Study casts of the teeth are routinely used for diagnosis and to assess treatment change: the crowding of the teeth or shortage of space available within the dental arch is usually assessed visually. A full cast analysis program has been developed previously, making use of the three-dimensional Reflex Plotter linked to a computer. This study examines the validity of the fit of computer generated parabolic curves to dental arches, as performed in the measurement of crowding. Using a visual analogue method it was found that the parabola appeared to fit lower post-treatment dental arches best. However, reservations regarding the fit of symmetrical curves are expressed and other solutions suggested.
AngleE. H. (1907) Treatment of malocclusion of the teeth, 7th edn, S. S. White Dental Company, Philadelphia.
2.
ArmitageP. (1971) Statistical methods in medical research, Blackwell Publishing, Oxford, 198–200.
3.
BegoleE. A. (1979) A computer program for the analysis of dental arch form using the cubic spline function, Computer Programs Biomedical, 10, 136–142.
4.
BlackG. V. (1902) Descriptive anatomy of the human tooth, 5th edn, S. S. White Dental Company, Philadelphia.
5.
BogueE. A. (1912) A collection of orthodontical data, Dental Record, xxxii, 875–876.
6.
BogueE. A. (1917) Orthodontia of the deciduous teeth, Dental Cosmos, lix, 246–246.
7.
BonwillW. G. A. (1886) Geometrical and mechanical laws of articulation, Transactions of the Odontological Society of Pennsylvania, 1886–87–88, 281–301.
8.
BraderA. C. (1972) Dental arch form related to intraoral forces: PR=C, American Journal of Orthodontics, 61, 541–561.
9.
CurrierH. H. (1969) A computerised geometric analysis of human dental arch form, American Journal of Orthodontics, 65, 164–179.
10.
HawleyC. A. (1905) Determination of the normal arch and its application to orthodontics, Dental Cosmos, 47, 541–557.
11.
HechterF. J. (1978) Symmetry and dental arch form of orthodontically treated patients, Journal of the Canadian Dental Association, 44, 173–184.
12.
HerrenP., SchmokerR., and JordiT. (1973) Arch shape and space balance determined by the Arcogramme Technique, Transactions of the European Orthodontic Society, 49, 61–73.
13.
HixonE. H. and OldfatherR. E. (1958) Estimation of the sizes of unerupted cuspid and bicuspid teeth, Angle Orthodontist, 28, 236–240.
14.
IzardG. (1927) New method for the determination of the normal arch by the function of the face, International Journal of Orthodontics, 13, 582–595.
15.
JacobsenA. (1975) The ‘Wits’ appraisal of jaw disharmony, American Journal of Orthodontics, 67, 125–138.
16.
JonesM. L. (1987) A quantitative three dimensional assessment of treatment change in a consecutively referred sample of malocclusion from a Welsh Town, PhD thesis, University of Wales.
17.
JonesM. L. and RichmondS. (1986) The performance and use of the 3D cast analysis system, British Journal of Orthodontics, 13, 54.
18.
JonesM. L. and RichmondS. (1985) Initial tooth movement: force application and pain—a relationship?, American Journal of Orthodontics, 88, 111–116.
19.
LuK. H. (1964) Analysis of dental arch symmetry, Journal of Dental Research, 43, 780–780 [abstr.].
20.
McConnailM. A. and ShurrE. A. (1949) The ideal form of the human dental arcade with some prosthetic application, Dental Record, 69, 285–302.
21.
MillsL. F. and HamiltonP. M. (1965) Epidemilogical studies of malalignment—a method for computing dental arch circumference, Angle Orthodontist, 35, 244–248.
22.
MusichD. R. and AckermanJ. I. (1973) The Calinometer; a reliable device for estimating dental arch perimeter, American Journal of Orthodontics, 63, 366–375.
23.
PontA. P. (1909) Der Zahn—Index in der Orthodontie, Zahnarztuche Orthopodie, 3, 306–321.
24.
RemsdenW. M. (1964) Co-ordinated arches: an investigation into the form and interrelationship of orthodontic arch wires, MSc thesis, Temple University.
25.
RichmondS. (1984) The feasibility of categorising orthodontic treatment difficulty—the use of three-dimensional plotting, MSc dissertation, University of Wales.
26.
RichmondS. (1987) Recording the dental cast in three dimensions, American Journal of Orthodontics, 92, 199–206.
27.
RichmondS. and JonesM. L. (1985) A comparison of two and three-dimensional incisor angles, British Journal of Orthodontics, 12, 90–96.
28.
RichmondS. and JonesM. L. (1986) The development of 3D cast analysis system, British Journal of Orthodontics, 13, 53–53.
29.
RobertsonN. R. E., JonesM. L., RichmondS., and MayE. (1987) The screening and categorization of patients: a case for natural selection?, British Journal of Orthodontics, 14, 182–186.
30.
RudgeS. J. (1982) A computer program for the analysis of study models, European Journal of Orthodontics, 5, 225–231.
31.
RudgeS. J., JonesP. T., HepenstalS., and BowdenD. E. J. (1983) The reliability of study model measurements in the evaluation of crowding, European Journal of Orthodontics, 5, 225–231.
32.
SicherH. (1952) Oral anatomy, 2nd edn, C. V. Mosby Company, St Louis.
33.
StantonF. L. (1922) A consideration of normal and abnormal dentures as a problem of three dimensional spaces and its bearing on orthodontic classification and terminology, International Journal of Orthodontics, Oral Surgery, and Radiology, viii, 185–204.
34.
TanakaM. M. and JohnstonL. E. (1974) The prediction of the size of unerupted canines and premolars in a contemporary orthodontic population, Journal of the American Dental Association, 88, 798–801.
35.
WheelerR. C. (1950) A textbook of dental anatomy and physiology, 2nd edn, W. B. Saunders Company, Philadelphia.
36.
WilliamsP. N. (1917) Determining the shape of the normal arch, Dental Cosmos, 59, 695–695.
37.
WhiteL. W. (1978) Individual ideal arches, Journal of Clinical Orthodontics, 72, 303–308.
