LightGuide: Projected Visualizations for Hand Movement Guidance

Size: px
Start display at page:

Download "LightGuide: Projected Visualizations for Hand Movement Guidance"

Transcription

1 LightGuide: Projected Visuliztions for Hnd Movement Guidnce Rjinder Sodhi 1,2 Hrvoje Benko 1 Andrew D. Wilson 1 1 Microsoft Reserch One Microsoft Wy Redmond, WA 9852 {enko, wilson}@microsoft.com 2 Deprtment of Computer Science University of Illinois 21 North Goodwin Avenue, Urn, IL 6181 rsodhi2@illinois.edu c d Figure 1. An overview of the rnge of 3D cues we creted to help guide user s movement. In (), user is shown 2D rrow with circle tht moves in the horizontl plne, () shows 3D rrow, (c) 3D pth where lue indictes the movement trjectory nd (d) uses positive nd negtive sptil coloring with n rrow on the user s hnd to indicte depth. ABSTRACT LightGuide is system tht explores new pproch to gesture guidnce where we project guidnce hints directly on user s ody. These projected hints guide the user in completing the desired motion with their ody prt which is prticulrly useful for performing movements tht require ccurcy nd proper technique, such s during exercise or physicl therpy. Our proof-of-concept implementtion consists of single low-cost depth cmer nd projector nd we present four novel interction techniques tht re focused on guiding user s hnd in mid-ir. Our visuliztions re designed to incorporte oth feedck nd feedforwrd cues to help guide users through rnge of movements. We quntify the performnce of LightGuide in user study compring ech of our on-ody visuliztions to hnd nimtion videos on computer disply in oth time nd ccurcy. Exceeding our expecttions, prticipnts performed movements with n verge error of 21.6mm, nerly 85% more ccurtely thn when guided y video. Author Keywords On-demnd interfces, on-ody computing, pproprited surfces, trcking. ACM Clssifiction Keywords H.5.2 [Informtion interfces nd presenttion]: User Interfces. Input devices & strtegies. Permission to mke digitl or hrd copies of ll or prt of this work for personl or clssroom use is grnted without fee provided tht copies re not mde or distriuted for profit or commercil dvntge nd tht copies er this notice nd the full cittion on the first pge. To copy otherwise, or repulish, to post on servers or to redistriute to lists, requires prior specific permission nd/or fee. CHI 12, My 5 1, 212, Austin, Texs, USA. Copyright 212 ACM /12/5...$1.. INTRODUCTION When performing gestures tht re intricte or tht require gret del of technique, physicl feedck from n instructor cn often e useful for performing movement. For exmple, when someone wnts to perform the proper technique for weight trining exercise, n instructor often gives instntneous feedck y grdully correcting the position of the user s ody through physicl touch. While this exchnge seems crucil, the vilility of such resource disppers when user is no longer in the presence of n instructor. Insted, directing humn movement is usully ccomplished through video recordings, digrms, nimtions, or textul descriptions. We rely on evy of online resources tht include detiled grphicl imgery or do-it-yourself videos (see Figure 2). However, without incrementl nd rel-time feedck, interpreting nd following set of movements cn still e chllenge. In this pper, we explore n lterntive pproch to movement guidnce where ody movement cn e directed using projected visul hints. Our system, LightGuide, provides users with rel-time incrementl feedck for movement guidnce tht is projected directly on their hnd (see Figure 1). LightGuide provides unique enefit to existing gesture guidnce methods: users cn focus their ttention directly on the ody-prt rther thn divide their ttention etween video screen nd the movement. Users cn move their ody-prts freely in spce, relesing the user from lwys eing orientted towrds video screen. All our system requires is projector nd depth-sensing

2 cmer. While our system does not require user to e physiclly instrumented with device, these hints cn lso e used in ody-worn [12,13] or on limited-screen spce hndheld devices, such s smrtphones. Thus, our work provides three primry contriutions: First, we introduce series of unique visuliztions for movement guidnce tht incorporte feedck nd feedforwrd cues. Second, we contriute prototype system, LightGuide, which is comprised of single overhed projector nd depth-sensing cmer to sense the user nd their movements. Our proof-of-concept system fcilittes the disply of our visul hints on user s ody nd llows us to reply pre-recorded or system-generted 3D pths t userdriven pce or dynmiclly controllle speeds. Finlly, we show results of our quntittive comprtive evlution, qulittive user feedck nd discuss the pros nd cons of our pproch. MOTIVATION We cn envision numer of prcticl pplictions tht leverge on-ody projected hints for guidnce. For exmple, imgine n mteur thlete working on punching exercises during mrtil rts trining. With projected hints, the system cn direct the user towrds the optiml rech of the rm to ensure tht the shoulder is not overextended to cuse injury. In nother exmple, physicl therpy ptients recovering from n injury cn e guided through prcticing exercises t home. Novice musicins lerning to ply n instrument cn y directed to the correct posture when their form egins to drift. We elieve tht ll of these movements cn e guided with correct sptilly registered projections on user's ody. RELATED WORK Our on-ody projection pproch drws from vriety of fields, including computer-ided instruction, ugmented relity, nd projection-sed guidnce. Here we focus on the relevnt relted work from these res to position nd understnd the contriutions of the present work. Computer-Aided Tsk Guidnce Receiving tsk guidnce through computer-ided instruction hs een reserch focus for decdes. Demonstrtion through nimted-videos hve shown tht computer-sed instruction cn improve tsk performnce, prticulrly in ssemly sed tsks [31]. Plmiter nd Elkerton showed tht well plced textul hints with nimted videos cn lso give immedite enefits for tsk performnce [23]. Others hve explored dding grphicl visul hints to video in post to help users explore rnge of dnce movements [29]. While these hints re stticlly plced in video, previous literture hs lso looked t using co-locted rel-time feedck nd feedforword mechnisms to provide on-demnd ssistnce to guide users through gesturl tsks [3,11]. Such systems led users in-situ, while user is in the process of performing the gesture. Our work drws upon this prior reserch where we explore how co- Figure 2. Exmples of how people currently follow instruction for movement (e.g. Kinect virtul vtr, stretching, rhythmic dnce nottion [4]). locted projection-sed on-ody hints cn help show similr improvements for movement tsks. Tsk Guidnce in Augmented Relity The field of Augmented Relity (AR) hs shown numer of methods to provide guidnce y using hed-mounted displys or moile devices to convey instructions tht re superimposed on virtul or rel world video feeds [1,8]. Feiner et l. explored using AR to guide users through repiring lser printers. More recently [21,22], AR hs een demonstrted for vriety of tsks, such s plying the guitr or mnufcturing. In tngile AR, White et l. explored using vriety of grphicl representtions through ghosting to enle the discovery nd completion of gestures [32]. While these pproches re promising, hed-mounted displys cn e cumersome for users to wer nd diminutive screens cn constrin the user experience. Augmenting Environments with Projectors Recent dvncements in projection technology hve mde it possile to imue user s environments with projection cpilities [24,26,27,33]. For exmple, Wilson nd Benko explored using series of depth-sensing cmers nd projectors to trnsform room-sized environment to enle un-instrumented surfces (e.g., desk) to emulte interctive displys. In ddition, the emergence of miniturized projection technology hs opened up the possiility of ppropriting the user s ody s disply surfce where even user s hnd lone contins more surfce re thn typicl smrt phone [12,13]. In ddition to ody-worn projection systems, hndheld [5,6] nd hed-mounted projectors [15] lso llow users to e moile, without requiring their environments to e permnently instrumented with projectors nd cmers [18,2,25]. All of these projection-sed pproches re similr to our pproch using depth-sensing cmer for trcking nd projector to turn n ritrry surfce into n interctive disply. Projection-Bsed Guidnce The use of projection-sed ugmented relity AR for guiding users through tsks hs een reserch vision in recent yers [1]. Kirk et l. looked t using projection in remote collortive scenrios (e.g., remote Lego uilding) with rel-time projection guidnce co-locted next to the user s hnd on sttic desk [19]. Similrly, Rosenthl et l.

3 found tht comining sttic text nd pictoril instructions on screen with micro-projection sed guidnce on physicl ojects improved overll tsk performnce [28]. In contrst to prior literture, we explore projecting visulhints with rel-time feedck directly on the user s hnd tht is trcked in mid-ir for movement guidnce. DESIGN CONSIDERATIONS FOR GUIDING MOVEMENT To provide in-situ guidnce for the user s movement, visul hints need to convey sense of where to move next. We re motivted y the ide tht one cn co-locte the instruction for the movement with the ody prt tht needs to e moved long desired pth. To inform the design of such hints nd the vlidity of the overll pproch, we focused this work on projected hints on the user s hnd s it moves freely in spce. We elieve tht our pproch llows the user to focus their ttention on ody prt nd the movement itself. Through our initil explortion s well s leverging prior literture, we highlight six criticl spects tht need to e considered when designing on-ody guidnce hints: (1) feedck, (2) feedforwrd, (3) scle, (4) dimension, (5) perspective nd (6) timing. Feedck Feedck components provide informtion out the current stte of the user during the execution of the movement. This feedck cn come in the form of user s current position, the pth the they took (e.g., [3]), or their error or devition from the pth, to nme few. For exmple, with position, the feedck cn either e relyed to the user in reltive sense (e.g. user s projected progress long movement pth) or in n solute sense (e.g. user s solute devition from movement pth). Feedforwrd Feedforwrd components provide informtion to the user out the movement s shpe prior to executing the movement. As descried in [3,11], the feedforwrd cn come in the form of showing the user where to go next, segment of the movement pth hed, or simply show the user the entire movement pth. One possile downside for showing the whole movement is for sufficiently complex pths, pth self-occlusions my ostruct user s view of where to move next. Scle To gin insight into how to convey scle, we consider Steven s Power Lw which descries reltionship etween mgnitude of stimulus (e.g., visul length, visul re, visul color) nd its perceived intensity or strength (projected line, projected circle, projected intensity) [2]. Tht is, the reltionship llows us to understnd how users perceive visul cues, e.g., the re of circle, color, or the length of line, nd descries how well they convey the scle of movement (e.g., wht is the distnce I should move my hnd to get from point A to point B when projected line denotes distnce versus using re or color to denote distnce?). Dimension As found in [17] the wy in which the user perceives the structure of the tsk gretly ffects their performnce for high-dimensionl input. As such, how we convey where to move in three-dimensions depends on how intuitive the user finds the visul hint. For certin users, the most intuitive wy to get from point A to point B my e in the form of visul hint tht is roken down into two distinct components, e.g. where to move horizontlly nd verticlly. In contrst, for others, single metphor hint my e the most perceptully intuitive, e.g. go from point A to B ll in one simultneous tsk. Perspective One spect of conveying n on-ody visul hint is to explore egocentric nd exocentric viewpoints [3] (e.g. first person nd third person perspective, respectively) With n egocentric viewpoint, we wnt users to get greter sense of presence where the hints ecome nturl extension of their odies, reinforcing guidnce y tugging the user s hnd long the movement pth. In contrst, with n exocentric viewpoint, rther thn seeing guided hints emodied in the user, they re seen t n overview (e.g., video). Timing In our design of n on-ody visul hint, we feel tht there re two min pproches tht my effectively communicte timing in motion: system imposed timing nd self-guidnce. For system imposed timing, users follow visul hint tht is displyed t system specified speed. A visul hint cn convey rnge of dynmics, such s in keeping the speed constnt or chnging it dynmiclly throughout the movement. For self-guidnce, the user cn see visul hint nd choose the pce t which they rect to the hint. LIGHTGUIDE PROJECTED HINTS We descrie set of visul hints tht follow importnt spects of the design spce we hve highlighted. Our visul hints cn e used to help guide user s movement in ll three trnsltionl dimensions. To our knowledge, this is the first implementtion of on-ody projected hints for reltime movement guidnce. While this is rther lrge design spce with mny possile solutions, our itertive design process included n nlysis of 1D, 2D nd 3D visul hints nd offers set of compelling solutions tht cn inform future designs. We focus our descriptions on the finl hint design which resulted from our itertive process, ut encourge the reder to see the ccompnying video for more complete reference of lterntives. In this initil explortion we hve chosen to focus nd verify our ides y tckling hnd trnsltion first (i.e., movements in the x, y nd z dimensions), without ny rottions of the hnd. As such, we leve visul voculry for 3D rottions to future work. Follow Spot The Follow Spot cn e seen in Figure 3()-(). Through our initil pilots, we found the most intuitive metphor for

4 Positive Negtive Positive Negtive c d Figure 3. In ()-() the Follow Spot shows user white circle nd lck rrow reduces in size when user moves their hnd up, (c)-(d) the Hue Cue shows positive coloring (lue) which represents the direction user should follow horizontlly while moving wy from the negtive coloring (red). users ws to use 1D visul length (e.g. distnce), which is reflected in the mpping specified y Steven s Lw [2]. To specify feedck in depth, the 1D rrow points wy from the user to signl moving up nd points the rrow towrds the user to signl moving down. The size of the rrow dicttes the distnce to the trget depth position communicting the scle of the movement. Tht is, s the user moves up in the z-direction to hit trget depth s specified y lrge lck rrow pointing wy from the user, the tip of the rrow decreses in size until it ecomes lck horizontl line. The visul hint otherwise contins no feedforwrd mechnism. Hue Cue We crete visul hint tht utilizes negtive nd positive sptil coloring to indicte direction nd the spce user should occupy, shown in Figure 3(c)-(d). The cue uses comintion of sptil coloring in x nd y nd depth feedck in z to guide user s movement in three dimensions. The feedforwrd component is conveyed in the positive coloring, shown in lue nd the negtive coloring for feedck in red. To perform the whole movement, user cn continuously move towrd the lue nd wy from the red. In order for user to see if they re moving t the correct depth, Follow Spot hint is projected in the middle of the hnd. 3D Arrow We crete more direct mpping to visulize direction y conveying simple 3D Arrow to the user, shown in Figure 4()-(). The enefit of using 3D Arrow is tht direction for ll three dimensions, x, y nd z cn e conveyed in single metphor. Additionlly, to engge the user s egocentric viewpoint, we render the 3D Arrow from the user s perspective nd dd shding to emphsize its 3D shpe. 3D Pthlet We crete 3D Pthlet metphor where users re shown smll segment of the pth hed in the movement. This visul hint llows users to see segment of the pth, denoted in lue in Figure 4(c)-(d) s form of feedforwd. The red dot provides users with their reltive position, projected on the movement pth. The enefit of the 3D Pthlet is tht users cn see chnges in direction of curved motions long the pth well efore they execute the movement. Figure 4(c)-(d) shows user completing movement shped in the form of the lphet letter N Figure 4. In ()-(), the 3D Arrow is shown pointing down nd up, (c)-(d) the 3D Pthlet, shows the user (red dot) smll segment of wht is hed in the pth (denoted in lue). displyed t 45-degree ngle. Additionlly, for perspective, similr shdow is used to emphsize the 3D Pthlet s shpe. As shown in Figure 5, when the user distorts their hnd significntly, the 3D illusion is diminished. Movement Guidnce Algorithm LightGuide cn reply ny pre-recorded movement (e.g., recorded with depth sensor) or idel generted pth (e.g., prmetric wve). For pth, we summrize our lgorithm (Figure 6) s follows: The pth is first pre-processed into segments, where segment is composed of two points in the order with which we wish to guide the user. The pth is then trnslted to the user s current hnd position where the visul hint is rendered. As the user follows visul hint, ny devition from the pth cn result in n solute, relxed-solute or reltive projection (Figure 6()-(c)). The user continues through the pth using one of these three pproches until the pth is complete. The solute projection results in visul hint tht immeditely guides the user ck to the movement pth once devited, the relxed-solute movement slowly guides the user ck to the movement pth nd the reltive projection simply shows the user the next direction of the movement without requiring the user to e directly on the pth. Ech projection type is tsk dependent. For exmple, dncing movement my e less stringent out following the exct pth nd could thus use reltive projection. In contrst, n exercise movement where user cn potentilly strin muscle if done incorrectly my use n solute or relxed-solute projection. Bsed on our initil pilots, we chose to hve the Follow Spot use n solute mpping, the Hue Cue to hve reltive mpping in x nd y nd n solute mpping in z, while the 3D Arrow nd 3D Pthlet use reltive mpping. Shdow c d Figure 5. In (), the 3D Pthlet cretes n illusion of the pth extending eyond your ody where the shdow emphsizes the 3D nture of the hint. In (), the illusion is diminished when the user s hnd is orientted t n extreme ngle.

5 1 3 Depth-Sening Cmer Projector Pth Segments Current User Position Current Segment 2 Current Segment User Strt Position Current User Position c Current User Position Current Segment Current Segment Figure 6. Our lgorithm first reks down the pth into smller segments. The pth is trnslted to the user s current hnd position nd the visul hint is rendered to egin guiding the user. When the user devites from the desired pth, the visul hint cn, () direct the user ck to the closest point on the pth, () incrementlly ring the user ck to the pth, or (c) guide the user through reltive movement. Dynimcs For system imposed timing, LightGuide cn reply the visul hint so tht it follows the movement pth utomticlly in spce t ny speed. To ensure tht the visul hints do not move off of the user s hnd, we followed the sme procedure s [12] in which we compute derivtive mp of the depth imge to check for lrge chnges in the oundries t the contours of the hnd. Tht is, if the visul hint reches the contour of the hnd, it stops moving until user hs dequtely cught up to the pth. For the self-guidnce pproch, the system relies on the user to direct themselves through the movement. A visul hint descries the motion trjectory through feedck nd feedfowrd cues nd user cn choose their own pce. LIGHTGUIDE IMPLEMENTATION Our proof-of-concept LightGuide system, seen in Figures 7, consists of two primry components. First is commercilly ville Microsoft Kinect Depth Cmer, which provides 64x48 pixel depth imges t 3Hz. The second component is stndrd off the shelf InFocus IN153 wide-ngle projector (128x124 pixels) [16]. The depth cmer nd projector re oth rigidly mounted to metl stnd positioned ove the user. This ensures tht we could dequtely see the user s hnd motions s well s to ensure tht our projected visul hints would fully cover the user s hnds. The visul hints re rendered from fixed perspective tht ssumes user is looking down 45-degree ngle towrds their hnd. While occlusion (prticulrly self-occlusion) is fundmentl prolem with ll projector-cmer systems, we do not feel tht this plyed significnt role in users interctions. In the future, multiple projectors nd cmers cn e used to help reduce the effects of occlusions on more complex unconstrined movements. Figure 7. () LightGuide uses single projector nd depth sensing cmer, () the projector nd depth cmer re fixed over the user s ody. Projector Cmer Clirtion For the visul hints to e correctly projected on user s hnd, we must first unify the projector nd cmer into the sme coordinte spce. We clirte our projector to the depth cmer s the cmer lredy reports rel world coordintes (mm). The intrinsic prmeters of the projector cn e modeled using the digonl field of view nd the center of projection. To compute the extrinsic prmeters, we require four non-coplnr correspondences etween points tht cn e seen in the depth cmer nd projector. Once we estlish correspondences etween the 2D points of the projector nd the 3D points of the cmer, we use the POSIT lgorithm [7] to find the position nd orienttion of the projector. Hnd Trcking The prototype system first trnsforms every pixel in the input imge into world coordintes nd then crops pixels outside of volume of 1 cuic meter. This removes the floor, wlls nd other ojects in the scene (e.g. desk). The prototype then identifies the user s rms y determining continuous regions long the depth imge. The system then finds the frthest point long the entire rm y trcing through the continuous region eventully reching the most distnt point long the hnd. To extrct the user s hnd, we ssume constnt hnd length [14] which worked well in our tests. A distnce trnsform [9] is then used on the resulting imge nd the mxim is ssumed to e the center position of the hnd. USER STUDY The purpose of this study ws to demonstrte the fesiility of our pproch nd to determine if our prototype is cple of guiding user s hnd in mid-ir. Specificlly, we wnted to know how ccurtely users follow on-ody projected visuliztions. We lso wnted to investigte how the ccurcy nd ehvior of user chnges for pths t vrying depth levels. In ddition to following, we lso explored the ccurcy nd speed of self-guided movements where users dictte their own pce of movement. To plce LightGuide s performnce in context, we compred our method to video s we felt it ws representtive of resource tht users currently utilize. The video condition, shown in Figure 8, is comprised of 3D

6 1 45 o 9 o 2 o 3 4 Figure 8. A rendering of the 3D hnd tht is used in our video condition. The motion is n rc tht moves towrds the user nd grdully increses in depth. model of hnd tht follows n idel, system-generted pth. Although our nimted video does not provide nerly s much visul context to prticipnts s rel life video, system controllle video llowed us to remove the effects of ny humn or trcking error tht could ffect the movement pths. More importntly, the nimted video llowed us to control the perspective of the video (e.g. rendered from the user s perspective) s well s precisely control the speed nd timing of replyed movements. While we feel tht the est performnce with our system cn e ttined y using oth video nd on-ody hints, our comprison independently mesures the effect of our visul hints nd video for movement guidnce. Prticipnts We recruited 1 right-hnded prticipnts from our locl metropolitn re (2 femle) rnging in ge from 18 to 4. All prticipnts were screened prior to the study to ensure their rnge of motion ws dequte to perform our tsks. The study took pproximtely 9 minutes nd prticipnts received grtuity for their time. Test Movements Our gol ws to support interctions on vriety of movements. For our user study, we included five different pths: line which must e trced ck nd forth, squre, circle, n N, nd line plus curve (Figure 9). These pths shre similr chrcteristics to the types of movements ptients re sked to perform in physicl therpy sessions (see Motivtion). The pths, seen in Figure 8, rnge in length from 3 to 63mm (men = mm, SD = 13.6mm). To ensure tht we dequtely tested vriety of depth levels, we vry the pths t three different ngles:, 45 nd 9 with respect to the horizontl plne in the prticipnt s frme of reference. Procedure During the experiment, prticipnts were instructed to stnd t comfortle position underneth the overhed projector nd depth-sensing cmer. Prior to strting, we verified tht Figure 9. In () the test pths used in our study, () ech pth is oriented t, 45 nd 9 (only circle pth is shown). ech prticipnt hd enough room to move their hnd while eing dequtely trcked y the system. The primry tsk consisted of prticipnt moving their hnd in spce following specific hnd guidnce visul hints. By following, we men tht visul hint would egin moving in spce t speed of 3 mm/sec. nd prticipnts would follow the hint nd respond to its cues. Our choice of 3mm/sec for visuliztion speed ws chosen through informl pilot studies tht hd users try out vriety of speeds. 3 mm/sec ws chosen to e the most comfortle constnt speed while still producing resonle hnd motions. To quntify how users perform movement t their own pce, secondry tsk ws included where the sme 3D Arrow ws used without ny system imposed timing. Tht is, the 3D Arrow would only chnge position if the user responded to the direction indicted y the 3D Arrow. We refer to this s self-guided. We performed within sujects experiment nd in totl, we tested 6 visul hints: Follow Spot, 3D Follow-Arrow, 3D Self-Guided Arrow, 3D Pthlet, Video on Hnd, nd Video on Screen. Here on, we refer to our two 3D Arrow conditions s 3D F-Arrow nd 3D SG-Arrow. All except the Video on Screen condition were projected on the prticipnt s hnd. Our seline Video on Screen condition ws shown to prticipnt on computer monitor situted directly in front of the user. Importntly, prticipnts were told to keep their hnds flt (fcing down) during the entire experiment to ensure tht the visul hints would consistently pper on their hnds etween trils s well s to ensure consistent hnd trcking performnce y our system. To provide consistent strt loction for ech movement, we mrked the desired strting hnd loction with mrkers on the floor in front of the prticipnt nd sked them to return to the mrker efore eginning ech new tril. In ech tril, prticipnts were instructed to hold out their hnd nd follow the guidnce cues completing single pth s ccurtely s possile. We sked the prticipnt to keep the visul hint t the center of their hnd. Once the pth ws completed, the system would sound chime nd red circle would pper on the prticipnt s hnd signling the user to return to the strt position. In totl, prticipnts were sked to follow single visuliztion over our 15 test pths;

7 Error (mm) Line Line 45 Line 9 Circle Circle 45 Circle 9 N N 45 N 9 Line + Curve Line + Curve 45 Line + Curve 9 Squre Squre 45 Squre 9 Follow Spot 3D F-Arrow 3D G-Arrow 3D Pthlet Video Hnd Video Screen Figure 1. Overll distriution of unscled devitions from pth. The circles denote users while colors show the 15 unique pths. presenttion order ws rndomized. The procedure ws repeted for ech of our conditions. Before ech mesurement phse, prticipnts were llowed to prctice using the visul hints to move through pth. Ech condition lsted pproximtely 1 minutes, of which 5 minutes ws used for prctice nd 5 minutes for mesurement. Between conditions, we llocted 5 minutes for prticipnts to rest in order to reduce the effects of hnd ftigue. Ech session produced 9 trils (6 conditions x 5 pths x 3 ngles) per prticipnt. To counter-lnce the conditions, the presenttion of ech condition ws rndomized to remove the effects of ordering. Users were interviewed fter ech session followed y short post-study interview. We recorded video of the prticipnts nd mesured their position, hnd-orienttion nd time. RESULTS We seprte our nlysis into two components: Movement Accurcy nd Movement Times. Our 1 prticipnts produced totl of 9 movement trils on 15 unique pths. During the study, we experienced only single type of outlier relting to the trcking of user s hnd. The trcking results would chnge depending on if the user would self-occlude their hnd (e.g., rotte towrds the principl xis of the cmer). Additionlly, we experienced 21 trils (2%) where users would len their odies into the cpture volume, leding to momentry erroneous hnd mesurements tht would only pper in the outer extents of the cpture volume. The erroneous mesurements in the outer extents were filtered in post-dt nlysis llowing us to use ll tril mesurements in our finl nlysis. Movement Accurcy We tke two-fold pproch on mesuring the ccurcy of movements: devition from the pth nd fit (e.g., see [14]). In oth cses, to determine ccurcy, we use the solute Euclidin distnce from the closest point s n error metric. As in prior literture [12], we highlight two sources of systemtic error: 1) non-linerity nd improper clirtion of the projector nd cmer (e.g., the loction of the projected visuliztion differs from where the cmer expects it to e) nd 2) inccurcy in the hnd trcking, especilly when the user s hnd egins to leve the cpture volume. Overll, we found smll glol systemtic offset etween the cmer nd projector where the verge X- offset cross users ws 9.2mm to the left of pth nd Y-offset of 1.5mm elow pth, which is in greement to findings in previous literture [12,14].We did not pply these glol X/Y offsets, s prticipnts would compenste for the system inccurcy in the following conditions y moving their hnd until the visuliztion ppered t the center of their hnd. In the self-guided condition, the loction of the 3D G-Arrow ws sufficiently well plced in ll our trils so tht prticipnts could see the visul hint. Movement Devitions We nlyzed the verge devitions of users cross ll pths nd visuliztions using their rw, unscled, distnces to the closest point on the pth, (see full distriution in Figure 1 nd single user s performnce in Figure 11). Using stndrd ANOVA, we found tht there ws significnt difference etween our visul hints (F [5, 894] = 276.5, p <.1). A post-hoc Bonfferroni-corrected t-test on the Follow spot nd 3D F-Arrow performed significntly etter thn oth video conditions with verge devitions of 24.6mm (SD = 9.mm) nd 49.9mm (SD = 29.17mm) respectively (t 16 = 25.6, p <.1, t 26 = 122.5, p <.1). Additionlly, the distriution highlights the difficulties users hd in perceiving scle for our nimted videos. Surprisingly, Bonfferroni-corrected t-test compring the ccurcy of our video conditions show tht significntly smller devitions cn e chieved y showing n identiclly rendered video, on the user s hnd (t 56 = 93., p <.1). Movement Shpe Although the unscled distriution in Figure 1 shows tht our users were not le to chieve the desired scling on pth with the video screen condition, the results do not explin how well users do t performing the shpe of the movement. To help nlyze shpe, we use the Itertive Closest Point (ICP) lgorithm to register the user s movements to our model pths [34]. With ICP, we hve the flexiility of rotting, trnslting nd scling n oject in ll three xes to find the est mtch. For our purposes, we

8 Figure 11. A single user s performnce on pths oriented t 45 using the Video Screen (top) nd Follow Spot (ottom row) visul hint. The ground truth is denoted in lck nd the user s movement is shown in red. Axis units re in mm. exclude rottion from our ICP trnsformtion s our pth s unique chrcteristics re defined y their ngle of rottion. Tht is, we wnted to see how well users perceived ngles in video nd excluding rottion llowed us to nlyze devitions from ngled motions. Figure 12 shows results on the chnge in devition when user s pth is scled nd trnslted with ICP. On verge, prticipnts using the video screen condition devited from the desired pth y 25.1mm (men SD = 7.3mm), while the video hnd condition fired comprly. Prticipnts using the Follow Spot condition showed significntly less devition t 13.7mm (men SD = 6.6mm) (t 16 = 11.4, p <.1). Additionlly, our results indicte tht there ws significnt performnce difference in orienttion of the pths in the video screen condition (F [2, 147] = 24.6, p <.1). On verge, prticipnts performed ngled movements with n verge devition of 43.2mm (SD = 9.3mm), pproximtely 4% less ccurtely thn flt or verticl movements. Movement Times We rek down movement mesurements into two components: self-guided times for the 3D SG-Arrow compred to the video conditions nd distnces hed or ehind pth for ech of our visul hints Figure 12. The Itertive Closest Point Algorithm is used to nlyze the performnce of user s shpe. A user s movement is trnslted nd scled itertively until their motion converges to the idel pth. Error rs encode stndrd error of the men. Figure 13. () Prticipnts movement times were nlyzed in the 3D SG-Arrow condition nd compred to video on hnd nd video on screen nd () shows prticipnt s verge distnce ehind ech projected visuliztion. Self-Guided Times The verge movement times cross ll users nd pths for the 3D G-Arrow, video screen, nd video hnd re visulized in Figure 13(). With the 3D SG-Arrow, lthough prticipnts were le to perform the movements with more ccurcy over oth video conditions, movement times for video were significntly fster (F [2, 447] = 54.9, p <.1). On verge, prticipnts performed video screen movements with men of 3.45s (SD = 1.67s), nerly twice s fst s the 3D SG-Arrow. These results reflect our oservtion tht prticipnt s tendencies were to first see the whole pth conveyed on video, where users cquire the gist of the entire movement. In contrst, users with the 3D SG-Arrow would perform movements in situ, figuring out direction s they moved long the pth. Distnce Ahed/Behind Pths Figure 13() displys the verge distnce (mm) prticipnts were in front, or ehind ech of the visuliztions in the following conditions. To illustrte how prticipnts follow 3D F-Arrow, Figure 14 displys single prticipnt s movement on circle tht is oriented t 45 degrees with the respect to cnonicl horizontl X-Y plne. User Feedck In the video condition, users were le to quickly perform movements, ut often expressed frustrtion with the lck of Follow Spot 3D F-Arrow 3D Pthlet

9 Figure 14. The plots show the sme movement from two perspectives of how fr in-front or ehind user s hnd is compred to the projected visul hint. Green denotes prticipnt s pth, the red line shows the ctul position of the hint nd the lue line shows the projected point on the pth. feedck. As one prticipnt descried for video, It ws hrder to reproduce sutle movements, then to follow. It ws lso hrder to judge elevtion sed on the size of the hnd. Importntly with video, users lso descried the lck of feedforwrd hints. As one prticipnt sid, With video, you hve glol fetures. You just never know wht s coming next. With the Follow spot visuliztion, users commented on the generl ese of understnding of the visuliztion. For exmple, s prticipnt explined, The circle one ws simplest, it ws only telling you up or down. Less displyed info mde it esier. Similrly, nother prticipnt noted, For me, the est visuliztion ws proly the circle with the rrow, s once I ws used to the mechnics of it, it ecme somewht second nture. With the 3D Pthlet, users commented on the enefits of knowing wht ws coming up hed in the movement. As prticipnt descried, The feedck ws gret nd I liked seeing where I ws going. Although occlusions were not prevlent in ll pths, users occsionlly commented on disppering red ll. As result, prticipnts would tend to overshoot pth, s they were unle to see how much of the pth they hd consumed. Following nd Leding A mjority of our users in our interviews (8/1) sid they preferred the 3D SG-Arrow over ll other visuliztions. The ility for users to shpe their own tempo ws importnt to their overll stisfction with the visuliztion. As prticipnt noted, Creting my own tempo mde it esier to concentrte on where I ws moving. Another prticipnt descried, If I go fster, I feel like I cn do it etter. Moving t my own speed lets me concentrte on wht the system wnts me to do. Becuse it s recting to me, I cn focus on the shpe of the pth. I didn t hve to follow slower system when I could do etter. DISCUSSION The results of our study support our pproch of guiding users movements with on-ody projections in tht users were le to perform more ccurtely with our system over video. Our resoning for using n nimted video ws to dequtely control for perspective, trcking error nd speed. However, we hypothesize tht the reson for the lrge difference in scle ws tht we only provided users with single shdow on white horizontl plne for visul context. Thus, more representtive mesure of ccurcy with our hints cn e seen in our nlysis with ICP, where the Follow Spot visul hint did significntly etter thn ll other conditions. In generl, users qulittive feedck lso reflected our empiricl findings where generl comments positively reflected the ese of understnding the hint. However, this ccurcy comes t cost. With our 3D SG- Arrow, users were le to ccurtely guide themselves through pth, ut were unle to do so t the sme speed s video. One reson for this ehvior my e ttriuted to users eing le to see the movement efore completing the pth, getting the gist of the motion. Although we hve highlighted scenrios where users re no longer in the position to look t video screen (e.g., when they re using ody-worn projection systems), more eneficil scenrio for on-ody projections my e ttined when comined with video. One strtegy users cn tke is to view the gist of the motion nd see the visul context in video, nd then use our on-ody hints to perfect the motions. Our findings lso showed tht when the exct sme video ws moved from the screen to the hnd, there ws significnt performnce difference in scle. While this my e ttriuted to the lck of visul context, or chnge in scle (e.g., the video on the hnd ws smller), nother possiility could e tht users were le to more ccurtely clirte for the desired movement of their hnd when the video ws rendered in the sme loction s the physicl ody-prt we were ttempting to guide. Surprisingly, t times users would ecome so immersed in the visul hints tht it ecme uncler to them whether they were moving their hnd or if it ws the visuliztion tht ws moving in spce. This rection reflects similr findings in previous literture [27] where projected light ws used to trick viewers into thinking sttic cr ws moving long rod. Among the visul hints, the 3D F-Arrow showed the most promising ehvior with regrd to user s consistently keeping pce with system imposed timing. Tht is, y simply conveying sense of the next point long the pth through direction lone, users were le to more ccurtely predict where to move next. Our user opinions suggest tht when the tsk is not rhythmic in nture or requires fixed speed/ccurcy, the most enefit my e otined y llowing the user to dictte their own pce. This llows users to hve the flexiility to decide how they wnt to interpret nd rect to the visul hints. CONCLUSION AND FUTURE WORK In this pper, we descried nd evluted four on-ody projected visul hints to help guide user s movement in mid-ir. In ddition, we introduced LightGuide, proof-of

10 concept system tht uses n overhed projector nd cmer to disply our visul hints which cn reply movements t user guided or system imposed speed. Our results suggest tht users cn follow our on-ody hints ccurtely for movement of single ody prt in spce nd cn do so t system controlled speed. While our chief gol with the present work ws to demonstrte tht on-ody projected hints could e used for movement guidnce, we hve only tested these visul hints on user s hnd. For exmple, these visul hints could just s esily e shown on the rest of your rms, torso nd legs ssuming the rest of the user s ody is trcked (e.g. with the Kinect skeletl trcker). Furthermore, we hve yet to explore guidnce of two or more ody prts (e.g. two hnds) simultneously. Another importnt question moving forwrd is how to dpt or dd rottionl visul hints to llow guiding user s full rnge of motion. Finlly, there re mny fscinting cognitive questions we would like to investigte. For exmple, does projecting the sme visul hint on screen llow the user to perform the movement just s ccurtely s projecting the hint on your ody? Cn on-ody visul hints e used to distort the user s sense of their spce, llowing us to control their rnge of motion? While we hve helped to define wht the design spce of projected hints might look like to explore guidnce first, we hve yet to nswer the question of how well users lern prticulrly movement. In ddition, we hve yet to explore how well users perform the dynmics of movement, prticulrly when users re guided through lternting speeds. Our work hs llowed us to nswer the fundmentl question of whether or not it is possile, ut mny interesting questions lie hed. ACKNOWLEDGMENTS We thnk the Microsoft Reserch VIBE nd ASI groups, s well s the 211 Microsoft Reserch interns, for helping us improve LightGuide. REFERENCES 1. Bird, K.M. nd Brfield, W. Evluting the effectiveness of ugmented relity displys for mnul ssemly tsk. Virtul Relity 4, 4, 1999, Bnji, M.R. Stevens, Stnley Smith (196 73). Journl of Personlity nd Socil Psychology, Bu, O. nd Mcky, W.E. OctoPocus: dynmic guide for lerning gesture-sed commnd sets. Proc. UIST, 28, Britnnic Co, X. nd Blkrishnn, R. Intercting with dynmiclly defined informtion spces using hndheld projector nd pen. Proc. UIST, 26, Co, X., Forlines, C., nd Blkrishnn, R. Multi-user interction using hndheld projectors. Proc. UIST, 27, Dniel Dementhon, L.D. Model-Bsed oject pose in 25 lines of code. Proc. of IJCV 15, 1 (1995), Feiner, Steve, Blire Mcintyre, D.S. Knowledge-Bsed ugmented relity. Commun. ACM 36, 7, 1993, Felzenszwl, P.F. nd Huttenlocher, D.P. Distnce trnsforms of smpled functions Flgg, M. nd Rehg, J.M. Projector guided pinting. Proc. UIST, 26, Freemn, D., Benko, H., Morris, M.R., nd Wigdor, D. ShdowGuides: Visuliztions for In-Situ Lerning of Multi- Touch nd Whole-Hnd Gestures. Proc. ITS, 29, Hrrison, C., Benko, H., Wilson, A.D., nd Wy, O.M. OmniTouch: Werle multitouch interction everywhere. Proc. UIST, 211, Hrrison, C., Tn, D., nd Morris, D. Skinput: Appropriting the ody s n input surfce. Proc. CHI, 21, Holz, C. nd Wilson, A. Dt miming: inferring sptil oject descriptions from humn gesture. Proc. CHI, 211, Hu, H., Brown, L.D., nd Go, C. Scpe: Supporting Stereoscopic Collortion in Projective Environments. Proc. CG, 24, InFocus Jco, R. The perceptul structure of multidimensionl input device selection. Proc. CHI, 1992, Kne, S.K., Avrhmi, D., Worock, J.O., nd Hrrison, B. Bonfire: A Nomdic system for hyrid lptop-tletop interction. Proc. UIST, 29, Kirk, D. nd Stnton Frser, D. Compring remote gesture technologies for supporting collortive physicl tsks. Proc. CHI, 26, Mistry, P. nd Mes, P. WUW-wer Ur world: werle gesturl interfce. Proc. CHI, 29, Motokw, Y. nd Sito, H. Support system for guitr plying using ugmented relity disply. Proc. ISMAR, 26, Neumnn, U. nd Mjoros, A. Cognitive, performnce, nd systems issues for ugmented relity pplictions in mnufcturing nd mintennce. Proc. of VR, 1998, Plmiter, S. nd Elkerton, J. An evlution of nimted demonstrtions of lerning computer-sed tsks. Proc. CHI, 1991, Pinhnez, C. The Everywhere Displys Projector: A Device to crete uiquitous grphicl interfces. Proc. UiComp, 21, Rskr, R., Berdsley, P., Vn Br, J., et l. RFIG Lmps: intercting with self-descriing world vi photosensing wireless tgs nd projectors. Proc. of SIGGRAPH, 24, Rskr, R., Welch, G., Cutts, M., Lke, A., Stesin, L., nd Fuchs, H. The office of the future: A unified pproch to imge-sed modeling nd sptilly immersive displys. Proc. SIGGRAPH, 1998, Rskr, R., Welch, G., Low, K.L., nd Bndyopdhyy, D. Shder lmps: Animting rel ojects with imge-sed illumintion. Proc. Eurogrphics, 21, Rosenthl, S., Kne, S.K., Worock, J.O., nd Avrhmi, D. Augmenting On-Screen Instructions with Micro-Projected Guides: When it works, nd when it fils. Proc. UiComp, 21, SynchronousOjects Tn, D.S., Pusch, R., nd Hodgins, J. Exploiting the cognitive nd socil enefits of physiclly lrge displys Wtson, G., Currn, R., Butterfield, J., nd Crig, C. The effect of using nimted work instructions over text nd sttic grphics when performing smll scle engineering ssemly. Proc. CE, 28, White, S., Lister, L., nd Feiner, S. Visul Hints for tngile gestures in ugmented relity. Proc. ISMAR, 27, Wilson, A.D. nd Benko, H. Comining multiple depth cmers nd projectors for interctions on, ove nd etween surfces. Proc. UIST, 21, Zhng, Z. Itertive point mtching for registrtion of free-form curves nd surfces. Journl of Computer Vision 13, ,

EQUATIONS OF LINES AND PLANES

EQUATIONS OF LINES AND PLANES EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint

More information

A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324

A.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324 A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................

More information

Section 5-4 Trigonometric Functions

Section 5-4 Trigonometric Functions 5- Trigonometric Functions Section 5- Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form

More information

Reasoning to Solve Equations and Inequalities

Reasoning to Solve Equations and Inequalities Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing

More information

Experiment 6: Friction

Experiment 6: Friction Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht

More information

AntiSpyware Enterprise Module 8.5

AntiSpyware Enterprise Module 8.5 AntiSpywre Enterprise Module 8.5 Product Guide Aout the AntiSpywre Enterprise Module The McAfee AntiSpywre Enterprise Module 8.5 is n dd-on to the VirusScn Enterprise 8.5i product tht extends its ility

More information

Small Businesses Decisions to Offer Health Insurance to Employees

Small Businesses Decisions to Offer Health Insurance to Employees Smll Businesses Decisions to Offer Helth Insurnce to Employees Ctherine McLughlin nd Adm Swinurn, June 2014 Employer-sponsored helth insurnce (ESI) is the dominnt source of coverge for nonelderly dults

More information

Pentominoes. Pentominoes. Bruce Baguley Cascade Math Systems, LLC. The pentominoes are a simple-looking set of objects through which some powerful

Pentominoes. Pentominoes. Bruce Baguley Cascade Math Systems, LLC. The pentominoes are a simple-looking set of objects through which some powerful Pentominoes Bruce Bguley Cscde Mth Systems, LLC Astrct. Pentominoes nd their reltives the polyominoes, polycues, nd polyhypercues will e used to explore nd pply vrious importnt mthemticl concepts. In this

More information

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.

Use Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions. Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd

More information

Enterprise Risk Management Software Buyer s Guide

Enterprise Risk Management Software Buyer s Guide Enterprise Risk Mngement Softwre Buyer s Guide 1. Wht is Enterprise Risk Mngement? 2. Gols of n ERM Progrm 3. Why Implement ERM 4. Steps to Implementing Successful ERM Progrm 5. Key Performnce Indictors

More information

P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn

P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn 33337_0P03.qp 2/27/06 24 9:3 AM Chpter P Pge 24 Prerequisites P.3 Polynomils nd Fctoring Wht you should lern Polynomils An lgeric epression is collection of vriles nd rel numers. The most common type of

More information

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered: Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you

More information

DlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report

DlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of

More information

How To Network A Smll Business

How To Network A Smll Business Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.

5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one. 5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous rel-vlued

More information

An Undergraduate Curriculum Evaluation with the Analytic Hierarchy Process

An Undergraduate Curriculum Evaluation with the Analytic Hierarchy Process An Undergrdute Curriculum Evlution with the Anlytic Hierrchy Process Les Frir Jessic O. Mtson Jck E. Mtson Deprtment of Industril Engineering P.O. Box 870288 University of Albm Tuscloos, AL. 35487 Abstrct

More information

2. Transaction Cost Economics

2. Transaction Cost Economics 3 2. Trnsction Cost Economics Trnsctions Trnsctions Cn Cn Be Be Internl Internl or or Externl Externl n n Orgniztion Orgniztion Trnsctions Trnsctions occur occur whenever whenever good good or or service

More information

Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom

Bayesian Updating with Continuous Priors Class 13, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom Byesin Updting with Continuous Priors Clss 3, 8.05, Spring 04 Jeremy Orloff nd Jonthn Bloom Lerning Gols. Understnd prmeterized fmily of distriutions s representing continuous rnge of hypotheses for the

More information

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( ) Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +

More information

APPLICATION NOTE Revision 3.0 MTD/PS-0534 August 13, 2008 KODAK IMAGE SENDORS COLOR CORRECTION FOR IMAGE SENSORS

APPLICATION NOTE Revision 3.0 MTD/PS-0534 August 13, 2008 KODAK IMAGE SENDORS COLOR CORRECTION FOR IMAGE SENSORS APPLICATION NOTE Revision 3.0 MTD/PS-0534 August 13, 2008 KODAK IMAGE SENDORS COLOR CORRECTION FOR IMAGE SENSORS TABLE OF FIGURES Figure 1: Spectrl Response of CMOS Imge Sensor...3 Figure 2: Byer CFA Ptterns...4

More information

Helicopter Theme and Variations

Helicopter Theme and Variations Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the

More information

ClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment

ClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment ClerPeks Customer Cre Guide Business s Usul (BU) Services Pece of mind for your BI Investment ClerPeks Customer Cre Business s Usul Services Tble of Contents 1. Overview...3 Benefits of Choosing ClerPeks

More information

Welch Allyn CardioPerfect Workstation Installation Guide

Welch Allyn CardioPerfect Workstation Installation Guide Welch Allyn CrdioPerfect Worksttion Instlltion Guide INSTALLING CARDIOPERFECT WORKSTATION SOFTWARE & ACCESSORIES ON A SINGLE PC For softwre version 1.6.5 or lter For network instlltion, plese refer to

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

Basic Analysis of Autarky and Free Trade Models

Basic Analysis of Autarky and Free Trade Models Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently

More information

Introducing Kashef for Application Monitoring

Introducing Kashef for Application Monitoring WextWise 2010 Introducing Kshef for Appliction The Cse for Rel-time monitoring of dtcenter helth is criticl IT process serving vriety of needs. Avilbility requirements of 6 nd 7 nines of tody SOA oriented

More information

Economics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999

Economics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999 Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

JaERM Software-as-a-Solution Package

JaERM Software-as-a-Solution Package JERM Softwre-s--Solution Pckge Enterprise Risk Mngement ( ERM ) Public listed compnies nd orgnistions providing finncil services re required by Monetry Authority of Singpore ( MAS ) nd/or Singpore Stock

More information

Graphs on Logarithmic and Semilogarithmic Paper

Graphs on Logarithmic and Semilogarithmic Paper 0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

Operations with Polynomials

Operations with Polynomials 38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply

More information

Basic Ultrasound Views

Basic Ultrasound Views Bsic Ultrsound Views 2 Kenneth D. Horton K.D. Horton Echo/Vsculr Lortory, Intermountin Medicl Center, Murry, UT, USA e-mil: kd.horton@comcst.net T.P. Arhm (ed.), Cse Bsed Echocrdiogrphy, DOI: 10.1007/978-1-84996-151-6_2,

More information

Vectors 2. 1. Recap of vectors

Vectors 2. 1. Recap of vectors Vectors 2. Recp of vectors Vectors re directed line segments - they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms

More information

6.2 Volumes of Revolution: The Disk Method

6.2 Volumes of Revolution: The Disk Method mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine so-clled volumes of

More information

Vector differentiation. Chapters 6, 7

Vector differentiation. Chapters 6, 7 Chpter 2 Vectors Courtesy NASA/JPL-Cltech Summry (see exmples in Hw 1, 2, 3) Circ 1900 A.D., J. Willird Gis invented useful comintion of mgnitude nd direction clled vectors nd their higher-dimensionl counterprts

More information

Multiblending: displaying overlapping windows simultaneously without the drawbacks of alpha blending

Multiblending: displaying overlapping windows simultaneously without the drawbacks of alpha blending Multilending: displying overlpping windows simultneously without the drwcks of lph lending Ptrick Budisch Microsoft Reserch One Microsoft Wy, Redmond, WA 98052, USA ABSTRACT Alph lending llows the simultneous

More information

Techniques for Requirements Gathering and Definition. Kristian Persson Principal Product Specialist

Techniques for Requirements Gathering and Definition. Kristian Persson Principal Product Specialist Techniques for Requirements Gthering nd Definition Kristin Persson Principl Product Specilist Requirements Lifecycle Mngement Elicit nd define business/user requirements Vlidte requirements Anlyze requirements

More information

Rotational Equilibrium: A Question of Balance

Rotational Equilibrium: A Question of Balance Prt of the IEEE Techer In-Service Progrm - Lesson Focus Demonstrte the concept of rottionl equilirium. Lesson Synopsis The Rottionl Equilirium ctivity encourges students to explore the sic concepts of

More information

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100

Mathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100 hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by

More information

Performance Monitoring Fundamentals: Demystifying Performance Assessment Techniques

Performance Monitoring Fundamentals: Demystifying Performance Assessment Techniques Performnce Monitoring Fundmentls: Demystifying Performnce Assessment Techniques Roert C. Rice, PhD Rchelle R. Jyringi Dougls J. Cooper, PhD Control Sttion, Inc. Deprtment of Chemicl Engineering Control

More information

How To Set Up A Network For Your Business

How To Set Up A Network For Your Business Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer

More information

The Velocity Factor of an Insulated Two-Wire Transmission Line

The Velocity Factor of an Insulated Two-Wire Transmission Line The Velocity Fctor of n Insulted Two-Wire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

Understanding camera trade-offs through a Bayesian analysis of light field projections

Understanding camera trade-offs through a Bayesian analysis of light field projections Understnding cmer trde-offs through Byesin nlysis of light field projections Ant Levin 1 Willim T. Freemn 1,2 Frédo Durnd 1 1 MIT CSAIL 2 Adoe Systems Astrct. Computer vision hs trditionlly focused on

More information

In addition, the following elements form an integral part of the Agency strike prevention plan:

In addition, the following elements form an integral part of the Agency strike prevention plan: UNITED STTES DEPRTMENT OF GRICULTURE Wshington, DC 20250 Federl Grin Inspection Service FGIS Directive 4711.2 6/16/80 STRIKE PREVENTION ND STRIKE CONTINGENCY PLNS I PURPOSE This Instruction: Estlishes

More information

Factoring Polynomials

Factoring Polynomials Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles

More information

Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.

Treatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3. The nlysis of vrince (ANOVA) Although the t-test is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the t-test cn be used to compre the mens of only

More information

Gaze Manipulation for One-to-one Teleconferencing

Gaze Manipulation for One-to-one Teleconferencing Gze Mnipultion for One-to-one Teleconferencing A. Criminisi, J. Shotton, A. Blke, P.H.S. Torr Microsoft Reserch Ltd, Cmridge, UK Astrct A new lgorithm is proposed for novel view genertion in one-toone

More information

Or more simply put, when adding or subtracting quantities, their uncertainties add.

Or more simply put, when adding or subtracting quantities, their uncertainties add. Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re

More information

9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes

9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes The Sclr Product 9.3 Introduction There re two kinds of multipliction involving vectors. The first is known s the sclr product or dot product. This is so-clled becuse when the sclr product of two vectors

More information

Integration. 148 Chapter 7 Integration

Integration. 148 Chapter 7 Integration 48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but

More information

Clipping & Scan Conversion. CSE167: Computer Graphics Instructor: Steve Rotenberg UCSD, Fall 2005

Clipping & Scan Conversion. CSE167: Computer Graphics Instructor: Steve Rotenberg UCSD, Fall 2005 Clipping & Scn Conersion CSE167: Computer Grphics Instructor: Stee Rotenberg UCSD, Fll 2005 Project 2 Render 3D hnd (mde up of indiidul boxes) using hierrchicl trnsformtions (push/pop) The hnd should perform

More information

Small Business Cloud Services

Small Business Cloud Services Smll Business Cloud Services Summry. We re thick in the midst of historic se-chnge in computing. Like the emergence of personl computers, grphicl user interfces, nd mobile devices, the cloud is lredy profoundly

More information

1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator

1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.

More information

9 CONTINUOUS DISTRIBUTIONS

9 CONTINUOUS DISTRIBUTIONS 9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete

More information

Regular Sets and Expressions

Regular Sets and Expressions Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite

More information

A Study on Autonomous Cooperation between Things in Web of Things

A Study on Autonomous Cooperation between Things in Web of Things A Study on Autonomous Coopertion etween Things in We of Things Jehk Yu, Hyunjoong Kng, Hyo-Chn Bng, MyungNm Be 2 Electronics nd Telecommunictions Reserch Institute, 38 Gjeongno, Yuseong-gu, Dejeon, 305-700,

More information

How To Make A Network More Efficient

How To Make A Network More Efficient Rethinking Virtul Network Emedding: Sustrte Support for Pth Splitting nd Migrtion Minln Yu, Yung Yi, Jennifer Rexford, Mung Ching Princeton University Princeton, NJ {minlnyu,yyi,jrex,chingm}@princeton.edu

More information

Gaze Manipulation for One-to-one Teleconferencing

Gaze Manipulation for One-to-one Teleconferencing Gze Mnipultion for One-to-one Teleconferencing A. Criminisi, J. Shotton, A. Blke, P.H.S. Torr Microsoft Reserch Ltd, Cmridge, UK Astrct A new lgorithm is proposed for novel view genertion in one-toone

More information

Homework 3 Solutions

Homework 3 Solutions CS 341: Foundtions of Computer Science II Prof. Mrvin Nkym Homework 3 Solutions 1. Give NFAs with the specified numer of sttes recognizing ech of the following lnguges. In ll cses, the lphet is Σ = {,1}.

More information

Curriculum for the Master Program in Business Education at the University of Innsbruck School of Management

Curriculum for the Master Program in Business Education at the University of Innsbruck School of Management The English version of the curriculum for the Mster Progrm in Business Eduction is not leglly inding nd is for informtionl purposes only. The legl sis is regulted in the curriculum pulished in the University

More information

New Internet Radio Feature

New Internet Radio Feature XXXXX XXXXX XXXXX /XW-SMA3/XW-SMA4 New Internet Rdio Feture EN This wireless speker hs een designed to llow you to enjoy Pndor*/Internet Rdio. In order to ply Pndor/Internet Rdio, however, it my e necessry

More information

Integration by Substitution

Integration by Substitution Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is

More information

** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand

** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand Modelling nd Simultion of hemicl Processes in Multi Pulse TP Experiment P. Phnwdee* S.O. Shekhtmn +. Jrungmnorom** J.T. Gleves ++ * Dpt. hemicl Engineering, Ksetsrt University, Bngkok 10900, Thilnd + Dpt.hemicl

More information

Simulation of operation modes of isochronous cyclotron by a new interative method

Simulation of operation modes of isochronous cyclotron by a new interative method NUKLEONIKA 27;52(1):29 34 ORIGINAL PAPER Simultion of opertion modes of isochronous cyclotron y new intertive method Ryszrd Trszkiewicz, Mrek Tlch, Jcek Sulikowski, Henryk Doruch, Tdeusz Norys, Artur Srok,

More information

5 a LAN 6 a gateway 7 a modem

5 a LAN 6 a gateway 7 a modem STARTER With the help of this digrm, try to descrie the function of these components of typicl network system: 1 file server 2 ridge 3 router 4 ckone 5 LAN 6 gtewy 7 modem Another Novell LAN Router Internet

More information

Warm-up for Differential Calculus

Warm-up for Differential Calculus Summer Assignment Wrm-up for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:

More information

AAPT UNITED STATES PHYSICS TEAM AIP 2010

AAPT UNITED STATES PHYSICS TEAM AIP 2010 2010 F = m Exm 1 AAPT UNITED STATES PHYSICS TEAM AIP 2010 Enti non multiplicnd sunt preter necessittem 2010 F = m Contest 25 QUESTIONS - 75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD

More information

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives

More information

TITLE THE PRINCIPLES OF COIN-TAP METHOD OF NON-DESTRUCTIVE TESTING

TITLE THE PRINCIPLES OF COIN-TAP METHOD OF NON-DESTRUCTIVE TESTING TITLE THE PRINCIPLES OF COIN-TAP METHOD OF NON-DESTRUCTIVE TESTING Sung Joon Kim*, Dong-Chul Che Kore Aerospce Reserch Institute, 45 Eoeun-Dong, Youseong-Gu, Dejeon, 35-333, Kore Phone : 82-42-86-231 FAX

More information

Vectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics

Vectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics Chpter 2 Vectors nd dydics Summry Circ 1900 A.D., J. Willird Gis proposed the ide of vectors nd their higher-dimensionl counterprts dydics, tridics, ndpolydics. Vectors descrie three-dimensionl spce nd

More information

Note: Principal version Modification Amendment Equivalence list Consolidated version from October 1 2014

Note: Principal version Modification Amendment Equivalence list Consolidated version from October 1 2014 Note: The following curriculum is consolidted version. It is leglly non-inding nd for informtionl purposes only. The leglly inding versions re found in the University of Innsruck Bulletins (in Germn).

More information

Section 5.2, Commands for Configuring ISDN Protocols. Section 5.3, Configuring ISDN Signaling. Section 5.4, Configuring ISDN LAPD and Call Control

Section 5.2, Commands for Configuring ISDN Protocols. Section 5.3, Configuring ISDN Signaling. Section 5.4, Configuring ISDN LAPD and Call Control Chpter 5 Configurtion of ISDN Protocols This chpter provides instructions for configuring the ISDN protocols in the SP201 for signling conversion. Use the sections tht reflect the softwre you re configuring.

More information

Assessing authentically in the Graduate Diploma of Education

Assessing authentically in the Graduate Diploma of Education Assessing uthenticlly in the Grdute Diplom of Eduction Dr Mree DinnThompson Dr Ruth Hickey Dr Michelle Lsen WIL Seminr JCU Nov 12 2009 Key ides plnning process tht embeds uthentic ssessment, workintegrted

More information

Babylonian Method of Computing the Square Root: Justifications Based on Fuzzy Techniques and on Computational Complexity

Babylonian Method of Computing the Square Root: Justifications Based on Fuzzy Techniques and on Computational Complexity Bbylonin Method of Computing the Squre Root: Justifictions Bsed on Fuzzy Techniques nd on Computtionl Complexity Olg Koshelev Deprtment of Mthemtics Eduction University of Texs t El Pso 500 W. University

More information

STUDY ON 3D TEXTURED BUILDING MODEL BASED ON ADS40 IMAGE AND 3D MODEL

STUDY ON 3D TEXTURED BUILDING MODEL BASED ON ADS40 IMAGE AND 3D MODEL STUDY ON 3D TEXTURED BUILDING MODEL BASED ON ADS4 IMAGE AND 3D MODEL Liu Zhen,, *, Gong Peng c, Shi Peijun Ssgw T d College of Resource Science & Technology, Beijing Norml University,1875, liuzhen@nu.edu.cn

More information

Numeracy across the Curriculum in Key Stages 3 and 4. Helpful advice and suggested resources from the Leicestershire Secondary Mathematics Team

Numeracy across the Curriculum in Key Stages 3 and 4. Helpful advice and suggested resources from the Leicestershire Secondary Mathematics Team Numercy cross the Curriculum in Key Stges 3 nd 4 Helpful dvice nd suggested resources from the Leicestershire Secondry Mthemtics Tem 1 Contents pge The development of whole school policy 3 A definition

More information

Unleashing the Power of Cloud

Unleashing the Power of Cloud Unleshing the Power of Cloud A Joint White Pper by FusionLyer nd NetIQ Copyright 2015 FusionLyer, Inc. All rights reserved. No prt of this publiction my be reproduced, stored in retrievl system, or trnsmitted,

More information

Physics 6010, Fall 2010 Symmetries and Conservation Laws: Energy, Momentum and Angular Momentum Relevant Sections in Text: 2.6, 2.

Physics 6010, Fall 2010 Symmetries and Conservation Laws: Energy, Momentum and Angular Momentum Relevant Sections in Text: 2.6, 2. Physics 6010, Fll 2010 Symmetries nd Conservtion Lws: Energy, Momentum nd Angulr Momentum Relevnt Sections in Text: 2.6, 2.7 Symmetries nd Conservtion Lws By conservtion lw we men quntity constructed from

More information

. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2

. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2 7 CHAPTER THREE. Cross Product Given two vectors = (,, nd = (,, in R, the cross product of nd written! is defined to e: " = (!,!,! Note! clled cross is VECTOR (unlike which is sclr. Exmple (,, " (4,5,6

More information

Revisions published in the University of Innsbruck Bulletin of 18 June 2014, Issue 31, No. 509

Revisions published in the University of Innsbruck Bulletin of 18 June 2014, Issue 31, No. 509 Plese note: The following curriculum is for informtion purposes only nd not leglly inding. The leglly inding version is pulished in the pertinent University of Innsruck Bulletins. Originl version pulished

More information

Morgan Stanley Ad Hoc Reporting Guide

Morgan Stanley Ad Hoc Reporting Guide spphire user guide Ferury 2015 Morgn Stnley Ad Hoc Reporting Guide An Overview For Spphire Users 1 Introduction The Ad Hoc Reporting tool is ville for your reporting needs outside of the Spphire stndrd

More information

EE247 Lecture 4. For simplicity, will start with all pole ladder type filters. Convert to integrator based form- example shown

EE247 Lecture 4. For simplicity, will start with all pole ladder type filters. Convert to integrator based form- example shown EE247 Lecture 4 Ldder type filters For simplicity, will strt with ll pole ldder type filters Convert to integrtor bsed form exmple shown Then will ttend to high order ldder type filters incorporting zeros

More information

Math 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1.

Math 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1. Mth 4, Homework Assignment. Prove tht two nonverticl lines re perpendiculr if nd only if the product of their slopes is. Proof. Let l nd l e nonverticl lines in R of slopes m nd m, respectively. Suppose

More information

Unit 6: Exponents and Radicals

Unit 6: Exponents and Radicals Eponents nd Rdicls -: The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N): - counting numers. {,,,,, } Whole Numers (W): - counting numers with 0. {0,,,,,, } Integers (I): -

More information

Vectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics

Vectors and dyadics. Chapter 2. Summary. 2.1 Examples of scalars, vectors, and dyadics Chpter 2 Vectors nd dydics Summry Circ 1900 A.D., J. Willird Gis proposed the ide of vectors nd their higher-dimensionl counterprts dydics, tridics, ndpolydics. Vectors descrie three-dimensionl spce nd

More information

Modular Generic Verification of LTL Properties for Aspects

Modular Generic Verification of LTL Properties for Aspects Modulr Generic Verifiction of LTL Properties for Aspects Mx Goldmn Shmuel Ktz Computer Science Deprtment Technion Isrel Institute of Technology {mgoldmn, ktz}@cs.technion.c.il ABSTRACT Aspects re seprte

More information

Vendor Rating for Service Desk Selection

Vendor Rating for Service Desk Selection Vendor Presented By DATE Using the scores of 0, 1, 2, or 3, plese rte the vendor's presenttion on how well they demonstrted the functionl requirements in the res below. Also consider how efficient nd functionl

More information

PROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1

PROBLEMS 13 - APPLICATIONS OF DERIVATIVES Page 1 PROBLEMS - APPLICATIONS OF DERIVATIVES Pge ( ) Wter seeps out of conicl filter t the constnt rte of 5 cc / sec. When the height of wter level in the cone is 5 cm, find the rte t which the height decreses.

More information

trademark and symbol guidelines FOR CORPORATE STATIONARY APPLICATIONS reviewed 01.02.2007

trademark and symbol guidelines FOR CORPORATE STATIONARY APPLICATIONS reviewed 01.02.2007 trdemrk nd symbol guidelines trdemrk guidelines The trdemrk Cn be plced in either of the two usul configurtions but horizontl usge is preferble. Wherever possible the trdemrk should be plced on blck bckground.

More information

The Acoustic Design of Soundproofing Doors and Windows

The Acoustic Design of Soundproofing Doors and Windows 3 The Open Acoustics Journl, 1, 3, 3-37 The Acoustic Design of Soundproofing Doors nd Windows Open Access Nishimur Yuy,1, Nguyen Huy Qung, Nishimur Sohei 1, Nishimur Tsuyoshi 3 nd Yno Tkshi 1 Kummoto Ntionl

More information

AREA OF A SURFACE OF REVOLUTION

AREA OF A SURFACE OF REVOLUTION AREA OF A SURFACE OF REVOLUTION h cut r πr h A surfce of revolution is formed when curve is rotted bout line. Such surfce is the lterl boundr of solid of revolution of the tpe discussed in Sections 7.

More information

Data replication in mobile computing

Data replication in mobile computing Technicl Report, My 2010 Dt repliction in mobile computing Bchelor s Thesis in Electricl Engineering Rodrigo Christovm Pmplon HALMSTAD UNIVERSITY, IDE SCHOOL OF INFORMATION SCIENCE, COMPUTER AND ELECTRICAL

More information

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001 CS99S Lortory 2 Preprtion Copyright W. J. Dlly 2 Octoer, 2 Ojectives:. Understnd the principle of sttic CMOS gte circuits 2. Build simple logic gtes from MOS trnsistors 3. Evlute these gtes to oserve logic

More information

2 DIODE CLIPPING and CLAMPING CIRCUITS

2 DIODE CLIPPING and CLAMPING CIRCUITS 2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of

More information

Why is the NSW prison population falling?

Why is the NSW prison population falling? NSW Bureu of Crime Sttistics nd Reserch Bureu Brief Issue pper no. 80 September 2012 Why is the NSW prison popultion flling? Jcqueline Fitzgerld & Simon Corben 1 Aim: After stedily incresing for more thn

More information

Gene Expression Programming: A New Adaptive Algorithm for Solving Problems

Gene Expression Programming: A New Adaptive Algorithm for Solving Problems Gene Expression Progrmming: A New Adptive Algorithm for Solving Prolems Cândid Ferreir Deprtmento de Ciêncis Agráris Universidde dos Açores 9701-851 Terr-Chã Angr do Heroísmo, Portugl Complex Systems,

More information

Physics 43 Homework Set 9 Chapter 40 Key

Physics 43 Homework Set 9 Chapter 40 Key Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nm-wide region t x

More information