Form at one scale may become inadequate at another.
For example, Linear Perspective may treat edges as straight and planes as flat across a particular range of scales. At a sufficiently different scale, curvature, irregularity or other physical structure may become important and the assumed geometrical model may no longer provide an adequate approximation.
The validity of a perspective model therefore depends partly upon the scale range over which its assumed geometry remains sufficiently close to Physical Form.
The Shape-Sufficiency Problem
A related question is whether the assumed geometrical form remains sufficiently close to Physical Form for the perspective system to remain useful or valid.
The Shape-Sufficiency Problem asks, in effect, over what range of scales and conditions Modelled Form and Apparent Form remain sufficiently adequate approximations of the Physical Form being analysed.
Physical Form is therefore not simply an abstract starting point. It provides the physical reference against which the sufficiency of a perspective model can ultimately be judged.
Perspective Phenomena Do Not Necessarily Change Physical Form
Perspective Phenomena can substantially change how a Physical Form appears without changing the underlying object itself.
These effects can include:
- apparent size change;
- foreshortening;
- apparent shape change;
- vanishing and convergence;
- occlusion;
- changes in visible detail;
- colour and contrast change;
- acuity change; and
- changes in apparent position or orientation.
Such phenomena primarily shape Apparent Form. They should not automatically be interpreted as alterations of Physical Form.
Physical Form and Perspective Images
A perspective image contains information produced from or related to Physical Form, but the image should not be confused with the Physical Form itself.
The physical object exists in Object Space. Its represented or optical appearance occupies Image Space or Perspective Space.
Thus:
Physical Form → Object Space
Apparent Form → Perspective / Image Space
This distinction prevents a perspective image from being treated as an exact physical copy of the spatial reality that produced it.
Why Physical Form Matters
Physical Form provides the essential reference to what actually exists in spatial reality.
Without distinguishing it from Modelled Form and Apparent Form, it becomes easy to confuse:
- physical structure with geometrical approximation;
- physical shape with perspective appearance;
- Object Space with Image Space;
- changes in appearance with changes in reality; and
- the information contained in an image with the complete structure of the object that produced it.
The distinction between Physical, Modelled and Apparent Form therefore provides a fundamental framework for understanding the relationship between spatial reality, geometrical modelling and perspective appearance.