Balance Rules
This theory is to help guide computer Art/Scientists in writing generative programs that use artistic balance rules that visually balance their compositions.
List of Terms:
Composition Frame is the boundary of the composition. It separates
what you are interested in from what you are not. (Figure 1.)
Composition Space is the total visual space contained within the Composition Frame. (Figure 1.)
Positive Space is a collection of all positive image fields (traditional Art theory)
Negative Space is a collection of the space that is not Positive Space (traditional Art theory)
Composition Centroid is the two dimensional center of gravity of the Composition Space. (Figure 1.)
Image Field is a two dimensional area within the composition space that has a definable boundary. Image field is related to the traditional compositional ideas of positive space and negative space in such that it is a definable portion of the positive or negative space. An Image Field has definable boundaries.
Major Positive Image field is one of the first noticed and most distinguishable concepts or ideas in the composition. It is an image in the composition that shares conceptual dominance with other image fields in the major collector. Compositions tend to have positive and negative spaces. A positive image field is part of the compositions positive space. (Figure 2.) Sometimes a positive image field will be a linier implication or a group of positive images that give the impression of a line or division of negative space (Figure 12.)
Positive Image Field Centroid is the visual two dimensional center of gravity for a positive image field. (Figure 2.)
Major Negative Image field is an area of negative space between the positive image fields. Its' boundaries are delineated by lines originating at the composition centroid and passing through two adjacent Positive image fields' centroids and ending at the composition frame.(Figure 3.) (Figure 4.)
Negative Image Field Centroid is the visual two dimensional center of gravity for a negative image field. (Figure 4.)
Minor Positive Image field is a positive image field with secondary conceptual importance to the composition and resides in a minor collector. (Figure 6.)
Linier implications are non-visual lines perceived in the composition (Figure 14.) (Figure 15.)
Linier divisions are visual line perceived in the composition. If they don't extend to a border or visual barrier they will imply and extension to that barrier. (Figure 18.)
Minor Negative Image field is a portion of the negative space surrounding a minor positive image field. The linier implications between the positive image fields create the boundaries for the minor negative image fields. (Figure 15.)
Standard Negative Field is the standard deviation for the area of all minor negative image fields.
Major Polygonic Collector is a polygon created by constructing lines between the centroids of the major positive image fields and the major negative image fields. Each of the lines become the sides of the polygonic collector. The centroid of the collector (polygon) is coincident with the composition centroid in a nominal balance. The polygon is transparent to the composition and is intended to exist only as a concept guiding the composition. (Figure 5.) (Figure 13.) (Figure 19.)
Minor Collector can be seen in two forms:
1.) Minor Polygonic Collector is a Minor collector with 3 or
more positive image fields. (Figure 7.)
2.) Minor Fill Collector is a Minor collector with 2 positive
image fields
The Minor Collector is a group of positive and or negative image
fields that have a conceptually minor significance in the composition.
The role of the minor collector is to break up the major negative
image fields into minor negative image fields of equal area (For
a nominal balance which has a Standard Negative Field of zero)
Nominal Balance is a composition where all
the Rules of Balance are satisfied, all resultant vectors sums
equal zero, and the Standard Negative Field equals zero. Nominal
Balance is a theoretical value and no artist will ever achieve
this without computational methods. ( Note: Most artists use a
slightly unbalanced composition to express visual tension )
Adjusted Balance is a composition where the balance has deviated
from the rules. The result of the adjusted balance can be described
as the resultant vector and a standard negative field. (Figure
20.)
Resultant Vector is a vector who's magnitude is equal to the distance from the composition centroid to the centroid of a major collector. And who's direction is measured from the composition centroid. (Figure 20.)
Total Resultant Vector Sum is the resultant vector sum of all resultant vectors.
Balance Rules: (Nominal Balance)
#1.) The centroid of the major polygonic collector
and the composition centroid is coincident ( in the same place).
#2.) The centroid of any minor polygonic collector and the composition
centroid is coincident.
#3.) All minor negative image fields contain the same amount of
area. (negative standard of zero)
#4.) If #1 and #2 are not satisfied then the resultant vector
sum from the polygonic collectors equal zero.