2. The central concept of ecological
optics
• The Ambient optic array at a point of
observation.
• To be an array means to have an
arrangement.
• To be ambient at a point means to
surround a position in an environment
that could be occupied by an observer.
4. What is implied by ambient at a
point?
• No picture can be ambient.
• Even a picture is said to be panoramic is
never a completely closed sphere.
• An array must surround the point
completely.
• The field must be closed, the sense in
which the surface of a sphere returns
upon itself.
• More precisely, the field is unbounded.
5. What is implied by the point in
the phrase point of observation?
• A position in ecological space, in a medium
instead of in a void.
• A place where an observer might be and from
which an act of observation could be made.
• Whereas abstract space consists of points,
ecological space consists of places—location and
position.
• When the position becomes occupied,
something very interesting happens to the
ambient array. It contains information about the
body of the observer.
7. How is ambient light structured?
• It is tempting to assume that the
environment consists of objects in space
and that, hence, the ambient array
consists of closed-contour forms in an
otherwise empty field, or “figure on
ground.”
• The environment does not consist of
objects.
8. Figure–ground (perception)
relating to or denoting the perception of images by the distinction of
objects from a background from which they appear to stand out,
12. Solid angles are divided and
subdivided into component parts
• For the terrestrial environment, the sky-earth
contrast divides the unbounded sphere field into
two hemispheres.
• The components of the earth are nested at
different levels of size.
• The components of the array from the earth also
fall into a hierarchy of subordinate level of size.
• The components of array are the visual angles
from..
• They are conventionally measured in degrees,
minutes, and seconds instead of kilometers,
meters, and millimeters.
13. The ambient optic array from a
wrinkled earth outdoors under the
sky
The dashed lines depict the envelope
of visual soild angles, not ray of light.
14. The components of arrays are the
visual angles
• As a nested hierarchy of solid angles all having a
common apex instead of as a set of rays
intersecting a point.
• Every solid angle, no matter how small, has form
in the sense that its cross-section has a form
unlike a ray in this respect.
• Each solid angle is unique.
• Solid angles can fill up a sphere in the way that
sectors fill up a circle.
• The surface of the sphere whose center is the
common apex of all the solid angles can be
thought of as a kind of transparent film or shell.
15. The structure of an optic array
• It is without gap: It does not consist of
points or spots that are discrete; it is
completely filled.
• The array is more like a hierarchy than like
a matrix.
• Loci are not defined by pairs of coordinates,
for the relation of location is not given by
degrees of azimuth and elevation but the
relation of inclusion.
• The difference between the relation of
metric location and relation of inclusion.
16. The laws of natural perspective
• The conception of the ambient optic array as a set
of solid angles corresponding to objects is thus a
continuation of ancient and medieval optics.
• Instead of only free standing objects present to an
eye, we postulate an environment of illuminated
surfaces.
• Natural perspective, as well as artificial perspective,
is restricted in scope, being concerned only with a
frozen optical structure.
• It omits motion from consideration. The ambient
optic array is treated as if its structure were frozen in
time and as if the point of observation were
motionless.
18. The same ambient array with the
point of observation occupied by
a person
19. The change of the optic array
brought by a locomotor
movement of the observer
20. Optical structure with a moving
point of observation
• A point of observation at rest is only the limiting case of a
point of observation in motion, the null case.
• Observation implies movement, locomotion with reference
of the rigid environment.
• Hence, the structure of an optic array at a stationary point
of observation is only a special case of the structure of an
optic array at a moving point of observation.
• Some features of the array do not persist and some do.
• The changes come from the locomotion and the
nonchanges come form the rigid layout of the
environmental surfaces.
• We have to distinguish between two kinds of structure in a
normal ambient array: the perspective structure and the
invariant structure.
21. Perspective structure and invariant
structure
• “The more it changes, the more it is the
same thing.”
• Consider, for example, how a rectangular
surface like a tabletop can be seen to sight.
• What are the invariants underlying the
transforming perspective in the array from
the tabletop?
• Optical change is not a transition from one
form to another but a reversible process.
22. • The geometrical habit of separating space from time and
imaging sets of frozen forms in space is very strong.
• One can think of each point of observation in the medium
at stationary and distinct.
• This is an elegant and abstract way of thinking, modeled on
projective geometry.
• The optic array flows in time instead of going from one
structure to another.
• We need for the formulation of ecological optics are not
the traditional notions of space and time but the concepts
of variance and invariance considered as reciprocal to one
another.
• The notion of a set of stationary points of observation in
the medium is appropriate for the problem of a whole
crowd of observers standing in different positions, each of
them perceiving the environment from his own point of
view.
23. The significance of changing
perspective in the ambient array
• The stationary pint of observation is more intelligible.
• It not longer is conceived as a single geometrical point in space
but as a pause in locomotion, as a temporarily fixed position
relative to the environment.
• In physics, the motion of an observer in space is “relative”,
inasmuch as what we call motion with reference to one chosen
frame of references.
• In ecology, the locomotion of an observer in the environment is
absolute.
• The information about the world that surrounds a point of
observation implies information about the point of observation
that is surrounded by a world.
• Each kind of information implies the other.
• The occupied point of observation resolve it into the former
extrospecific information and the latter propriospecific in
formation.
Editor's Notes
The hills in this aerial photo, the convexities or protuberances, can be compared to the “humps” shown the other photos.
The visual angle is the angle a viewed object subtends at the eye, usually stated in degrees of arc. It also is called the object's angular size. The diagram on the right shows an observer's eye looking at a frontal extent (the vertical arrow) that has a linear size , located in the distance from point .
In geometry, a solid angle (symbol: Ω) is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large the object appears to an observer looking from that point. In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a steradian (symbol: sr).
Definition: That part of a circle that lies between two lines that intersect it.
Try this Drag one of the orange dots that control the angle ∠AOB. The red arc is the arc intercepted by that angle.
It is assumed that illumination has reached a steady state. The earth is hown as wrinkled or bumped, but not cluttered. This is an optid array at a single fixed point of observation. It illustrates the main invariants of natural perspective: the separation of two hemisphere of the ambient array at the horizon, and the increasing density of the optical texture toward its maximum at the horizon. Theses are invariants even the array flows, as it does when the point of observation moves.
It shows a cluttered environment where some surfaces are projected at the point of observation and the remainder are not, where some are unbidden and the others are hidden. The hidden surfaces are indicated by dotted lines. Only the faces of the layout of surfaces sre shown, not the facets of their surfaces, their textures.
When an observer is present at a point of observation, the visdual system begins to function.
The thin solid lines indicate the ambient optic array for the seated observer, and the thin dashed lines thre latered optic array after standing up and moving forward. The differences between the two arrays is specific to the difference between the ppint of observation. To the path of locomotion. Note that ambient array is changes, including th eposiiton begind the head. And note that whgat was preciously hidden becomes unhidden.,