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A best practice is to use a dual display mode with one image demonstrating the stomach, then the second image demonstrating the heart (Fig. 20-2). This gives the interpreting physician confidence of heart/stomach situs. Bony elements cause shadowing that may obstruct the view of anatomy deep to the bones. Therefore, the spine is best visualized when the fetal spine is up (prone), whereas the abdominal organs and most of the heart structures are better visualized then the fetal spine is down (supine) or lateral. To determine fetal lie, follow the transverse spine from head to rump, observing the location of the head and rump as the transducer is moved across the patient. Once the location of the head and rump is identified, fetal position can be determined (breech, vertex, transverse, or oblique). Next, determine how the fetus is lying within the gestational sac by identifying the transverse spine’s location on the display monitor. If the transverse spine is toward the top of the monitor, the fetus is prone. If the transverse spine is toward the bottom of the monitor, the fetus is supine (Table 20-1). When the fetus is vertex and the transverse spine is on the right of the monitor, the fetus is lying on its left side. When the fetus is breech and the transverse spine is on the right side of the monitor, the fetus is lying on its right side. When the fetus is vertex and the transverse spine is on the left side of the monitor, the fetus is lying on its right side. When the fetus is breech and the transverse spine is on the left side of the monitor, the fetus is lying on its left side (Table 20-2). Imaging success depends on scanning technique. Higher frequency transducers produce increased resolution. Lower frequency transducers have increased penetration. Always use the highest frequency transducer that allows for proper depth penetration. Additionally,... [стр. 523 ⇒]

FETAL PRESENTATION The fetal presentation varies throughout the pregnancy and is described in terms of what fetal part is closest to the cervix. The term vertex refers to the topmost point of the skull. In obstetrics, the term vertex (also called cephalic) is used to indicate when the fetal head is down (toward the cervix), which is the normal presentation for birth. The fetus may be vertex facing toward the maternal back or vertex facing toward the maternal abdomen. Occasionally, the fetus does not move into the vertex position. When the fetus lies transverse in the maternal uterus, it is common practice to indicate the fetal presentation according to which side the fetal head is located in reference to the mother (e.g., “transverse fetal lie–head maternal left”). The term breech indicates that the fetal buttocks are down (toward the cervix). This is an abnormal presentation for birth and may require a cesarean delivery. There are several variations of breech. Complete breech refers to when the buttocks present first (toward the cervix) and both the hips and knees are flexed. Incomplete or “footling” breech indicates that the fetus has one or both feet down (toward the cervix), so its leg(s) are poised to deliver first. Frank breech indicates that the fetal buttocks present first (toward the cervix) and the hips are flexed so the legs are straight and completely drawn up toward the fetal chest. And finally, the fetus may lie in an oblique position. When the fetus lies obliquely, it’s good practice for the examiner to indicate either vertex or breech oblique presentation plus which side the fetal head is lying (e.g., “breech oblique fetal lie– head maternal right”)(Fig. 20-3). [стр. 523 ⇒]

29 Often – but not always – there is a history of a prolonged labor. The hair loss is manifest at birth, or shortly thereafter, as a band of alopecia ranging in width from 1 to 4 cm, usually located over the vertex (Fig. 8.7A). There is typically an associated caput succedaneum and in some instances, frank tissue necrosis (Fig. 8.7B). If the injury is mild, the alopecia is usually temporary;29,30 however, scarring alopecia may result if the injury is severe (Fig. 8.7C).31,32 The areas of scarring can often be corrected with plastic surgery. The presence of halo scalp ring implies soft-tissue hypoxia and as such, infants with this condition should be monitored for developmental defects, which could have accompanied prolonged labor and associated hypoxic states. Lacerations Scalpel lacerations to the infant during cesarean section represent a potential form of injury. Smith and coworkers33 found an incidence of fetal injury of 1.9% in a series of 896 cesarean deliveries. Lacerations were much more common in those deliveries where the indication was nonvertex presentation (breech or transverse lie). In these infants, the injuries were almost always located on the lower portion of the body, whereas infants in a vertex presentation usually sustained their lacerations on the head. Failure to recognize the injury in the delivery room was a common occurrence. [стр. 127 ⇒]

The most common location is at the vertex of the scalp, but they may also be found anterior to the vertex, off the midline on the lateral parietal scalp, or even extending down onto the forehead along a line from the lateral forehead to the lateral edge of the eyebrows. Rarely, lesions of membranous aplasia cutis occur on the face, in a line extending from the preauricular region to the angles of the mouth.76 The term focal facial dermal hypoplasia has been used to describe these lesions (Fig. 9.25). Lesions of temporal aplasia cutis may be associated with Setleis syndrome and found with additional... [стр. 155 ⇒]

INFANTILE SEBORRHEIC DERMATITIS (ISD) First described by Unna in 1887,29 ISD (see also Chapter 15) is a disease that affects infants usually in the first 2 years, with a distinct inflammatory eruption that primarily involves the scalp, retroauricular area, face, chest, diaper, and intertriginous areas. A precise definition is lacking; some physicians confine the entity to the presence of scalp scaling without inflammation called ‘cradle cap’ that affects the vertex of the scalp, whereas others only use the term if there is inflammation of the scalp and in other seborrheic sites. Cutaneous features The eruption usually begins under 6 weeks of age, but may occur up to 1 year or even later.30 Both sexes are equally affected. The vast majority of infants develop cradle cap alone; this is a collection of asymptomatic, greasy keratin on the vertex of the scalp (retention hyperkeratosis), without inflammation or involvement of other areas. A few patients develop multiple areas of involvement, including erythematous well-demarcated patches in the retroauricular area, eyebrows, along the sides of the nose, and involving the axillae, chest, and diaper area. The most commonly involved areas are the scalp and diaper area... [стр. 363 ⇒]

ABSTRACT Comparison of the clinical efficacy of loop diuretics in the treatment of chronic heart failure. Gorbunova M. L., Vlasova T. V. Nizhny Novgorod State Medical Academy Introduction. The article discusses the features of the diuretics action mechanism. There is a comparative analysis of diuretics depending on the action point, as well as a comparison of the pharmacological properties of drugs of the same class (loop diuretics - furosemide and torasemide). The authors conducted monitoring of patients with chronic heart failure (CHF). Aim. Evaluation of the effectiveness and safety of torasemide (Lotonel, «Vertex») for the patients with CHF. Patients and methods. 48 patients with heart failure were randomized into 2 groups: 20 patients received torasemide (Lotonel, «Vertex») in addition to the basic therapy for 3 months, and 18 patients received furosemide. Patients included in the study had clinical signs of heart failure of II-III stage. Examination of patients included determination of FC of CHF according to NYHA, severity of the clinical condition, using a rating scale of clinical state (RSCS), the registered ECG in 12 leads, EchoCG, blood sampling to determine electrolyte metabolism and creatinine, as well as a 6-minute walk test. Results and conclusion: at baseline and after 3 months of therapy all the patients were examined for their clinical condition, hemodynamic status, quality of life and functional status of the left ventricle (LV), the levels of electrolyte metabolism and creatinine were also determined. The effects of both diuretics on body weight, edema, shortness of breath were comparable. After 3 months in both groups the results of EchoCG showed an improved decrease in the enddiastolic volume (EDV), as well as a significant increase in LVEF. There was a significant increase in the distance of a 6-min walk test in the torasemide group, torasemide had less influence on the potassium excretion. The results confirmed the safety and efficacy of the use of torasemid and furosemide in the assessment of the clinical condition severity and improvement of the quality of life of the patients with moderate compensated CHF. However, clinical and hemodynamic characteristics of torasemid were superior to furosemide. Key words: chronic heart failure, loop diuretics, torasemid, furosemide. For citation: Gorbunova M. L., Vlasova T. V. Comparison of the clinical efficacy of loop diuretics in the treatment of chronic heart failure // RMJ. 2017. № 4. P. 252–256. [стр. 14 ⇒]

Svenningsen L, Lindemann R, Eidal K: Measurements of fetal head compression pressure during bearing down and their relationship to the condition of the newborn, Acta Obstet Gynecol Scand 67:129-133, 1988. 205. Leviton A, Pagano M, Kuban KC: Etiologic heterogeneity of intracranial hemorrhages in preterm newborns, Pediatr Neurol 4:274-278, 1988. 206. Shankaran S, Bauer CR, Bain R, Wright LL, et al: Prenatal and perinatal risk and protective factors for neonatal intracranial hemorrhage, Arch Pediatr Adolesc Med 150:491-497, 1996. 207. Newton TH, Gooding CA: Compression of superior sagittal sinus by neonatal calvarial molding, Radiology 115:635-640, 1975. 208. Cowan F, Thoresen M: Changes in superior sagittal sinus blood velocities due to postural alterations and pressure on the head of the newborn infant, Pediatrics 75:1038-1047, 1985. 209. Pellicer A, Gaya F, Madero R, Quero J, et al: Noninvasive continuous monitoring of the effects of head position on brain hemodynamics in ventilated infants, Pediatrics 109:434-440, 2002. 210. Barrett JM, Boehm FH, Vaughn WK: The effect of type of delivery on neonatal outcome in singleton infants of birth weight of 1,000 g or less, JAMA 250:625-629, 1983. 211. Beverley DW, Chance GW, Inwood MJ, Schaus M, et al: Intraventricular haemorrhage and haemostasis defects, Arch Dis Child 59:444-448, 1984. 212. Horbar JD, Pasnick M, McAuliffe TL, Lucey JF: Obstetric events and risk of periventricular hemorrhage in premature infants, Am J Dis Child 137:678-681, 1983. 213. Kauppila O, Gronroos M, Aro P, Aittoniemi P, et al: Management of low birth weight breech delivery: Should cesarean section be routine? Obstet Gynecol 57:289-294, 1981. 214. Low JA, Galbraith RS, Sauerbrei EE, Muir DW, et al: Maternal, fetal, and newborn complications associated with newborn intracranial hemorrhage, Am J Obstet Gynecol 154:345-351, 1986. 215. Tejani N, Rebold B, Tuck S, Ditroia D, et al: Obstetric factors in the causation of early periventricular-intraventricular hemorrhage, Obstet Gynecol 64:510-515, 1984. 216. Welch RA, Bottoms SF: Reconsideration of head compression and intraventricular hemorrhage in the vertex very-low-birth-weight fetus, Obstet Gynecol 68:29-34, 1986. 217. Meidell R, Marinelli P, Pettett G: Perinatal factors associated with earlyonset intracranial hemorrhage in premature infants: A prospective study, Am J Dis Child 139:160-163, 1985. 218. Bada HS, Korones SB, Anderson GD, Magill HL, et al: Obstetric factors and relative risk of neonatal germinal layer/intraventricular hemorrhage, Am J Obstet Gynecol 148:798-804, 1984. 219. Tejani N, Verma U, Hameed C, Chayen B: Method and route of delivery in the low birth weight vertex presentation correlated with early periventricular/intraventricular hemorrhage, Obstet Gynecol 69:1-4, 1987. 220. Tejani N, Verma U, Shiffman R, Chayen B: Effect of route of delivery on periventricular/intraventricular hemorrhage in the low birth weight fetus with a breech presentation, J Reprod Med 32:911-914, 1987. 221. Hansen A, Leviton A: Labor and delivery characteristics and risks of cranial ultrasonographic abnormalities among very-low-birth-weight infants, Am J Obstet Gynecol 181:997-1006, 1999. 222. Wadhawan R, Vohr BR, Fanaroff AA, Perritt RL, et al: Does labor influence neonatal and neurodevelopmental outcomes of extremely-lowbirth-weight infants who are born by cesarean delivery? Am J Obstet Gynecol 189:501-506, 2003. 223. Synnes AR, Chien L-Y, Peliowski A, Baboolal R, et al: Variations in intraventricular hemorrhage incidence rates among Canadian neonatal intensive care units, J Pediatr 138:525-531, 2001. 224. Osborn DA, Evans N, Kluckow M: Hemodynamic and antecedent risk factors of early and late periventricular/intraventricular hemorrhage in premature infants, Pediatrics 112:33-39, 2003. 225. O’Shea M, Savitz DA, Hage ML, Feinstein KA: Prenatal events and the risk of subependymal/intraventricular haemorrhage in very low birthweight neonates, Paediatr Perinat Epidemiol 6:352-362, 1992. 226. Bucciarelli RL, Nelson RM, Egan EA, Eitzman DV, et al: Transient tricuspid insufficiency of the newborn: A form of myocardial dysfunction in stressed newborns, Pediatrics 59:330-337, 1977. 227. Cabal LA, Devaskar U, Siassi B, Hodgman JE, et al: Cardiogenic shock associated with perinatal asphyxia in preterm infants, J Pediatr 96:705710, 1980. 228. DiSessa TG, Leitner M, Ti CC, Gluck L, et al: The cardiovascular effects of dopamine in the severely asphyxiated neonate, J Pediatr 99:772-776, 1981. 229. Donnelly WH, Bucciarelli RL, Nelson RM: Ischemic papillary muscle necrosis in stressed newborn infants, J Pediatr 96:295-300, 1980. 230. Finley JP, Howman-Giles RB, Gilday DL, Bloom KR, et al: Transient myocardial ischemia of the newborn infant demonstrated by thallium myocardial imaging, J Pediatr 94:263-270, 1979. 231. Lees MH: Perinatal asphyxia and the myocardium, J Pediatr 96:675-678, 1980. 232. Nelson RM, Bucciarelli RL, Eitzman DV, Egan EA 2nd, et al: Serum creatine phosphokinase MB fraction in newborns with transient tricuspid insufficiency, N Engl J Med 298:146-149, 1978. 233. Rowe RD, Hoffman T: Transient myocardial ischemia of the newborn infant: A form of severe cardiorespiratory distress in full-term infants, J Pediatr 81:243-250, 1972. [стр. 592 ⇒]

Similarly, axonal rupture when associated with severance of the nerve sheath and thus loss of a ‘‘guide’’ for regenerating axons (neurotmesis) is associated with a poor spontaneous outcome. However, axonal rupture with an intact nerve sheath is intermediate in severity; axonal regeneration occurs at a rate of approximately 1.8 mm/day,129 somewhat faster than the rate of approximately 1 mm/day in older individuals. Pathogenesis Brachial plexus injury is thought to result from stretching of the brachial plexus, with its roots anchored to the cervical cord, by extreme lateral traction. The traction is exerted by the shoulder, in the process of delivering the head with breech deliveries, and by the head, in the process of delivering the shoulder in cephalic deliveries. The upper roots of the plexus are most vulnerable, but with marked traction, all roots are affected and total paralysis results. The relatively rare occurrence of intrauterine injury to the brachial plexus has been secondary to abnormalities of fetal position or of uterine structure.118,130-132 The pathogenetic events just mentioned occur secondary to, especially, obstetrical factors and large fetal size.12,110,112-115,117-125,127,133-135a Thus, in a large, essentially unselected series reported by Gordon and colleagues,110 abnormal presentations occurred in 56% of cases; this group consisted of 14% breech and 42% abnormal vertex presentations (occiput posterior and occiput transverse). Shoulder dystocia was present in 51% of all vertex deliveries and in 30% of all breech deliveries. Labor was augmented in 50% of these cases. In the large series (n = 276) studied in the United Kingdom and Ireland, 65% had shoulder dystocia.120 In several series of shoulder dystocia, approximately 20% of infants sustained some degree of brachial plexus injury.115,124,135 Birth weight of affected infants exceeds 3500 g in 50% to 85% of cases.110,114,115,120,122-124,133,135-137 In a large Swedish series, the incidence of brachial plexus palsy was 45fold greater at a birth weight of more than 4500 g than at a birth weight of less than 3500 g.117 In an older study, intrauterine asphyxia with fetal depression was suggested by the signs of fetal distress in 44% and Apgar score at 1 minute of less than 4 in 39%.110 Thus, a large, depressed infant after abnormal labor and delivery appears to be at added risk. [стр. 987 ⇒]

Trace Alternant: An electroencephalographic pattern of sleeping newborns, characterized by bursts of slow waves, at times intermixed with sharp waves, and intervening periods of relative quiescence with extreme low-amplitude activity. Tumescence (Penile): Hardening and expansion of the penis (penile erection). When associated with REM sleep, it is referred to as a sleep-related erection. Twitch (Body Twitch): A very small body movement such as a local foot or finger jerk; this movement usually is not associated with arousal. Vertex Sharp Transient: Sharp negative potential, maximal at the vertex, occurring spontaneously during sleep or in response to a sensory stimulus during sleep or wakefulness. The amplitude varies but rarely exceeds 250 µV. Use of the term vertex sharp wave is discouraged. Wake Time: The total time occurring between sleep onset and final wake-up time that is scored as wakefulness in a polysomnogram. Waxing and Waning: A crescendo-decrescendo pattern of activity, usually electroencephalographic activity. Zeitgeber: An environmental time cue, such as sunlight, noise, social interaction, alarm clocks, that usually helps an individual entrain to the 24-hour day. [стр. 183 ⇒]

However Hunner’s original descriptions of his cystoscopic findings12 read well alongside cystoscopic pictures using modern endoscopic equipment:1 ‘The crucial test in cystoscopy is the finding of a small abrasion on the mucosa surface which, if not bleeding on discovery, will easily bleed on being touched.’ (Figure 8.1) ‘Occasionally the distention of the bladder by air as the patient assumes the knee-breast posture causes this area to split and a tiny stream of blood flows to the vertex.’ (Figure 8.2) ‘The ulcer is usually found in the vertex or free portion of the bladder.’ (Figure 8.3) ‘On cystoscopy one’s attention is not infrequently first arrested by a glazed, dead, white appearance of a portion of the bladder mucosa.’ (Figure 8.4) ‘One may see a dead white scar area with a small congested area in the immediate neighbourhood and while one is examining this area the congestion becomes marked and may even begin to ooze blood.’ (Figure 8.5) In clinical practice today, cystoscopy is performed at some time in the work-up of most patients presenting with bladder pain, frequency, and urgency. The aim of cystoscopy is to exclude other conditions, positively diagnose interstitial cystitis, and record the extent of changes such as fissuring or ulceration, glomerulations, and bladder capacity, and to provide a therapeutic benefit by... [стр. 95 ⇒]

Общим для этих подходов является то, что в них используются графовые модели различных видов. Кроме того, и модель ВС принято изображать в виде графа. В связи с этим в рассматриваемую систему включены классы Vertex (Вершина), Arc (Дуга) и Graph (Граф), позволяющие задавать различные графовые модели. Класс Vertex предназначен для описания типов вершин и их атрибутов. Класс Arc — для описания дуг и их атрибутов, и, наконец, класс Graph — для описания различных типов графов, допустимых в них типов вершин и дуг и их сопоставления. В систему включено несколько предопределенных видов графа, то есть подклассов класса Graph, например, DecisionGraph (Дерево решений), который позволяет строить с помощью визуальных средств простые деревья решений, а затем проводить на них прямой и обратный вывод. В качестве примера рассмотрим упрощенное дерево решений для некоторых аспектов выбора оборудования в ВС. Дерево решений состоит из вершин двух типов (рис. 16). Вершины решений, содержащие вопросы, обозначаются окружностью. Цели или логические выводы обозначаются прямоугольниками. Условия задаются на дугах. Каждая вершина нумеруется. Представление дерева решений в визуальной среде показано на рис. 17. На этапе визуализации в каждой вершине устанавливается в качестве свойства имя переменной отождествляемой с ней табл. 1. Таблица 1 Назначения вершин дерева Имя переменной... [стр. 58 ⇒]

4. Графический процессор Графический процессор (ГП или GPU) предназначен для хранения, обработки и передачи на монитор данных о выводимом на экран изображении. ГП существенно повышает производительность компьютера, освобождая центральный процессор (ЦП) от обработки графических данных. По своей сложности современные ГП могут превосходить ЦП. Обработки графических данных включает определение объектов, составляющих сцену, расчет местоположения вершин, задающих эти объекты, построение по вершинам граней, наложение на грани текстур и т.п. Графические процессоры имеют конвейерную архитектуру. В классическом варианте различают вершинные и пиксельные процессоры — конвейеры. Поступающие в ГП данные об изображаемом объекте сначала обрабатываются в вершинном процессоре (Vertex Pipeline) с помощью программ, называемых вершинными шейдерами (Vertex Shader). Шейдер - функция и программа компьютерной графики для создания тех или иных эффектов в изображениях. Вершинный шейдер рассчитывает геометрию сцены и параметры вершин (координаты, цвет, освещение и др.), может выполнять такие операции, как деформация и анимация объектов. Геометрический шейдер — программа, обрабатывающая данные не на уровне отдельных вершин, как в вершинных шейдерах, а на уровне графических примитивов, то есть наборов вершин, например линий, полосок, треугольников и т.д. Геометрические шейдеры позволяют существенно повысить эффективность преобразования сложных трехмерных объектов. 95... [стр. 95 ⇒]

2.2 Single-Query Planners: Incremental Search Single-query planning methods focus on a single initial– goal configuration pair. They probe and search the continuous C-space by extending tree data structures initialized at these known configurations and eventually connecting them. Most single-query methods conform to the following template: 1. Initialization: Let G(V, E) represent an undirected search graph, for which the vertex set V contains a vertex for one (usually q I ) or more configurations in Cfree , and the edge set E is empty. Vertices of G are collision-free configurations, and edges are collision-free paths that connect vertices. 2. Vertex selection method: Choose a vertex q cur ∈ V for expansion. [стр. 167 ⇒]

RAPIDLY EXPLORING DENSE TREES k: the exploration steps of the algorithm —————————————————————— G.init(q I ); for i = 1 to k do G.add_vertex(α(i)); q n ← nearest(S(G), α(i)); G.add_edge(q n , α(i)); end for The tree starts at q I , and in each iteration, an edge and vertex are added. So far, the problem of reaching q G has not been explained. There are several ways to use RDTs in a planning algorithm. One approach is to bias α(i) so that q G is frequently chosen (perhaps once every 50 iterations). A more efficient approach is to develop a bidirectional search by growing two trees, one from each of q I and q G . Roughly half of the time is spent expanding each tree in the usual way, while the other half is spend attempting to connect the trees. The simplest way to connect trees is to let the newest vertex of one tree be a substitute for α(i) in extending the other. This tricks one RDT into attempting to connect to the other while using the basic expansion algorithm [5.38]. Several works have extended, adapted, or applied RDTs in various applications [5.37, 39–42]. Detailed descriptions can be found in [5.5, 7]. Other Tree Algorithms Planners based on the idea of expansive spaces are presented in [5.43–45]. In this case, the algorithm forces exploration by choosing vertices for expansion that have fewer points in a neighborhood around them. In [5.46], additional performance is obtained by self-tuning random walks, which focus virtually all of their effort on exploration. Other successful tree-based algorithms include the path-directed subdivision tree algorithm [5.47] and some of its variants [5.48]. In the literature, it is sometimes hard to locate tree-based planners for ordinary path planning problems as many of them (including RRT) were designed and/or applied to more complex problems (see Sect. 5.4.4). Their performance is nevertheless excellent for a variety of path planing problems. [стр. 168 ⇒]

5.5 for all possible pairs, computing their intersections, and tracing out the roadmap. Several algorithms exist that provide better asymptotic running time [5.50], but they are considerably more difficult to implement. The best-known algorithm runs in O(n lg n) time in which n is the number of roadmap curves [5.51]. An alternative is to compute a shortest-path roadmap [5.52], as shown in Fig. 5.6. This is different than the roadmap presented in the previous section because paths may actually touch the obstacles, which must be allowed for paths to be optimal. The roadmap vertices are the reflex vertices of Cobs , which are vertices for which the interior angle is greater than π. An edge exists in the roadmap if and only if a pair of vertices is mutually visible and the line through them pokes into Cfree when extended outward from each vertex (such lines are called bitangents). An O(n 2 lg n)-time construction algorithm can be formed by using a radial sweep algorithm from each reflex vertex. It can theoretically be computed in time O(n 2 + m), in which m is the total number of edges in the roadmap [5.53]. Figure 5.7 illustrates the vertical cell decomposition approach. The idea is to decompose Cfree into cells that are trapezoids or triangles. Planning in each cell is trivial because it is convex. A roadmap is made by placing a point in the center of each cell and each boundary between cells. Any graph search algorithm can be used to find a collision-free path quickly. The cell decomposition can be constructed in O(n lg n) time using the plane-sweep principle [5.54, 55]. Imagine that a vertical line sweeps from x = −∞ to x = ∞, stopping at places where a polygon vertex is encountered. In these cases,... [стр. 169 ⇒]

4.4 Kinodynamic Planning Due to the great difficulty of planning under differential constraints, many successful planning algorithms that address kinodynamic problems directly in the phase space X are sampling based. Sampling-based planning algorithms proceed by exploring one or more reachability trees. Many parallels can be drawn with searching on a grid; however, reachability trees are more complicated because they do not necessarily involve a regular lattice structure. The vertex set of reachability trees is dense in most cases. It is therefore not clear how to search a bounded region exhaustively at a fixed resolution. It is also difficult to design approaches that behave like a multiresolution grid, in which refinements can be made arbitrarily to ensure resolution completeness. Many algorithms attempt to convert the reachability tree into a lattice. This is the basis of the original kinodynamic planning work [5.63], in which the discrete-time approximation to the double integrator, q̈ = u, is forced onto a lattice as shown in Fig. 5.14. This enables an approximation algorithm to be developed that solves the kinodynamic planning problem in time polynomial in the approximation quality 1/ and the number of primitives that define the obstacles. Generalizations of the methods to fully actuated systems are described in [5.7]. Surprisingly, it is even possible to obtain a lattice for some underactuated, nonholonomic systems [5.77]. If the reachability tree does not form a lattice, then one approach is to force it to behave as a lattice by imposing a regular cell decomposition over X (or C), and allowing no more than one vertex per cell to be expanded in the reachability graph; see Fig. 5.15. This idea was... [стр. 174 ⇒]

Different contact state representations essentially differ only in how primitive contacts are defined. One common representation [26.23] defines primitive contacts as point contacts in terms of vertex–edge contacts for two-dimensional (2-D) polygons, and vertex–face and edge–edge contacts for three-dimensional (3-D) polyhedra. Another representation [26.24] defines a primitive contact as between a pair of topological surface elements (i. e., faces, edges, and vertices). Here a contact primitive can characterize a contact region that is either a point, a line segment, or a planar face, unlike the point-contact notion. From the viewpoint of contact identification via sensing, however, both representations can result in states that are different by definition but indistinguishable in identification due to uncertainties. Figure 26.16 shows such an example. The notion of a principal contact [26.25,26] presents a high-level primitive contact that is more robust to recognition. A principal contact (PC) denotes a contact between a pair of topological surface elements that are not boundary elements of other contacting topological surface elements. The boundary elements of a face are the edges and vertices bounding it, and the boundary elements of an edge are the vertices bounding it. Different PCs between two objects correspond to different degrees of freedom of the objects, which often also correspond to significant differences in the contact forces and moments. As shown in Fig. 26.16, the indistinguishable states in terms of the other contact primitives are grouped as a single contact state in terms of PCs. Thus, there are also fewer contact states in terms of PCs, leading to a more concise characterization of contact states. In fact, every contact state between two convex polyhedral objects is described by a single PC. [стр. 671 ⇒]

Есть много других задач поиска для графов. В задаче о вершинном покрытии (vertex cover problem) для данного графа и числа b требуется найти b вершин, которые «задевают» каждое ребро (для любого ребра графа хотя бы один из концов ребра лежит в этом множестве). Можете ли вы покрыть все рёбра графа рис. 8.5 семью вершинами? А шестью? Как связана эта задача с задачей о независимом множестве? Задача о вершинном покрытии (vertex cover problem) является частным случаем задачи о покрытии множествами (см. главу 5). В задаче о покрытии множествами на вход даются множество E и несколько его подмножеств S1 , ‌, Sm , а также число b. Найти необходимо b из заданных подмножеств, объединение которых покрывает E. (Как свести задачу о трёхдольном сочетании к задаче о покрытии множествами?) В задаче о вершинном покрытии элементами E являются рёбра графа, а для каждой вершины графа есть множество Si , содержащее все смежные с ней рёбра. Наконец, в задаче о клике (clique problem) по данному графу и числу g необходимо найти множество из g вершин, каждые две из которых соединены ребром. Каков размер максимальной клики в графе на рис. 8.5? Как задача о клике связана с задачей о независимом множестве? Максимальный путь Мы уже знаем, что задача о кратчайшем пути в графе решается эффективно. А что можно сказать про задачу о максимальном пути (longest path problem)?... [стр. 239 ⇒]

Section 3.4: Topological Sort A topological ordering, or a topological sort, orders the vertices in a directed acyclic graph on a line, i.e. in a list, such that all directed edges go from left to right. Such an ordering cannot exist if the graph contains a directed cycle because there is no way that you can keep going right on a line and still return back to where you started from. Formally, in a graph G = (V, E), then a linear ordering of all its vertices is such that if G contains an edge (u, v) ? Efrom vertex u to vertex v then u precedes v in the ordering. [стр. 22 ⇒]

It is important to note that each DAG has at least one topological sort. There are known algorithms for constructing a topological ordering of any DAG in linear time, one example is: 1. Call depth_first_search(G) to compute finishing times v.f for each vertex v 2. As each vertex is finished, insert it into the front of a linked list 3. the linked list of vertices, as it is now sorted. A topological sort can be performed in ?(V + E) time, since the depth-first search algorithm takes ?(V + E) time and it takes ?(1) (constant time) to insert each of |V| vertices into the front of a linked list. Many applications use directed acyclic graphs to indicate precedences among events. We use topological sorting so that we get an ordering to process each vertex before any of its successors. Vertices in a graph may represent tasks to be performed and the edges may represent constraints that one task must be performed before another; a topological ordering is a valid sequence to perform the tasks set of tasks described in V. Problem instance and its solution Let a vertice v describe a Task(hours_to_complete: int), i. e. Task(4) describes a Task that takes 4 hours to complete, and an edge e describe a Cooldown(hours: int) such that Cooldown(3) describes a duration of time to cool down after a completed task. Let our graph be called dag (since it is a directed acyclic graph), and let it contain 5 vertices: A B C D E... [стр. 22 ⇒]

Section 17.1: Algorithm Pseudo Code Algorithm PMinVertexCover (graph G) Input connected graph G Output Minimum Vertex Cover Set C Set C <- new Set<Vertex>() Set X <- new Set<Vertex>() X <- G.getAllVerticiesArrangedDescendinglyByDegree() for v in X do List<Vertex> adjacentVertices1 <- G.getAdjacent(v) if !C contains any of adjacentVertices1 then C.add(v) for vertex in C do List<vertex> adjacentVertices2 <- G.adjacentVertecies(vertex) if C contains any of adjacentVertices2 then C.remove(vertex)... [стр. 108 ⇒]

Chapter 44: Travelling Salesman Section 44.1: Brute Force Algorithm A path through every vertex exactly once is the same as ordering the vertex in some way. Thus, to calculate the minimum cost of travelling through every vertex exactly once, we can brute force every single one of the N! permutations of the numbers from 1 to N. Psuedocode minimum = INF for all permutations P current = 0 for i from 0 to N-2 current = current + cost[P[i]][P[i+1]] current = current + cost[P[N-1]][P[0]] first if current < minimum minimum = current... [стр. 208 ⇒]

Thus we can have the following algorithm (C++ implementation): int cost[N][N]; //Adjust the value of N if needed int memo[1 << N][N]; //Set everything here to -1 int TSP(int bitmask, int pos){ int cost = INF; if (bitmask == ((1 << N) - 1)){ //All vertices have been explored return cost[pos][0]; //Cost to go back } if (memo[bitmask][pos] != -1){ //If this has already been computed return memo[bitmask][pos]; //Just return the value, no need to recompute } for (int i = 0; i < N; ++i){ //For every vertex if ((bitmask & (1 << i)) == 0){ //If the vertex has not been visited cost = min(cost,TSP(bitmask | (1 << i) , i) + cost[pos][i]); //Visit the vertex } } memo[bitmask][pos] = cost; //Save the result return cost; } //Call TSP(1,0)... [стр. 209 ⇒]

More generally, suppose X is any graph with finitely many vertices and edges. If the two endpoints of any edge of X are distinct, we can collapse this edge to a point, producing a homotopy equivalent graph with one fewer edge. This simplification can be repeated until all edges of X are loops, and then each component of X is either an isolated vertex or a wedge sum of circles. This raises the question of whether two such graphs, having only one vertex in each component, can be homotopy equivalent if they are not in fact just isomorphic graphs. Exercise 12 at the end of the chapter reduces the question to the case of W connected graphs. Then the task is to prove that a wedge sum m S 1 of m circles is not W homotopy equivalent to n S 1 if m ≠ n . This sort of thing is hard to do directly. What one would like is some sort of algebraic object associated to spaces, depending only W W on their homotopy type, and taking different values for m S 1 and n S 1 if m ≠ n . In W fact the Euler characteristic does this since m S 1 has Euler characteristic 1−m . But it... [стр. 20 ⇒]

As our general theory will show, these examples for n ≥ 1 together with the helix example exhaust all the connected coverings spaces of S 1 . There are many other disconnected covering spaces of S 1 , such as n disjoint circles each mapped homeomorphically onto S 1 , but these disconnected covering spaces are just disjoint unions of connected ones. We will usually restrict our attention to connected covering spaces as these contain most of the interesting features of covering spaces. The covering spaces of S 1 ∨ S 1 form a remarkably rich family illustrating most of the general theory very concretely, so let us look at a few of these covering spaces to get an idea of what is going on. To abbreviate notation, set X = S 1 ∨ S 1 . We view this as a graph with one vertex and two edges. We label the edges a and b and we choose orientations for a and b . Now let e be any other graph with four edges meeting at each vertex, X e have been assigned labels a and b and orientations in and suppose the edges of X such a way that the local picture near each vertex is the same as in X , so there is an... [стр. 66 ⇒]

As the reader will discover by experimentation, it seems that every graph having four edges incident at each vertex can be 2 oriented. This can be proved for finite graphs as follows. A very classical and easily shown fact is that every finite connected graph with an even number of edges incident at each vertex has an Eulerian circuit, a loop traversing each edge exactly once. If there are four edges at each vertex, then labeling the edges of an Eulerian circuit alternately a and b produces a labeling with two a and two b edges at each vertex. The union of the a edges is then a collection of disjoint circles, as is the union of the b edges. Choosing orientations for all these circles gives a 2 orientation. It is a theorem in graph theory that infinite graphs with four edges incident at each vertex can also be 2 oriented; see Chapter 13 of [König 1990] for a proof. There is also a generalization to n oriented graphs, which are covering spaces of the wedge sum of n circles. [стр. 66 ⇒]

This graph is connected since every element of G is a product of gα ’s, so there is a path in the graph joining each vertex to the identity vertex e . Each relation rβ determines a loop in the graph, starting at any vertex g , and we attach a 2 cell for each such loop. The resulting cell eG is the Cayley complex of G . The group G acts on X eG by multiplication complex X on the left. Thus, an element g ∈ G sends a vertex g ′ ∈ G to the vertex gg ′ , and the edge from g ′ to g ′ gα is sent to the edge from gg ′ to gg ′ gα . The action extends to... [стр. 86 ⇒]

One says that X has the weak topology with respect to the subspaces eα . In this topology a sequence of points in the interiors of distinct edges forms a closed subset, hence never converges. This is true in particular if the edges containing the sequence all have a common vertex and one tries to choose the sequence so that it gets ‘closer and closer’ to the vertex. Thus if there is a vertex that is the endpoint of infinitely many edges, then the weak topology cannot be a metric topology. An exercise at the end of this section is to show the converse, that the weak topology is a metric topology if each vertex is an endpoint of only finitely many edges. A basis for the topology of X consists of the open intervals in the edges together with the path-connected neighborhoods of the vertices. A neighborhood of the latter sort about a vertex v is the union of connected open neighborhoods Uα of v in eα for all eα containing v . In particular, we see that X is locally path-connected. Hence a graph is connected iff it is path-connected. If X has only finitely many vertices and edges, then X is compact, being the ` continuous image of the compact space X 0 α Iα . The converse is also true, and more generally, a compact subset C of a graph X can meet only finitely many vertices and... [стр. 92 ⇒]

1. If X is a tree and v0 is any vertex of X , then the construction of a maximal tree Y ⊂ X starting with Y0 = {v0 } yields an increasing sequence of subtrees Yn ⊂ X whose union is all of X since a tree has only one maximal subtree, namely itself. We can think of the vertices in Yn − Yn−1 as being at ‘height’ n , with the edges of Yn − Yn−1 connecting these vertices to vertices of height n − 1 . In this way we get a ‘height function’ h : X →R assigning to each vertex its height, and monotone on edges. [стр. 94 ⇒]

For each vertex v of X there is exactly one edge leading downward from v , so by following these downward edges we obtain a path from v to the base vertex v0 . This is an example of an edgepath, which is a composition of finitely many paths each consisting of a single edge traversed monotonically. For any edgepath joining v to v0 other than the downward edgepath, the height function would not be monotone and hence would have local maxima, occurring when the edgepath backtracked, retracing some edge it had just crossed. Thus in a tree there is a unique nonbacktracking edgepath joining any two points. All the vertices and edges along this edgepath are distinct. A tree can contain no subgraph homeomorphic to a circle, since two vertices in such a subgraph could be joined by more than one nonbacktracking edgepath. Conversely, if a connected graph X contains no circle subgraph, then it must be a tree. For if T is a maximal tree in X that is not equal to X , then the union of an edge of X − T with the nonbacktracking edgepath in T joining the endpoints of this edge is a circle subgraph of X . So if there are no circle subgraphs of X , we must have X = T , a tree. For an arbitrary connected graph X and a pair of vertices v0 and v1 in X there is a unique nonbacktracking edgepath in each homotopy class of paths from v0 to v1 . e , which is a tree since it is simplyThis can be seen by lifting to the universal cover X e0 of v0 , a homotopy class of paths from v0 to v1 lifts to connected. Choosing a lift v... [стр. 95 ⇒]

Let us look at some examples to see what the idea is. Consider the graph X1 shown in the figure, consisting of two vertices joined by four edges. When studying the fundamental group of X1 we consider loops formed by sequences of edges, starting and ending at a fixed basepoint. For example, at the basepoint x , the loop ab−1 travels forward along the edge a , then backward along b , as indicated by the exponent −1 . A more complicated loop would be ac −1 bd−1 ca−1 . A salient feature of the fundamental group is that it is generally nonabelian, which both enriches and complicates the theory. Suppose we simplify matters by abelianizing. Thus for example the two loops ab−1 and b−1 a are to be regarded as equal if we make a commute with b−1 . These two loops ab−1 and b−1 a are really the same circle, just with a different choice of starting and ending point: x for ab−1 and y for b−1 a . The same thing happens for all loops: Rechoosing the basepoint in a loop just permutes its letters cyclically, so a byproduct of abelianizing is that we no longer have to pin all our loops down to a fixed basepoint. Thus loops become cycles, without a chosen basepoint. Having abelianized, let us switch to additive notation, so cycles become linear combinations of edges with integer coefficients, such as a − b + c − d . Let us call these linear combinations chains of edges. Some chains can be decomposed into cycles in several different ways, for example (a − c) + (b − d) = (a − d) + (b − c) , and if we adopt an algebraic viewpoint then we do not want to distinguish between these different decompositions. Thus we broaden the meaning of the term ‘cycle’ to be simply any linear combination of edges for which at least one decomposition into cycles in the previous more geometric sense exists. What is the condition for a chain to be a cycle in this more algebraic sense? A geometric cycle, thought of as a path traversed in time, is distinguished by the property that it enters each vertex the same number of times that it leaves the vertex. For an arbitrary chain ka + ℓb + mc + nd , the net number of times this chain enters y is k + ℓ + m + n since each of a , b , c , and d enters y once. Similarly, each of the four edges leaves x once, so the net number of times the chain ka + ℓb + mc + nd enters x is −k − ℓ − m − n . Thus the condition for ka + ℓb + mc + nd to be a cycle is simply k + ℓ + m + n = 0 . To describe this result in a way that would generalize to all graphs, let C1 be the free abelian group with basis the edges a, b, c, d and let C0 be the free abelian group with basis the vertices x, y . Elements of C1 are chains of edges, or 1 dimensional chains, and elements of C0 are linear combinations of vertices, or 0 dimensional chains. Define a homomorphism ∂ : C1 →C0 by sending each basis element a, b, c, d to y − x , the vertex at the head of the edge minus the vertex at the tail. Thus we have ∂(ka + ℓb + mc + nd) = (k + ℓ + m + n)y − (k + ℓ + m + n)x , and the cycles are precisely the kernel of ∂ . It is a simple calculation to verify that a−b , b −c , and c −d... [стр. 108 ⇒]

Also H3 (X4 ) = Ker ∂3 = 0 . The group H1 (X4 ) is the same as H1 (X3 ) , namely Z× Z , so this is the only nontrivial homology group of X4 . It is clear what the general pattern of the examples is. For a cell complex X one has chain groups Cn (X) which are free abelian groups with basis the n cells of X , and there are boundary homomorphisms ∂n : Cn (X)→Cn−1 (X) , in terms of which one defines the homology group Hn (X) = Ker ∂n / Im ∂n+1 . The major difficulty is how to define ∂n in general. For n = 1 this is easy: The boundary of an oriented edge is the vertex at its head minus the vertex at its tail. The next case n = 2 is also not hard, at least for cells attached along cycles that are simply loops of edges, for then the boundary of the cell is this cycle of edges, with the appropriate signs taking orientations into account. But for larger n , matters become more complicated. Even if one restricts attention to cell complexes formed from polyhedral cells with nice attaching maps, there is still the matter of orientations to sort out. The best solution to this problem seems to be to adopt an indirect approach. Arbitrary polyhedra can always be subdivided into special polyhedra called simplices (the triangle and the tetrahedron are the 2 dimensional and 3 dimensional instances) so there is no loss of generality, though initially there is some loss of efficiency, in restricting attention entirely to simplices. For simplices there is no difficulty in defining boundary maps or in handling orientations. So one obtains a homology theory, called simplicial homology, for cell complexes built from simplices. Still, this is a rather restricted class of spaces, and the theory itself has a certain rigidity that makes it awkward to work with. The way around these obstacles is to step back from the geometry of spaces decomposed into simplices and to consider instead something which at first glance seems wildly more complicated, the collection of all possible continuous maps of simplices into a given space X . These maps generate tremendously large chain groups Cn (X) , but the quotients Hn (X) = Ker ∂n / Im ∂n+1 , called singular homology groups, turn out to be much smaller, at least for reasonably nice spaces X . In particular, for spaces like those in the four examples above, the singular homology groups coincide with the homology groups we computed from the cellular chains. And as we shall see later in this chapter, singular homology allows one to define these nice cellular homology groups for all cell complexes, and in particular to solve the problem of defining the boundary maps for cellular chains. [стр. 110 ⇒]

There is a nontrivial homomorphism from this group to the group G of rotational symmetries of a regular dodecahedron, sending a to the rotation ρa through angle 2π /5 about the axis through the center of a pentagonal face, and b to the rotation ρb through angle 2π /3 about the axis through a vertex of this face. The composition ρa ρb is a rotation through angle π about the axis through the midpoint of an edge abutting this vertex. Thus the relations a5 = b3 = (ab)2 defining π1 (X) become ρa5 = ρb3 = (ρa ρb )2 = 1 in G , which means there is a well-defined homomorphism ρ : π1 (X)→G sending a to ρa and b to ρb . It is not hard to see that G is generated by ρa and ρb , so ρ is surjective. With more work one can compute that the kernel of ρ is Z2 , generated by the element... [стр. 151 ⇒]

As in calculus, if a solution of δϕ = ψ exists, it will be unique up to adding an element of the kernel of δ , that is, a function that is constant on each component of X . The equation δϕ = ψ is always solvable if X is a tree since if we choose arbitrarily a value for ϕ at a basepoint vertex v0 , then if the change in ϕ across each edge of X is specified, this uniquely determines the value of ϕ at every other vertex v by induction along the unique path from v0 to v in the tree. When X is not a tree, we first choose a maximal tree in each component of X . Then, since every vertex lies in one of these maximal trees, the values of ψ on the edges of the maximal trees determine ϕ uniquely up to a constant on each component of X . But in order for the equation δϕ = ψ to hold, the value of ψ on each edge not in any of the maximal trees must equal the difference in the already-determined values of ϕ at the two ends of the edge. This condition need not be satisfied since ψ can have arbitrary values on these edges. Thus we see that the cohomology group H 1 (X; G) is a direct product of copies of the group G , one copy for each edge of X not in one of the chosen maximal trees. This can be compared with the homology group H1 (X; G) which consists of a direct sum of copies of G , one for each edge of X not in one of the maximal trees. [стр. 196 ⇒]

For many manifolds there is a very nice geometric proof of Poincaré duality using the notion of dual cell structures. The germ of this idea can be traced back to the five regular Platonic solids: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Each of these polyhedra has a dual polyhedron whose vertices are the center points of the faces of the given polyhedron. Thus the dual of the cube is the octahedron, and vice versa. Similarly the dodecahedron and icosahedron are dual to each other, and the tetrahedron is its own dual. One can regard each of these polyhedra as defining a cell structure C on S 2 with a dual cell structure C ∗ determined by the dual polyhedron. Each vertex of C lies in a dual 2 cell of C ∗ , each edge of C crosses a dual edge of C ∗ , and each 2 cell of C contains a dual vertex of C ∗ . The first figure at the right shows the case of the cube and octahedron. There is no need to restrict to regular polyhedra here, and we can generalize further by replacing S 2 by any surface. A portion of a more-or-less random pair of dual cell structures is shown in the second figure. On the torus, if we lift a dual pair of cell structures to the universal cover R2 , we get a dual pair of periodic tilings of the plane, as in the next three figures. The last two figures show that the standard CW structure on the surface of genus g , obtained from a 4g gon by identifying edges via the product of commutators [a1 , b1 ] ··· [ag , bg ] , is homeomorphic to its own dual. Given a pair of dual cell structures C and C ∗ on a closed surface M , the pairing of cells with dual cells gives identifications of cellular chain groups C0∗ = C2 , C1∗ = C1 , and C2∗ = C0 . If we use Z coefficients these identifications are not quite canonical since there is an ambiguity of sign for each cell, the choice of a generator for the corresponding Z summand of the cellular chain complex. We can avoid this ambiguity by considering the simpler situation of Z2 coefficients, where the identifi∗ cations Ci = C2−i are completely canonical. The key observation now is that under... [стр. 241 ⇒]

Two of these 2 tori intersect along a circle when the corresponding 3 tori of X intersect along a 2 torus. This happens when the triples of ± ’s for the two 3 tori differ in exactly one entry. The pattern of intersection of the eight 2 tori of Z can thus be described combinatorially via the 1 skeleton of the cube, with vertices (±1, ±1, ±1) . There is a torus of Z for each vertex of the cube, and two tori intersect along a circle when the corresponding vertices of the cube are the endpoints of an edge of the cube. All eight tori contain the single 0 cell of Z . To obtain a model of Z itself, consider a regular octahedron inscribed in the cube with vertices (±1, ±1, ±1) . If we identify each pair of opposite edges of the octahedron, each pair of opposite triangular faces becomes a torus. However, there are only four pairs of opposite faces, so we get only four tori this way, not eight. To correct this problem, regard each triangular face of the octahedron as two copies of the same triangle, distinguished from each other by a choice of normal direction, an arrow attached to the triangle pointing either inside the octahedron or outside it, that is, either toward the nearest vertex of the surrounding cube or toward the opposite vertex of the cube. Then each pair of opposite triangles of the octahedron having normal vectors pointing toward the same vertex of the cube determines a torus, when opposite edges are identified as before. Each edge of the original octahedron is also replaced by two edges oriented either toward the interior or exterior of the octahedron. The vertices of the octahedron may be left unduplicated since they will all be identified to a single point anyway. With this scheme, the two tori corresponding to the vertices at the ends... [стр. 434 ⇒]

Если включить эту опцию, то материал будет обрабатываться в максимальном качестве. Учтите, в таком случае время обработки значительно увеличивается; ♦ Sky (Небо) — в этом случае цвет материала меняется на цвет фона сцены (Sky); ♦ Use Mist (Использовать туман) — Blender имеет возможность использовать в сцене туман (не путать с режимом Volume материала). Отключите ее, если не хотите, чтобы объект реагировал на туман; ♦ Face Textures (Текстурированные грани) и Face Textures Alpha (Текстурированные грани с прозрачностью). В этом случае основной цвет материала будет заменен на вывод текстуры в обычном режиме и с альфа-каналом (с прозрачностью); ♦ Vertex Color Paint (Окраска вершин)— Blender позволяет раскрашивать в разные цвета вершины объекта. Установка этой опции заменит базовый цвет материала на раскраску вершин; ♦ Vertex Color Light (Освещение вершин) — дополнительное освещение от окрашенных вершин; ♦ Light G roup (Группа света)— материал можно поместить в группу отдельного источника света; ♦ Z Offset (Смещение по Z) — настройка слоев при работе с прозрачностью. [стр. 143 ⇒]

Помимо раскраски текстуры Blender предлагает окраску вершин (Vertex Paint). Причем выполняется это действие непосредственно на модели в окне 3D View. Vertex P a in t— это возможность ручной окраски вершин объекта любыми цветами палитры и совмещение их с текстурами по необходимости. Нужно знать, что одновременная работа базового цвета Diffuse объекта и окрашенных вершин невозможна. Для включения режима рисования нужно выбрать Vertex Paint в меню Mode (см. рис. 4.93). Разработчики постарались облегчить изучение программы и максимально унифицировали похожие функции. Поэтому нет ничего удивительного в том, что режимы Sculpt Mode, Texture Mode и Vertex Mode имеют одинаковый набор панелей и инструментов. Рассмотрим только предлагаемые для окраски вершин кисти: ♦ Add (Добавление)— смешивание цветов вершин путем прибавления нового цвета к старому;... [стр. 203 ⇒]

Построение поверхности крыши 1. Настроить единицы измерения. Выбрать в главном меню команду Customize (Настройки) → Units setup… (Настройка единиц) → Metric → Millimeters, для системных единиц System Units setup установить Millimeters. 2. Настройка шага сетки. Выбрать в главном меню команду Customize (Настройки) → Grid and Snap Settings (Настройки сетки и шага)→ Home Grid (базовая сетка) → Grid Spacing установить 100 mm. Вкладка Snap (Шаг) выбрать Grid Points (Точки сетки). Установить двухмерную привязку. 3. Создание линий опорных сечений. а) На виде сверху (Top) построить два горизонтальных отрезка длиной 1000 мм. Для этого использовать команду Create (Создать)→Shapes (Формы)→ Line (линия). Тип вершин Corner (C изломом). Координаты точек первого отрезка (-2000,-2000), (-1000,-2000), второго – (1000,-2000), (2000,-2000). На виде спереди (Front) построить дугу (Arc) с координатами конечных точек(-1000,0) и (1000,0), радиусом 1000 мм. Перенести дугу на 2000 мм вперед до совмещения с отрезками. В команде Modify (Редактирование) преобразовать дугу в редактируемый сплайн выбрав команду Edit Spline. Присоединить к дуге два отрезка командой Attach. Включить режим Vertex, слить точки соединения концов дуги с отрезками командой Weld. Проконтролировать направление нумерации вершин слева направо, включив флажок параметра Show Vertex Number (Показать нумерацию вершин). В этом же направлении создавать следующую линию. б) На виде сверху построить отрезок с координаттами точек (-100,-100), (100,-100). 4.Построение направляющей линии. На виде сверху построить отрезок с координатами (0,-2000) и (0, -100). 5. Построение поверхности опорных сечений Loft. Выделить линию–траекторию. В команде Create (Создать) → Geometry (Геометрия) → Compound Objects (Составные объекты) выбрать Loft. Нажав кнопку Get Shapes (Указать форму), указать первое опорное сечение, ввести значение Path (Путь) 100% и активировав кнопку Get Shapes, указать второе сечение. Для редактирования поверхности открыть свиток Skin Parameters (Параметры оболочки) в разделе Options установить количество шагов пути Path Steps =0. При необходимости изменить направление нормалей поверхности флажком Flip Normals. [стр. 1 ⇒]

Редактирование поверхности. В команде Modify раскрыть список подчиненных объектов поверхности Loft, выбрать Shape (Форма), выделить линейное сечение и перенести его вверх на высоту 1500 мм. Выделить сечение сложной формы, спуститься на уровень редактирования элементов сплайна, выбрать подчиненный объект Spline, командой Detach отсоединить копию сплайна, предварительно поставив флажок Copy . Выбрать для редактирования новую форму, в команде Modify, выбрать подчиненный объект сегмент, выделить и удалить линейные сегменты. Выбрать подученный объект вершина и соединить конечные точки командой Connect. Применить модификатор Extrude (Выдавить), величину выдавливания Amount задать 1 мм. 7. Создание группы. Выделить поверхность Loft и выдавленный контур. Объединить их в группу командой Group. 8. Создание кругового массива. Для выделенной группы назначить центром трансформации начало координат. Выбрать команду Tools (Инструменты) →Array (Массив) в разделе Rotate (Вращение) назначить угол между соседними объектами относительно оси Z 900, количество объектов для 1D (одномерного массива) задать 4. 9. Верхнее отверстие закрыть пирамидой высотой 100 мм, основание привязать к вершинам отверстия используя для этого трехмерную привязку Vertex. 10. Построение основы крыши. Повернуть перспективное окно таким обзором, чтобы отображалась нижняя основа. Используя привязку к вершинам Vertex построить прямоугольник размером 4000х4000 мм. На любой проекции построить замкнутый контур сечения, которое будет формировать профиль бордюра крыши. Выделить прямоугольник, присвоить ему модификатор Bevel Profile, выбрать с помощью кнопки Pick Profile построение сечение. Если построенная поверхность ориентирована неверно, необходимо повернуть Profile Gizmo в нужном направлении. С помощью стандартного примитива Plane закрыть основу крыши, привязываясь к крайним вершинам бордюра трехмерной привязкой Vertex. [стр. 2 ⇒]

Вполне возможно, что вам будет сложно выделить нужные объекты. Дело в том, что поверхности односторонние, и с внутренней стороны 3ds Max не позволяет их выделять. Не стесняйтесь вращать вид в окне проекции, "загляните" снизу. • Выделите все объекты верхней части (либо нижней, не важно), включите трехмерную привязку по вершинам, "схватитесь" за угловую вершину одного из лепестков и перенесите все объекты к вершине соответствующего лепестка другой половины (рис. 2.31, д). Главная панель -> Select and Move (или клавиша ) Главная панель -> выберите View в выпадающем списке координатных систем Главная панель -> включите привязки (или клавиша ) Панель Snaps -> включите кнопку Snap To Vertex Toggle (если вы сделали эту панель видимой, в противном случае откройте диалогавое окно Grid and Snaps Settings и установите флажок Vertex во вкладке Snaps, остальные флажки снимите) • Выделите любой объект, но лучше, если это будет нижняя крышка, и преобразуйте его к типу редактируемых полигонов и присоедините (Attach) к нему все остальные объекты. Квадрупольное меню -> Convert to -> Convert to Editable Poly Квадрупольное меню -> "окошко" в строке Attach В открывшемся диалоговом окне выберите все обьекты и нажмите Attach... [стр. 130 ⇒]

Vertex attribute arrays are naturally assigned to the vertices of the output graph and commonly contain properties such as vertex name, size, or spatial position (where appropriate). Edge attributes are likewise assigned to the edges of the output graph but also encode the graph connectivity. The vtkTableToGraph filter creates one or more edges for each row in the edge table by following a template called the link graph. The link graph is a graph which has one vertex for every column in the edge table. The edges in the link graph specify how to create edges from each table row. Figure 12 demonstrates this translation. On the left is the input edge table, in the center is the link graph, and on the right is the resulting graph. The link graph may connect an arbitrary number of columns in arbitrary patterns such as full connectivity (cliques), paths, or stars. To D E... [стр. 6 ⇒]

Although vtkTableToGraph can create graphs of nearly arbitrary complexity, we do not often need its power when creating trees. Instead, we use two filters, vtkTableToTree and vtkGroupLeafNodes, that in combination produce arbitrary hierarchies. First, vtkTableToGraph takes a table as input and creates a simple two-level tree as output. A single vertex is created to be the root of the tree. Next, we create one new child of the root vertex for each row in the input table. Once all the data exist in this trivial tree structure we use vtkGroupLeafNodes to organize it. We use a series of vtkGroupLeafNodes filters to organize a tree into multiple levels. Each instance of vtkGroupLeafNodes adds one level to a tree, just above the leaf nodes, that groups the leaves based on the values of some vertex attribute. The order in which these groupings are applied is reflected in the order of the vtkGroupLeafNodes instances within the pipeline. This is illustrated in Figure 13. 7... [стр. 6 ⇒]

Если созданная форма вас не устраивает, подкорректируйте ее. Для этого на командной панели перейдите на вкладку Modify (Редактирование). В стеке модификаторов щелкните на плюсике справа от названия Line (Линия), переключитесь на уровень редактирования Vertex (Вершины) и измените положение и тип вершин. Когда форма будет готова, перейдите на уровень редактирования Spline (Сплайн). Сплайнпуть должен быть двойным, так как он задает толщину стенок будущей модели. По этой причине в свитке Geometry (Геометрия) найдите кнопку Outline (Контур), в счетчик рядом с кнопкой введите 2 см и нажмите Enter (рис. 3.31). 4. Есть еще одна проблема: сплайн замкнут. Это неправильно, путь должен быть незамкнутой фигурой. Для решения этой проблемы переключитесь на уровень редактирования Segment (Сегмент), выделите маленький сегмент, замыкающий форму внизу (рис. 3.32), и удалите его. Переключитесь на уровень редактирования объекта, то есть в стеке модификаторов щелкните на строке Line (Линия). 5. Выделите звезду. Активизируйте вкладку Modify (Редактирование) командной панели и раскройте список модификаторов. Выберите модификатор Bevel Profile (Скос по профилю). В свитке Parameters (Параметры) нажмите кнопку Pick Profile (Выбрать профиль) и щелкните на сплайн Line (Линия) в любом окне проекции. 6. Получившийся трехмерный объект зависит от двухмерных, из которых был создан. Поэтому, если модель не соответствует желаемой, выделите сплайнпуть Line (Линия), переключитесь на уровень редактирования Vertex (Вершина) и, управляя вершинами, измените размер сплайна. При изменении сплайна будет изменяться и сама трехмерная форма. Сохраните файл под именем Цветочный горшок. [стр. 74 ⇒]

Магическая Применение модификаторов, создание составных объектов, сплайновое моделирование — это далеко не все возможности программы 3ds Max. Чтобы сделать объект со сложной геометрией, необходимо использовать и другие средства, например полигональное моделирование. Это, пожалуй, самый интересный способ моделирования. Дело в том, что поверхность любого объекта программа рассматривает как набор вершин, ребер, граней и других элементов, положение которых можно изменять. Элементы, входящие в состав трехмерной модели, называются подобъектами. Поверхность, которая состоит из управляющих подобъектов, называется редактируемой. Редактируемую поверхность можно сравнить, условно, конечно, с глиной, из которой вы можете вылепить любую форму. В 3ds Max есть несколько типов редактируемых поверхностей: Editable Mesh (Редактируемая сетка) — поверхность, состоящая из треугольных граней. При работе с редактируемой сеткой можно использовать режимы редактирования Vertex (Вершина), Edge (Ребро), Face (Грань), Polygon (Полигон) и Element (Элемент); Editable Polу (Редактируемая полисетка) — поверхность, состоящая из многоугольников. Для работы с такими объектами можно использовать режимы редактирования Vertex (Вершина), Edge (Ребро), Border (Граница), Polygon (Полигон) и Element (Элемент); Editable Patch (Редактируемая патчповерхность) — поверхность, состоящая из лоскутов тре... [стр. 107 ⇒]

Оно содержит уже известные вам структурные элементы: Vertex (Вершина), Edge (Ребро), Face (Грань), Polygon (Полигон) и Element (Элемент). Переключаясь на тот или иной уровень редактирования подобъектов, можно выделять соответствующие подобъекты и работать с ними. Как вы уже знаете, прежде чем чтонибудь сделать с объектом в 3ds Max, его обязательно нужно выделить. При работе с подобъектами действует тот же принцип: для выполнения любых операций с подобъектами их нужно выделить, а уже затем применять различные инструменты. Активный уровень подобъектов подсвечивается желтым цветом, а сам выделенный подобъект имеет красный цвет. В 3ds Max есть набор удобных инструментов, которые заметно упрощают выделение подобъектов. Их можно найти в свитке Selection (Выделение). В верхней части свитка Selection (Выделение) есть кнопки для быстрого переключения между уровнями подобъектов (рис. 5.3). Основные возможности изменения геометрии сетчатой поверхности собраны в свитке Edit Geometry (Правка геометрии) (рис. 5.4). Команды редактирования на уровне объекта (то есть при выделенной строке Editable Mesh (Редактируемая сетка) в стеке модификаторов) действуют на всю сетку, но, как и в случае сплайнового моделирования, для редактирования подобъектов используется соответствующий уровень, то есть редактирование вершин осуществляется на уровне редактирования Vertex (Вершина) и т. д. [стр. 110 ⇒]

Many of these viruses are “temperate,” meaning that they have available an alternative life-style in which they coexist with the host as a “prophage,” with the expression of most but not all phage genes shut off. In most cases, the prophage is integrated into the host chromosome (e.g., Escherichia coli phage ␭), but some prophages are extrachromosomal plasmids, either circular (e.g., E. coli phage P1) or linear (e.g., E. coli phage N15). The lysogenic life cycle, as this association is called, is thought to exert an important influence on both the evolution of the virus and the evolution of the host. In the case of virus evolution, this is because any phage infecting a cell is likely to encounter prophage DNA with which it might potentially recombine. In the case of host evolution, one of the most efficient ways for novel genes to enter a bacterial genome is as part of a prophage, and there are many examples of prophage-harbored genes that alter the phenotype of the host (34, 35). The virion capsid, known as the “head” for these viruses, is made of protein with no lipid. There is typically one major structural subunit (the major capsid protein) making up the protein lattice of the capsid, arranged in hexamers and pentamers, closely following the icosahedral symmetry and “quasiequivalent” packing predicted by Caspar and Klug (40). In some cases, the capsid is prolate, that is, elongated along one axis of the icosahedron (e.g., myovirus T4). There are also usually other proteins associated with the capsid in various roles, and all of these phages have a “portal” (called a “connector” in some phages), a dodecameric ring located at one vertex of the capsid. The portal, among other duties, marks the vertex of the capsid to which the tail will attach. The tail is the structure that attaches the virion to the cell and engineers the entry of the DNA into the cell at the beginning of infection (208). For purposes of taxonomy, the order Caudovirales is divided into three families based on tail morphology (111): the Siphoviridae, with long noncontractile tails; the Myoviridae, with long contractile tails; and the Podoviridae, with stubby tails (Fig. 1). These divisions provide a convenient way for us to talk about the differences in the phages’ tail... [стр. 4 ⇒]

Figure41 Системы Координат Координатные углы цилиндрической и сферической систем координат ( q и F) всегда выражаются в градусах. Позже, при создании КЭ модели, системы координат помогают установить основные направления отображения результатов анализа. В MSC.Patran очень просто использовать переменные системы координат, и они тесно связаны с операциями геометрического моделирования. Почти все опции, использующие координатные данные, имеют возможность создания локальной системы координат для ввода данных. Примитивы низшего порядка Топологические примитивы определяют смежность геометрических примитивов и устанавливают подкомпоненты примитивов более высокого порядка. Каждый геометрический примитив имеет свой номер. MSC.Patran устанавливает номер топологического примитива, соответствующего смежному объекту более высокого порядка. Например, ввод в строку данных Surface 4.2 определит ребро Edge 2 поверхности Surface 4. Каждая кривая, поверхность и тело в MSC.Patran имеет набор определенных топологических примитивов: Определяет топологическую конечную точку кривой или угол поверхности или Vertex (вершина) тела. Vertex - это подкомпонент кривой. (Каждая точка ссылается на vertex, но не наоборот) Определяет топологическую кривую на поверхности или теле. Edge - это Edge подкомпонент поверхности или тела. (ребро)... [стр. 55 ⇒]

Смотреть страницы где упоминается термин "vertex": [42] [9] [175] [189] [12] [13] [209] [162] [22] [27] [28] [114] [38] [67] [4] [5] [28] [327] [334] [442] [443] [475] [486] [78] [7] [63] [152] [116] [131] [132] [269] [270] [270] [425] [505] [35] [48] [12] [4] [60] [308] [93] [113] [116] [17] [31] [59] [60] [67] [1]