Fiber-dependent Approach For Fast Dynamic Character Animation
Fiber-dependent Approachfor Fast Dynamic Character AnimationAyano KanedaWaseda Universitydizzy-miss-lizzy@moegi.waseda.jpTsukasa FukusatoWaseda Research Institute for Science and Engineeringtsukasa@moegi.waseda.jpYoshihiro FukuharaWaseda Universityfyoshi@ruri.waseda.jpTakayuki NakatsukaWaseda Universityt59nakatsuka@fuji.waseda.jpShigeo MorishimaWaseda Research Institute for Science and Engineeringshigeo@waseda.jpAbstracting, linear blend skinning, multi-layer systemCreating secondary motion of character animation including jiggling of fat is demanded inthe computer animation. In general, secondarymotion from the primary motion of the character are expressed based on shape matchingapproaches. However, the previous methodsdo not account for the directional stretch characteristics and local stiffness at the same time,that is problematic to represent the effect ofanatomical structure such as muscle fiber. Ourframework allows user to edit the anatomicalstructure of the character model correspondingto creature’s body containing muscle and fatfrom the tetrahedral model and bone motion.Our method then simulates the elastic deformation considering anatomical structures defineddirectional stretch characteristics and stiffnesson each layer. In addition, our method can addthe constraint for local deformation (e.g. biceps)considering defined model’s characteristics.Keywords: fiber definition,shape match-1 IntroductionCharacter animation has been advanced usingphysically-based simulations for expressive animation, in particular, secondary motion, whichbreathe life into characters with the jiggling andwobbly action. Using a rig or a skeleton is anefficient method for generating the secondarymotion of a character. One of the approachesis skinning, which conditions the surface meshof the object by mapping from a skeletal structure. In some approaches, the model is deformed into the required shape using exampledata (e.g., character pose designed by artists andresult shapes based on physical simulation) assigned to each model. Others approaches integrate voxels or anatomical construction into thecharacter model to generate more lifelike movement and to preserve the volume of the character model. However, due to the complexity of setting anatomical effects such as inter-CASA 20171
action between muscle and fat, dynamic animation remains an unintuitive and time-consumingprocess. Moreover, the anisotropic deformation based on muscle fiber orientation requiresheavy burden on setting apposite parameters todesign lifelike character animation. In this paper, we propose a novel method for expressing secondary motion easily from a skeletalcharacter animation with a multi-layer systemand anatomical fiber vectors. We integratethe anatomical parameters (local anisotropy andstiffness) into the input model, which is a volumetric tetrahedral mesh. Then, we simulate theelastic deformation using the shape matching algorithm owing to the small computational costand robust simulation. Our method can add stiffness and fiber orientation to local regions in themodel and can express elastic deformation withanisotropy response. To consider secondary motion, our framework propagates both the internaland the external force over the object volume. Inaddition, the volume of the model is preserved.Our method makes three contributions to the developments of the lifelike character animation: allows easy setting of anatomical parameters based on intuition incorporates elastic deformation considering the fiber orientation adds constraint for the partial deformation(e.g., biceps)2 Related WorkIn character animation linear blending / interpolation approaches, as well as non-linear mapping approaches, which involve controlling askeleton using a range of values from real-timeand closed-form skinning, are used. Jacobson etal. [1] propose an efficient algorithm that computes skinning weights by minimizing the nonlinear rigidity energy. In addition, Kavan et al.[2] improve skeleton-based character animation,which approximates a non-linear elastic deformation to an elastic energy function and a jointbased deformer. While these approaches deliverhigh-quality primary animations, designing lifelike animations including secondary motion isstill difficult using these methods only. In general, dynamic skin deformation with interactiveapplications and frequent conformations of theresult action are in high demand for animators.Mukai et al. [3] propose a helper bone controller that maps the primary skeleton motionto the dynamic movement of helper bones using the trained motion sequences consisting ofskeleton motions and corresponding skin deformations. The helper bone controller enables non-linear and complicated deformationsby considering the effect of soft-tissue dynamics, but does not consider mesh-to-mesh interaction (collision and self-collision) against external force. To overcome these problems, two approaches have been investigated: (1) rig-spaceapproaches (the subspace energy minimizationwith rigging controls and (2) physically-basedapproaches. Rig-space approaches [4, 5, 6] describe the mesh deformation as linear modes.In these approaches, it is difficult to consideran anisotropic response and design a multi-layersystem composed of spaces of bone, muscle, fat,and skin to simulate the interaction between layers. In addition, rig-space approaches requirehigh computational costs due to the non-linearproperties of the rig. In contrast, physicallybased approaches integrate anatomical knowledge into computing. Teran et al. [7] and Fanet al. [8] indicate that the volumetric shape withbones, which function as rigid constraints andpreserving the pose is informative for a lifelikecharacter animation. Liu et al. [9] and Rumman et al. [10] report handling of mesh deformation with collisions against surrounding environment. In particular, McAdams et al. [11]demonstrated self-collision of the model withsoft tissue deformation in interactive time. Unfortunately, previous physically-based proposalshave common problems: the stability of simulation and the computational cost depend on timestep width. We solve these problems using ashape matching algorithm [12], which is a fastand robust method for simulating elastic deformations.Use of a shape matching algorithm allowssecondary movements to be controlled withphysical parameters and designed intuitively bya multi-layer model. Shape matching imposesgeometric constraints which optimize the positions of vertexes using elastic energy to thesimulation of a deformable object. Chen et al.[13] propose a robust method to preserve the ob-CASA 20172
Figure 1: Overview: We make the clusters for each body layer to the mesh model. Each layer has theconstraints (stiffness and fiber vector) set by a user. We then compute the mesh deformationusing Linear Blending Skinning for the primary deformation and fiber-dependent ShapeMatching for the secondary deformation.ject volume during deformation. However, theydo not focus on anatomical feature of character model with a multi-layer system because thevolume spaces overlap each other. Their methoddoes not properly account for secondary motionsuch as fat jiggling because of its strong volume preservation. Iwamoto et al. [14] suggesta simple multi-layer approach which can handle secondary motion. They divide the modelinto multiple layers imitating anatomical structure such as bone, muscle, and fat. They thensimulate elastic deformation of the body by considering stiffness defined on each layer. Thissimple multi-layer approach succeeded in simulating secondary motion with the different stiffness values for each layer. However, as the directional stretch characteristics in the model arenot considered, that is problematic to considerthe effect of anatomical structure such as muscle fiber. Ijiri et al. [15, 16] add fiber orientation constraints which represent the expansionand contraction direction of the motion to generate character animation of flexible bodies. However, many complicated inputs are required toadjust the model behavior. In addition, as thepartial stiffness cannot be represented withoutdirectly adding motion data into local regions,generating secondary motion such as jiggling offat from the skeletal motion remains problematic.Our method solves these problems by elastic deformation considering partial directionalstretch characteristics and stiffness at the sametime. Our goal is to express the effect of anatomical fiber vectors which have the local directional stretch characteristic for secondary motion.3 MethodsOur system generates 3D dynamic animationfrom skeletal motion data and a tetrahedroncharacter model. We construct a local region,a set of one vertex connecting its immediateneighbors. The local region can represent overlap of neighboring local regions, which playa role in transmitting the force from the outside gradually using shape matching. We firstspecify several fiber orientations of local regionsuch as muscle and skin for stretchable (or nonstretchable) constraints. When a user sets theconstraints, the global fiber field is calculatedautomatically calculated automatically from acharacter structure such as the bone direction,and the user specified constraints.(Section 3.1).Based on the fiber vector field, it is possible tohandle stretchable orientation of model mainlyinspired by the human body structure. In ad-CASA 20173
other layers. Our method allows a user to chooseβ [0.0, 1.0] in each layer.3.3 Global Fiber Vector Field DefinitionFigure 2: Layer clustering with the bunnymodel: (a) bone, (b) muscle and (c)fat. Each layer is clustered by the distance from bone. A user can edit thevolume of each layer.dition, we define a multi-layered model, whereeach layer has two parameters for designingdifferent movements. In addition, our methodenables to represent the locally large deformation using the constraints based on joints’ angleinformation with volume preservation (Section3.5).3.1 Body Structure ClassificationWe partition the model into multi-layers to formthe anatomical structure of the character modelcorresponding to creature’s body. These layers mainly imitate the anatomical tissue layerssuch as bone, muscle, and fat, and each cluster can be given different motion. In the bonelayer, we manipulate the surface mesh of bonelayer by linear blend skinning. This illustratesthe primary deformation of the model. To express the secondary deformation, the other clusters simulate the elastic deformation based onshape matching (Section 3.4). In this paper, wedivide into the layers by distance from the bone.In addition, our method allows a user to set optional layers manually to improve the quality ofthe mesh deformation.3.2 Setting Fiber ParametersWe set the fiber parameters on each body layerto express the detailed secondary deformation.Each body layer has two parameters: (1) α [0.0, 1.0] is the stiffness that determines howthe model maintain the original shape, and (2)β [0.0, 1.0] is the weight of the fiber vector,which represents how the fiber vector effect. Weadopt α which decreases the value according tothe distance from the bone layer. In addition,the muscle layer has bigger value of β than theWe need to assign the fiber vector δ R3 toeach local region (one-ring neighborhood) in order to apply the fiber orientation to the model.Given the sets of the constraint vectors, ourmethod automatically computes the global fibervectors by interpolating. In this paper, the interpolation is propagated for the entire tetrahedralmesh by Laplacian smoothing [17] as follows:li δ i ρij δ j(1)j M(minδi li 22 λi ) δ k ck 22(2)k Cwhere N i is the number of vertexes, M j is the set of one-ring neighboring vertexes ofi th vertex, C k is the number of user inputs,q i is the position of a vertex, λ is the coefficient(in this paper, λ 1.0 103 ), ρij is the weightfrom Nj and ck is the user-specified constraint.The weight ρij is given by the following:exp ( rij )k Nij exp ( rij )ρij (3)where rij is the Euclidean distance between theposition q i and q j . In consequence, the globalfiber vector field can be automatically generated.For a character model, we set the constraints onthe bone layer and the surface mesh based on theanatomical structure of the body. Our methodis inspired from Saito et al. [18] that musclefibers tend to point in the same direction fromone tendon to another. We set the constraint vectors on the bone layer, to be parallel to the bonedirection. In addition, we add constraint vectorsalong the surface using an orthogonal unit vectorto the the surface.3.4 Fiber-dependent Shape MatchingAlgorithmWe update the position q i and the velocity piof i-th vertex of the model based on the shapeCASA 20174
where Nr i is the set of vertexes in the local shape, Tr is the scaling matrix, and ci is thecenter of the mass for the local region Nr as following equation: ri Nr wi q i ci r .i Nr wiFigure 3: The orientation of fibers for each local region. The result is interpolatedby constraints tangential to bone andsurface mesh.(8)where wir represents orientation-dependentweights of the local shape and we explain inSection 3.5. The relation between the restposition q 0i and its center of the mass c0i is thesame as q i and ci in equation (8). In addition,we compute the rotation matrix R to fit theprevious pose into the current pose for eachlocal shape. In our method, we determine Rr ofNr using the method of Muller et al. [19].argminRr ()2wir Rr brest bcurrii(9)i NrGiven the fitting rotation matrix Rr , we estimatethe goal position of i-th vertex in Nr as followequation:Figure 4: Algorithm of shape matching. Tocompute the goal position g i of particle i in local region r, the rest pose ofthe region is appropriately deformedby scale matrix Tr . We then minimizethe rotation matrix Rr between a current pose and a rest pose.matching algorithm as follow:gi qif ext h ihmi′′q i q i hpip′i pi α()g ri Rr Tr q 0i c0r crThen, as one vertex presents in multiple localregions, the goal position g i is obtained by thelinear sum which is weighted from the each local shape and the fiber constraints as followingequation: r r{r i Nr } wi g ir{r i Nr } wi(4)gi (5)where h is the time step, f extis the externaliforce against i-th vertex, mi is the mass, and g iis the goal position for i-th vertex respectively.α [0.0, 1.0] is the stiffness parameter. Then,we need to determine the goal position g i . To focus on the local region Nr i, the relative vectors with respect to its center of mass ci , bcurriand brestare described as below:ibcurr (q i ci )i(6)brest Tr (θ)(q 0i c0i )i(7)(10)(11)3.5 Fiber-dependent Anisotropy ResponseFiber OrientationWe deform the vertexes considering the fiberorientation defined for each local region, whichrepresents the direction of easy contraction. Inthe process of computing the mass center of local regions and blending the effect of belonging local regions on the given vertex, weighting coefficients could affect the deformationCASA 20175
anisotropy.(s · r i )2(12) r i 22 0k Nr mk q k0ri qi (13)k Nr mk1(14)s β 2 (1 β)2()ri βv i (1 β) r i wir mi Figure 5: Using the additional constraint on biceps. Biceps are induced by the anglebetween an upper arm and a lower armwith the constraint.By setting β for each layer (Section 3.1), we adjust the effect of fiber vector on each layer. Inour framework, for the fat layer β is set as 0.0,denoting the layer has no fiber, and in musclelayer almost 1.0, which expresses that the muscle is difficult to move in the direction along thefiber orientation.3.6 Muscle-inspired constraint andVolume PreservingOur method can add local deformation intothe model easily, by setting a additional constraint. In character animation, when the character bends his arm, his biceps builds. Whenthe human flexes his arm, biceps brachii musclestands out and triceps brachii muscle extend atthe same time. In addition, we assume that upper muscle bulges perpendicularly to the muscle fiber orientation as in [18]. In this paper, weadd a simple constraint to elbow joint, and represent the flexing model’s biceps using definedfiber orientation.Ti (θ) DMDT c(θ)01 c(θ) 2M 000 (15)0 0 (16)1 2c(θ)c (θ) β sin θ ni · τ 1.0(17)where θ is horn angle of the forearm and bicep,ni is the unit vector, perpendicularly to the fiberorientation of i-th local region from the closestbone layer’s surface, and τ represent the unitvector orthogonal to the plane made by the armsections. Matrix D consists of three vectors, d1is represented by ni and two vectors d2 and d3 ,and d1 , d2 , d3 constructs a normalized orthogonal basis at Ni . D represents the orientationFigure 6: The effect of the fiber vector undergravity. The results show that thebar stretches when the the fiber vector is orthogonal to gravity (b), andnot when parallel (c) compared withno fibers (a).Table 1: The parameter of Figure 8modelαM βM αF βFIwamoto et al.1.0 0.0 0.3 0.0our method (i)1.0 1.0 0.3 0.3our method (ii) 1.0 1.0 0.3 0.3our method (iii) 1.0 1.0 0.3 1.0field. This effect is added on the muscle layerby adjusting β, which is almost zero in fat layer.In addition, the determinant of matrix Ti 1.0.Matrix Ti represents the scale change of the local region Ni . Therefore, the volume could bepreserved in each region when the determinantof matrix Ti 1.0. In particular, it is difficultto handle the partial deformation without precomputation and example data. However, ourapproach allows users to easily design the motion in the local region using defined fiber vectorfield.CASA 20176
Figure 7: Comparison with different settings of β parameters under gravity.Figure 8: Comparison with various setting of α and β parameters in multi-layers.Figure 9: Dynamic character deformation, ”a jumping animation,” simulated by our method.4 Resultconsequence, our method can add fiber properties to the model using this weight.Bar (gravity): Figure 6 shows the dependencyof fiber vector. As shown in Figure 6, the baris more rigid parallel to the fiber vector than orthogonal to one. As set the weight in equation(12), calculated goal position tends to get thelarger weighted parallel to the fiber vectors. InBar (beta): We also represent the effect of βparameter in Figure 7. These four bars have different β parameter, the left as β 0.0, the leftmiddle as β 0.6, the right middle as β 0.75and the right as β 1.0 and all fiber vectorsCASA 20177
using these two parameters (our method (i), (ii)and (iii)). Our method allows user to extend theexpression.Patrik (jumping-animation): As a result, wegenerate character animation in Figure 9 underthe effect of α and β. In Figure 9, we set musclelayer as αM 1.0, βM 1.0, and fat layeras αF 0.3, βF 0.0. As shown in Figure 9, the movements of the fat lags behind theinput skeletal movement when the model jumps.Based on fiber vector field defined by constrainton bone and surface mesh, we easily add thefiber vectors effect to secondary motion generation.Figure 10: Arm simulation with the additionalconstraint on biceps. The results obviously prove the difference in thedeformation because of the value ofβ. (a) and (b) set β as 0.0, and (c)and (d) set β as 1.0.are orthogonal to the floor. As shown in Figure 7, each bar demonstrates different deformation due to the effect of β. The bar with β 0.0represents the isotropic rigidness and then tendsto have directional stretch feature with increasing β. In these model, the fiber vectors work asbellows structure . Then, as increasing β parameter, these model tend to more and more hangdown under gravity.Bar (multi-layer): We also compare the barmodel deformation under only the effect of αand α and β in Figure 8. These bars divided intomulti layers. The left layer as α 1.0and layeras α 0.3 and two layer set β as zero. It showsthe deformation like Iwamoto et al. [14] withonly stiffness parameter model. The layer set assmall β to decrease the rigidness and Iwamotoet al. [14] expresses the jiggling of fat using thedifference of rigidness. The other bars are setnon-zero value for each layer and α, β. In addition to the effect of the difference of the rigidness, these model represent the effect of fibervectors and its difference of weights betweenlayers. The bar bends more smoothly by the effect of the fiber vectors and we can design thedeformation than only stiffness model. As a result, we design these three differential motionBiceps: In Figure 10, we simulate the biceps.Figure 10 shows the effect of constraint for biceps. The results obviously prove the differencein the deformation from the value of β. (a) and(b) set β as 0.0, and (c) and (d) set β as 1.0. Weevaluate the volume change rate of (c) and (d) βas 1.0 for (a) and (b) β as 0.0 through the armbending motion. Then, we success in expressing biceps building with constraint. The average rate of the volume change of the model withMuscle-inspired constraint is only 0.291 percentfrom non-constraint model’s volume. Althoughwe contract local regions in the model with constraint, the total volume of the computed goalposition is almost same as the result of normalshape matching. Thus, our framework can design the partial deformation using defined fibervector field and additional constraint.Computational cost: In table 2, we reports ourtesting scenarios and the run time of our method.We executed on an Intel i7-4910MQ CPU at2.90GHz. All scenarios are produced relativelyfast. In addition, we would also like to furtherenhance the computational speed by implementing GPU-based solutions in the future.4.1 LimitationOur approach is inherently limited in physicalaccuracy because of its pure and geometrical nature, since it is based on shape matching algorithm. However, allowing a user to edit and simulate in real time is more important in the context of art-directed animation than physical ac-CASA 20178
Table 2: Model statistics and simulation timingsmodelbar (gravity)bar (beta)bar curacy. Our framework can express secondarymotion such as jiggling of fat and biceps. However, computing sagging faces is challenging inour framework. It needs additional constraintbetween skin and fat, then we have to considerskin layers. Due to lack of muscle fiber connections, when a character twists his arm, thestreaks of muscles’ effect need optional constraints on fibers.4.2 Conclusion and Future workWe have presented a system for generating dynamic character animation from a skeletal motion. Our proposed method consists two steps:(i) defining the multi-layer system with fibervectors ,(ii) computing a global shape withanisotropy responses using the shape matching algorithm. Our method employs fiberdependent parameters into the shape matchingalgorithm; it consequently achieves the simpleand intuitive control for the anisotropic stiffnessand motion of the character shape. As a result,our method performs expressing the effects ofanatomical fiber vectors which have the localdirectional stretch characteristics for secondarymotion. We believe that our system can assist toapply the unwieldly physically-based animationinto user-friendly application systems. In addition, we would like to attempt automatically estimating the parameters from captured data suchas sensing devices or video sequence.AcknowledgementsWe would like to thank Naoya Iwamoto and Tatsuya Yatagawa for their precious advices.Thisproject was supported in part by ACCEL, JST.References[1] A. Jacobson, I. Baran, L Kavan, J. Popovi,and O. Sorkine. Fast automatic skinningtransformations. ACM Transactions onGraphics, 31:1–10, 2012.[2] L. Kavan and O. Sorkine. Elasticityinspired deformers for character articulation. ACM Transactions on Graphics,31:1, 2012.[3] T. Mukai and S. Kuriyama. Efficient dynamic skinning with low-rank helper bonecontrollers. ACM Transactions on Graphics, 35:1–11, 2016.[4] F. Hahn, S. Martin, B. Thomaszewski,R. Sumner, S. Coros, and M. Gross. Rigspace physics. ACM Transactions onGraphics, 31:1–8, 2012.[5] F. Hahn, B. Thomaszewski, S. Coros,R. Sumner, and M. Gross. Efficient simulation of secondary motion in rig-space.ACM Transactions on Graphics, 31:165,2013.[6] H. Xu and J. Barbic. Pose-space subspacedynamics. ACM Transactions on Graphics, 35:1–14, 2016.[7] J. Teran, E. Sifakis, S. Blemker, V. Hing,C. Lau, and R. Fedkiw. Creating and simulating skeletal muscle from the visible human data set. IEEE Transaction on Visualization and Computer Graphics, 11:317–328, 2005.[8] Y. Fan, J. Litven, and D. Pai. Active volumetric musculoskeletal systems. ACMTransactions on Graphics, 33:1–9, 2014.[9] L. Liu, K. Yin, B. Wang, and B. Guo. Simulation and control of skeleton-driven softbody characters. ACM Transactions onGraphics, 32:1–8, 2013.[10] N. Rumman and M. Fratarcangeli. Position based skinning of skeleton-drivendeformable characters. Proceedings ofthe 30th Spring Conference on ComputerGraphics - SCCG ’14, 1:83–90, 2014.CASA 20179
[11] A. McAdams, Y. Zhu, A. Selle, M. Empey,R. Tamstorf, J. Teran, and E. Sifakis. Efficient elasticity for character skinning withcontact and collisions. ACM Transactionson Graphics, 33:153:1–153:12, 2014.[12] M. Muller, B. Heidelberger, M. Teschner,and M. Gross. Meshless deformationsbased on shape matching. ACM Transactions on Graphics, 24:471–478, 2005.[13] C.-H. Chen, M.-H. Tsai, I.-C Lin, and P.H. Lu. Skeleton-driven surface deformation through lattices for real-time character animation. User Modeling and UserAdapted Interaction, 29:241–251, 2013.[14] N. Iwamoto, H. Shum, L. Yang, andS. Morishima. Multi-layer lattice modelfor real-time dynamic character deformation. Computer Graphics Forum, 34:99–109, 2015.[15] T. Ijiri, K. Takayama, H. Yokota, andT. Igarashi. Procdef: Local-to-global deformation for skeleton-free character animation.Computer Graphics Forum,7:1821–1828, 2009.[16] T. Ijiri, T. Ashihara, N. Umetani,T. Igarashi, R. Haraguchi, H. Yokota,and K. Nakazawa. A kinematic approachfor efficient and robust simulation of thecardiac beating motion. PLoS ONE, 5:1–9,2012.[17] K. Takayama, T. Igarashi, R. Haraguchi,and K. Nakazawa. A sketch-based interface for modeling myocardial fiber orientation. Proceedings of the 8th internationalsymposium on Smart Graphics, pages 1–9,2007.[18] S. Saito, Z. Zhou, and L. Kavan. Computational bodybuilding: Anatomically-basedmodeling of human bodies. ACM Transactions on Graphics, 34:41, 2015.[19] M. Muller, J. Bender, N. Chentanez, andM. Macklin. A robust method to extractthe rotational part of deformations. Proceedings of ACM SIGGRAPH Conferenceon Motion in Games, pages 2–7, 2016.CASA 201710
3.3 Global Fiber Vector Field Definition We need to assign the fiber vector 2 R3 to eachlocalregion(one-ringneighborhood)inor-der to apply the fiber orientation to the model. Given the sets of the constraint vectors, our method automatically computes the global fiber vectors by interpolating. In this paper, the inter-
Bruksanvisning för bilstereo . Bruksanvisning for bilstereo . Instrukcja obsługi samochodowego odtwarzacza stereo . Operating Instructions for Car Stereo . 610-104 . SV . Bruksanvisning i original
10 tips och tricks för att lyckas med ert sap-projekt 20 SAPSANYTT 2/2015 De flesta projektledare känner säkert till Cobb’s paradox. Martin Cobb verkade som CIO för sekretariatet för Treasury Board of Canada 1995 då han ställde frågan
service i Norge och Finland drivs inom ramen för ett enskilt företag (NRK. 1 och Yleisradio), fin ns det i Sverige tre: Ett för tv (Sveriges Television , SVT ), ett för radio (Sveriges Radio , SR ) och ett för utbildnings program (Sveriges Utbildningsradio, UR, vilket till följd av sin begränsade storlek inte återfinns bland de 25 största
Hotell För hotell anges de tre klasserna A/B, C och D. Det betyder att den "normala" standarden C är acceptabel men att motiven för en högre standard är starka. Ljudklass C motsvarar de tidigare normkraven för hotell, ljudklass A/B motsvarar kraven för moderna hotell med hög standard och ljudklass D kan användas vid
LÄS NOGGRANT FÖLJANDE VILLKOR FÖR APPLE DEVELOPER PROGRAM LICENCE . Apple Developer Program License Agreement Syfte Du vill använda Apple-mjukvara (enligt definitionen nedan) för att utveckla en eller flera Applikationer (enligt definitionen nedan) för Apple-märkta produkter. . Applikationer som utvecklas för iOS-produkter, Apple .
Fiber damage, changes in the fiber wall structure, reduced single softwood kraft fiber strength and fiber deformations (curl, kinks and dislocations) all affected the fiber network properties. Mechanical treatment at the end of kraft cooking conditions resulted in fiber damage such that single fiber strength was reduced.
C A B L E B L O w i N ghand held Fiber Blower The Condux hand held fiber blower is ideal for shorter run fiber optic cable or micro fiber optic cable installations. The unit's hinged design makes it easy to install and remove duct and fiber. The Condux hand held fiber blower installs fiber from 0.20 inches (5.8 mm) to 1.13 inches (28.7 mm)
properties of fiber composites [1]. A number of tests involving specimens with a single fiber have been developed, such as single fiber pull-out tests, single fiber fragmentation tests and fiber push-out tests [2-4]. Yet it still remains a challenge to characterize the mechanical properties of the fiber/matrix interface for several reasons.
