A Spatial Model for Nested Multiscale Interfaces
Chris Olston
Stanford University
olston@https://www.doczj.com/doc/9619056942.html,
Abstract
Signi?cant recent interest has been devoted to the multiscale interface as a paradigm for user-driven exploration of large or complex information worlds.Multiscale interfaces sometimes permit nesting
of worlds,a notion that underpins a diverse variety of navigation aides and multiple-view tools such
as visual hyperlinks,bookmarks,?lters,magnifying glasses,overview and detail views,and coordinated
views,all of which can be used to enhance the effectiveness of information exploration.These constructs
often behave in accordance with underlying spatial relationships among nested views.Unfortunately,re-
searchers and designers currently lack tools to help them describe and reason formally about spatial
relationships tying together nested virtual worlds.The absence of appropriate formalisms is problem-
atic because multiple spatial models are available and,even under a consistent model different nested
constructs can exhibit different behaviors,many of which have complex and asymmetric properties.In
this paper we describe a spatial model for nested multiscale interfaces that we constructed based on ex-
perience with a prototype data visualization system.We show how behaviors of nested components can
be described succinctly in our model and provide a comprehensive taxonomy of32distinct behaviors.
Finally,we make use of our spatial model to design techniques to help maintain user orientation during
navigation between nested worlds by smoothly animating transitions between outer and inner views.
1Introduction
Multiscale interfaces[FB95]represent a powerful and?exible paradigm for user-driven exploration of large information worlds in which users can adjust the scale with which information is displayed while browsing. Multiscale interfaces have been proposed or deployed in a diverse set of applications including information visualization tools,e.g.,[AW95,BHP+96,DKR97,LRB+97,STH02,WOA+01],WYSIWYG tools for creating and viewing documents,e.g.,[Cora,Corb,MPBH95],geographic information system(GIS)and cartographic tools,e.g.,[AA99,BGS99],and even Web browsers[BHS+96].Many multiscale interface environments including[ACSW96,BHP+96,BHS+96,BSP+93,PF93,PM99,SFB94,WOA+01]permit nesting,whereby one information world appears as a sub-window of another.Nested sub-windows are called portals[BHP+96,WOA+01]1,which serve as a uni?ed way to implement a number of useful constructs that can enhance the ability of users to explore large or complex information worlds effectively.First of all,portals provide a convenient mechanism for linking together different information worlds or different locations within the same world via a useful navigation shortcut:Users can“enter”a portal to change the main view to be the one displayed inside the portal.Aside from serving as visual hyperlinks,portals can also be used as bookmarks(also called indexes)[BHP+96]as well as a variety of nested multiple-view constructs including?lters[BHP+96,SFB94],magnifying glasses[Bel00,SFB94],overview and detail views[CMS98],and coordinated views[Bel00,SFB94].We refer to nested constructs that can be created using portals in multiscale environments collectively as portal tools.
Montmartre Pulgas Mission 5
371
5
5
101
101
45
45
371
Figure1:Magnifying glass tool.
Firelight
Cuesta
Magdalena
Stuart
Park
Street Map
(miles)
Satellite Image
(kilometers) Figure2:Coordinated view tool.
1.1Portal Tools and Complexity
Portal tools often obey an underlying spatial model that ties together the views shown at different levels of nesting and dictates how the views change in response to user actions.For example,consider a typical magnifying glass tool,which covers a region of the world displayed on the screen and in its place displays an increased-scale representation of the occluded region.Figure1illustrates a cartographic application with a magnifying glass portal https://www.doczj.com/doc/9619056942.html,ers may reposition the magnifying glass,causing its contents to shift,and the relationship between the change in position on the screen and the shift in contents of the magnifying glass portal is based on an implicit spatial model that incorporates scale as well as horizontal and vertical https://www.doczj.com/doc/9619056942.html,ers may also change the scale of the world being explored,automatically triggering a corresponding change in the scale of the magnifying glass contents to maintain a?xed scale ratio derived from a spatial model.
Different types of portal tools exhibit different spatial properties,e.g.,bookmark tools typically behave differently than magnifying glasses when repositioned by a user.Moreover,the behaviors of some tools can be complex.For example,consider coordinated view tools,which contain an inner world consisting of an alternative representation of the portion of the outer information world currently displayed on the screen. Figure2shows an example of a coordinated view tool that might be used in a GIS application to show a street map(inner world)in conjunction with a satellite image(outer world)of the same area.In many applications users may pan,or scroll,in the information world,causing the view of the outer world to shift while the coordinated view tool remains stationary on the screen.Meanwhile,the content of the coordinated view is shifted automatically to maintain the inner and outer views coordinated.Since the coordinated view tool remains?xed on the screen,when a pan occurs the position of the tool in the coordinates of the outer information world changes.However,if a user repositions the coordinated view tool directly,also altering its position relative to the outer information world,its contents remain unchanged.This apparent inconsistency in behavior has the useful property of allowing the tool to be freely repositioned on the screen to avoid occluding essential information without affecting the contents of the coordinated view tool,which continues to display an alternative representation of the portion of the outer information world currently displayed on the screen.In some applications,complexities such as this are warranted due to useful properties that arise such as the ability to affect which information is occluded without resorting to navigation.In fact, behaviors that are complex to describe may seem quite intuitive to expert users.On the other hand,for simple applications or novice users,it may be appropriate to remove complexities by,for example,locking the screen position of a coordinated view tool,which requires altering the way the tool behaves in response to user actions.
Even a single type of portal tool such as a coordinated view can be alternatively con?gured to behave in
one of several ways.Interestingly,some con?gurations may result in asymmetric properties.For example, consider a magnifying glass tool,illustrated in Figure1,in which the magni?ed scale of the nested world inside the magnifying glass is typically a function of the current scale of the outer world.Therefore,when a user alters the scale of the outer world,the scale of the inner world changes automatically,and the relation-ship is typically governed by a multiplicative magni?cation factor.In some instances,users are permitted to alter the scale of the inner world directly.If so,the portal may be con?gured so that the change,divided by the magni?cation factor,propagates to the outer world,having the same overall effect that would have occurred had the user altered the scale of the outer world directly and leaving the magni?cation factor un-changed.On the other hand,in an alternative con?guration,a change made by a user to the scale of the inner world does not propagate to the outer world,having the effect of programming the magni?cation factor of the magnifying glass.In this alternative con?guration,changing the scales of the inner and outer worlds are not symmetric actions:the former programs the magni?cation factor between the two worlds,while the latter alters the scales of both worlds while holding the magni?cation factor constant.
1.2Formalism to Combat Complexity
As we have seen in Section1.1,different portal tools exhibit different spatial behaviors in response to user actions,a single type of tool can be con?gured to exhibit several alternative behaviors,and these behaviors can be complex and asymmetric.Due to the presence of signi?cant complexity,we feel that an overarching formal model for portal behavior that describes the space of possible behaviors in a systematic way would be of signi?cant bene?t to researchers,designers,programmers,and users.First,researchers of nested mul-tiscale interfaces can leverage a formal model to help them understand,describe,communicate,and reason about properties of portal tools and the alternative con?gurations available.Second,by providing a clear enumeration and description of possible behaviors,a good formalism can assist designers faced with the nontrivial tasks of deciding which behaviors to make available,how best to present the available options to end-users,and what control mechanisms to provide,when offering portal tools in a nested multiscale inter-face environment.A formal model may also be of signi?cant help to programmers of multiscale interfaces, which can use it as a basis for a simple and elegant implementation of portals with?exible con?gurations. Finally,a spatial model of portal behavior can be incorporated into documentation to guide non-expert users of systems like DataSplash[WOA+01]as they create portal tools that have?exible,visually programmable behaviors.
This paper presents a formal model for the spatial properties of nested user interface constructs.Al-though nesting has been proposed in a variety of contexts,we are aware of no previous attempt to model spatial relationships among nested information worlds formally.Our initial work in[OW00]developed a basic model for nested interfaces based on Boolean properties that describe whether certain actions such as navigating in worlds or repositioning portals trigger other actions to occur.The abstract model of[OW00] is intended to be very general,and does not specify the exactly way in which actions are correlated,which depends on the speci?c spatial or non-spatial model in use.In this paper we describe a detailed spatial model based on space-scale diagrams[FB95]that captures the semantics of a wide variety of portal tools and con?gurations in a uni?ed way.The speci?c contributions of this paper are:
?We extend space-scale diagrams,originally designed for analyzing non-nested multiscale interfaces, to incorporate nesting in a natural way(Section2).
?Drawing from our experience with a nested multiscale data visualization environment,we propose a model describing the way portals behave in response to user actions based on geometric relationships among elements in a space-scale diagram(Section3).
?We provide a comprehensive taxonomy of32varieties of portal tools that obey our spatial model,and
Figure3:Example canvas.Figure4:Space-scale diagram.
provide an accompanying online Java demonstration program for readers to experiment with different tool types and con?gurations in our taxonomy(Section4).
?We propose techniques for animating the entrance into a portal while maintaining the user’s orienta-tion that exploit our spatial model(Section5).
We now proceed with a short review of non-nested multiscale interfaces and space-scale diagrams,and then introduce nesting formally.
2Multiscale Interfaces,Space-Scale Diagrams,and Nesting
In a typical multiscale interface a user navigates within a two-dimensional world that can be very large or even in?nite.For our purposes it is convenient to think of it as a?nite,two-dimensional rectangle with x and y coordinates called a canvas2.Figure3shows a simple canvas containing three concentric circles.The user is able to view portions of the canvas inside a?xed-size rectangle of screen real-estate called the viewer window.To control which portion of the two-dimensional canvas appears in the viewer window,the user can navigate in three dimensions by panning and zooming.The effect of panning is to change the portion of the canvas that appears in the viewer window without affecting the degree of magni?cation,or scale.The effect of zooming is to change the scale,causing a greater or smaller portion of the canvas to become visible in the viewer window.
2.1Review of Space-Scale Diagrams
Multiscale interfaces are perhaps easiest understood with the help of space-scale diagrams,introduced by Furnas and Bederson[FB95],which represent scale explicitly,leading to a convenient way to model nav-igation and,in particular,zooming.We review space-scale diagrams brie?y here(the reader is referred to [FB95]for a more comprehensive description and discussion).Figure4shows a space-scale diagram for the canvas in Figure3.The two-dimensional canvas appears multiple times in the three-dimensional diagram that has dimensions u,v,and s,and each copy of the canvas lies in a different u–v plane and is scaled by a different amount.Scale is determined by the s coordinate.In the u–v plane at scale coordinate s=1,the canvas is drawn at its“natural”scale,so that u=x and v=y.At other s positions,the x and y dimensions are scaled multiplicatively(linearly)by s:u=x·s and v=y·s.Due to this scaling effect,an(x,y)point
in a canvas becomes a great ray(see Figure4)in(u,v,s)-space originating at(0,0,0)and passing through all points on the line parameterized by s as follows:u=x·s;v=y·s.Objects in the canvas such as the circles in Figure3become generalized cones in the space-scale diagram.
The portion of the canvas currently displayed on the screen in the viewer window is represented in a space-scale diagram as a2D shape in u and v of?xed size and shape called an aperture,which is usually rectangular,as shown in Figure4.The canvas is rendered by taking the portion that lies inside an aperture called the parent frame(for reasons that will soon become clear)and drawing it on the screen,scaled to ?t exactly inside the viewer window.(The shape of the parent frame aperture must match the shape of the viewer window.)Since apertures are?xed in size and shape,their coordinates can be encoded by their center position,a(u,v,s)point that can be edited by the user via navigation(panning and zooming)operations. Editing the position of the parent frame aperture causes the contents of the viewer window to change.
2.2Nesting in Space-Scale Diagrams
We can extend space-scale diagrams in a natural way to represent nested canvases(those containing portals). For simplicity,we assume only a single level of nesting,whereby a single child canvas is nested within a single parent canvas.Our model can be extended to incorporate multiple levels of nesting,as found in some environments such as[BHP+96,WOA+01].We also simplify our discussion by focusing on parent canvases containing a single portal,although in general canvases may contain multiple portals,possibly linking to different child canvases.
Portals can be thought of as having two aspects:outline and contents.An outline in the parent canvas designating where the contents of a portal are to be drawn is called the portal frame.As with all objects in the parent canvas,a portal frame has an(x,y)location,a shape,and a size,all of which can potentially be edited by the user.The contents of a portal are de?ned by the child frame,an aperture(?xed-size2D shape) in the space-scale diagram of the child canvas.Figure5(a)shows an example of a space-scale diagram containing the three frames(parent,portal,child)of our model(the canvas contents have been omitted from the space-scale diagram to reduce clutter),augmented with a recursive portal.A recursive portal is one in which the child canvas is the same as the parent canvas,so the portal goes to another location and/or scale in the same canvas.With recursive portals,all three frames to be drawn in the same space-scale diagram.
(A non-recursive portal can be drawn using two diagrams to represent the parent and child canvases.)The reason the portal frame has(x,y)coordinates while the other two frames have(u,v,s)coordinates is that the portal frame,like any graphical object within a canvas,is manifest at all scales while the parent and child frames each have a corresponding scale.For simplicity,we assume throughout this paper that all three frames in our model are rectangular,as is common,so the portal frame appears in the space-scale diagram as a pyramid composed of four great rays.
Figure5(b)shows the viewer window as seen by the user when the parent and child canvases are both the one shown in Figure3and are rendered using the frames shown in Figure5(a).A portal is rendered for the user by taking the region of the child canvas enclosed by the child frame,scaling it appropriately, and drawing it inside the portal frame in the parent canvas,which in turn is rendered on the screen inside the viewer window as discussed in Section2.1.(The shape of the child frame must match the shape of the portal frame.)In Figure5(a),the cross-section of the portal frame taken at the current scale coordinate of the parent frame is smaller than the parent frame,and is enclosed by the parent frame.Consequently,the portal outline is rendered inside the viewer window in Figure5(b).The cross-section of the portal frame at the scale of the parent frame is also smaller than the child frame,meaning that the portion of the canvas bounded by the child frame is demagni?ed(reduced in scale)when rendered inside the portal in Figure5(b). To enable rendering and simplify animation of portal entering(see Section5),the aspect ratios of the three rectangular frames should match,and for simplicity we assume that all three aspect ratios remain?xed and equal at all times.
Figure5:A space-scale diagram containing the three frames of our model for a canvas with a recursive portal(a),and the corresponding viewer window(b).
Figure6:A space-scale diagram showing a new interface state(a),and the corresponding viewer window (b),obtained by beginning with Figure5and editing either the parent or portal frame with the parent-portal latch active.
Our basic three-frame model for a parent canvas containing a single portal to a child canvas was orig-inally introduced in[OW00],which presented an equivalent notion of frames not based on space-scale diagrams.As justi?ed in[OW00],the three frames can be assigned the ordering parent frame portal frame child frame based on the conceptual distance from the user:the parent frame encloses the main display,the portal frame is an element inside that display,and the portal frame is conceptually located be-neath the main display,inside the portal frame.For convenience,we use the notation X+(and X?)to refer to the frame immediately succeeding(preceding)frame X in the conceptual order.Next we discuss user interaction.
3Spatial Model for Behavior During User Interaction
One way in which users can interact with nested multiscale interfaces is by editing the coordinates of the three frames in our model.Editing the(u,v,s)position of the parent frame,which always remains?xed in size,is accomplished via parent navigation operations,i.e.,pan and zoom.Many environments including [BHP+96,WOA+01]also support child navigation,which allows users to edit the(u,v,s)position of the child frame.For example,a user could potentially pan and zoom the child canvas in Figure5(b)to enlarge and recenter its contents without affecting the parent canvas.Panning either the parent or child frames alters the u and v position in the space-scale diagram of the center of the frame in a manner independent of the current scale.For example,a“pan left”operation performed at any scale will set u:=u?K for some constant K that does not depend on s.Zooming the parent or child frame changes the s position of the frame, typically while keeping it centered on the same great ray,thereby holding the x and y coordinates constant. Therefore,whenever zooming is performed,changing the scale from s to s ,the other two coordinates are updated automatically to u =u·s s.
In addition to editing the parent and child frames via parent and child navigation,users can edit the portal frame by manipulating the portal object.A portal can be thought of as an object having the special property that it displays another canvas,and some environments including[BHP+96,WOA+01]permit users to move and resize portal objects in the same manner as other non-portal objects.For example,a user could make the portal in Figure5(b)larger and reposition it.The effect on the space-scale diagram would be to enlarge and reposition the pyramid representing the portal frame.Under the simplest of behaviors,each frame can be freely edited by the user and each is independent,meaning that edits to one frame have no effect on the other two frames.However,many other behaviors are possible in which the user is prevented from editing certain frames,or,more interestingly,in which editing one frame causes changes to other frames.We now describe two types of fundamental properties,frame editability and dependencies,that govern these more complex behaviors.
3.1Frame Editability and Dependencies
As introduced in[OW00],there are two types of Boolean properties governing the fundamental behavior of portals during user interaction.Each frame has an editability property,and each ordered pair of frames has a dependency property,resulting in nine Boolean properties overall.We review these basic properties here before introducing our detailed model for frame dependencies based on spatial relationships among frames in Section3.2.
The user can be prevented from editing a frame by disabling the frame’s editability property.The editability of each frame can be con?gured independently.By default,editing one frame has no effect on the other two frames,although it may change the contents of the viewer window.For example,making the portal in Figure5(b)smaller does not affect the child frame,which remains in the same position in the space-scale diagram,so the same contents(two concentric circles)would be displayed in the smaller
s?nav
sticky
lens ?1
sticky lens ?1s?nav ?1portal frame
parent frame child frame
Figure 7:The three frames in our model,in order of conceptual distance from the user,with arcs between them representing potential dependencies between frames.
portal frame.Frame dependencies are properties that cause one frame to change automatically when the user edits another frame.Dependencies are one-way links between ordered pairs of frames,of which there are six.Each dependency can either be enabled or disabled.If a dependency from frame A to frame B ,written A →B ,is enabled,then whenever the user edits the position and/or size of frame A ,the position and/or size of frame B changes automatically.Of course,a dependency A →B cannot be enabled unless frame A is editable.On the other hand,even if frame B is not editable,the dependency can still be enabled.Editability only restricts direct editing,while still allowing indirect editing via frame dependencies.
There are six possible frame dependencies in our three-frame model.We classify the dependencies into forward and reverse dependencies.A dependency A →B is forward if A B ,and reverse otherwise.Each forward dependency A →B has an inverse,B →A that is a reverse dependency.It is helpful to think of the frame dependency properties of a portal as a directed graph with three vertices,one for each frame (parent,portal,and child),as shown in Figure 7with frames displayed in order of conceptual distance from the user,from left to right.Each arc in the graph is labeled with the name we give to the corresponding dependency.The three forward dependencies are named as follows:parent →portal ≡sticky ,parent →child ≡s-nav (for synchronous navigation),and portal →child ≡lens .We name their inverses sticky ?1,s-nav ?1,and lens ?1,respectively.
There are a total of 125distinct fundamental behaviors,considering only the Boolean editability and dependency properties,and accounting for the restriction that outgoing dependencies are only allowed from editable frames.Many of these behaviors are unintuitive and can be confusing,and three usability rules were proposed in [OW00]to eliminate unintuitive behaviors,reducing the number of allowed behaviors to 32.These 32intuitive behaviors are abstract,in the sense that our general model from [OW00]only considers whether dependencies between frames are enabled or disabled,and not what effect enabled dependencies have,which depends on the way dependencies are implemented.
The appropriate dependency implementation depends on the characteristics desired,which vary across applications.In some applications,the relationships among frames may not have any spatial signi?cance.For example,consider a political map visualization of the United States in which a recursive portal displays the home town of the governor of the state displayed in the main viewer window.The portal exhibits,among others,the s-nav dependency because edits to the parent frame (navigation in the main viewer window)can trigger a change to the child frame (portal contents),but the relationship is not spatial.On the other hand,in many common and natural applications of nested multiscale interfaces,dependent frames exhibit a spatial relationship.We describe our model for a spatial implementation of frame dependencies next.
3.2Spatial Implementation of Dependencies
Frame dependencies can be implemented in a way that obeys a spatial metaphor.There are at least two plausible metaphors for nested multiscale interfaces.In one,the portal frame is treated as a physical window, where moving closer spreads out the viewing angle,thereby enlarging the visible area of the child canvas. Alternatively,portals can be treated like hanging pictures rather than windows in this respect.Our original intuition when we helped develop portals in the DataSplash system[WOA+01]was to follow the physical window metaphor due to its correspondence with windows in the real world.However,after extensive experimentation it became clear that the physical window model was impractical because the portal contents could not be made invariant during zooming,making it dif?cult to program useful nested visualizations. Therefore,it was decided that the hanging picture metaphor would likely be superior for most purposes. We now present our spatial model for implementing frame dependencies,which is based on the hanging picture metaphor,and which satis?es the mapping transitivity and inversion properties de?ned in[OW00] and deemed essential for intuitive nested interface environments.For simplicity,we focus on recursive portals,but our model extends easily to non-recursive ones.
3.2.1Latches
The basic conceptual constructs in our spatial model are latches,which temporarily fasten together pairs of frames.There are two latches in our three-frame model,one between each pair of frames that are adjacent in conceptual order:the parent-portal latch and the child-portal latch.Each of the two latches involves one aperture(parent or child frame),represented as a?xed-size rectangle in the space-scale diagram,and the portal frame,represented as a pyramid of variable size.Consider the four points at which the four great rays making up the pyramid of the portal frame intersect the plane of one of the aperture frames.These are called the intersection points of the aperture frame,and their four(u,v)coordinates relative to the(u,v)position of the aperture frame center are called the relative intersection coordinates.When a latch is active,it fastens the relevant aperture frame to the portal frame by maintaining the relative intersection coordinates invariant, causing the movements of the two frames to be coordinated.
By physical analogy,an aperture frame can be thought of as being embedded in a thin,?at plate pierced by four rods representing the great rays of the portal frame,the ends of which are anchored to the origin. The holes in the plate made by the rods represent the relative intersection coordinates,which remain in the same position in the plate.The rods are permitted to slide freely up and down in the holes.When the latch is active,the effect is that moving the plate laterally(panning the aperture)causes the rods(portal frame) to move along with it.Moving the plate up(increasing the scale coordinate of the aperture by zooming) causes the angle between the rods to decrease and the portal frame to become smaller.Conversely,moving the plate down(decreasing the scale coordinate of the aperture by zooming)spreads the rods farther apart and causes the portal frame to grow larger,as illustrated in the transition from Figure5to Figure6,in which both panning and zooming of the parent frame aperture have been performed with the parent-portal latch active.Edits made to the portal frame transfer to the aperture frame via the same mechanism when the latch is active.Moving the rods in unison laterally(repositioning the portal frame)causes the plate to move along with them,indirectly panning the aperture.Bringing the rods closer together(reducing the size of the portal frame)causes the plate to move up,increasing the scale coordinate of the aperture such that the relative intersection coordinates remain unchanged.Conversely,spreading the rods apart(increasing the size of the portal frame)causes the plate to move down,decreasing the scale coordinate of the aperture.This effect is illustrated in the transition from Figure5to Figure6,which could have been accomplished by spreading out the portal frame rods with the parent-portal latch active.
We now describe the effect of latches mathematically.Let the parent aperture frame coordinates be (u p,v p,s p),and the coordinates of the lower-left and upper-right corners of the portal frame be(x1,y1)
Dependency
parent-portal
child-portal
child-portal
parent-portal
parent-portal
child-portal
s p
,y1·s p+(v p?v p)s
p
,y2·s p+(v p?v p) x 2?x 1
,v p+s p·
y2·y 1?y1·y 2
x 2?x 1
3
As before,it can be veri?ed that the relative intersection coordinates between the portal and parent frames remain unchanged.The corresponding formulae for the child-portal latch are similar.
As we will see in Section5,the concept of latches is useful for creating an animation sequence for entering a portal.The primary purpose of latches,however,is to link together the motions of dependent frames during editing by the user,as discussed next.
3.2.2Activation of Latches
Latches are inactive by default,and they may be activated temporarily during frame editing,depending on which dependencies are enabled.While the user is editing frame A,a latch is activated for each outgoing dependency A→X that is enabled.If A→X is a forward dependency,i.e.,A X,then the latch between X and X?(the frame immediately preceding X in the conceptual order)is activated while frame A is edited.Otherwise,if A→X is a reverse dependency,i.e.,X A,then the latch between X and X+ (the frame immediately succeeding X in the conceptual order)is activated.Put simply,if any dependency A→X is enabled,then while frame A is edited,the latch between X and the frame before X on the path from A to X is activated.For example,suppose the parent frame is edited,i.e.,the user pans or zooms in the parent canvas.If the sticky dependency(parent→portal)is enabled,then the parent-portal latch is activated during editing.If the s-nav dependency(parent→child)is enabled,then the child-portal latch is activated.If both dependencies are enabled,then both latches are activated while the parent frame is edited. Table1lists,for each dependency A→B,which latch is activated while the user edits frame A.Note that latch activation is not necessarily symmetric,e.g.,if the parent-portal latch is activated while the user edits the parent frame,it may not necessarily be activated while the user edits the portal frame.
Forward Dependencies Enabled Non-recursive Portal Tool Type {}canvas-stationary visual hyperlink
{lens} {
viewer-stationary magnifying glass
{sticky,s-nav}
?Visual hyperlinks are analogous to hypertext hyperlinks(e.g.,between Web pages)in that they allow the user to navigate instantly from a location on one canvas to a new location on the same can-vas,or some location on another canvas.Additionally,visual hyperlinks display the contents of the destination in a sub-window,providing a“preview”of the destination.Hyperlinks use no forward dependencies.
?Filter/transformers[BHP+96,SFB94]are portals that show an alternative representation of the region of the parent canvas that is occluded by the portal.For this type of tool,the lens dependency is enabled,causing the contents of a?lter/transformer to be correlated with its position and size in the parent canvas.
?Magnifying glasses[ACSW96,PF93]show a magni?ed view of the region of the canvas underneath.
See Figure1for an illustration.As with?lter/transformers,the lens dependency is enabled,causing the contents of a magnifying glass to be correlated with its position and size in the outer canvas.
?Overview tools are?xed on the screen and show a demagni?ed view of the portion of the canvas surrounding the current viewer window contents,creating an overview and detail view[CMS98].The s-nav dependency is enabled,causing the contents of an overview to be correlated with the contents of the main viewer window.The sticky dependency is also enabled,causing an overview tool to remain the same size and in the same position on the screen despite parent navigation.
?Coordinated views[Bel00,SFB94]remain on the screen at all times and show an alternative repre-sentation of the region of the parent canvas displayed in the main viewer window.See Figure2for an illustration.In contrast to?lter/transformers,the view displayed inside a coordinated view tool depends only on what is displayed in the main viewer window,and is not related to the position of the portal.As with overview tools,coordinated views have the sticky and s-nav dependencies enabled, causing them to remain stationary on the screen and their contents to be correlated with the contents of the viewer window.
Visual hyperlinks,?lter/transformers,and magnifying glasses can be either canvas-stationary or viewer-stationary.(Overview tools and coordinated views are always viewer-stationary by nature.)The position and size of a canvas-stationary tool are?xed relative to the canvas,and therefore the observed position relative to the viewer window changes during panning in the parent canvas and the observed size changes during zooming.In contrast,the position and size of viewer-stationary tools relative to the viewer window remains ?xed while parent navigation is performed.Canvas-stationary portal tools can be made viewer-stationary by enabling the sticky dependency and taking the transitive closure of the resulting dependency graph to guarantee dependency transitivity as required by the usability rules of[OW00].Viewer-stationary visual hyperlinks are also called bookmarks(known as indexes in Pad++[BHP+96]).For simplicity,throughout the remainder of this paper we focus on recursive portal tools and commonly refer to the?ve tool types by abbreviation:hyperlinks,bookmarks,canvas magni?ers,viewer magni?ers,and overviews.
4.2Programmability Options
Before we describe the second component of our taxonomy,frame programmability,we must?rst introduce the concept of interface state,upon which our notion of programmability is based.Let(x1,y1)and(x2,y2) be the lower-right and upper-left corners,respectively,of the portal frame,and let(u p,v p,s p)and(u c,v c,s c) be the coordinates of the parent and child frames,respectively.The interface state S of a parent canvas con-taining a nested child canvas speci?es the current coordinates of all three frames in our model.However,it is useful to reformulate the interface state in terms of relative relationships among frames.Recall from Sec-tion3.2.1that the points at which the portal frame intersects the plane of an aperture(parent or child frame),
in(u,v)coordinates relative to the aperture center are called the relative intersection coordinates.Since we require portals to have a?xed aspect ratio,we can encode the parent-portal relative intersection coordinates as the three-tuple I p= x1·s p?u p,y1·s p?v p,x2·s p?u p ,and the child-portal relative intersection coordinates similarly as I c= x1·s c?u c,y1·s c?v c,x2·s c?u c .The overall interface state can be rewritten
by encoding the coordinates of each frame relative to those of the previous frame in the conceptual order. The result is the following three-tuple of three-tuples:S= S parent,S portal,S child = u p,v p,s p ,I p,I c . The three components of the interface state,S parent,S portal,and S child,each correspond to one frame in our model,and together they specify unambiguously the coordinates of all three frames.S parent speci?es which part of the parent canvas is displayed inside the viewer window and S portal speci?es the placement and size of the portal within the viewer window.S child pertains to the contents of the portal and speci?es which portion of the child canvas is displayed inside the portal,relative to the placement and size of the portal outline within the parent canvas.For example,with a magnifying glass,S child determines the magni?cation factor as well as the offset between the portion of the outer canvas occluded by the magnifying glass and the portion of the canvas displayed inside it.
When a forward dependency between two frames is enabled,the interface state component of the de-pendent frame encodes the spatial relationship between the two frames.For example,in the case of the lens dependency for magnifying glasses,S child encodes the magni?cation factor and offset.Altering the inter-face state of the dependent frame can be thought of as a way to program the spatial relationship between the frames.When a frame is not dependent on any other frames,spatial relationships among frames are not rel-evant because its coordinates remain?xed unless it is edited directly,as with the child frame of a bookmark. In that case,altering its interface state can be thought of as a way to program its absolute coordinates.In either case,we refer to the act of altering a frame’s interface state by editing that frame as programming the frame.
We say that frame A is programmable if users can alter S A directly by editing A.If all frames are editable and no reverse dependencies are enabled,then all frames are programmable.Frame A can be made nonprogrammable in one of two ways.The?rst way is to make frame A non-editable,which has the indirect consequence of disabling any outgoing dependencies from A of the form A→X(recall from Section3.1that dependencies from non-editable frames are not allowed).Second,if any incoming forward dependencies to frame A are enabled,then A can be made nonprogrammable by adding inversion,which proceeds in two steps.First,for each forward incoming dependency X→A enabled,we enable its inverse A→X,which is a reverse dependency.Second,to guarantee dependency transitivity as required by the usability rules of[OW00],we take the transitive closure of the resulting dependency graph.Adding inversion is only applicable if at least one forward dependency into frame A is enabled.Note that both methods for making a frame nonprogrammable,adding inversion and disabling editability,can result in a change to the tool type by affecting which forward dependencies are enabled.Adding inversion can in some cases lead to additional forward dependencies being enabled due to the transitive closure step.Disabling editability can lead to one or more forward dependencies being disabled since outgoing dependencies from non-editable frames are not permitted.We revisit this apparent oddity below in Section4.3.
To illustrate the two options for making frames nonprogrammable,we take as an example a fully pro-grammable canvas magni?er,which has only the lens dependency enabled.Since a magnifying glass shows a detailed view of a small area of the canvas,users may wish to explore the immediate neighborhood of that view without affecting the outer view by panning inside the magnifying glass.Performing this action amounts to editing the child frame,which alters S child and programs the offset between the position of the magnifying glass in the canvas and the location viewed within the magnifying glass.Normally,the offset of a magnifying glass is kept at zero,so programming the offset may,for novice users,result in unexpected behavior during further interaction.Therefore,it may be appropriate to disable programming of the child frame for novice users.For magnifying glasses,which have the lens forward dependency enabled,there are two ways to disable child frame programmability.The simplest is to disable editing of the child frame,
disallowing users from panning or zooming the contents of the portal directly.The second way to make
the child frame nonprogrammable is to add inversion by enabling the lens?1dependency.In the resulting
behavior,if a user pans the contents of the magnifying glass,the magnifying glass itself moves within the
outer canvas to remain centered over the portion of the canvas shown in the magni?ed inner view.The effect
is the same as if the user had instead repositioned the magnifying glass over a new area of the outer canvas,
keeping the offset?xed at zero.
Both options for making the child frame nonprogrammable are possible with canvas-stationary magni-
fying glasses,but for tools with no forward dependencies into the child frame enabled,it is not possible to
add inversion.For example,consider a bookmark tool,which does not use the lens dependency.It is not ap-
propriate to attempt to prevent the user from programming the bookmark contents(child frame)by enabling
the lens?1dependency,thereby causing the bookmark tool to be repositioned or resized in the parent canvas
in response to child navigation.In fact,this behavior is not permitted by the usability rules.
In summary,there are?ve types of tools,de?ned by which forward dependencies are enabled.For each
type of tool,each frame can be either programmable or nonprogrammable,depending on which frames
are editable and which reverse dependencies are enabled.A frame can always be made nonprogrammable
by disabling editability of that frame.In some cases,the same frame can alternatively be made nonpro-
grammable by adding inversion.Note that the programmability of the parent frame is a global option,which
affects the entire interface by preventing the user from panning and zooming the parent canvas.In contrast,
the programmability of the portal and child frames only pertains to an individual portal,and can be con?g-
ured differently for each portal present in the interface.We now present our overall taxonomy of portal tools
that obey our spatial model,which classi?es them by tool type and programmability.
4.3Portal Tool Taxonomy
Table3lists every allowed combination of tool type and programmability options,along with the resulting
behavior.Behaviors are represented as three strings of three T/F values each.The?rst string encodes which
forward dependencies are enabled,in the order sticky,s-nav,lens,and the second string encodes which
reverse dependencies are enabled,in the order sticky?1,s-nav?1,lens?1.The third string encodes which
frames are editable,in the order parent,portal,child.For each tool type,the?rst eight rows correspond to
the23=8options available by making each frame either programmable(indicated by“Y”),or nonpro-grammable by disabling editability(indicated by“N-noned”),which are always possible for each frame.
Additional rows,if any,correspond to options resulting from making one or more frames nonprogrammable
by adding inversion(indicated by“N-inv”),which is only possible in some cases.Each unique behavior
obtained by selecting a tool type and choosing a programmability option for each frame is assigned a unique
identi?cation number.As discussed above,in some cases disabling programmability of frames(either by
disabling editability or by adding inversion)may enable or disable one or more forward dependencies,
causing the behavior to be equivalent to that of another tool type.We indicate such cases in Table3by
referencing the identi?cation number of the equivalent behavior in parentheses.While the number of valid
tool type and programmability options is greater,there are32nonequivalent behaviors,accounting for all 32behaviors that satisfy the usability rules of[OW00].
To illustrate how a portal tool can become equivalent to another due to making some aspect nonpro-
grammable,we present two examples.First,making the parent frame nonprogrammable by disabling ed-
itability removes the sticky and s-nav dependencies of any portal tools present since outgoing dependencies
are not allowed in the absence of editability.Therefore,when the parent frame is not editable,a book-
mark,which normally employs the sticky dependency,is equivalent to a hyperlink,which has the sticky
dependency disabled(see the?fth through eighth rows for the bookmark tool type in Table3).This equiv-
alence makes intuitive sense:if the user is not permitted to pan or zoom the parent canvas,then there is no
detectable difference between canvas-stationary and viewer-stationary tools.
Programmability Options
Reverse Deps.
Y Y FFF TTT1
Y N-noned FFF TTF2
Y Y FFF TFT3
Y N-noned FFF TFF4
N-noned Y FFF FTT5
N-noned N-noned FFF FTF6
N-noned Y FFF FFT7
N-noned N-noned FFF FFF8 bookmark Y FFF
Y FFF
N-noned FFF
N-noned FFF
Y FFF
Y FFF
N-noned FFF
N-noned FFF
N-inv TFF
N-inv TFF
Y Y FFT TTT15
Y N-noned FFT TTF16
Y Y FFF TFT(3)
Y N-noned FFF TFF(4)
N-noned Y FFT FTT17
N-noned N-noned FFT FTF18
N-noned Y FFF FFT(7)
N-noned N-noned FFF FFF(8)
Y N-inv FFT TTT19
N-noned N-inv FFT FTT20 viewer Y FFF
magni?er Y FFF
N-noned FFF
N-noned FFF
Y FFF
Y FFF
N-noned FFF
N-noned FFF
Y FFT
Y FFT
N-noned FTT
N-inv TFF
N-inv TFF
N-inv TTT
Y Y TTF TTT27
Y N-noned TTF TTF28
Y Y TTF TFT29
Y N-noned TTF TFF30
N-noned Y FFF FTT(5)
N-noned N-noned FFF FTF(6)
N-noned Y FFF FFT(7)
N-noned N-noned FFF FFF(8)
Y N-inv TTF TTT31
Y N-inv TTF TFT32
Y Y TTT TTT(24)
Y N-noned TTT TTF(25)
Y N-inv TTT TTT(26)
As a second example,consider a coordinated view tool(as in Figure2),which,like an overview tool, has both the sticky and s-nav forward dependencies enabled,and whose contents remain unchanged when the user edits the position or size of the portal in the viewer window.As suggested in Section1.1,it may be appropriate to make the portal frame nonprogrammable to simplify the behavior and avoid confusing novice users.Making the portal frame nonprogrammable by adding inversion causes the sticky?1dependency to be enabled,and taking the transitive closure causes the lens dependency to be enabled as well.Therefore, a coordinated view tool with a portal frame made nonprogrammable by adding inversion is equivalent to a viewer magni?er,which has all three forward dependencies enabled(see the last three rows of Table3). This equivalence makes intuitive sense as well:the only difference between a coordinated view tool and a viewer magni?er is that with a viewer magni?er,the contents of the portal change when the user edits the portal’s position or size relative to the viewer window.If the user is not permitted to reposition or resize the portal relative to the viewer window then the effective difference between the two tool types is removed. (Of course,although the two tool types share a common behavior in this case,they may be instantiated differently,i.e.,have opposite magni?cation factors.)
5Animating the Entrance Into a Portal
An important feature in some nested multiscale interface environments is the ability of the user to“enter”
a portal[WOA+01],causing the parent canvas and frame to be replaced by the child canvas and frame. This feature is clearly useful for navigation aides such as visual hyperlinks and bookmarks.Interestingly, it can also be a convenient feature for other types of tools.For example,entering a magnifying glass is a convenient shortcut for increasing the scale of the canvas(magnifying the main view).Conversely,entering an overview is a simple way to demagnify the view rapidly.Entering a?lter/transformer or coordinated view tool offers a convenient method of converting the main view into the alternative one shown inside the portal tool.
When the user enters a portal,to maintain the user’s orientation it may be helpful for the system to perform an animated transition from the current interface state to the?nal state resulting from entering the portal.There are many ways to execute this animation,and we propose three alternatives based on nested space-scale diagrams here.One alternative is to deactivate both latches and navigate the parent frame to the position in which its four corners meet the four great rays of the portal frame pyramid,following one of the pan-zoom trajectories proposed in[FB95]such as a hyperbolic trajectory.The effect seen by the user of navigating along this path is that of“zooming in”on the portal until it?lls the entire viewer window.A second alternative is to deactivate both latches and enlarge the portal frame gradually until its four great rays reach the four corners of the parent frame,causing the portal to appear to grow progressively until it?lls the entire viewer window.In both these alternatives,after the animation has been performed,the?nal step is to replace the parent canvas and frame by the child canvas and frame,which will have the effect of deleting the portal outline from the viewer window perimeter and completing the seamless transformation from parent view to child view.
The previous two approaches,which align the parent and portal frames by animating the motion of one of them with both latches deactivated,can be used to animate the entrance into any portal.The following third approach may be the most effective in maintaining user orientation during the entrance into a recursive portal,or more generally any portal to another canvas with equivalent coordinates,such as a?lter.This approach aligns all three frames and proceeds in two phases:one to align the portal and child frames,and a second to bring the parent frame into alignment with the other two frames.In the?rst phase,the parent-portal latch is activated while the parent frame is displaced(along with the latched portal frame)using a smooth animation to a new location in which the four great rays of the latched portal frame intersect the four corners of the child frame,as illustrated in the transition from Figure5to Figure6.(A pan-zoom trajectory
from[FB95]such as a hyperbolic trajectory can be used for this phase.)In the second phase,both latches are deactivated and the parent frame is moved to the position of the child frame,again using a pan-zoom trajectory from[FB95].At the end of the second phase,the child frame replaces the parent frame,now at the same position,and for non-recursive portals the child canvas replaces the parent canvas,completing the transition.The overall effect of this approach seen by the user of the?rst phase is that the parent canvas is panned and zoomed to align the outer view to the inner one like a jigsaw puzzle.In the second phase,the main viewer“zooms in”on the portal until it?lls the entire viewer window.
6Summary and Future Work
In this paper we have described a spatial model for nested multiscale interfaces that we constructed based on experience with spatial metaphors in a prototype data visualization system.Our model uses space-scale diagrams and a physical analogy of rods piercing plates to describe the behavior of portals in response to user actions such as panning,zooming,and repositioning the portal.We also provided a taxonomy of tools that can be constructed using portals that obey our spatial model,classifying them by tool type and programmability by users.(To accompany our spatial model and portal tool taxonomy,we created an online demonstration program[Ols02],which may aid in understanding how the portal tools in our taxonomy behave in response to user actions.)Finally,we used our model of spatial relationships to propose techniques for smoothly animating the transition from the outer view to the inner view displayed inside a portal,helping to maintain user orientation during navigation between nested worlds.
The design of animated transitions between nested worlds serves as an example of how our formalisms might be used in practice.In general,it is our belief that the formal model presented here can be of signi?cant bene?t to researchers,designers,programmers,and users of nested multiscale interfaces.Researchers can use our framework as a basis for reasoning about properties of portal tool con?gurations including spatial dependencies and programmability options.Also,our taxonomy of possible behaviors can assist designers faced with the nontrivial tasks of deciding which of the32recommended behaviors to make available and how best to offer control over the tool type and programmability options to end-users.In addition,our formal model can serve as a speci?cation for implementors of nested user interfaces.Finally,our physical analogy of plates and rods along with our interactive demonstration program may be useful in documenting the behavior of nested interface components for end-users.
As future work we plan to re?ne our taxonomy to allow frames in our model to be partially pro-grammable,in addition to the existing options of full programmability and strictly non-programmability. For example,with a magnifying glass for novice users it may be appropriate to allow programming of the magni?cation factor,but at the same time require that the offset between the portion of the outer canvas occluded by the magnifying glass and the magni?ed portion displayed inside it remain?xed at zero.Doing so would require making the child frame partially programmable,since both the magni?cation factor and offset are encoded in the child component of the interface state.We believe that our notion of interface state,overall model,and taxonomy can be extended in a straightforward manner to accommodate partial programmability of frames.
Acknowledgments
We thank the other members of the Tioga DataSplash research group at UC Berkeley for many useful discussions over the years:Alexander Aiken,Michael Chu,Vuk Ercegovac,Mark Lin,Mybrid Spalding, Michael Stonebraker,and Allison Woodruff.We also thank Chris Stolte for helpful feedback.This research was supported by a Chambers Stanford Graduate Fellowship.
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8字模型与飞镖模型模型1：角的8字模型 如图所示，AC 、BD 相交于点O ，连接AD 、BC ． 结论：∠A ＋∠D ＝∠B ＋∠C ． O D C B A 模型分析 证法一： ∵∠AOB 是△AOD 的外角，∴∠A ＋∠D ＝∠AOB ．∵∠AOB 是△BOC 的外角， ∴∠B ＋∠C ＝∠AOB ．∴∠A ＋∠D ＝∠B ＋∠C ． 证法二： ∵∠A ＋∠D ＋∠AOD ＝180°，∴∠A ＋∠D ＝180°－∠AOD ．∵∠B ＋∠C ＋∠BOC ＝180°， ∴∠B ＋∠C ＝180°－∠BOC ．又∵∠AOD ＝∠BOC ，∴∠A ＋∠D ＝∠B ＋∠C ． （1）因为这个图形像数字8，所以我们往往把这个模型称为8字模型． （2）8字模型往往在几何综合题目中推导角度时用到． 模型实例 观察下列图形，计算角度： （1）如图①，∠A ＋∠B ＋∠C ＋∠D ＋∠E ＝________； 图图① F D C B A E E B C D A 图③ 2 1O A B 图④ G F 12 A B E 解法一：利用角的8字模型．如图③，连接CD ．∵∠BOC 是△BOE 的外角， ∴∠B ＋∠E ＝∠BOC ．∵∠BOC 是△COD 的外角，∴∠1＋∠2＝∠BOC ． ∴∠B ＋∠E ＝∠1＋∠2．（角的8字模型），∴∠A ＋∠B ＋∠ACE ＋∠ADB ＋∠E ＝∠A ＋∠ACE ＋∠ADB ＋∠1＋∠2＝∠A ＋∠ACD ＋∠ADC ＝180°． 解法二：如图④，利用三角形外角和定理．∵∠1是△FCE 的外角，∴∠1＝∠C ＋∠E ．
∵∠2是△GBD 的外角，∴∠2＝∠B ＋∠D ． ∴∠A ＋∠B ＋∠C ＋∠D ＋∠E ＝∠A ＋∠1＋∠2＝180°． （2）如图②，∠A ＋∠B ＋∠C ＋∠D ＋∠E ＋∠F ＝________． 图② F D C B A E 312图⑤ P O Q A B F C D 图⑥ 2 1 E D C F O B A （2）解法一： 如图⑤，利用角的8字模型．∵∠AOP 是△AOB 的外角，∴∠A ＋∠B ＝∠AOP ． ∵∠AOP 是△OPQ 的外角，∴∠1＋∠3＝∠AOP ．∴∠A ＋∠B ＝∠1＋∠3．①（角的8字模型），同理可证：∠C ＋∠D ＝∠1＋∠2．② ，∠E ＋∠F ＝∠2＋∠3．③ 由①＋②＋③得：∠A ＋∠B ＋∠C ＋∠D ＋∠E ＋∠F ＝2（∠1＋∠2＋∠3）＝360°． 解法二：利用角的8字模型．如图⑥，连接DE ．∵∠AOE 是△AOB 的外角， ∴∠A ＋∠B ＝∠AOE ．∵∠AOE 是△OED 的外角，∴∠1＋∠2＝∠AOE ． ∴∠A ＋∠B ＝∠1＋∠2．（角的8字模型） ∴∠A ＋∠B ＋∠C ＋∠ADC ＋∠FEB ＋∠F ＝∠1＋∠2＋∠C ＋∠ADC ＋∠FEB ＋∠F ＝360°．（四边形内角和为360°） 练习： 1．（1）如图①，求：∠CAD ＋∠B ＋∠C ＋∠D ＋∠E ＝ ； 图 图① O O E E D D C C B B A A 解：如图，∵∠1=∠B+∠D ，∠2=∠C+∠CAD ， ∴∠CAD+∠B+∠C+∠D+∠E=∠1+∠2+∠E=180°． 故答案为：180° 解法二：
美国常青藤名校的由来 以哈佛、耶鲁为代表的“常青藤联盟”是美国大学中的佼佼者，在美国的3000多所大学中，“常青藤联盟”尽管只是其中的极少数，仍是许多美国学生梦想进入的高等学府。 常青藤盟校(lvy League)是由美国的8所大学和一所学院组成的一个大学联合会。它们是：马萨诸塞州的哈佛大学，康涅狄克州的耶鲁大学，纽约州的哥伦比亚大学，新泽西州的普林斯顿大学，罗德岛的布朗大学，纽约州的康奈尔大学，新罕布什尔州的达特茅斯学院和宾夕法尼亚州的宾夕法尼亚大学。这8所大学都是美国首屈一指的大学，历史悠久，治学严谨，许多著名的科学家、政界要人、商贾巨子都毕业于此。在美国，常青藤学院被作为顶尖名校的代名词。 常青藤盟校的说法来源于上世纪的50年代。上述学校早在19世纪末期就有社会及运动方面的竞赛，盟校的构想酝酿于1956年，各校订立运动竞赛规则时进而订立了常青藤盟校的规章，选出盟校校长、体育主任和一些行政主管，定期聚会讨论各校间共同的有关入学、财务、援助及行政方面的问题。早期的常青藤学院只有哈佛、耶鲁、哥伦比亚和普林斯顿4所大学。4的罗马数字为“IV”，加上一个词尾Y，就成了“IVY”，英文的意思就是常青藤，所以又称为常青藤盟校，后来这4所大学的联合会又扩展到8所，成为现在享有盛誉的常青藤盟校。 这些名校都有严格的入学标准，能够入校就读的学生，自然是品学兼优的好学生。学校很早就去各个高中挑选合适的人选，许多得到全国优秀学生奖并有各种特长的学生都是他们网罗的对象。不过学习成绩并不是学校录取的惟一因素，学生是否具有独立精神并且能否快速适应紧张而有压力的大一新生生活也是他们考虑的重要因素。学生的能力和特长是衡量学生综合素质的重要一关，高中老师的推荐信和评语对于学生的入学也起到重要的作用。学校财力雄厚，招生办公室可以完全根据考生本人的情况录取，而不必顾虑这个学生家庭支付学费的能力，许多家境贫困的优秀子弟因而受益。有钱人家的子女，即使家财万贯，也不能因此被录取。这也许就是常青藤学院历经数百年而保持“常青”的原因。 布朗大学(Brown University) 1754年由浸信会教友所创，现在是私立非教会大学，是全美第七个最古老大学。现有学生7000多人，其中研究生近1500人。 该校治学严谨、学风纯正，各科系的教学和科研素质都极好。学校有很多科研单位，如生物医学中心，计算机中心、地理科学中心、化学研究中心、材料研究实验室、Woods Hole 海洋地理研究所海洋生物实验室、Rhode 1s1and反应堆中心等等。设立研究生课程较多的系有应用数学系、生物和医学系、工程系等，其中数学系海外研究生占研究生名额一半以上。 布朗大学的古书及1800年之前的美国文物收藏十分有名。 哥伦比亚大学(Columbia University) 私立综合性大学，位于纽约市。该校前身是创于1754年的King’s College，独立战争期间一度关闭，1784年改名力哥伦比亚学院，1912年改用现名。
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网络仿真文献综述 摘要:网络仿真技术是一种通过建立网络设备和网络链路的统计模型, 并模拟网络流量的传输, 从而获取网络设计或优化所需要的网络性能数据的仿真技术。网络仿真技术以其独有的方法能够为网络的规划设计提供客观、可靠的定量依据，缩短网络建设周期，提高网络建设中决策的科学性，降低网络建设的投资风险。 网络仿真技术是一种通过建立网络设备和网络链路的统计模型, 并模拟网络流量的传输, 从而获取网络设计或优化所需要的网络性能数据的仿真技术。由于仿真不是基于数学计算, 而是基于统计模型，因此，统计复用的随机性被精确地再现。 关键词：网络仿真；统计模型；仿真技术
1.前言 目前，数据网络的规划和设计一般采用的是经验、试验及计算等传统的网络设计方法。不过，当网络规模越来越大、网元类型不断增多、网络拓扑日趋复杂、网络流量纷繁交织时，以经验为主的网络设计方法的弊端就越来越显现出来了。网络规划设计者相对来说缺乏大型网络的设计经验，因此在设计过程中主观的成分更加突出。 数学计算和估算方法对于大型复杂网络的应用往往是非常困难的，得到的结果的可信性也是比较低的，特别是对于包交换、统计复用的数据网络，情况更是如此。因此，随着网络的不断扩充，越来越需要一种新的网络规划和设计手段来提高网络设计的客观性和设计结果的可靠性，降低网络建设的投资风险。网络仿真技术正是在这种需求拉动下应运而生的。网络仿真技术以其独有的方法能够为网络的规划设计提供客观、可靠的定量依据，缩短网络建设周期，提高网络建设中决策的科学性，降低网络建设的投资风险。 网络仿真技术是一种通过建立网络设备和网络链路的统计模型, 并模拟网络流量的传输, 从而获取网络设计或优化所需要的网络性能数据的仿真技术。由于仿真不是基于数学计算, 而是基于统计模型，因此，统计复用的随机性被精确地再现。它以其独有的方法为网络的规划设计提供客观、可靠的定量依据，缩短网络建设周期，提高网络建设中决策的科学性，降低网络建设的投资风险。 2.网络仿真软件比较分析 网络仿真软件通过在计算机上建立一个虚拟的网络平台，来实现真实网络环境的模拟，网络技术开发人员在这个平台上不仅能对网络通信、网络设备、协议、以及网络应用进行设计研究，还能对网络的性能进行分析和评价。另外，仿真软件所提供的仿真运行和结果分析功能使开发人员能快速、直观的得到网络性能参数，为优化设计或做出决策提供更便捷、有效的手段。因此运用网络仿真软件对网络协议、算法等进行仿真已经成为计算机网络通信研究中必不可少的一部分。 2.1 OPNET仿真软件介绍
第四章景观模型制作 第一节主要工具的使用方法 —、主要切割材料工具的使用方法 （—）美术刀 美术刀是常用的切割工具，一般的模型材料（纸板，航模板等易切割的材料）都可使用它来进行切割，它能胜任模型制作过程中，从粗糙的加工到惊喜的刻划等工作，是一种简便，结实，有多种用途的刀具。美术刀的道具可以伸缩自如，随时更换刀片;在细部制作时，在塑料板上进行划线，也可切割纸板，聚苯乙烯板等。具体使用时，因根据实际要剪裁的材料来选择刀具，例如，在切割木材时，木材越薄越软，刀具的刀刃也应该越薄。厚的刀刃会使木材变形。 使用方法：先在材料商画好线，用直尺护住要留下的部分，左手按住尺子，要适当用力（保证裁切时尺子不会歪斜），右手捂住美术刀的把柄，先沿划线处用刀尖从划线起点用力划向终点，反复几次，直到要切割的材料被切开。 （二）勾刀 勾刀是切割切割厚度小于10mm的有机玻璃板，ABS工程塑料版及其他塑料板材料的主要工具，也可以在塑料板上做出条纹状机理效果，也是一种美工工具。 使用方法：首先在要裁切的材料上划线，左手用按住尺子，护住要留下的部分，右手握住勾刀把柄，用刀尖沿线轻轻划一下，然后再用力度适中地沿着刚才的划痕反复划几下，直至切割到材料厚度的三分之二左右，再用手轻轻一掰，将其折断，每次勾的深度为0.3mm 左右。 （三）剪刀 模型制作中最常用的有两种刀：一种是直刃剪刀，适于剪裁大中型的纸材，在制作粗模型和剪裁大面积圆形时尤为有用；另外一种是弧形剪刀，适于剪裁薄片状物品和各种带圆形的细部。 （四）钢锯 主要用来切割金属、木质材料和塑料板材。 使用方法：锯材时要注意，起锯的好坏直接影响锯口的质量。为了锯口的凭证和整齐，握住锯柄的手指，应当挤住锯条的侧面，使锯条始终保持在正确的位置上，然后起锯。施力时要轻，往返的过程要短。起锯角度稍小于15°，然后逐渐将锯弓改至水平方向，快钜断时，用力要轻，以免伤到手臂。 （五）线锯 主要用来加工线性不规则的零部件。线锯有金属和竹工架两种，它可以在各种板材上任意锯割弧形。竹工架的制作是选用厚度适中的竹板，在竹板两端钉上小钉，然后将小钉弯折成小勾，再在另一端装上松紧旋钮，将锯丝两头的眼挂在竹板两端即可使用。 使用方法：使用时，先将要割锯的材料上所画的弧线内侧用钻头钻出洞，再将锯丝的一头穿过洞挂在另一段的小钉上，按照所画弧线内侧1左右进行锯割，锯割方向是斜向上下。 二、辅助工具及其使用方法 （一）钻床 是用来给模型打孔的设备。无论是在景观模型、景观模型还是在展示模型中，都会有很多的零部件需要镂空效果时，必须先要打孔。钻孔时，主要是依靠钻头与工件之间的相对运动来完成这个过程的。在具体的钻孔过程中，只有钻头在旋转，而被钻物体是静止不动的。 钻床分台式和立式两种。台式钻床是一种可以放在工台上操作的小型钻床，小巧、灵活，使
O D C B A 图12图E A B C D E F D C B A O O 图12图E A B C D E D C B A H G E F D C B A 第一章 8字模型与飞镖模型 模型1 角的“8”字模型 如图所示，AB 、CD 相交于点O ， 连接AD 、BC 。 结论：∠A+∠D=∠B+∠C 。 模型分析 8字模型往往在几何综合 题目中推导角度时用到。 模型实例 观察下列图形，计算角度： （1）如图①，∠A+∠B+∠C+∠D+∠E= ； （2）如图②，∠A+∠B+∠C+∠D+∠E+∠F= 。 热搜精练 1．（1）如图①，求∠CAD+∠B+∠C+∠D+∠E= ； （2）如图②，求∠CAD+∠B+∠ACE+∠D+∠E= 。 2．如图，求∠A+∠B+∠C+∠D+∠E+∠F+∠G+∠H= 。
D C B A M D C B A O 135E F D C B A 105O O 120 D C B A 模型2 角的飞镖模型 如图所示，有结论： ∠D=∠A+∠B+∠C 。 模型分析 飞镖模型往往在几何综合 题目中推导角度时用到。 模型实例 如图，在四边形ABCD 中，AM 、CM 分别平分∠DAB 和∠DCB ，AM 与CM 交于M 。探究∠AMC 与∠B 、∠D 间的数量关系。 热搜精练 1．如图，求∠A+∠B+∠C+∠D+∠E+∠F= ； 2．如图，求∠A+∠B+∠C+∠D = 。
O D C B A O D C B A O C B A 模型3 边的“8”字模型 如图所示，AC 、BD 相交于点O ，连接AD 、BC 。 结论：AC+BD>AD+BC 。 模型实例 如图，四边形ABCD 的对角线AC 、BD 相交于点O 。 求证：（1）AB+BC+CD+AD>AC+BD ； （2）AB+BC+CD+AD<2AC+2BD. 模型4 边的飞镖模型 如图所示有结论： AB+AC>BD+CD 。
描写常青藤优美句段写常青藤作文散文句子 描写常青藤优美句段写常青藤作文散文句子第1段： 1.睁开朦胧的泪眼，我猛然发觉那株濒临枯萎的常春藤已然绿意青葱，虽然仍旧瘦小，却顽强挣扎，嫩绿的枝条攀附着窗格向着阳光奋力伸展。 2.常春藤是一种常见的植物，我家也种了两盆。可能它对于很多人来说都不足为奇，但是却给我留下了美好的印象。常春藤属于五加科常绿藤本灌木，翠绿的叶子就像火红的枫叶一样，是可爱的小金鱼的尾巴。常春藤的叶子的长约5厘米，小的则约有2厘米，但都是小巧玲珑的，十分可爱。叶子外圈是白色的，中间是翠绿的，好像有人在叶子上涂了一层白色的颜料。从叶子反面看，可以清清楚楚地看见那凸出来的，一根根淡绿色的茎。 3.渴望到森林里探险，清晨，薄薄的轻雾笼罩在树林里，抬头一看，依然是参天古木，绕着树干一直落到地上的常春藤，高高低低的灌木丛在小径旁张牙舞爪。 4.我们就像马蹄莲，永不分开，如青春的常春藤，紧紧缠绕。 5.我喜欢那里的情调，常春藤爬满了整个屋顶，门把手是旧的，但带着旧上海的味道，槐树花和梧桐树那样美到凋谢，这是我的上海，这是爱情的上海。 6.当我离别的时候，却没有你的身影；想轻轻地说声再见，已是人去楼空。顿时，失落和惆怅涌上心头，泪水也不觉悄悄滑落我伫立很久很久，凝望每一条小路，细数每一串脚印，寻找你
的微笑，倾听你的歌声――一阵风吹过，身旁的小树发出窸窸窣窣的声音，像在倾诉，似在安慰。小树长高了，还有它旁边的那棵常春藤，叶子依然翠绿翠绿，一如昨天。我心头不觉一动，哦，这棵常春藤陪伴我几个春秋，今天才惊讶于它的可爱，它的难舍，好似那便是我的生命。我蹲下身去。轻轻地挖起它的一个小芽，带着它回到了故乡，种在了我的窗前。 7.常春藤属于五加科常绿藤本灌木，翠绿的叶子就像火红的枫叶一样，是可爱的小金鱼的尾巴。常春藤的叶子的长约5厘米，小的则约有2厘米，但都是小巧玲珑的，十分可爱。叶子外圈是白色的，中间是翠绿的，好像有人在叶子上涂了一层白色的颜料。从叶子反面看，可以清清楚楚地看见那凸出来的，一根根淡绿色的茎。 8.常春藤是多么朴素，多么不引人注目，但是它的品质是多么的高尚，不畏寒冷。春天，它萌发出嫩绿的新叶；夏天，它郁郁葱葱；秋天，它在瑟瑟的秋风中跳起了欢快的舞蹈；冬天，它毫不畏惧呼呼作响的北风，和雪松做伴常春藤，我心中的绿色精灵。 9.可是对我而言，回头看到的只是雾茫茫的一片，就宛如窗前那株瘦弱的即将枯死的常春藤，毫无生机，早已失去希望。之所以叫常春藤，可能是因为它一年四季都像春天一样碧绿，充满了活力吧。也许，正是因为如此，我才喜欢上了这常春藤。而且，常春藤还有许多作用呢！知道吗？一盆常春藤能消灭8至10平
XXX理工大学 CHANGSHA UNIVERSITY OF TECHNOLOGY&TECHNOLGY 题目：多领域建模理论与方法 学院： XXX 学生： XXX 学号: XXX 指导教师： XXX 2015年7月2日
多领域建模理论和方法 The theories and methods of Multi-domain Modeling Student:XXX Teacher:XXX 摘要 建模理论和方法是推动仿真技术进步和发展的重要因素，也是系统仿真可持续发展的基础[1]文中综述了多领域建模主要采用的四种方法，并重点对基于云制造的多领域建模和仿真进行了叙述，并对其发展进行了展望。 关键词：多领域建模仿真；云制造；展望 Abstract：The theory and method of system model building is not only the key factor to stimulate the development and improvement of simulation technique but also the base of system simulation. This paper analysis four prevails way in Multi-domain Modeling, especially to the Multi-domain Modeling and Simulation in cloud manufacturing environment. We give a detail on its development and future. Keywords: Multi-domain Modeling and simulation; Cloud manufacturing; Future development 一引言 随着科学技术的发展进步和产品的升级需求，对产品提出了更高的要求，使得建模对象的组成更加复杂，涉及到各个学科、进程的复杂性以及设计方法的多元化。这些需求都是以前单领域建模方案无法满足的，因此，必须建立一个建模方式在设计过程中完成对繁杂目标的多领域建模、结构仿真、多元化分析等。 多领域建模是将机械、控制、电子等不同学科领域的模型“组装”成一个更大的模型进行仿真。根据需要的不同，实际建模过程中，可以将模型层层分解。将不同领域的仿真模型“零件”组装成“部件”，“子系统”则是由不同学科下的部件装配而成，与此同时装配完成的不同学科的分子系统还能再装配成为一个全面仿真模型，称之为“系统”，由此可见多领域建模技术在繁杂产品设计过程中具有出众的优势。 本文对多领域建模常用的四种方法：基于各领域商用仿真软件接口的建模方法；基于高层体系结构的建模方法；基于统一建模语言的多领域建模方法和基于云制造环境下多领域建模的方法进行了分析并对基于云制造环境下多领域建模方法进行了展望。
一、常青藤大学 目录 联盟概述 联盟成员 名称来历 常春藤联盟（The Ivy League）是指美国东北部八所院校组成的体育赛事联盟。这八所院校包括：布朗大学、哥伦比亚大学、康奈尔大学、达特茅斯学院、哈佛大学、宾夕法尼亚大学、普林斯顿大学及耶鲁大学。美国著名的体育联盟还有太平洋十二校联盟（Pacific 12 Conference）和大十联盟（Big Ten Conference）。常春藤联盟的体育水平在美国大学联合会中居中等偏下水平，远不如太平洋十校联盟和大十联盟。 联盟概述 常春藤盟校（Ivy League）指的是由美国东北部地区的八所大学组成的体育赛事联盟（参见NCAA词条）。它们全部是美国一流名校、也是美国产生最多罗德奖学金得主的大学联盟。此外，建校时间长，八所学校中的七所是在英国殖民时期建立的。 美国八所常春藤盟校都是私立大学，和公立大学一样，它们同时接受联邦政府资助和私人捐赠，用于学术研究。由于美国公立大学享有联邦政府的巨额拨款，私立大学的财政支出和研究经费要低于公立大学。 常青藤盟校的说法来源于上世纪的50年代。上述学校早在19世纪末期就有社会及运动方面的竞赛，盟校的构想酝酿于1956年，各校订立运动竞赛规则时进而订立了常青藤盟校的规章，选出盟校校长、体育主任和一些行政主管，定期聚会讨论各校间共同的有关入学、财务、援助及行政方面的问题。早期的常青藤学院只有哈佛、耶鲁、哥伦比亚和普林斯顿4所大学。4的罗马数字为"IV"，加上一个词尾Y，就成了"IVY"，英文的意思就是常青藤，所以又称为常青藤盟校，后来这4所大学的联合会又扩展到8所，成为如今享有盛誉的常青藤盟校。 这些名校都有严格的入学标准，能够入校就读的学生，必须是品学兼优的好学生。学校很早就去各个高中挑选合适的人选，许多得到全国优秀学生奖并有各种特长的学生都是他们网罗的对象。不过学习成绩并不是学校录取的惟一因素，学生是否具有独立精神并且能否快速适应紧张而有压力的大一新生生活也是他们考虑的重要因素。学生的能力和特长是衡量学生综合素质的重要一关，高中老师的推荐信和评语对于学生的入学也起到重要的作用。学校财力雄厚，招生办公室可以完全根据考生本人的情况录取，而不必顾虑这个学生家庭支付学费的能力，许多家境贫困的优秀子弟因而受益。有钱人家的子女，即使家财万贯，也不能因
幻想之旅角色模型制作流程 1.拿到原画后仔细分析角色设定细节，对不清楚的结构、材质细节及角色身高等问题与 原画作者沟通，确定对原画理解准确无误。 2.根据设定，收集材质纹理参考资料。 3.开始进行低模制作。 4.制作过程中注意根据要求严格控制面数（以MAX为例，使用Polygon Counter工具查 看模型面数）。 5.注意关节处的合理布线，充分考虑将来动画时的问题。如有疑问与动作组同事讨论咨 询。 6.由于使用法线贴图技术不能使用对称复制模型，可以直接复制模型，然后根据具体情 况进行移动、放缩、旋转来达到所需效果。 7.完成后，开始分UV。 分UV时应尽量充分利用空间，注意角色不同部位的主次，优先考虑主要部位的贴图（例如脸，前胸以及引人注意的特殊设计），为其安排充分的贴图面积。使用Relax Tool 工具确保UV的合理性避免出现贴图的严重拉伸及反向。 8.低模完成后进入法线贴图制作阶段。 现在我们制作法线贴图的方法基本上有三种分别是： a.在三维软件中直接制作高模，完成后将低模与高模对齐，然后使用软件工具生成法 线贴图。 b.将分好UV的低模Export成OBJ格式文件，导入ZBrush软件。在ZB中添加细节 制作成高模，然后使用Zmapper插件生成法线贴图。 c.在Photoshop中绘制纹理或图案灰度图，然后使用PS的法线贴图插件将灰度图生成 法线贴图。 （具体制作方法参见后面的制作实例） 建议在制作过程中根据实际情况的不同，三种方法结合使用提高工作效率。 9.法线贴图完成后，将其赋予模型，查看法线贴图的效果及一些细小的错误。 10.进入Photoshop,打开之前生成的法线贴图，根据其贴在模型上的效果对法线贴图进行 修整。（例如边缘的一些破损可以使用手指工具进行修补，或者在绿色通道中进行适当的绘制。如需加强某部分法线贴图的凹凸效果可复制该部分进行叠加可以起到加强
https://www.doczj.com/doc/9619056942.html, 有意向申请美国大学的学生，大部分听过一个名字，常青藤大学联盟。那么美国常青藤大学盟校到底是怎么一回事，又是由哪些大大学组成的呢？下面为大家介绍一下美国常青藤大学联盟。 立思辰留学360介绍，常青藤盟校(lvy League)是由美国的七所大学和一所学院组成的一个大学联合会。它们是：马萨诸塞州的哈佛大学，康涅狄克州的耶鲁大学，纽约州的哥伦比亚大学，新泽西州的普林斯顿大学，罗德岛的布朗大学，纽约州的康奈尔大学，新罕布什尔州的达特茅斯学院和宾夕法尼亚州的宾夕法尼亚大学。这8所大学都是美国首屈一指的大学，历史悠久，治学严谨，许多著名的科学家、政界要人、商贾巨子都毕业于此。在美国，常青藤学院被作为顶尖名校的代名词。 常青藤由来 立思辰留学介绍，常青藤盟校的说法来源于上世纪的50年代。上述学校早在19世纪末期就有社会及运动方面的竞赛，盟校的构想酝酿于1956年，各校订立运动竞赛规则时进而订立了常青藤盟校的规章，选出盟校校长、体育主任和一些行政主管，定期聚会讨论各校间共同的有关入学、财务、援助及行政方面的问题。早期的常青藤学院只有哈佛、耶鲁、哥伦比亚和普林斯顿4所大学。4的罗马数字为“IV”，加上一个词尾Y，就成了“IVY”，英文的意思就是常青藤，所以又称为常青藤盟校，后来这4所大学的联合会又扩展到8所，成为现在享有盛誉的常青藤盟校。 这些名校都有严格的入学标准，能够入校就读的学生，自然是品学兼优的好学生。学校很早就去各个高中挑选合适的人选，许多得到全国优秀学生奖并有各种特长的学生都是他们网罗的对象。不过学习成绩并不是学校录取的惟一因素，学生是否具有独立精神并且能否快速适应紧张而有压力的大一新生生活也是他们考虑的重要因素。学生的能力和特长是衡量学生综合素质的重要一关，高中老师的推荐信和评语对于学生的入学也起到重要的作用。学校财力雄厚，招生办公室可以完全根据考生本人的情况录取，而不必顾虑这个学生家庭支付学费的能力，许多家境贫困的优秀子弟因而受益。有钱人家的子女，即使家财万贯，也不能因此被录取。这也许就是常青藤学院历经数百年而保持“常青”的原因。
动画精度模型制作与探究 Animation precision model manufacture and inquisition 前言 写作目的：三维动画的制作，首要是制作模型，模型的制作会直接影响到整个动画的最终效果。可以看出精度模型与动画的现状是随着电脑技术的不断发展而不断提高。动画模型走精度化只是时间问题，故精度模型需要研究和探索。 现实意义：动画需要精度模型，它会让动画画面更唯美和华丽。游戏需要精度模型，它会让角色更富个性和激情。广告需要精度模型，它会让物体更真实和吸引。场景需要精度模型，它会让空间更加开阔和雄伟。 研究问题的认识：做好精度模型并不是草草的用基础的初等模型进行加工和细化，对肌肉骨骼，纹理肌理，头发毛发，道具机械等的制作更是需要研究。在制作中对于层、蒙版和空间等概念的理解和深化，及模型拓扑知识与解剖学的链接。模型做的精，做的细，做的和理，还要做的艺术化。所以精度模型的制作与研究是很必要的。 论文的中心论点：对三维动画中精度模型的制作流程，操作方法，实践技巧，概念认知等方向进行论述。 本论 序言：本设计主要应用软件为Zbrsuh4.0。其中人物设计和故事背景都是以全面的讲述日本卡通人设的矩阵组合概念。从模型的基础模型包括整体无分隔方体建模法，Z球浮球及传统Z球建模法（对称模型制作。非对称模型制作），分肢体组合建模法（奇美拉，合成兽），shadow box 建模和机械建模探索。道具模型制作，纹理贴图制作，多次用到ZBURSH的插件，层概念，及笔刷运用技巧。目录： 1 角色构想与场景创作 一初步设计：角色特色，形态，衣装，个性矩阵取样及构想角色的背景 二角色愿望与欲望。材料采集。部件及相关资料收集 三整体构图和各种种类基本创作 2 基本模型拓扑探究和大体模型建制 3 精度模型大致建模方法 一整体无分隔方体建模法 二Z球浮球及传统Z球建模法（对称模型制作。非对称模型制作） 三分肢体组合建模法（奇美拉，合成兽） 四shadow box 建模探索和机械建模 4 制作过程体会与经验：精度细节表现和笔刷研究 5 解剖学，雕塑在数码建模的应用和体现（质量感。重量感。风感。飘逸感）
2019年美国常春藤八所名校排名享有盛名的常春藤盟校现在是什么情况呢？接下来就来为您介绍一下！以下常春藤盟校排名是根据2019年美国最佳大学进行的。接下来我们就来看看各个学校的状态以及真实生活。 完整的常春藤盟校名单包括耶鲁大学、哈佛大学、宾夕法尼亚大学、布朗大学、普林斯顿大学、哥伦比亚大学、达特茅斯学院和康奈尔大学。 同时我们也看看常春藤盟校是怎么样的？也许不是你所想的那样。 2019年Niche排名 3 录取率5% 美国高考分数范围1430-1600 财政援助：“学校选择美国最优秀的学生，想要他们来学校读书。如果你被录取，哈佛会确保你能读得起。如果你选择不去入学的话，那一定不是因为经济方面的原因。”---哈佛大三学生2019年Niche排名 4 录取率6% 美国高考分数范围1420-1600 学生宿舍：“不可思议！忘记那些其他学校的学生宿舍吧。在耶鲁，你可以住在一个豪华套房，它更像是一个公寓。一个公寓有许多人一起住，包括一个公共休息室、洗手间和多个卧室。我再不能要求任何更好的条件了。这个套房很大，很干净，还时常翻修。因为学校的宿舍深受大家喜爱，现在有90%的学生都住在学校！”---耶鲁大二学生
2019年Niche排名 5 录取率7% 美国高考分数范围1400-1590 综合体验：“跟任何其他学校一样，普林斯顿大学有利有弊。这个学校最大的好处也是我选择这个学校的主要原因之一就是它的财政援助体系，任何学生想要完成的计划，它都会提供相应的财政支持。”---普林斯顿大二学生 2019年Niche排名 6 录取率9% 美国高考分数范围1380-1570 自我关心：“如果你喜欢城市的话，宾夕法尼亚大学是个不错的选择。这里对于独立的人来说也是一个好地方，因为在这里你必须学会自己发展。要确保进行一些心理健康的训练，因为这里的人通常会过量工作。如果你努力工作并且玩得很嗨，二者都会使你精疲力尽，所以给自己留出点儿时间休息。”---宾夕法尼亚大一学生 2019年Niche排名7 录取率7% 美国高考分数范围1410-1590 综合体验：“学校的每个人都很关心学生，包括我们的身体状况和学业成绩。在这里，你可以遇到来自世界各地的多种多样的学生。他们在学校进行的安全防范教育让我感觉受到保护。宿舍生活非常精彩，你会感觉跟室友们就像家人一样。总之，能成为学校的一员我觉得很棒，也倍感荣幸！”---哥伦比亚大二学生2019年Niche排名9 录取率9% 美国高考分数范围1370-1570 学术点评：“新的课程培养学术探索能力，在过去的两年中我
电力自动化设备 Electric Power Automation Equipment Vol．33No．1Jan.2013 第33卷第1期2013年1月 0引言 近年来，绝缘栅双极型晶体管IGBT （Insulated Gate Bipolar Transistor ）因其不断改善的电压、电流承受能力和工作频率、功率损耗等性能指标而被广泛应用到机车牵引、开关电源、新能源发电等电能变换和处理领域中［1］，因此IGBT 的可靠性受到国内外科研工作者的广泛关注。研究表明，与IGBT 器件结温（T j ）相关的热循环过程和器件封装材料热膨胀系数不一致是致其故障的主要诱因［2-3］，IGBT 的电热仿真模型可以估计结温的变化情况，从而可用于IGBT 可靠性的评估。国内外对IGBT 的电热仿真模型开展了大量研究工作［4-6］，其中基于半导体物理并考虑自热效应（Self -heating ）的IGBT A.R.Hefner 器件模型［6］ 和反映其封装传热过程的Cauer 网络［7-9］联合组成的IGBT 电热模型准确度较高，并已在Saber 、Pspice 等电路仿真软件中得到应用［10-11］，但是，仿真软件有限的器件模型库无法满足仿真需要，同时出于技术保密的缘故，半导体制造商并不会提供建立电热模型需要的模型参数，因此如何建立一种有效并准确的参数提取方法就显得十分必要。 IGBT 电热仿真模型参数同半导体物理、器件以 及封装结构直接相关，无法直接测量，只能通过一定 的技术方法和手段获取。一个有效的参数提取过程是获得有效的电热模型的前提条件；此外，实现模型参数的准确提取对于分析IGBT 的性能、优化驱动电路的设计、指导其应用以及选型都具有重要意义。在参数提取之后，有效性验证也至关重要，可以让使用者合理选择器件的工作范围。由于非穿通（NPT ）型 IGBT 目前在工业领域中已获得了广泛而成熟的应 用［12］，本文将以其作为参数提取的研究对象。本文从NPT 型IGBT 电热仿真模型的工作原理出发，首先将模型参数分为电参数和热参数两大类。然后对近年来模型参数提取方法的研究情况进行讨论，依据提取手段的不同将文献中出现的IGBT 电参数提取方法归纳为4类：仿真提取［13］；经验估计，如利用经验公式［12，14-18］、数据手册［15-16］或者参数典型范围［12］；参数隔离［19-27］；参数优化，包括直接搜索技术［14］、模拟退火算法［28-29］、变量轮换法［30-32］等。同时归纳Cauer 网络的参数提取可以从IGBT 的封装结构［8-9，33-34］和封装瞬态热阻曲线［7，35-36］2个方向出发，并列表给出了提取电参数和热参数的不同方法之间的优缺点。最后对各种提取方法进行了总结，并讨论了一个模型电参数提取步骤，以增强参数提取工作的有序性和可靠性，这对于提高IGBT 电热仿真模型的应用水平，扩大其使用范围起到了积极的作用。 1IGBT 电热仿真模型及其参数 IGBT 的电热仿真模型是建立在考虑了半导体 自热效应的Hefner 物理模型基础之上，耦合了受结温影响的器件模型及与散热路径相关的动态热模型。在分析器件损耗特性、辅助电力电子设计以及研究因器件老化衰退引起的变换器端口特性等方面， ＮＰＴ型ＩＧＢＴ电热仿真模型参数提取方法综述 徐铭伟，周雒维，杜 雄，沈 刚，杨 旭 （重庆 大学输配电装备及系统安全与新技术国家重点实验室，重庆400044） 摘要：对NPT 型IGBT 电热仿真模型的工作原理进行了概述，并将模型参数分为电参数（即基于半导体物理的Hefner 器件模型参数）和热参数（即反映器件封装传热的Cauer 网络参数）两大类，然后对近年来模型参数提取方法的研究情况进行讨论。依据提取技术手段的不同将IGBT 电参数提取方法归纳为仿真提取、经验估计、参数隔离和参数优化4类，并从时效性、准确性、复杂性等方面对各种方法进行了比较和评价；从IGBT 的封装结构和封装瞬态热阻曲线2个方向出发讨论了Cauer 网络参数的提取。最后讨论了一个模型电参数的提取步骤。 关键词：绝缘栅双极型晶体管；电热；仿真；模型；参数提取；热网络；电参数；热参数中图分类号：TM 322 文献标识码：A DOI ：10.3969／j.issn.1006-6047.2013.01.026 收稿日期：2011－08－09；修回日期：2012－10－19 基金项目：科技部国际合作项目（2010DFA72250）；国家自然科学基金资助项目（51077137）；输配电装备及系统安全与新技术国家重点实验室重点资助项目（2007DA10512711101）；中央高校基本科研业务费资助项目（CDJXS11150022） Project supported by the International Cooperation Project of the Minister of Science and Technology of China （2010DFA -72250），the National Natural Science Foundation of China （51077137），the Key Program in State Key Laboratory of Power Transmission Equipment &System Security and New Tech -nology （2007DA10512711101）and the Fundamental Research Funds for the Central Universities of China （CDJXS11150022）
我国很多学子都想前往美国的常青藤大学就读于研究生，所以美国常青藤大学研究生申请条件都有哪些? 美国常青藤大学研究生申请条件： 1、高中或本科平均成绩(GPA)高于3.8分，通常最高分是4分，平均分越高越好; 2、学术能力评估测试I(SAT I，阅读+数学)高于1400分，学术能力评估测试II(SAT II，阅读+数学+写作)高于2000分; 3、托福考试成绩100分以上，雅思考试成绩不低于7分; 4、美内国研究生入学考试(GRE)成绩1400分以上，经企管理研究生入学考试(GMAT)成绩700分以上。 大学先修课程(AP)考试成绩并非申请美国大学所必需，但由于大学先修课程考试对于高中生来说有一定的挑战性及难度，美国大学也比较欢迎申请者提交大学先修课程考试的成绩，作为入学参考标准。
有艺术、体育、数学、社区服务等特长者优先考容虑。获得国际竞赛、辩论和科学奖等奖项者优先考虑，有过巴拿马国际发明大赛的得主被破例录取的例子。中国中学生在奥林匹克数、理、化、生物比赛中获奖也有很大帮助。 常春藤八所院校包括：哈佛大学、宾夕法尼亚大学、耶鲁大学、普林斯顿大学、哥伦比亚大学、达特茅斯学院、布朗大学及康奈尔大学。 新常春藤包括：加州大学洛杉矶分校、北卡罗来纳大学、埃默里大学、圣母大学、华盛顿大学圣路易斯分校、波士顿学院、塔夫茨大学、伦斯勒理工学院、卡内基梅隆大学、范德比尔特大学、弗吉尼亚大学、密歇根大学、肯阳学院、罗彻斯特大学、莱斯大学。 纽约大学、戴维森学院、科尔盖特大学、科尔比学院、瑞德大学、鲍登学院、富兰克林欧林工程学院、斯基德莫尔学院、玛卡莱斯特学院、克莱蒙特·麦肯纳学院联盟。 小常春藤包括：威廉姆斯学院、艾姆赫斯特学院、卫斯理大学、斯沃斯莫尔学院、明德学院、鲍登学院、科尔比学院、贝茨学院、汉密尔顿学院、哈弗福德学院等。
计算机仿真技术简介 计算机仿真技术是一门综合性信息技术，它通过专用软件，整合图像、声音、动画等，将三维的现实环境、物体模拟成多维表现形式的计算机仿真，再由数字媒介作为载体传播给人们。当人们通过该媒体浏览观赏时就如身临其境一般。并且可以选择任意角度，观看任意范围内的场景或选择观看物体的任意角度。正是由于对身临其境的真实感和对超越现实的虚拟性，以及建立个人能够沉浸其中、超越其上、进出自如、具有交互作用的多维信息系统的追求，推动了计算机仿真技术在各个领域中的应用与发展。并且，因其有效性、经济性、安全性、直观性等特点而受到广泛的应用。它是在计算机图形学基础上发展起来的一种仿真应用技术。 计算机仿真已成为系统仿真的一个重要分支，系统仿真很大程度上指的就是计算机仿真。计算机仿真技术的发展与控制工程、系统工程及计算机工程的发展有着密切的联系。一方面，控制工程、系统工程的发展，促进了仿真技术的广泛应用；另一方面，计算机的出现以及计算机技术的发展，又为仿真技术的发展提供了强大的支撑。工业方面，计算机仿真一直作为一种必不可少的工具，在减少损失、节约经费开支、缩短开发周期、提高产品质量等方面发挥着重要的作用。 综上所述，计算机仿真技术是以数学理论、相似原理、信息技术、系统技术及其应用领域有关的专业技术为基础，以计算机和各种物理效应设备为工具，利用系统模型对实际的或设想的系统进行试验研究的一门综合性技术。它集成了计算机技术、网络技术、图形图象技术、面向对象技术、多媒体、软件工程、信息处理、自动控制等多个高新技术领域的知识。 计算机仿真技术原理 对于需要研究的对象，计算机一般是不能直接认知和处理的，这就要求为之建立一个既能反映所研究对象的实质，又易于被计算机处理的数学模型。关于研究对象、数学模型和计算机之间的关系，可以用图1来表示。
1 O D C B A 图1 2图E A B C D E F D C B A O O 图12图E A B C D E D C B A 第一章 8字模型与飞镖模型 模型1 角的“8”字模型 如图所示，AB 、CD 相交于点O ， 连接AD 、BC 。 结论：∠A+∠D=∠B+∠C 。 模型分析 8字模型往往在几何综合 题目中推导角度时用到。 模型实例 观察下列图形，计算角度： （1）如图①，∠A+∠B+∠C+∠D+∠E= ； （2）如图②，∠A+∠B+∠C+∠D+∠E+∠F= 。 热搜精练 1．（1）如图①，求∠CAD+∠B+∠C+∠D+∠E= ； （2）如图②，求∠CAD+∠B+∠ACE+∠D+∠E= 。
2 H G E F D C B A D C B A M D C B A O 135 E F D C B A 2．如图，求∠A+∠B+∠C+∠D+∠E+∠F+∠G+∠H= 。 模型2 角的飞镖模型 如图所示，有结论： ∠D=∠A+∠B+∠C 。 模型分析 飞镖模型往往在几何综合 题目中推导角度时用到。 模型实例 如图，在四边形ABCD 中，AM 、CM 分别平分∠DAB 和 ∠DCB ，AM 与CM 交于M 。探究∠AMC 与∠B 、∠D 间的数量关系。
3 105O O 120 D C B A O D C B A 热搜精练 1．如图，求∠A+∠B+∠C+∠D+∠E+∠F= ； 2．如图，求∠A+∠B+∠C+∠D = 。 模型3 边的“8”字模型 如图所示，AC 、BD 相交于点O ，连接AD 、BC 。 结论：AC+BD>AD+BC 。
2021中考数学易错题飞镖模型8字模型探究试题模型一：角的飞镖模型基础 结论：C + ∠ ∠ = ∠ B + A BDC∠ 解答： ①方法一：延长BD交AC于点E得证 ②方法二：延长CD交AB于点F得证 ③方法三：延长AD到在其延长方向上任取一点为点G得证 总结： ①利用三角形外角的性质证明
模型二：角的8字模型基础结论：D ∠ ∠ = + + C B A∠ ∠
解答： ①方法一：三角形内角和得证 ②方法二：三角形外角【BOD 】的性质得证总结： ①利用三角形内角和等于 180证明 推出 ②利用三角形外角的性质证明
角的飞镖模型和8字模型进阶 【例1】如图，则= ∠E D B A + C + + ∠ ∠ ∠ + ∠ 解答： ①方法一：飞镖ACD得证 ∠E + D C A B ∠ ∠ = 180 ∠ + + ∠ +
②方法二：8字BECD得证 + ∠ ∠E B A + C D ∠ = + 180 + ∠ ∠ 【例2】如图，则= E ∠F + D C A B ∠ ∠ ∠ + + ∠ ∠ + + 解答：飞镖ABF+飞镖DEC得证 ∠F + ∠ E D B + A C ∠ = ∠ + 210 ∠ ∠ + + 【例3】如图，求= E D ∠F B A + C ∠ + ∠ + ∠ ∠ + ∠ + 解答：8字模型得证 ∠F + ∠ E D A B C + 360 + = ∠ ∠ ∠ + ∠ + 【例4】如图，求= ∠D C A + B ∠ + ∠ + ∠
解答：连接BD得飞镖BAD+飞镖DBC得证 + ∠D A ∠ C B = + ∠ 220 + ∠ 【例5】如图，求= ∠H G ∠ F + D A C + E B + ∠ + ∠ ∠ + + ∠ + ∠ ∠ 解答：飞镖EHB+飞镖FAC得证 ∠H ∠ + + ∠ G F A B C D E ∠ + + = 360 ∠ ∠ ∠ + + ∠ + 模型三：边的飞镖模型基础 结论：CD + > AC BD AB+