Molecular Surface Abstraction

Molecular Surface Abstraction

Gregory Cipriano,Student Member,IEEE,and Michael Gleicher Abstract—

In this paper we introduce a visualization technique that provides an abstracted view of the shape and spatio-physico-chemical properties of complex molecules.Unlike existing molecular viewing methods,our approach suppresses small details to facilitate rapid comprehension,yet marks the location of signi?cant features so they remain visible.Our approach uses a combination of ?lters and mesh restructuring to generate a simpli?ed representation that conveys the overall shape and spatio-physico-chemical properties(e.g.electrostatic charge).Surface markings are then used in the place of important removed details,as well as to supply additional information.These simpli?ed representations are amenable to display using stylized rendering algorithms to further enhance comprehension.Our initial experience suggests that our approach is particularly useful in browsing collections of large molecules and in readily making comparisons between them.

Index Terms—molecular surfaces,molecular visualization,surfaces,textures,cartographic labeling

1I NTRODUCTION

One goal of structural biology is to understand the chemical and phys-ical properties of macro-molecules(especially proteins)and how this enables the chemical reactions behind life’s processes.In order to study these large and complex molecules,biochemists rely on visual-izations that provide various levels of abstraction.The more abstract visualizations portray a molecule’s internal structure.However,pro-tein interactions involve the“functional surface”presented:to a large degree,the internal structure simply exists as scaffolding to place vari-ous forces and chemical properties in proper spatial relationships with one another.While visualizations of these functional surfaces exist, they portray all of the detail and complexity of large molecules.The complexity of these visualizations is problematic as they do not afford rapid assessment,and details may obscure larger scale phenomena.To date,the degree of abstraction provided for internal structure has not been shown for external properties.

In this paper,we introduce abstracted molecular surfaces,a visual-ization technique that provides for abstracted views of the boundary of a molecule and the physical and chemical properties at this boundary. Our goal is to provide simpli?ed visual representations of molecules such that scientists can rapidly assess the most signi?cant features of their surfaces,even when drawn at a small size.Such abstracted views are useful for rapid browsing and comparison,but also to study molecules while unencumbered by small details.Once general no-tions are determined from the abstracted views,a scientist can make a focused examination of a more detailed representation.

Our abstraction mechanism processes the detailed information about the molecule to provide a visually simpli?ed representation.The shape of the molecular surface is simpli?ed,removing small details to better convey the basic shape.Signi?cant shape features,such as clefts and pockets,become more prominent when the visual clutter of smaller features is removed.A comparison with other display methods is shown in Figure1and Figure2.Additionally,our abstracted display is more amenable to stylized rendering that accentuates the shape,re-tains readability at lower resolutions allowing gallery displays,and allows for the use of surface markings to display other information.

Our technique also uses abstraction on properties other than shape. Scalar?elds along the surface,such as electrostatic charge,are sim-pli?ed for clarity,and other properties are displayed as symbols on the surface.These presentations allow signi?cant features to be seen ?Authors are with the Department of Computer Sciences,University of Wisconsin,Madison,E-mail:gregc@https://www.wendangku.net/doc/1f11237373.html, gleicher@https://www.wendangku.net/doc/1f11237373.html,.

Manuscript received31March2007;accepted1August2007;posted online2 November2007.

For information on obtaining reprints of this article,please send e-mail to: tvcg@https://www.wendangku.net/doc/1f11237373.html,.quickly and clearly.

We are motivated by an increased need for tools that enable quick and comparative visual analysis.Advances in structural biology,such as high-throughput crystallography and NMR spectroscopy,together with better prediction and simulation,have led to a marked increase in the number of proteins for which the three-dimensional atomic struc-ture is known.Repositories for structural information,such as the PDB[2],have in turn grown dramatically.This wealth of information creates the need to look at large collections of molecules,requiring quick judgement.

Our technique,detailed in§3,relies on?ltering of both the shape and surface?elds to form abstractions.We describe how we adapt standard methods for shape smoothing by explicitly removing regions where the methods are likely to fail.§3.2describes how surface de-cals can be used to display removed features,as well as other infor-mation.§3.3describes the methods we use for more effectively por-traying scalar?elds on the surfaces,and§3.4describes how stylized rendering techniques are used.

1.1Background

Because proteins predominantly interact with other molecules non-covalently,their atomic forces effectively create shells that must?t together.The metaphor of a“lock and key”dates back over a century —[33]cites an1894paper by Fisher.While?exible water balloons or bean bags may be more appropriate metaphors than rigid pieces of metal,the central property governing how proteins interact is the non-penetration of their boundaries.Because the forces fall off rapidly with distance,treating the boundary as a surface(in the mathematical sense)is appropriate.

The de?nition of this geometric boundary surface is varied.The pi-oneering work of Richards(see[8]for a historical survey)introduced functional notions of these surfaces.The notion of solvent accessibil-ity leads to molecular surfaces that provide a smooth description of the boundary.The molecular(solvent excluded)surface is the surface that a spherical probe can contact without intersecting the molecule.Con-nolly provided practical methods for sampling these surfaces[6,7], which have subsequently been re?ned in both ef?ciency and quality [3,29,39].Even more recent works provide methods,such as in[5], that can produce high quality representations of these surfaces.

The geometric molecular surface is only one of many properties that contribute to protein interactions.There is considerable evidence that electrostatics play a critical role in protein-protein interactions(see [32]for a survey of early work).Other properties that in?uence in-teractions include hydrogen bonds(and a molecule’s ability to form them),polarity,and hydrophobicity.Because these properties fall off rapidly with distance,it is reasonable to consider them as scalar?elds on the molecular surface when studying molecular interactions.

Molecules are continually in motion.In proteins,the motions

range

(a)Molecular surface with charge (b)Qutemol (c)Stylized display (d)Abstracted with our method

Fig.1.Depictions of the surface and electrostatic charge distribution of Adenylate Kinase (1ANK).The standard approach (a),drawn with Pymol [11],shows the molecular surface pseudo-colored (from red to blue)with the charge distribution.Qutemol [34](b),applies stylized lighting to a space ?lling representation.(c)applies stylized shading directly to the molecular surface.(d)shows our abstracted surface depicted with stylized rendering.This molecule has binding partners that ?t into channels formed in each of its lobes.From this view,one such channel should be visible in the center of the right lobe.This is made more readily visible by

abstraction.

Fig.2.A ball-and-stick representation (left)of adenylate kinase (Figure 1)contains too much information to be easily understandable.For larger scale views,biologists use abstracted representations such as ribbon diagrams (right).Such abstractions show major internal features of the molecule but do not convey the external surface.

from thermal vibrations to large conformational changes.This inces-sant movement,coupled with uncertainty in the measurement of the atomic coordinates,means that any static con?guration of a molecule is merely a snapshot of its possible state.Therefore,smaller details of the shape and other ?elds of the molecule are of reduced signi?cance as they are likely changing continuously.2

R ELATED W ORK

2.1Molecular Visualization

Because of the importance of molecular shape,structural biologists have depended on visual tools from the beginning.Visual tools predate computers and continue to be developed to this day (see [8,35,16]for historically oriented surveys).Current state-of-the-art systems,such as Chimera [27],PyMol[11],and their competitors,provide large feature sets giving many options for the display of molecules.

Any visualization of a molecule necessarily involves some degree of abstraction.The ?eld has developed a range of visual representa-tions that provide different levels of abstraction;see [16]for a survey.For showing the internal composition of a molecule,many abstrac-tions exist ranging from models that show every atom and bond,such as a ball and stick model,to highly abstracted representations,such as ribbon diagrams (Figure 2).These highly abstracted diagrams are valuable for providing a summary of a large molecule.However,be-cause they do not indicate the “exterior”shape of the molecule,they provide less help in studying how the molecule would interact with others.Our methods provide such abstract representations for external properties.

There are two primary ways for showing the exterior shape of a molecule:space ?lling diagrams,where each atom is drawn as a solid sphere,and solvent-excluded surfaces,or molecular surfaces.Both views provide the shape of the molecule,however they provide it with a large amount of atomic-scale detail.Such detail is problematic as it can obscure larger scale phenomena and hinder effective portrayal of the shape.Raising the size of the probe sphere leads to molecular surfaces that exclude smaller crevices but may lose important pockets without discarding distracting bumps (Figure 3).Our methods can retain important features while reducing distracting detail.

Surface simpli?cation (see [23]for a survey)creates approximate models with fewer polygons.These methods are useful in improving

ef?ciency while preserving the appearance.Simpli?cation is an es-sential part of large molecule surface display [13,28].In contrast,our approach seeks to alter the appearance to be more abstract,and does not necessarily provide a performance bene?t,although abstracted sur-faces are amenable to simpli?cation.[13]applies smoothing,similar to our approach,to reduce the blocky appearance of coarse models of large molecules.

Display of other spatio-physico-chemical properties by color cod-ing molecular surfaces became common as soon as surface represen-tations were readily available.An early example was GRASP [24],which showed electrostatic potentials on surfaces.[4]unfolded the surfaces to better show their property distributions.Our methods pro-vide abstracted display of these properties as well as molecular shape.Work on displaying molecular motion shows the uncertainty in molecular shape.[21]shows uncertainty and vibrational motion by blurring standard representations,and [31]clusters states to provide visual representations of ranges of conformations.[18]uses a com-bination of point-based rendering and random displacement to convey surface uncertainty in volumetric data.While our work does not ex-plicitly depict motion,it does convey a sense of uncertainty through the lack of detail.

The work of biochemist and artist David Goodsell inspires us by showing the merit of using artistically stylized depictions of molecules.His stunning ?gures require considerable artistic talent and effort to create.In [15]he describes a system for image processing molecular graphics that simulates a black-and-white line-art look,but which makes no abstraction of the shape.2.2Conveying Shape

The complexity of molecular shape is hard to convey,as some spatial cues such as size and familiarity are not applicable.To help assist in shape comprehension,biochemists often rely on motion and stereo display to enhance more standard graphics cues,such as lighting,fog,and depth-cueing.

Texture can be an effective cue for aiding in shape perception [17].To date,it has not been applied in large-molecule visualizations as the molecular surfaces or space ?lling views are ill-suited for texturing.Our abstracted views make use of texture.

Clever lighting design can greatly enhance the perception of lo-cal shape [22].To provide for better comprehension of global shape,molecular visualizations have recently begun to use both global illumi-nation and stylized shading.QuteMol [34]demonstrates the effective-ness of these techniques and shows how they can be implemented ef?-ciently in hardware.However,QuteMol does not provide for shape ab-straction;it provides only all-atom displays or space-?lling diagrams.By providing abstracted surfaces,our approach can more easily apply a range of stylized depiction effects.

[26]shows how identi?ed features can be better presented using stylized display.We apply this idea in a new domain and extend it by explicitly removing the features and only portraying them in a stylized fashion.

(a)Original,1.5angstrom probe (b)With a 4angstrom probe (c)Abstraction of original mesh

Fig.3.A demonstration of how using a larger probe size,while resulting in a slightly smoother mesh,will destroy ?ne details.Bright yellow,blue and red surfaces denote ligands,included to emphasize the important pockets.In particular,channels containing important ligands are completely removed in (b),along with other structural detail.Our method (c)preserves these features.

3A BSTRACTED S URFACES

Our abstraction process removes small details from molecular surfaces and their associated properties.These details are unlikely to be biolog-ically signi?cant,but will certainly detract from a viewer’s ability to interpret larger patterns.

To create an abstracted representation of a molecule,our approach takes as input a triangle mesh of the molecular surface as well as in-formation about the properties of the molecule.Our implementation uses external tools to create these inputs from PDB ?les.For the ?g-ures in this paper,MSMS[29]was used to create surface meshes and APBS[1]was used to compute electrostatic charge.The triangle mesh must be sampled ?nely enough to appear smooth at the scale of in-terest,but need not be uniform.Properties are associated with mesh vertices;scalar ?elds are sampled at these points before abstraction.The primary step of abstraction is to remove small details in shape by smoothing the mesh.The choice of the scale of “small”is chosen to be smaller than a residue,but larger than an atom.Our implementation uses Taubin’s ?lter [36,37]as it is ef?cient and suf?ciently volume-preserving.Local operations are performed on vertices lying in disc surrounding a given point,with importance falling off with the inverse of distance,as given by Fujiwara [12].We have emprically determined the ?lter parameters λ=.8and μ=?.87,disc radius 4angstroms,and 10iterations to correspond to the desired feature size to remove.These parameters are a function of the scale at which we are interested in studying (https://www.wendangku.net/doc/1f11237373.html,rger than atomic scale interactions),not of particular molecules.All examples use the same parameter values.

The smoothing process creates a potential problem:“Mid-sized”features that are larger than what is removed reliably by the ?lter are often distorted by it.These features,such as peaks formed by protrud-ing chemical groups and small divots,may be biologically signi?cant.While a more sophisticated ?ltering mechanism might better preserve them,even undistorted,these features are undesirable for abstraction as they are still dif?cult to portray.

To handle mid-sized features,we apply a different strategy shown in Figure 4.Our approach identi?es the features and removes them from the mesh,leaving a smoother surface.However,it remembers that a feature was removed and depicts that feature using a surface marking.This approach has the advantages that it avoids artifacts from ?ltering and provides more control over how features are displayed.Small surface markings are better for abstracted representations than small bumps and divots because they do not detract from the overall shape and are visible from a wide range of viewpoints (see Figure 11).3.1Removing Mid-Sized Features

Mid-sized features are identi?ed and removed.At present,our meth-ods identify bumps and bowls that are large enough to be potentially interesting,but small enough to be problematic for smoothing.Simi-lar approaches could be applied for other shape features,such as ridges and valleys.

Our process for removing bumps and bowls consists of several steps,illustrated in Figure 4.Features are identi?ed by ?nding points of that have high curvature after smoothing,which is indicative of a ?ltering artifact.An initial round of smoothing is applied

speci?cally

(a)Original surface (b)After initial

smoothing

(c)With bumps removed (d)Abstracted result

Fig.4.The molecular surface (a)is ?rst smoothed,then “mid-sized”features are identi?ed (b).Those features are removed from the original surface (c),then smoothing is applied and decals are used to represent the removed features (d).

for feature detection.Vertices whose curvature are outliers are chosen as features.The system computes the 10th percentile of the absolute value of principle curvatures (κ1and κ2)for all vertices over the mesh.Vertices are chosen to be outliers if their Gaussian curvature (K =κ1κ2)is greater than P times the square of the 10th percentile princi-ple curvature.Empirically,we have chosen P =30to provide a good balance between mesh smoothness and overly aggressive feature re-moval.The exact value of this parameter does not matter since precise identi?cation is unimportant;an excess or missed point is likely to be grouped with another point in a later stage.

For each of these seed vertices,our system constructs a group con-taining other vertices within 2.5angstroms along the surface.This distance was empirically found to correspond to the approximate size of individual mid-size features.If groups overlap,then it is likely that they are larger aggregates of individual features on the original mesh,so the process repeatedly merges groups until no overlaps are found.This step results in a collection of patches on the surface repre-senting mid-sized features.These regions are then removed from the original,unsmoothed mesh.To “sand them off,”our system removes the majority of the vertices in the region and simultaneously “de?ates”those that remain.To accomplish both,it ?rst sorts the vertices accord-ing to how far away they are from their nearest seed vertex.It then takes the closest 80%and removes them,one by one,by edge con-tracting each with its closest neighbor in the graph,provided this con-traction doesn’t cause topological problems.This ensures that smaller triangles will be removed ?rst,and also that vertices will be removed top-down,in the case of peaks,or bottom-up for divots.

The edge contraction process produces a mesh with its mid-sized features “sanded off”but the removal process often negatively impacts mesh connectivity,leaving many high-order vertices.Our system per-forms edge ?ips to improve the mesh by identifying high order ver-tices and for each one ?ipping its outgoing edge that is connected the highest order neighbor.It also ?nds extremely low-order vertices and contracts the outgoing edge connecting to their lowest order neighbor.

Fig.5.We texture the surface using local parameterizations generated using an exponential map.First,a plane is constructed tangent to the desired position of the texture.Next,points surrounding that point(here in dark red)are mapped to that plane.Finally,the texture is placed on the surface according to that map.

After these methods remove mid-sized features,the resulting sur-face is smoothed.

3.2Decaling

We would like to create surface markings that are independent of the underlying triangulation.Otherwise,a coarse or uneven triangulation might lead to jagged,irregular shaped markings.

Texture mapping provides for surface markings independent of tri-angulation,but requires a parameterization of the surface to provide texture coordinates.The molecular surfaces are dif?cult to parame-terize globally.We apply the approach of[30]to place textures on regions of the surface.Their approach creates a local parameterization of a region of the surface.This approach works well for our needs because our abstracted surface is relatively smooth,and because the markings we wish to apply are local.

3.2.1Decal Parameterization

[30]use a discrete exponential map to create a local parameterization of a surface in the neighborhood of a point.Exponential maps take a point on the surface and map the surface surrounding that point to its tangent plane(see Figure5),in a manner that yields mappings that pre-serve distances well.That plane serves as a local parameterization of the surface,and can be used to apply a texture with minimal distortion.

The methods of[30]were presented to support interactive decal placement.To apply it within our molecular abstraction process,we must automate the process of choosing the seed point,and of limiting the mapped region.These issues are challenging because poor choices can lead to parameterizations that distort the textures as they get fur-ther from the seed point.

To solve these problems our system attempts to locate an ideal start-ing vertex within the patch.Two competing goals intersect here:this vertex should lie as close as possible to the center of the region it rep-resents,and also the normals on the surface should deviate as little as possible from its normal.This latter property is much more impor-tant to the overall quality of the parameterization,so our system?rst removes from consideration any vertices where it doesn’t hold(i.e. N vertex·N plane<.05).

If all vertices are removed,then the patch cannot form a good pa-rameterization,and so that patch is not shown.Otherwise,the starting vertex is picked that has minimal distance to its most remote neighbor, which most often is a vertex lying roughly in the center of the patch.

3.2.2Choosing Decal Placement

We consider two types of markings:?xed sized glyphs centered at a point,and arbitrary shaped regions.The former are used in our system to display symbols,such as circles and checks,to denote various fea-tures on the surface.To create a glyph decal,the point position is used as the seed for creating the parameterization.

Regions are represented as a subset of the mesh vertices.To create a decal corresponding to a region on the surface,our approach selects the best vertex(using the criteria in§3.2.1)and builds a parameteri-zation around it.This parameterization determines where each of the vertices in the region lie in the texture plane,providing a2D mesh

that

has only one other neighbor that is also in the patch.We remove these.At right,a vertex,denoted by a’*’, joins two otherwise locally disconnected sets.We will add its neighbors, denoted by a’+’,to the

patch.

Fig.7.At left,a patch before boundary smoothing.Nodes on the bound-ary are placed directly on vertices on the mesh,leaving a jagged exte-rior.At right,after smoothing.

can be drawn on that plane.This patch is drawn to a texture such that the region outside of it is made transparent with alpha blending.

The shape of a feature may have been distorted by both the?lter-ing operations to create the smooth mesh and the mapping process, which may lead to patches with small holes,disconnected or poorly-connected vertices,and a jagged boundary.Removing these artifacts leads to abstracted markings that not only prevent problems in display, but also?t better into an abstracted representation and dispel any illu-sion that the?ne details of the patch boundary are signi?cant.

Our system abstracts patches in a number of steps.First,it ap-plies standard binary image processing operations adapted to the non-uniform lattice of the2D mesh.We use morphological operations[14] to remove outlying points and?ll in small niches and holes.Dilation and erosion operators are de?ned based on the neighbors of a vertex. One step of dilation expands the patch out to include all immediate neighbors of the outermost vertices,while one step of erosion con-tracts the patch to remove all outermost vertices.

Rather than de?ning larger structuring elements,these immediate connectivity operators are applied repeatedly.We use4iterations of the close operator(dilation followed by erosion)to provide a good balance of problem removal and shape preservation.

Morphological operators may leave thin threads and bridges,as shown in Figure6.These are removed by eliminating vertices with only one connected neighbor,and by expanding the patch around bridge vertices,which are de?ned as any vertex in the patch that has at least two neighbors not in the patch,and which do not themselves share a neighbor that is not in the patch.

After these cleaning steps,our system then?nds all closed loops that lie on the border of the patch.This boundary is then smoothed(in the2D map)by applying a low-pass?lter to the2D positions in the chains.This boundary is drawn with a stroke around its edge and the enclosed region?lled,either with a?at color or with a texture de?ned over the plane.See Figure7for an example.

3.2.3Using Decals

Our system uses decals to present information about the molecule in several ways.Because decals are semi-transparent,they overlay nicely on one another.However,displaying too much information may lead to clutter,so our system can optionally disable certain types of de-

Fig.8.Left:surface containing peaks and bowls.Right:same surface

abstracted;peaks replaced by an X decal and bowls replaced by an

O.

Fig.9.At left,surface features are obscured by binding ligands.At right, projecting each ligand’s location onto the surface allows simultaneous viewing of both ligand location and underlying surface properties. cals,if desired.Decal positions can be determined from a number of tools,or can be provided manually for annotation.New methods for identifying features to mark can be easily added to our system.

For speci?c positional features,such as the location of hydrogen bond acceptors,our system chooses a single position on the surface and places a symbolic decal like the X in Figure5.A surface point near an internal feature,such as an atom center,is chosen somewhat arbitrarily as small differences in positions are not important in the abstracted representation.

Our approach uses decals to indicate the mid-sized features re-moved in§3.1.While the set of vertices in the feature that remain after the removal process could be used to denote a region,our experi-ence is that after contraction and smoothing,this patch bears little re-lationship in shape that of the removed feature.Therefore,our system instead uses a circular symbol of?xed size(1.5angstroms in radius), as a circle doesn’t imply anything(for better or worse)about the orig-inal shape.Glyphs within the circles are used to differentiate peaks from bowls.Examples can be seen in Figure8.

Our system also uses decals to indicate larger regions correspond-ing to other information that is known about the molecule.Biologists use a myriad of tools to attempt to locate biologically signi?cant areas on a molecule’s surface.When binding partners are known,regions of the surface near ligands can be marked.This representation makes vis-ible the portion of the surface involved in the interactions(Figure9). The output of region detectors,such as pocket?nders,can also be dis-played this way.Our system presently includes an an implementation of Ligsite[19]to identify potential pockets.The output of these de-tectors is noisy,so before constructing decals,small or low-con?dence regions are removed to avoid clutter,and excessively large regions are also culled because they are usually errors from the pocket?nder and are problematic for the exponential map creator.

The system displays the output of different region detectors using different patterns for each,allowing multiple features to be shown si-multaneously and compared(Figure10).

3.3Abstracting Surface Fields

Many important properties beyond the atomic forces that form the molecular surfaces,such as electrostatic charge and hydrophobicity are typically represented as scalar?elds on the molecular surface and displayed using pseudo-coloring.Such properties suffer from the same profusion of small details as the shape itself,with similar issues in comprehension and display at small size.

Therefore,we abstract the scalar?elds on the surface of the molecule.The scalar properties are attached to vertices before any simpli?cation.This is particularly important because the true geome-try determines the value(i.e.the position used to sample a volumetric scalar?eld such as electrostatic charge).Simpli?cation should account for the real geometry in?nding features(such as regions)in the scalar ?eld as property values attached to vertices can be moved by the shape simpli?cation.While this will distort the shape of the?eld,signi?cant features of the?eld,such as regions of large magnitude,will remain with approximately the same shape and value.

The?eld abstraction process aims to remove small,less relevant details but to also preserve the coherent regions where the?eld has a de?nite value.Therefore,we apply a boundary-preserving low-pass ?lter to the surface scalar?eld.Speci?cally,we adapt the bilateral ?lter[38]to the irregular lattice of the triangle mesh.

As in the image case,the bilateral?lter computes a new value at a vertex by taking a weighted average of the other vertices in its neigh-borhood,where these weights are determined by using both the spatial and value differences.We achieve larger kernel sizes by iterated ap-plication of smaller ones.

The general formula for our bilateral?lter at iteration i for vertex v with value val i(v),where d(v,w)represents Euclidean distance from vertex v to w,and N(v)represents the set of v’s neighbors,is:

val i+1(v)=

1

k i(v)

·∑

w∈N(v)

val i(w)·c i(w,v)(1)

c i(w,v)=e?d(v,w)

2

2·e

(val i(v)?val i(w))2

2·σ2i,k i(v)=∑

w∈N(v)

c i(w,v)(2)

Thus,our system applies a Gaussian?lter for both distance and value-similarity weights.For the latter,though,we have found that by using a larger kernel(σi)for the?rst few iterations and then progressively reducing it at later iterations,we can prevent areas of uniform value from completely diffusing into areas of different value.

Our method to adapt kernel size is to use a kernel proportional to the standard deviation over the values at each vertex.Since the variance of the values themselves will be converging as a result of smoothing, this results in a progressively smaller sigma,which in turn gives higher weight to the value-similarity kernel.

Our system iterates until asymptotic convergence,which is reached when the average over all vertices v of val i+1(v)?val i(v)is less than ε.In our experiments,ε=.005.

When a mid-sized feature is removed,scalar?eld information con-tained in that feature is lost.This information is potentially important: for example,highly charged protrusions may be biologically signi?-cant.To preserve this important?eld information,the removal process associates a?eld value with the decal representing a removed feature, determined by averaging the values of that feature’s vertices.

3.4Display of Abstracted Surfaces

The resulting abstracted surfaces still provides a shape display prob-lem.The visual presentations must not impede the use of the surface markings indicating small shape features.Also,we prefer a visual style consistent with the abstraction,rather than the“realistic”shiny plastic more commonly used to display molecular surfaces.There-fore,our system’s primary display is stylized.Qutemol[34]showed the utility of stylized shading for molecular depiction.We apply sev-eral of their concepts to molecular surfaces.Our system also applies the stylized rendering to non-abstracted surface models(seen in many ?gures throughout the paper).

To enhance shape portrayal,we apply per-pixel silhouette shading [20],which sets brightness=1?p cos

?1(n z)

π/2,where n z is the z compo-nent of the surface normal and p is a tunable constant that we have set to.3in our?gures.This shading sets pixels on faces that orient directly toward the viewer at maximal brightness,with decreasing brightness as the face normal orients away.

(a)Pymol(b)Stylized(b)Abstracted

Fig.10.An example of Bullfrog Ribonuclease(1M07)before and after our abstraction process.The green striped areas represent parts of the surface that were identi?ed as putative ligand binding sites.The yellow,ligand shadows,or areas of the surface nearest to known ligand locations.

Ambient occlusion(AO)lighting[20]is applied as it accentuates

global shape.As pointed out by[34],the regions made darker by

ambient occlusion because of lower lighting accessibility are related

to the regions with lower chemical accessibility.Interior points of

clefts and pockets are made darker.Our implementation of AO uses

the graphics hardware to sample light directions.

As a?nal step,our system strokes along contours of the mesh,

which can be de?ned as those edges that border both a front-facing

and a back-facing face.This not only enhances shape perception,but

gives a stylized look that gives a constant reminder of the degree of ab-

straction in the representation.The smoothness of abstracted surfaces

makes more sophisticated contouring methods unnecessary.Experi-

ments with Suggestive Contours[10,9],show that they add few con-

tours beyond the simple ones on our surfaces,and that these additional

contours were typically small enough to be dif?cult to notice.

As in traditional molecular surface display,scalar?elds are indi-

cated on the surface by pseudo-coloring.For the examples shown in

this paper,electrostatic charge is displayed using the red to blue scale

that is commonly used.Colors for other decals are chosen such that

they can be seen when overlayed on these colors.

4R ESULTS

We have implemented our molecular surface abstraction techniques in

our bespoke visualization testbed that runs under Windows on PCs.

Our system relies on standard tools for computing the surfaces and

other properties.For all examples in this paper,we use MSMS[29]

to generate the molecular surface meshes,APBS[1]to compute elec-

trostatic charge distributions,and an implementation of Ligsite[19]to

identify putative binding pockets.

We emphasize that abstraction is not the same as changing the probe

https://www.wendangku.net/doc/1f11237373.html,rger probe sizes will?ll in crevices that may be important

pockets,while leaving bumpy details that detract from comprehension

as shown in Figure3.Indeed,abstraction can be applied to surfaces

generated with any probe size.All examples in this paper were gener-

ated using a probe size of1.5Angstroms,(except Figure3b).

Figures throughout the paper show the results of our methods ap-

plied to various molecules.Figure10shows how important aspects

of the molecule are made clear by abstraction.Figure12provides a

gallery of examples.

Major shape features,such as pockets and clefts,become very clear

on abstracted surfaces because there are fewer small details to distract

the viewer,and the smoothness allows silhouette shading,contouring

and ambient occlusion lighting to emphasize the shape.

The asymptotic complexity of our method scales linearly with the

number of vertices of the input mesh,which scales(at worst)linearly

with the number of atoms in the molecule.This was con?rmed empir-

ically in our performance evaluation.

To assess performance of our prototype,we selected60proteins of

various sizes from the Astex test set[25].When determining the tim-

ings for the abstraction process,we consider smoothing,decal con-

struction,and surface?eld relaxation;but not the preprocesses to de-

termine the initial mesh,electrostatic charges,or binding pockets.

We

Fig.11.A sphere with a bump facing upward,rotated forward45?,and

at right90?.Top:traditional geometric display.Bottom:our abstracted

view makes the location more apparent.

also exclude the time required to load data from disk and compute am-

bient occlusion lighting.Timings were performed on a PC with an

Athlon4400CPU,2GB of RAM,and NVidia7900GT graphics.

On our test set,the time needed to perform abstraction ranged be-

tween7and113seconds.These correspond to the smallest molecule

in the set(1CBS,137residues,1092atoms)and the largest(1CX2,

2200,21764).The expected linear performance scaling was observed.

Once abstracted,the models are displayed in real time using the

graphics hardware.Our system maintained at least30fps on all

molecules in the test set.Our ambient occlusion precomputation im-

plementation is not realtime(about10seconds for the largest molecule

in the test set),but is computed in parallel and its results continuously

displayed on the model’s surface.The abstracted model,including its

ambient occlusion lighting,could be precomputed and stored.

5D ISCUSSION

The symbolic display of smaller features has a number of advantages.

It makes shape features more readily apparent from a wider range of

viewing directions(Figure11).Symbols are visible in static displays,

while shape features often are only obvious in regular displays when

the object is moving.At small sizes,sampling issues may make small

geometric features dif?cult to display.With surface textures,texture

sampling hardware can perform sampling using mip-mapping,and de-

cals can be omitted at very small sizes.

Displaying symbols as decals on the surface provides a mechanism

for indicating a variety of properties about the underlying molecule.

Such decaling would be dif?cult on non-abstracted surfaces:their non-

smoothness would make parameterization dif?cult,and the small fea-

tures would obscure the symbols with clutter and occlusion.Because

the symbolic display is imprecise,they?t in better with the abstracted

surfaces as abstracted surfaces imply a lack of positional precision.

Abstracted surfaces are also more amenable to mesh decimation for

performance enhancement.This can be particularly important when

displaying multiple molecules simultaneously in an interactive system.

Together,these features of abstracted surfaces suggest that they will be useful in creating gallery views that allow a number of molecules to be shown simultaneously for browsing and comparison.Without a reduction in detail,a gallery of surfaces would be overwhelming.In a gallery display,the size and resolution of each molecule’s depiction is limited.There is also less opportunity for interactively rotating each molecule to?nd views that show shape features.

Many of the the limitations of our initial prototype should be ad-dressed.Better shape feature?nding would allow us to translate more of the shape into surface symbols to provide further abstraction.In-corporating dynamics would help us better target unstable features for removal.Better decal design should include textures that help con-vey shape more precisely.And methods are required to apply decals correctly on decimated meshes and patches with non-planar topology. To be truly useful,abstracted surfaces will need to be integrated into existing tools and work?ows.

Our abstraction has been applied to study features at a speci?c scale. Exploring other scales would require retuning the methods,and pos-sibly designing a new set of feature detectors.Studying molecules at scales much different than the atomic level interactions we consider, such as macro-molecular assemblies,would provide more challenges, including performance.

The most important step for our work is to assess how effective these representations are for scientists.To date,our testing of ab-stracted molecular surfaces with our biochemist collaborators has been limited,so our observations are anecdotal.In all cases,their initial re-actions were extremely positive.They immediately appreciated the simpli?ed views.On molecules familiar to them the views matched what they“expected”them to look like.In several cases they would make comments like“I never noticed that before,I wonder...”which is particularly encouraging as it implies a new way of looking at things might lead to new hypotheses.In viewing unfamiliar molecules,they were able to spot important functional areas quickly.

A CKNOWLEDGEMENTS

We thank George Phillips Jr.and his lab for their guidance in this project.Aaron Bryden helped with software pipeline issues and Py-Mol?gures,and Cody Robson contributed some of our mesh process-ing implementation.Nick Reiter provided molecules and feedback. Rachel Heck assisted with video production.Cipriano was supported by NIH training grant NLM-5T15LM007359.

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Fig. 12. A gallery of example proteins of various sizes, shown before and after abstraction. Traditional images, rendered with [11], show molecular surfaces for the proteins, and spheres for the ligands. Stylized images use our rendering techniques on non-abstracted surfaces.

Pymol

Abstracted

1F3D

1FLR

Pymol

Pymol

Abstracted

Abstracted

1AI5

Pymol Abstracted

Pymol Abstracted

Stylized

1A6W

Pymol Abstracted

Stylized 1CBS

Pymol

Abstracted

Stylized

1BMA

Pymol Abstracted

Stylized

2POR

Pymol Abstracted

Stylized Stylized 1GLQ

1AQW

1AOE

Pymol Abstracted

Stylized

十款公认最实用的绘图软件评测

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指南针：北方是罗盘针通常指向的方向。在平面图中，北方箭头显示了平面图的哪一边是北边。 空调几位：是放置空调的地方。 实心墙：描绘了墙壁的相对厚度 剪式楼梯：通常由楼梯相连的两个主要航程构成，从上方观察时形成“U”形。 扶手：是设计用于抓住手的轨道，以提供稳定性或支撑。 抽水马桶：是厕所的象征。 电梯：是一个移动的楼梯，由一个由马达驱动的无休止的循环带组成，它传达公共建筑物的地板之间的人。 四：电气和电信符号 用途：不同的电气符号用来标明开关，电话线，热水器，水龙头等安装的位置，以及不同地方插座的安装类型（是安装三孔插座，双控插座甚至是四孔插座），以便安装电气时更能方便快捷操作。 五：墙，门，窗户和结构图形

FANUC系统数据备份与恢复教学内容

F A N U C系统数据备份 与恢复

一、FANUC系统数据备份与恢复 （一）概述 FANUC数控系统中加工程序、参数、螺距误差补偿、宏程序、PMC程序、PMC数据，在机床不使用是是依靠控制单元上的电池进行保存的。如果发生电池时效或其他以外，会导致这些数据的丢失。因此，有必要做好重要数据的备份工作，一旦发生数据丢失，可以通过恢复这些数据的办法，保证机床的正常运行。 FANUC数控系统数据备份的方法有两种常见的方法： 1、使用存储卡，在引导系统画面进行数据备份和恢复； 2、通过RS232口使用PC进行数据备份和恢复。 （二）使用存储卡进行数据备份和恢复 数控系统的启动和计算机的启动一样，会有一个引导过程。在通常情况下，使用者是不会看到这个引导系统。但是使用存储卡进行备份时，必须要在引导系统画面进行操作。在使用这个方法进行数据备份时，首先必须要准备一张符合FANUC系统要求的存储卡（工作电压为5V）。具体操作步骤如下： 1、数据备份： （1）、将存储卡插入存储卡接口上(NC单元上，或者是显示器旁边)； （2）、进入引导系统画面；（按下显示器下端最右面两个键，给系统上电）； （3）、调出系统引导画面；下面所示为系统引导画面： （4）、在系统引导画面选择所要的操作项第4项，进入系统数据备份画面；（用UP或DOWN键）

（5）、在系统数据备份画面有很多项，选择所要备份的数据项，按下YES键，数据就会备份到存储卡中； （6）、按下SELECT键，退出备份过程； 2、数据恢复： （1）、如果要进行数据的恢复，按照相同的步骤进入到系统引导画面； （2）、在系统引导画面选择第一项SYSTEM DATA LOADING; （3）、选择存储卡上所要恢复的文件； （4）、按下YES键，所选择的数据回到系统中； （5）、按下SELECT键退出恢复过程； （三）使用外接PC进行数据的备份与恢复 使用外接PC进行数据备份与恢复，是一种非常普遍的做法。这种方法比前面一种方法用的更多，在操作上也更为方便。操作步骤如下： 1、数据备份： （1）、准备外接PC和RS232传输电缆； （2）、连接PC与数控系统； （3）、在数控系统中，按下SYSTEM功能键，进入ALLIO菜单，设定传输参数(和外部PC匹配); （4）、在外部PC设置传输参数（和系统传输参数相匹配）； （5）、在PC机上打开传输软件，选定存储路径和文件名，进入接收数据状态； （6）、在数控系统中，进入到ALLIO画面，选择所要备份的文件（有程序、参数、间距、伺服参数、主轴参数等等可供选择）。按下“操作”菜单，进入到操作画面，再按下“PUNCH”软键，数据传输到计算机中； 2、数据恢复： （1）、外数据恢复与数据备份的操作前面四个步骤是一样的操作；

CAD快捷键命令大全图文版文字版键盘版

在CAD操作中我们常用一些快捷键来代替鼠标操作从而提高绘图效率，以下是小编为大家整理的常用快捷键大全，涵盖图文版、文字版、键盘版。 图文版： 文字版： 一、常用功能键 F1: 获取帮助 F2: 实现作图窗和文本窗口的切换 F3: 控制是否实现对象自动捕捉 F4: 数字化仪控制 F5: 等轴测平面切换 F6: 控制状态行上坐标的显示方式 F7: 栅格显示模式控制 F8: 正交模式控制 F9: 栅格捕捉模式控制 F10: 极轴模式控制 F11: 对象追踪模式控制 （用ALT+字母可快速选择命令，这种方法可快捷操作大多数软件。） 二、常用CTRL，ALT快捷键 ALT+TK 如快速选择 ALT+NL 线性标注 ALT+VV4 快速创建四个视口 ALT+MUP 提取轮廓 Ctrl+B: 栅格捕捉模式控制（F9） Ctrl+C: 将选择的对象复制到剪切板上 Ctrl+F: 控制是否实现对象自动捕捉（F3） Ctrl+G: 栅格显示模式控制（F7） Ctrl+J: 重复执行上一步命令 Ctrl+K: 超级链接 Ctrl+N: 新建图形文件 Ctrl+M: 打开选项对话框 Ctrl+O：打开图象文件 Ctrl+P：打开打印对说框 Ctrl+S：保存文件 Ctrl+U：极轴模式控制（F10）

Ctrl+v：粘贴剪贴板上的内容 Ctrl+W：对象追踪式控制（F11）Ctrl+X：剪切所选择的内容 Ctrl+Y：重做 Ctrl+Z：取消前一步的操作 Ctrl+1：打开特性对话框 Ctrl+2：打开图象资源管理器 Ctrl+3：打开工具选项板 Ctrl+6：打开图象数据原子 Ctrl+8或QC：快速计算器 双击中键：显示里面所有的图像三、尺寸标注 DLI:线性标注 DRA：半径标注 DDI：直径标注 DAL：对齐标注 DAN：角度标注 DCO: 连续标注 DCE:圆心标注 LE:引线标注 TOL:公差标注 四、捕捉快捷命令 END：捕捉到端点 MID：捕捉到中点 INT：捕捉到交点 CEN：捕捉到圆心 QUA：捕捉到象限点 TAN：捕捉到切点 PER：捕捉到垂足 NOD：捕捉到节点 NEA：捕捉到最近点 五、基本快捷命令 AA：测量区域和周长（area) ID：指定坐标 LI：指定集体（个体）的坐标AL：对齐（align)

信息安全系统备份与恢复管理办法

信息安全系统备份与恢复管理办法 1.总则 第一条为保障公司信息系统的安全，使得在计算机系统失效或数据丢失时，能依靠备份尽快地恢复系统和数据，保护关键应用和数据的安全，保证数据不丢失，特制定本办法。第二条对于信息系统涉及到的网络设备、网络线路、加密设备、计算机设备、应用系统、数据库、维护人员，采取备份措施，确保在需要时有备用资源可供调配和恢复。 第三条本管理办法中涉及到的设备主要指运行在信息技术部主机房中的网络设备、加密设备及计算机设备。 第四条信息系统备份手段根据不同信息的重要程度及恢复时间要求分为实时热备份和冷备份等。同一平台的系统应尽量使用同样的备份手段，便于管理和使用。信息技术部负责信息系统的备份与恢复管理，并制定数据备份计划，对数据备份的时间、内容、级别、人员、保管期限、异地存取和销毁手续等进行明确规定。 第五条信息技术部应根据各系统的重要程度、恢复要求及有关规定要求制定系统配置、操作系统、各应用系统及数据库和数据文件的备份周期和保存期限。 第六条对于重要系统和数据的备份周期及备份保存期限应遵循以下原则：

(一) 至少要保留一份全系统备份。 (二) 每日运行中发生变更的文件，都应进行备份。 (三) 生产系统程序库要定期做备份，每月至少做一次。 (四) 生产系统有变更时，须对变更前后的程序库进行备份。 (五) 批加工若有对主文件的更新操作，则应进行批加工前备份。 (六) 每天批加工结束后都要对数据文件进行批后备份，对核心数据须进行第二备份。 (七) 对批加工生成的报表也要有相应的备份手段，并按规定的保留期限进行保留。 (八) 用于制作给用户数据盘的文件应有备份。 (九) 各重要业务系统的月末、半年末、年末以及计息日等特殊日的数据备份须永久保留。 (十) 定期将生产系统的数据进行删减压缩，并将删减的数据备份上磁带，永久保留。 (十一) 以上未明确保存期限的各项备份的保存至少应保存一周。 2.设备备份 第七条信息系统电源设备应尽量保证有两套电源来源。 第八条对关键通讯线路和网点通讯线路必须采用双通讯线路；网络的运行线路和备份线路必须选用不同的网络服务供

流程图常用的绘图软件

流程图，是一种比较简单的图表，画起来虽然简单，但是却也需要耗费不少时间和精力。说到绘制流程图的工具，可能很多人会想到Office，微软的Word、Excel、PPT确实是办公中使用率最高的软件。但是用来画流程图，并非是最佳的选择。因此，寻找一款能够替代且专业好用的流程图绘制软件，也许是作为流程图用户的您，需要花费大量时间与精力去做的事情。今天，终于不用再去苦苦找寻了。让我来为大家介绍一款超高性价比的流程图软件。 在很多日常用到Linux，Mac系统的人们开始烦恼，似乎就没有一款软件类似Visio，一款软件就能可以解决所有问题。这时，亿图图示出现了。当下受很多人欢迎的绘图软件亿图绘图专家，这款神奇之处在哪里，在这里我给大家介绍一下。 下面是出自设计师们绘制的智能选择颜色模板

绘图小白可以访问亿图软件的动态帮助，点开它，你能找到亿图的产品研发团队准备的软件说明介绍，以及详细的图文、视频教程，让你可以更轻松、更快的熟悉软件，开始绘制你的业务流程图。

不少用户使用亿图绘制一份业务流程图时发现，亿图的功能是符合办公工具在用户心中位置的，可以用来做很多演示要用的图，可以添加很多很难画的图形：

专业的形状是必不可少的，基本流程图形状里具备了所有绘制流程图时需要用的形状： 业务流程图用到的符号很多，能够满足用户这个需求的软件很少。 符号库里的图形是根据模拟真实场景设计的：

这款软件厉害之处是去掉了操作中的“繁文缛节”，简单直接的配合用户画图，但用户依然可以使用工具绘制自己想要的图，最大程度的贴合用户体验。 所有符号的颜色都具备商务、美观、整洁的视觉效果：

AI(Illustrator)常用快捷键大全和技巧

Illustrator常用快捷键大全和技巧 Illustrator的全部快捷键 Illustrator工具箱 移动工具【V】 直接选取工具、组选取工具【A】 钢笔、添加锚点、删除锚点、改变路径角度【P】 添加锚点工具【+】删除锚点工具【-】 文字、区域文字、路径文字、竖向文字、竖向区域文字、竖向路径文字【T】 椭圆、多边形、星形、螺旋形【L】 增加边数、倒角半径及螺旋圈数（在【L】、【M】状态下绘图）【↑】 减少边数、倒角半径及螺旋圈数（在【L】、【M】状态下绘图）【↓】 矩形、圆角矩形工具【M】画笔工具【B】 铅笔、圆滑、抹除工具【N】旋转、转动工具【R】 缩放、拉伸工具【S】镜向、倾斜工具【O】 自由变形工具【E】混合、自动勾边工具【W】 图表工具（七种图表）【J】渐变网点工具【U】 渐变填色工具【G】颜色取样器【I】 油漆桶工具【K】剪刀、餐刀工具【C】 视图平移、页面、尺寸工具【H】放大镜工具【Z】 默认前景色和背景色【D】切换填充和描边【X】 标准屏幕模式、带有菜单栏的全屏模式、全屏模式【F】 切换为颜色填充【<】切换为渐变填充【>】切换为无填充【/】 临时使用抓手工具【空格】 精确进行镜向、旋转等操作选择相应的工具后按【回车】 复制物体在【R】、【O】、【V】等状态下按【Alt】+【拖动】 工具箱(多种工具共用一个快捷键的可同时按【Shift】加此快捷键选取,当按下【CapsLock】键时，可直接用此快捷键切换) Illustrator文件操作 新建图形文件【Ctrl】+【N】 打开已有的图像【Ctrl】+【O】 关闭当前图像【Ctrl】+【W】 保存当前图像【Ctrl】+【S】 另存为... 【Ctrl】+【Shift】+【S】 存储副本【Ctrl】+【Alt】+【S】 页面设置【Ctrl】+【Shift】+【P】 文档设置【Ctrl】+【Alt】+【P】 打印【Ctrl】+【P】 打开“预置”对话框【Ctrl】+【K】 回复到上次存盘之前的状态【F12】 Illustrator编辑操作 还原前面的操作(步数可在预置中) 【Ctrl】+【Z】 重复操作【Ctrl】+【Shift】+【Z】 将选取的内容剪切放到剪贴板【Ctrl】+【X】或【F2】 将选取的内容拷贝放到剪贴板【Ctrl】+【C】

常用地质绘图软件

常用的地质绘图软件 一、地质绘图、矢量化、CAD软件 1. Geomap 3.2地质绘图软件包 版本3.2 平台Windows 98/NT/2000/XP 简介：GeoMap3.2适用于制作各种地质平面图（如构造图、等值线图、沉积相图、地质图等）、剖面图（如地质剖面图、测井曲线图地震剖面图、岩性柱状图、连井剖面图等）、统计图、三角图、地理图、工程平面图（公路分布图、管道布线图等）多种图形。GeoMap地质制图系统能广泛应用于石油勘探与开发、地质、煤炭、林业、农业等领域，也是目前国内在石油地质上应用较广的CAD软件之一。 相关软件还包括以下几个专业制图系统：GeoCon油藏连通图生成系统、GeoCol综合地质柱状图编辑系统、GeoMapD油藏开发制图系统、GeoStra地层对比图编辑系统、GeoMapBank网上图文资料库管理系统、GeoReport地质多媒体汇报系统OE目标评价软件。 2. MAPGIS 版本6.5 平台Windows 98/NT/2000/XP 简介：图形矢量化及编辑软件,是一个大型工具型地理信息系统软件，可对数字、文字、地图遥感图像等多源地学数据进行有效采集、一体化管理、综合空间分析以及可视化表示。可制作具有出版精度的复杂地质图，能进行海量无缝地图数据库管理以及高效的空间分析。具有强大的图形编辑功能。 3. NDS测井曲线矢量化 版本4.16 平台Windows 98/NT/2000

简介：测井曲线矢量化,NDSlog、Ndsmap等 4. SDI CGM Editor 版本2.00.50 平台Windows 简介：CGM绘图工具，包括图形转换及拼图。与Larson CGM Studio相比，有以下优点：1、Larson将已作好的CGM文件，作为整体导入，不能修改; 2、Larson添加的热区不能在同一文件的对象之间跳转。而这些SDI CGM Editor都可以。 5. SDI CGM Office 版本2.00.50 平台Windows 简介：显示CGM v1 - v4, ATA, CGM+, PIP, WebCGM，dwg/dxf, pdf, ps, hpgl, plt, emf, tiff, jpeg,png, bmp & xwd文件。转换CGM文件到CGM, EMF, JPEG, PNG, TIFF & BMP格式。拷贝/粘贴CGM图形到Microsoft Office。 6. SDI Convert 版本7.9.0 平台Windows 简介:可以批量和交互进行各种图形格式之间的相互转化，包括CGM、PS和其它常用光栅文件格式。 7. SDI Dgn 1/9 版本1.12.8 平台Windows