MSW:Mathematical Model

4. Mathematical Model
If you use information correctly, the model will behave correctly. Mathematics is not subjective, but deterministic. Access to the subsystem internals make it easier to understand. This provides knowledge independent of experience.

Through trial and evaluation, the model has been successively refactored to reduce the complexity and the computation cost of the implementations. Several generations of empirical data has been created by applying the model to real world situations. The consequences of the model has been observable by the senses. Problem areas and shortcomings have been resolved to create a robust solution.

4.A. Abstract Structure
The abstract structure of the formal strings is governed by a set of laws. The grammar of the formal strings are based on syntactic rules that define their internal structure.

4.C. Regular Expressions
A regular expression is used to examine text and identify strings that match a stated pattern. A regular expression is written in a concise and flexible formal language. It contains literals and metacharacters. A literal is any character that we literally want to find in the string. A metacharacter is a special character with a unique meaning that is not literally in the string, but represents a type of search pattern.

4.D. Variability
The symbols and their meaning are based on an international agreement that does not allow for variability. Everyone should understand the individual symbols to mean the same thing regardless of language or writing style.

Beyond the individual symbols, there are two primary spelling rules for writing a sign as a 2 dimension cluster of symbols: 1) write the position of contact and 2) every sign has a center.

Beyond the individual symbols, there exists a vast amount of variability in how people write: horizontal or vertical, minimalist or exacting detail, few heads or lots of heads, stick figures or detached hands.

Even within the same style, there exists five types of variability for SignWriting Text.

4.D.1. Viewpoint Variability
Some signs can be written from the front perspective (straight-on view of the signer) or from the top perspective (top-down view of the signer). Although these written signs represent the same sign, they will not use the same string.

4.D.2. Symbol Variability
Symbol choice is sometimes subjective. A sign can be written with more, less, or different details. The choice of detail will affect the choice of symbol and hence the string.

4.D.3. Center Variability
Every 2 dimensional cluster of symbols has a center by definition. This center is defined as the origin of the signbox space (0,0). The center of a signbox is important for layout.

All signs that do not contain a head or trunk symbol will center the same regardless of writing direction. Horizontal writing will center on the head symbols only. Vertical writing will center on both the head and the trunk symbols.

A custom center allows the user to specifically set the center of a sign and override any predetermined value.

4.D.4. Order Variability
The order of symbols in a signbox string is only meaningful for issues of overlap when one symbol is positioned on top of another and the negative space of the top symbol obscures part of the positive space of a lower symbol. Otherwise, the order of the symbols is irrelevant to the visual representation of a string. The relationship is surjective with several strings mapping to a single visual image. Order variability can be exploited to resolve issues of ambiguity. Two different signs with the same visual appearance but different meanings can have different spellings based on order variability.

4.D.5. Position Variability
Within the formal strings, the precise position of each symbol is user defined. Unless written against an accepted dictionary, a user has the ability to fine tune the position of each symbol. For a single symbol, there is no positional variability. Two symbols will have dozens of approximate relations. More than two, and the number of approximate relations increases exponentially.