Apparent Form

Apparent Form is the perspective appearance of a Physical Form: the visible outcome produced when spatial reality is viewed, imaged, projected or otherwise subjected to a Perspective Process.

A single Physical Form can produce many different Apparent Forms because appearance depends upon the relationship between the object, the Viewpoint and the conditions under which the view or image is formed.

Apparent Form is therefore the principal bridge between spatial reality and classified Perspective Form.

What Is Apparent Form?

Apparent Form is the appearance of a Physical Form from a particular:

Viewpoint;
Viewing Direction;
distance;
orientation;
Projection Mode;
Field of View;
optical condition;
scale;
resolution; and
Perspective Process.

It belongs to the resulting Image Space or Perspective Space rather than to the physical structure of the object itself.

A cube, for example, possesses a Physical Form but can produce many different Apparent Forms when viewed from different directions and distances.

Apparent Form = Perspective-Space appearance of a particular Form

Physical Form Appears Through Perspective as Apparent Form

A basic relationship of perspective can be stated as:

Physical Form → Perspective Process → Apparent Form

The Physical Form itself need not change for the Apparent Form to change.

Moving around an object, altering the Viewing Direction, changing the distance or changing another Perspective Condition can produce a new Apparent Form while the object itself remains physically unchanged.

This is one of the fundamental distinctions of perspective:

Physical Form is not Apparent Form.

Perspective Phenomena Shape Apparent Form

Apparent Form is shaped by a wide range of Perspective Phenomena.

Perspective Phenomena are apparent and generalised changes in visual features arising through Perspective Processes.

They may affect:

apparent size;
shape;
aspect;
position;
orientation;
outline;
foreshortening;
line direction;
vanishing;
colour;
contrast;
acuity;
visible detail; and
light and shade.

Different phenomena therefore act upon different facets of Apparent Form.

The Level 3 diagram links Apparent Form to these different classes of Perspective Phenomena and shows how geometrical, optical and combined effects contribute to the resulting appearance.

Apparent Form and Classified Perspective Form

When an Apparent Form is considered not merely as the appearance of one particular object but as a characteristic form of perspective output, it can be classified as a Perspective Form.

Perspective Form identifies the characteristic visual, optical, geometrical or spatial appearance produced by a Perspective Process.

Examples include:

Linear Perspective Form;
Spherical Perspective Form;
Curvilinear Perspective Form;
Parallel Perspective Form;
Axonometric Perspective Form; and
Photographic Form.

Here, Form is a generalised classification of output, rather than the particular Physical Form of one individual object.

Geometrical, Optical and Combined Perspective Form

At the level of classified output, Perspective Form can involve:

GEOMETRICAL — where the principal characteristics concern geometrical organisation and transformation.

OPTICAL — where the principal characteristics arise through optical conditions and visible effects.

GEOMETRICAL + OPTICAL — where geometrical and optical characteristics operate together in the resulting Apparent Form.

The distinction is important because perspective appearance is not produced by geometry alone.

A Perspective Image can simultaneously contain geometrical transformations of size, shape and position together with optical changes of colour, acuity, contrast, illumination or detail.

Perspective of Form — Geometrical Facets

Perspective of Form is the geometrical division of Perspective Form.

It is concerned principally with apparent changes in:

SIZE · SHAPE · POSITION · ORIENTATION · OUTLINE

These changes concern the geometrical appearance of spatial Forms within Perspective Space.

Linear Perspective provides an important example, involving apparent size, edges, outlines, planes, recession and vanishing relationships.

Perspective of Form should therefore not be treated as a synonym for Perspective Form.

Perspective Form → broad classified perspective output
Perspective of Form → geometrical division concerned with Form

Perspective of Forms

The related expression Perspective of Forms concerns the projected appearance or outline of geometrical Forms present in spatial reality.

These may include:

points;
lines;
planes;
polygons;
surfaces;
solids;
outlines; and
other geometrically defined Forms.

Perspective therefore transforms not only complete objects but also the geometrical elements and relationships from which their spatial organisation can be analysed.

Principal Divisions of Perspective Form

1. Perspective of Form — Geometrical Facets

Perspective of Form concerns apparent changes in geometry, outline, size, shape, position and orientation.

Important phenomena include diminution, proportion, foreshortening, aspect and vanishing.

2. Gradient of Colour Perspective — Optical Facets

Gradient of Colour Perspective concerns apparent changes in colour, hue or saturation associated with distance or optical conditions.

Aerial Perspective and Atmospheric Perspective provide important examples.

3. Gradient of Acuity Perspective — Optical and Geometrical Facets

Gradient of Acuity Perspective concerns apparent changes in clarity, sharpness, resolution and visible detail.

The amount of Form that can be distinguished therefore depends partly upon image scale and detector or visual resolution.

4. Gradient of Chiaroscuro Perspective — Optical Facets

Gradient of Chiaroscuro Perspective concerns changes in illumination, light, shade and contrast that contribute to spatial appearance.

These divisions demonstrate why classified Perspective Form may be geometrical, optical or a combination of both.

Depth Cues Help Interpret Apparent Form

A Perspective Image provides visual information from which an observer can attempt to infer the spatial structure that produced it.

Important monocular or pictorial cues include:

occlusion and overlapping contours;
relative size;
relative height in the visual field;
texture gradients;
linear convergence;
aerial colour changes;
contrast changes; and
acuity changes.

Binocular cues include retinal disparity and convergence.

Motion cues include motion parallax, optic flow and Viewpoint change.

Contextual and perceptual cues include familiar size, object recognition, scene structure and known spatial relationships.

These cues assist in the interpretation of Apparent Form and in the inference of possible underlying Physical Form.

Apparent Form Does Not Uniquely Determine Physical Form

A fundamental problem follows from the distinction between Physical and Apparent Form:

A single Apparent Form does not always determine one unique Physical Form.

The same or a very similar Image-Space Form may sometimes correspond to more than one possible Object-Space arrangement.

Perspective interpretation may therefore require:

geometrical assumptions;
context;
recognition of familiar Forms;
Viewpoint information;
scale information;
multiple views;
depth cues; and
other Perspective Framework structures.

This is part of the wider Correspondence or Equivalence Problem: determining how reliably Image-Space information can be related to the Physical Form and spatial structure that produced it.

Apparent Form and Scale

Apparent Form also depends upon scale and resolution.

A Physical Form contains structure at many possible scales. At one scale small details may disappear; at another they may become significant features of apparent shape.

Apparent Shape may therefore change with scale and resolution even when the Physical Form and Viewpoint remain unchanged.

This connects Apparent Form directly with the Scale–Shape–Size Problem.

Why Apparent Form Matters

Apparent Form lies at the centre of perspective because it is the point at which spatial reality becomes visible perspective appearance.

Apparent Form is not Physical Form;
Apparent Form belongs to Perspective Space or Image Space;
Perspective Phenomena shape different features of Apparent Form;
Apparent Form may contain geometrical, optical or combined characteristics;
Perspective of Form concerns its geometrical facets;
size, shape, position, orientation and outline are principal geometrical variables;
colour, acuity and chiaroscuro contribute further optical or combined effects;
depth cues assist the interpretation of Apparent Form; and
one Apparent Form does not necessarily identify one unique Physical Form.

Apparent Form therefore provides the connection between the Physical and Modelled Form of spatial reality and the wider classification of Perspective Forms and Perspective Phenomena.

Explore Theory

Explore the principal theories, classifications, types, forms, geometries, spatial concepts and visual phenomena of perspective.