Perspective requires a distinction between what physically exists and the geometrical Form through which its perspective appearance is analysed.
These are Physical Form and Modelled Form.
Physical Form is the actual structure of an object or scene in spatial reality. Modelled Form is the idealised or assumed geometrical Form used to analyse, describe or construct the relationship between that Physical Form and its perspective appearance.
Together they form the principal Object-Space and modelling side of the relationship that produces Apparent Form.
Physical Form
Physical Form is the actual physical configuration, structure, shape, outline or volume of a real object or scene in Object Space.
It describes how a spatial object is physically organised independently of the particular Perspective View through which it is observed.
For example, the Physical Form of a rigid cube consists of its actual three-dimensional spatial structure.
Physical Form may therefore be expressed as:
Physical Form = actual Object-Space Form
The Physical Form of an object does not need to change simply because its perspective appearance changes.
A change of Viewpoint, Viewing Direction, distance or another Perspective Condition can produce a different appearance while the underlying Physical Form remains unchanged.
Physical Form and the Perspective Process
Physical Form becomes visually or representationally accessible through a Perspective Process.
The process establishes the relationship between spatial reality and its resulting appearance and may be analysed through both:
- Modelled Form; and
- Perspective Phenomena.
Perspective Phenomena describe systematic changes or effects arising through perspective.
Important phenomena affecting the appearance of Form include:
- Aspect of Form;
- Diminution of Size;
- Perspective of Proportion;
- Degradation of Form; and
- Foreshortening.
These phenomena do not necessarily represent changes in the Physical Form itself. They concern the way in which spatial structure becomes transformed, reduced or differently presented through perspective.
A rectangular plane, for example, may appear foreshortened when viewed obliquely without undergoing any physical change. Likewise, equal physical dimensions situated at different distances can have different apparent sizes.
Modelled Form
Modelled Form is the idealised or assumed geometrical Form used to analyse, describe, calculate or construct the relationship between Physical Form and Apparent Form.
It is therefore neither simply the Physical Form itself nor merely another appearance of it.
Geometry necessarily abstracts spatial reality. A complex Physical Form may, for analytical purposes, be treated as:
- a point;
- a line;
- a plane;
- a rectangle;
- a cube;
- a sphere;
- a polygon;
- a surface; or
- another defined geometrical Form.
Modelled Form may therefore be expressed as:
Modelled Form = assumed geometrical approximation used for analysis or construction
Modelling Physical Form
A geometrical model reduces the complexity of physical reality to Forms that can be defined and analysed.
The degree of approximation depends upon the object, the scale at which it is considered and the purpose of the analysis.
A building might be modelled as a combination of planes and solids. A curved surface might be approximated by a sphere, cylinder or another defined surface. A complex natural object may require a much less exact geometrical description.
The model does not replace the Physical Form. It provides the geometrical framework through which its perspective behaviour can be studied.
Modelled Form as an Assumed Geometrical Limit
Modelled Form can provide an assumed geometrical limit towards which the Apparent Form may be interpreted under specified conditions of scale, geometry and observation.
For a simple object such as a nominal cube, the relationship may be comparatively straightforward. For an irregular, natural or highly detailed Physical Form, the correspondence can be much less exact.
The Modelled Form should therefore not be treated as an arbitrary alternative that is continually exchanged for another model. It is the geometrical assumption through which the particular relationship between appearance and spatial Form is being analysed.
The adequacy of the approximation depends upon such factors as:
- scale;
- resolution;
- complexity of the Physical Form;
- geometrical assumptions employed; and
- purpose of the analysis.
Physical, Modelled and Apparent Form
Physical Form and Modelled Form belong to a larger three-part relationship:
Physical Form — what spatially exists
Modelled Form — the assumed geometrical approximation through which it is analysed
Apparent Form — how that spatial Form appears through perspective
For analytical purposes, the production relationship can be represented as:
Physical Form + Modelled Form → Apparent Form
The arrow represents a relationship of production and dependence rather than a simple temporal sequence.
The three Forms belong together, but they should not simply be assumed to coincide. Their correspondence varies with scale, geometry, Viewpoint, Projection Mode and other Perspective Conditions.
Form, Object Space and Perspective Space
The distinction is closely related to the difference between Object Space and Perspective Space:
Physical Form → Object-Space Form
Modelled Form → geometrical relationship used to analyse the correspondence
Apparent Form → Perspective-Space appearance
Perspective therefore concerns not simply the existence of Forms, but the relationship between Forms existing in spatial reality and their appearances through perspective.
Image Space is not Object Space, just as Apparent Form is not Physical Form.
Form and the Scale–Shape–Size Problem
Physical Form contains structure at many possible scales. At one observational or representational scale, small details may be invisible; at another, those same details may become significant features of the Form.
Modelled Form therefore necessarily represents spatial structure at some assumed level of geometrical description.
This is central to the Scale–Shape–Size Problem: a geometrical Form sufficient at one scale of analysis may not remain sufficient at another.
Scale therefore affects not only how much of a Form can be seen, but also how adequately its Physical Form can be geometrically modelled.
Why Physical and Modelled Form Matter
The distinction between Physical and Modelled Form prevents geometrical description from being confused with physical reality.
- Physical Form is the actual spatial structure;
- Modelled Form is its geometrical approximation or analytical representation;
- a model does not necessarily reproduce every feature of the Physical Form;
- the adequacy of a model depends partly upon scale and resolution;
- Perspective Phenomena alter or shape appearance without necessarily changing Physical Form; and
- Physical and Modelled Form participate in the production and analysis of Apparent Form.
The resulting visible appearance is examined separately as Apparent Form.