Faceted Knobs and Geometric Objects


Allen Klinger and Samuel M. Genensky

Prof. Allen Klinger Dr. Samuel M. Genensky

School of Engineering and Applied Science Center for the Partially Sighted

University of California at Los Angeles 720 Wilshire Boulevard, Suite 200

Los Angeles, California 90095-1596 Santa Monica, California 90401

<klinger@cs.ucla.edu> <harpoons@ucla.edu>

Key Words: Solids, Geometry, Shape, Reasoning, Recognition, Concepts, User Interfaces,

Colors, Textures, Pictorial, Picture Grammars, Hierarchical, Discrimination, Categories


This paper describes uses of models of three-dimensional solids in computer interfaces. The suggestions here were inspired by a State of California requirement of geometric signs to assist functionally blind and partially sighted people, and a project to expand world wide web access for such individuals. The paper describes using sharp contrast in color and/or texture, to locate cues in regular and semi-regular solids. Issues discussed are features, current and potential future visual systems for computers, and the role of human pattern recognition.


This paper describes possible uses of models of three-dimensional solids in computer interfaces. This effort began with the display of regular shapes [1, p. 5] - see Figure 1; and others that are semi-regular, as in Figure 2. The work is now part of augmenting the tools available for visually-limited computer users. That process provokes larger considerations of dividing the pattern recognition task between computers and people. The purpose here is to extend work in the State of California on signs of particular value to functionally blind and partially sighted individuals. The practicality of using solid geometric objects on a computer video display terminal screen centers on their recognizable nature. People readily perceive cube versus tetrahedron or octahedron. Solids can aid where human recognition of icons, letters and numbers, is marginal.

Convex Polyhedra With Equal Faces and Vertices Surrounded Alike

(Above description of regular solids is from Coxeter [1, p. 5])

Fig. 1 Three Regular Solids (drawn by Mathematics [2])

1. Simple Geometrical Triggers

Several groups of shapes can be distinguished even by partially sighted individuals. The Fig. 1 regular solids are different in nature than one with two types of faces as those in Fig. 2. Presence of both triangles and rectangles is a simple geometric trigger: an easily recognized feature.

Convex Polyhedra With Two Types of Faces

The left semiregular solid is fourteen-faced, hexagonal at the equator. It is called the cuboctahedron (Coxeter [1, pp. 18, 19], [3]). The right one has eighteen faces and an octagonal equator.

Fig. 2 Two Semiregular Solids (Created Using Mathematica - See [2])

One of us (SG) proposed, and the State of California has mandated, that equilateral-triangle and circle signs be posted at public restrooms, visible cues to aid selection. This use of planar shapes suggests applying human pattern recognition to facilitate user-computer interaction. Geometric entities, entire solids as in Figs. 1 and 2, faces (triangle or rectangle in Fig. 2), and distinct edges (hexagon or octagon equators in Fig. 2) could constitute handles, knobs, or buttons. As in the restroom selection, geometric shapes, viewed on a computer display terminal as interface objects, can help people overcome limitations, or perform more effectively in stressful situations. In the case of the physical signs used to distinguish California restrooms, the patterns are recognizable by the partially sighted (definitions of this term, and others in the field of vision, appear below in Table 1). Also they can be categorized successfully tactilely by functionally blind people. The analogous computer interface approach is to use sound in place of touch; we will say more on this elsewhere. Similarly, computer displays of solid entities, as in Figs. 1, 2, can be linked to, and trigger, an action. We explore some examples of geometric objects that easily can be recognized and suggest how they can trigger concepts or actions.

Planar roundness is an example of a geometric trigger of simple nature. Consider the wealth of detail present in icons on computer displays. In contrast regular polyhedra, three-dimensional objects are perceptually repetitive in some feature, and could act in a computer interface as a trigger to recognition. [The tetrahedron repeats four equilateral triangles; the cube six squares.]

Sections and parts of solids can make up more complex triggers. Sectioning an octahedron into two pyramids is like the half-symbol evolution of Greek and Roman numbers described in [5, p. 5]. We suggest using solids because they are more easily distinguished by all kinds of sight capable people. Further these objects can be part of a new kind of computer interface. Geometric objects can aid in traversing an information hierarchy, through highlighting/coloring displayed edges or faces. The computer can color, darken, or suffuse with texture, locations on the solids. [To offer a new interface widely limitation to black-white displays may eliminate color and force reliance on texture and intensity variation.] Color, texture, and intensity are primary visual features to apply to geometric entities to render them distinguishable. Other features can also support or trigger human decision-making, but these can highlight and make immediately-recognizable the distinction between regular and semiregular.

2. Interface Abilities

Human pattern recognition considerations can be part of interface design to extend computer access. The use of polyhedral [1] entities as computer intereface signs, buttons or knobs could enlarge the number of people able to work comfortably with digital technology. Such new interface options described here could help people losing aspects of their vision through aging.

The central technical issues involve classification of three dimensional signs on the computer display. Related topics are replacing text labels and facilitating user actions. Many people with disabilities need assistance from computer interface designers to work with current technology.

Individuals with motor control problems (e.g., from cerebral palsy), functional blindness, and partial sight can be successful with computers. Table 1 lists definitions describing visual functioning levels and parallel ideas about computer interface capability. Extending visual function to selection among alternative icons enables examining computer interface effectiveness. The tabulated interface-definitions (italics) range from (at the low) an action-impaired individual who cannot use all the offered alternatives, to a fully selection-capable person. Though a person who can distinguish all possibilities (and initiate any of them by an action) is a maximum capability that represents the traditional design assumption. In pattern recognition algorithm terms, no undecided cases, all items correctly classified. Actually, beginning with the visual domain definitions in Table 1 there are many levels of capability in user computer-interface skill. The most reasonable design would seek to enable practically all users to function at half the level of one who is fully selection-capable.

3. Mandated Practice

The law described in Section 1 offers a model of how more functional interfaces could become the norm. Prevailing systems' increases in functioning via (Macintosh) file folder or (Windows) hierarchic selection by text-windows, can be replaced by requiring simpler user selection of alternatives. Just as, first in California, and gradually elsewhere, laws require supporting rapid classification decisions from physical signs can be augmented for the computer. [State of California requires all buildings new or being remodeled, to have doors to public restrooms, or entrance walls, labelled with recognizable gender-designating signs. The following excerpts from the law describe how government may mandate change: "... entrances to restroom ... to be used by men an equilateral triangle ... at eye level with one vertex of the triangle pointing directly upward. ... color and gray value ... of the triangle should contrast sharply with ... door or entranceway wall" A similar statement for women substitutes circle for triangle. Labeling by international man/woman symbols and a printed word completes the mandate. Since functionally blind individuals can distinguish circular from rectangular/triangular signs., and partially sighted people usually can distinguish them at a distance of several feet, the law has strong results. It overcomes the inability of both populations to distinguish either international man/woman symbols or words, while the added geometric shapes create no difficulties for fully sighted people. California's mandate extends to Nevada, Washington and British Columbia; New York and Montana may join.] Just as with geographic extensions of geometric restroom signs, control knob standards could become widespread and lead to replacing icons on computer displays to aid users.

4. Knobs and Controls

Colored groups of faces can define objects we can cause to act as knobs. Table 2 covers a range of features for computer interface controls. This table describes application of the regular and semi-regular solids to creating geometric entities that can aid human pattern recognition.

Computer displays label similar entities by words. However, when words are difficult to read the alternatives become indistinguishable. Words or print in icons or menus is unhelpful for partially sighted and functionally blind people: it provides them no way todistinguish labels. But geometric means can readily aid classifying controls, as with restroom signs. Table 2 presents the principal considerations about geometry, color, intensity, and features for computer interfaces. Groups of faces describe distinguishable objects. E.g., square-based pyramid, tetrahedron, and upper or lower part of an octahedron are all sorts of "four-triangle-sides" handles. Fig. 3 displays ways to build hierarchic and action-selection into an interface that uses solid models as knobs.

Initiating Actions

Fig. 3a Solids in Interfaces - Objects Shown


Employing sharp contrast in color, texture, or intensity provides the means to distinguish entities.

Faces of solids, and edges can be associated with an object, creating selections users can initiate to Fig. 3b Ways to Use Solids in Interfaces - Actions Selected

relate to a hierarchy. Sound descriptions of icons and pointer position can enhance users' capability.

Recognition, deciding between categories, is a fundamental aspect of computer interfaces. Geometric solids, algorithms to construct them, and means to highlight their parts enable new computer interfaces. Access for people with different sorts of visual perception extends progression to recognizable text-labeled icon symbols to solids suited to the aging population. Greater computer interface visual discrimination could help people stay intellectually aware and economically active.

Computer Display Considerations

Improve Discrimination

Variation of Color, Gray-Level Between Entities Themselves

Variation of Color, Gray-Level Between Entity Ensemble and Control Panel Background

Diverse Features

Same Geometry With Different Size Entities. Different Shapes or Varied Geometries.

Handle Selection

Knob Stems Small Right Circular Cylinders

Stems Topped By Geometrically-Varied Solids

Circular, Triangular, Square, Hexagonal or Octagonal Cross-Section.

Complex Solids

Multifaceted Three-Dimensional Geometric Objects [1].

Sectioned Multifaceted Three-Dimensional Geometric Objects [1]. .

Table 2. Possible Geometric Controls


[1] Coxeter, H.S.M. Regular Polytopes, MacMillan Co., New York, 2nd edition, 1963.

[2] Wolfram, S. The Mathematica Book, Champaign, IL: Wolfram Media, 1996.

[3] http://www.astro.virginia.edu/ eww6n/math/Cuboctahedron.html

[4] Ghyka, M. The Geometry of Art and Life, New York: Dover, 1977.

[5] Neugebaurer, O. The Exact Sciences in Antiquity, New York: Dover, 1969.

Six Fundamental Definitions For Visual Interfaces

* I: Persons are functionally blind if they either: 1. Cannot see at all (totally blind); or, 2. Have better-eye vision limited to light projection. * Ia: Persons are called functionally incapable if they either: 1. Cannot chose the most effective action presented (totally unskilled); or, 2. Are reduced in possible actions to being icon discrimination limited.

*II: Persons are totally blind if unable to visually detect light of any intensity with either eye.

*IIa: Persons are totally incapable if unable to visually detect displayed icons and text.

*III: Persons are limited to light projection if only able to detect light and tell the direction of its source with their better eye. *IIIa: Persons are limited to icon discrimination if able to detect the existence of clickable entities but unaware of their destination.

*IV: Partially sighted individuals have better-eye best corrected visual acuity at 20/70 or worse and light projection limit. Another criterion is: better-eye best corrected visual acuity exceeds 20/70, but maximum angular diameter of visual field is 30 degrees or less.

*IVa: Partially selection-capable individuals can choose between three entities but are icon discrimination limited (unable to decide between two similar visuals).

*V: Persons visually impaired are either functionally blind or partially sighted.

*Va: Persons action impaired are either: 1. functionally unable to work with a computer interface; or, partially selection-capable.

*VI: Persons not visually impaired are fully sighted.

* VIa: Persons not action impaired are fully selection-capable.

Table 1. Definitions Concerning Sight and Computer-Use Capability