Transformations quasi-conformes de maillages volumiques et applications en infographie

La modélisation géométrique est importante autant en infographie qu'en ingénierie. Notre capacité à représenter l'information géométrique fixe les limites et la facilité avec laquelle on manipule les objets 3D. Une de ces représentations géométriques est le maillage volumique, formé de polyèdres assemblés de sorte à approcher une forme désirée. Certaines applications, tels que le placage de textures et le remaillage, ont avantage à déformer le maillage vers un domaine plus régulier pour faciliter le traitement. On dit qu'une déformation est \emph{quasi-conforme} si elle borne la distorsion. Cette thèse porte sur l’étude et le développement d'algorithmes de déformation quasi-conforme de maillages volumiques. Nous étudions ces types de déformations parce qu’elles offrent de bonnes propriétés de préservation de l’aspect local d’un solide et qu’elles ont été peu étudiées dans le contexte de l’informatique graphique, contrairement à leurs pendants 2D. Cette recherche tente de généraliser aux volumes des concepts bien maitrisés pour la déformation de surfaces. Premièrement, nous présentons une approche linéaire de la quasi-conformité. Nous développons une méthode déformant l’objet vers son domaine paramétrique par une méthode des moindres carrés linéaires. Cette méthode est simple d'implémentation et rapide d'exécution, mais n'est qu'une approximation de la quasi-conformité car elle ne borne pas la distorsion. Deuxièmement, nous remédions à ce problème par une approche non linéaire basée sur les positions des sommets. Nous développons une technique déformant le domaine paramétrique vers le solide par une méthode des moindres carrés non linéaires. La non-linéarité permet l’inclusion de contraintes garantissant l’injectivité de la déformation. De plus, la déformation du domaine paramétrique au lieu de l’objet lui-même permet l’utilisation de domaines plus généraux. Troisièmement, nous présentons une approche non linéaire basée sur les angles dièdres. Cette méthode définit la déformation du solide par les angles dièdres au lieu des positions des sommets du maillage. Ce changement de variables permet une expression naturelle des bornes de distorsion de la déformation. Nous présentons quelques applications de cette nouvelle approche dont la paramétrisation, l'interpolation, l'optimisation et la compression de maillages tétraédriques.

Coût bioenergetique des modes de déplacements irréguliers en sport

The objective of this thesis was to quantify the physiological responses such as O2 uptake (VO2), heart rate (HR) and blood lactate ([LA]) to some types of activities associated with intermittent sports in athletes. Our hypothesis is that the introduction of accelerations and decelerations with or without directional changes results in a significative increase of the oxygen consumption, heart rate and blood lactate. The purpose of the first study was to measure and compare the VO2 and the HR of 6 on-court tennis drills at both high and low displacement speeds. These drills were done with and without striking the ball, over full and half-width court, in attack or in defense mode, using backhand or forehand strokes. Results show that playing an attacking style requires 6.5% more energy than playing a defensive style (p < 0.01) and the backhand stroke required 7% more VO2 at low speed than forehand stroke (p < 0.05) while the additional cost of striking the ball lies between 3.5 and 3.0 mL kg-1 min-1. Finally, while striking the ball, the energy expanded during a shuttle displacement on half-width court is 14% higher than running on full-width court. Studies #2 and #3 focused on different modes of displacement observed in irregular sports. The objective of the second study was to measure and compare VO2, HR and [LA] responses to randomly performed multiple fractioned runs with directional changes (SR) and without directional changes (FR) to those of in-line running (IR) at speeds corresponding to 60, 70 and 80% of the subject’s maximal aerobic speed (MAS). All results show that IR’s VO2 was significantly lower than SR’s and FR’s (p<0.05). SR’s VO2 was greater than FR’s only at speeds corresponding to 80%MAS. On the other hand, HR was similar in SR and FR but significantly higher than IR’s (p<0.05). [LA] varied between 4.2 ± 0.8 and 6.6 ± 0.9 mmol L-1 without significant differences between the 3 displacement modes. Finally, the third study’s objective was to measure and compare VO2 , HR and [LA] responses during directional changes at different angles and at different submaximal running speeds corresponding to 60, 70 and 80% MAS. Subjects randomly performed 4 running protocols 1) a 20-m shuttle running course (180°) (SR), 2) an 8-shaped running course with 90-degree turns every 20 m (90R), 3) a Zigzag running course (ZZR) with multiple close directional changes (~ 5 m) at different angle values of 91.8°, 90° and 38.6°, 4) an In-line run (IR) for comparison purposes. Results show that IR’s was lower (p<0.001) than for 90R’s, SR’s and ZZR’s at all intensities. VO2 obtained at 60 and 70%MAS was 48.7 and 38.1% higher during ZZR when compared to IR while and depending on the intensity, during 90R and SR was between 15.5 and 19.6% higher than during IR. Also, ZZR’s VO2 was 26.1 and 19.5% higher than 90R’s, 26.1 and 15.5% higher than SR’s at 60 and 70%MAS. SR’s and 90R’s VO2 were similar. Changing direction at a 90° angle and at 180° angle seem similar when compared to continuous in-line running. [LA] levels were similar in all modalities. Overall, the studies presented in this thesis allow the quantification of the specific energetic demands of certain types of displacement modes in comparison with conventional forward running. Also, our results confirm that the energy cost varies and increase with the introduction of accelerations and decelerations with and without directional changes.

Changements climatiques et stratégies de mitigation : Assistons-nous à une décarbonisation de l’économie mondiale ?

Note d'analyse

Dénombrement dans les empilements apolloniens généralisés et distribution angulaire dans les extensions quadratiques imaginaires.

Cette thèse traite de deux thèmes principaux. Le premier concerne l'étude des empilements apolloniens généralisés de cercles et de sphères. Généralisations des classiques empilements apolloniens, dont l'étude remonte à la Grèce antique, ces objets s'imposent comme particulièrement attractifs en théorie des nombres. Dans cette thèse sera étudié l'ensemble des courbures (les inverses des rayons) des cercles ou sphères de tels empilements. Sous de bonnes conditions, ces courbures s'avèrent être toutes entières. Nous montrerons qu'elles vérifient un principe local-global partiel, nous compterons le nombre de cercles de courbures plus petites qu'une quantité donnée et nous nous intéresserons également à l'étude des courbures premières. Le second thème a trait à la distribution angulaire des idéaux (ou plutôt ici des nombres idéaux) des corps de nombres quadratiques imaginaires (que l'on peut voir comme la distribution des points à coordonnées entières sur des ellipses). Nous montrerons que la discrépance de l'ensemble des angles des nombres idéaux entiers de norme donnée est faible et nous nous intéresserons également au problème des écarts bornés entre les premiers d'extensions quadratiques imaginaires dans des secteurs.

Clinical methods for quantifying body segment posture: a literature review

Purpose. Clinicians commonly assess posture in persons with musculoskeletal disorders and tend to do so subjectively. Evidence-based practice requires the use of valid, reliable and sensitive tools to monitor treatment effectiveness. The purpose of this article was to determine which methods were used to assess posture quantitatively in a clinical setting and to identify psychometric properties of posture indices measured from these methods or tools. Methods. We conducted a comprehensive literature review. Pertinent databases were used to search for articles on quantitative clinical assessment of posture. Searching keywords were related to posture and assessment, scoliosis, back pain, reliability, validity and different body segments. Results. We identified 65 articles with angle and distance posture indices that corresponded to our search criteria. Several studies showed good intra- and inter-rater reliability for measurements taken directly on the persons (e.g., goniometer, inclinometer, flexible curve and tape measurement) or from photographs, but the validity of these measurements was not always demonstrated. Conclusion. Taking measurements of all body angles directly on the person is a lengthy process and may affect the reliability of the measurements. Measurement of body angles from photographs may be the most accurate and rapid way to assess global posture quantitatively in a clinical setting.

Reliability of a quantitative clinical posture assessment tool among persons with idiopathic scoliosis

Objective To determine overall, test–retest and inter-rater reliability of posture indices among persons with idiopathic scoliosis. Design A reliability study using two raters and two test sessions. Setting Tertiary care paediatric centre. Participants Seventy participants aged between 10 and 20 years with different types of idiopathic scoliosis (Cobb angle 15 to 60°) were recruited from the scoliosis clinic. Main outcome measures Based on the XY co-ordinates of natural reference points (e.g. eyes) as well as markers placed on several anatomical landmarks, 32 angular and linear posture indices taken from digital photographs in the standing position were calculated from a specially developed software program. Generalisability theory served to estimate the reliability and standard error of measurement (SEM) for the overall, test–retest and inter-rater designs. Bland and Altman's method was also used to document agreement between sessions and raters. Results In the random design, dependability coefficients demonstrated a moderate level of reliability for six posture indices (ϕ = 0.51 to 0.72) and a good level of reliability for 26 posture indices out of 32 (ϕ ≥ 0.79). Error attributable to marker placement was negligible for most indices. Limits of agreement and SEM values were larger for shoulder protraction, trunk list, Q angle, cervical lordosis and scoliosis angles. The most reproducible indices were waist angles and knee valgus and varus. Conclusions Posture can be assessed in a global fashion from photographs in persons with idiopathic scoliosis. Despite the good reliability of marker placement, other studies are needed to minimise measurement errors in order to provide a suitable tool for monitoring change in posture over time.

Differences in Standing and Sitting Postures of Youth with Idiopathic Scoliosis from Quantitative Analysis of Digital Photographs

The objective of this study was to explore whether differences in standing and sitting postures of youth with idiopathic scoliosis could be detected from quantitative analysis of digital photographs. Standing and sitting postures of 50 participants aged 10–20-years-old with idiopathic scoliosis (Cobb angle: 15° to 60°) were assessed from digital photographs using a posture evaluation software program. Based on the XY coordinates of markers, 13 angular and linear posture indices were calculated in both positions. Paired t-tests were used to compare values of standing and sitting posture indices. Significant differences between standing and sitting positions (p < 0.05) were found for head protraction, shoulder elevation, scapula asymmetry, trunk list, scoliosis angle, waist angles, and frontal and sagittal plane pelvic tilt. Quantitative analysis of digital photographs is a clinically feasible method to measure standing and sitting postures among youth with scoliosis and to assist in decisions on therapeutic interventions.

Validity of a Quantitative Clinical Measurement Tool of Trunk Posture in Idiopathic Scoliosis

STUDY DESIGN: Concurrent validity between postural indices obtained from digital photographs (two-dimensional [2D]), surface topography imaging (three-dimensional [3D]), and radiographs. OBJECTIVE: To assess the validity of a quantitative clinical postural assessment tool of the trunk based on photographs (2D) as compared to a surface topography system (3D) as well as indices calculated from radiographs. SUMMARY OF BACKGROUND DATA: To monitor progression of scoliosis or change in posture over time in young persons with idiopathic scoliosis (IS), noninvasive and nonionizing methods are recommended. In a clinical setting, posture can be quite easily assessed by calculating key postural indices from photographs. METHODS: Quantitative postural indices of 70 subjects aged 10 to 20 years old with IS (Cobb angle, 15 degrees -60 degrees) were measured from photographs and from 3D trunk surface images taken in the standing position. Shoulder, scapula, trunk list, pelvis, scoliosis, and waist angles indices were calculated with specially designed software. Frontal and sagittal Cobb angles and trunk list were also calculated on radiographs. The Pearson correlation coefficients (r) was used to estimate concurrent validity of the 2D clinical postural tool of the trunk with indices extracted from the 3D system and with those obtained from radiographs. RESULTS: The correlation between 2D and 3D indices was good to excellent for shoulder, pelvis, trunk list, and thoracic scoliosis (0.81>r<0.97; P<0.01) but fair to moderate for thoracic kyphosis, lumbar lordosis, and thoracolumbar or lumbar scoliosis (0.30>r<0.56; P<0.05). The correlation between 2D and radiograph spinal indices was fair to good (-0.33 to -0.80 with Cobb angles and 0.76 for trunk list; P<0.05). CONCLUSION: This tool will facilitate clinical practice by monitoring trunk posture among persons with IS. Further, it may contribute to a reduction in the use of radiographs to monitor scoliosis progression.