Abstract A Flexible Framework for Hardware-Accelerated High-Quality Volume Rendering

A Flexible Framework for Hardware-Accelerated

High-Quality Volume Rendering

Christoph Berger?Markus Hadwiger?Helwig Hauser?

VRVis Research Center for Virtual Reality and Visualization

Vienna/Austria

http://www.VRVis.at/vis/

Abstract

Because of an enormous development of graphics hard-ware and the invention of new rendering algorithms in the past it is now possible to perform interactive hardware-accelerated high quality volume rendering and iso-surface reconstruction on low cost standard PC platforms.

In this paper we introduce a framework that integrates sev-eral different rendering techniques which signi?cantly im-prove both performance and image quality of standard tex-ture based rendering approaches.Furthermore the most common graphics adapters are supported without addi-tional need for setup as well as several vendor-dependent OpenGL-extensions like pixel-,texture-and fragment-shaders.Therefore it is easy to compare the varying re-sults of different rendering algorithms on diverse graphics adapters with respect to quality and performance. Keywords:volume rendering,volume visualization, graphics hardware,isosurface-reconstruction,OpenGL

1Introduction

For visualization of volumetric data direct volume render-ing[7,8]is an important technique to get insight into data. The key advantage of direct volume rendering over surface rendering approaches is the potential to show the structure of the value distribution throughout the volume.Due to the fact that each volume sample contribution to the?nal image is included,it is a challenge to convey that value distribution simple and precisely.

Because of an enormous development of low-cost3D hardware accelerators in the last few years(driven by the computer games industry)the features supported by consumer-oriented graphics boards like the NVIDIA GeForce family[17]or the ATI Radeon family[15]are also very interesting for professional graphics develop-ers.Especially NVIDIA’s pixel-and texture shader and ATI’s fragment shader are powerful extensions to stan-dard2D and3D texture mapping capabilities.Therefore ?boerga@https://www.sodocs.net/doc/9b6027389.html,

?hadwiger@vrvis.at

?hauser@vrvis.at high-performance and high-quality volume rendering at very low costs is now possible.Several approaches of hardware-accelerated direct volume rendering have been introduced to improve rendering speed and accuracy of vi-sualization algorithms.Thus it is possible to provide inter-active volume rendering on standard PC platforms and not only on special-purpose hardware.

In this paper we present an application that includes sev-eral different visualization algorithms for direct volume rendering as well as direct iso-surface rendering(no polyg-onal representation has to be extracted,instead special fea-tures of current rendering hardware are used).The major objective of the prototype is to provide comparison possi-bilities for several hardware accelerated volume visualiza-tions with respect to performance and quality.On startup of the software,the installed graphics adapter is detected automatically and regarding to the supported OpenGL-features the user can switch between the available render-ing modes supported by the current graphics hardware. The full functionality includes pre-and post classi?ca-tion modes as well as pre-integrated classi?cation modes (more details on classi?cation will follow in Section3.2 and3.3).All algorithms are implemented exploiting both 2D or3D texture mapping as well as optional diffuse and specular lighting.Additionally we have adopted the high-quality reconstruction technique based on PC-hardware, introduced by Hadwiger et al.[5],to enhance the render-ing quality through high-quality?ltering.

The major challenge is combining diverse approaches in one simple understandable framework that supports sev-eral graphics adapters which have to be programmed com-pletely different and still provide portability for implemen-tation of new algorithms and support of new hardware-features.

The paper is structured as follows.Section2gives a short overview of work that has been done on volume rendering and especially on hardware-accelerated methods.Section 3is then going to introduce the main topic,namely volume rendering in hardware(texture based),providing a brief overview of the major approaches and describing different classi?cation techniques.In Section4we will then discuss the implementation in detail and problems that have to be overcome if supporting graphics adapters from different

vendors.This section will also cover some performance issues and other application speci?c problems we encoun-tered during prototype implementation.Section5summa-rizes what we have presented and additionally some future work that we are planning at the moment will be brie?y mentioned.

2Related Work

For scalar volume data several visualization approaches have been https://www.sodocs.net/doc/9b6027389.html,ually they can be classi?ed into indirect volume rendering,such as iso-surface reconstruc-tion,and direct volume rendering techniques that immedi-ately display the voxel data.

In contrast to indirect volume rendering,where an inter-mediate representation through surface extraction methods (e.g.the Marching Cube algorithm[10])is generated and then displayed,direct volume rendering uses the original data.Although the original implementation did not use texturing hardware,the basic idea of using object-aligned slices to substitute trilinear by bilinear interpolation was introduced by Lacroute and Levoy[6],the ShearWarp al-gorithm.

Cabral[2]presented a texture-based approach,exploiting the3D texture mapping capabilities of high-end graph-ics workstations.This method has been expanded by Westermann und Ertl[19],who store density values and corresponding gradients in texture memory and ex-ploit OpenGL extensions for unshaded volume rendering, shaded iso-surface rendering,and application of clipping geometry.Based on their implementation,Mei?ner et al.

[12]have expanded the method to enable diffuse illumi-nation for semi-transparent volume rendering.However, this approach requires multiple passes through the rasteri-zation hardware,resulting in a signi?cant loss in rendering performance.

Rezk-Salama et al.[13]presented a technique that sig-ni?cantly improves both performance and image quality of the2D-texture based approach.But in contrast to the techniques presented previously(all based on high-end graphics workstations),they show how multi-texturing ca-pabilities of modern consumer PC graphics boards are ex-ploited to enable interactive volume visualization on low-cost hardware.Furthermore they introduced methods for using NVidia’s register combiner OpenGL extension for fast shaded isosurfaces,interpolation and volume shading. Engel at al.[3]expanded the usage of low-cost hardware and introduced a novel texture-based volume rendering approach based on pre-integration(presented by R¨o ttger, Kraus and Ertl in[14]).This method provides high image quality even for low-resolution volume data and non-linear transfer functions with high frequencies by exploiting multi-texturing,advanced texture fetch and pixel-shading operations,available on current programmable consumer graphics hardware.3Hardware-Accelerated Volume Rendering

This section gives a brief overview of general direct volume rendering,especially the theoretical background. Then we focus on how to exploit graphics hardware for direct volume rendering purposes and afterwards we dis-cuss the varying classi?cation methods that we have im-plemented.Additionally we brie?y mention the hardware-accelerated?ltering method,that we use for quality en-hancements.

3.1Volume Rendering

Algorithms for direct volume rendering differ in the way the complex problem of image generation is split up into several subtasks.A common classi?cation scheme differentiates between image-order and object-order ap-proaches.An example for an image-order method is ray-casting,in contrast object-order methods are cell-projection,shear-warp,splatting,or texture-based algo-rithms.

In general all methods use an emission-absorption model for the light transport.The common theme is an(approxi-mate)evaluation of the volume rendering integral for each pixel,in other words an integration of attenuated colors (light emission)and extinction coef?cients(light absorp-tion)along each viewing ray.The viewing ray x(λ)is parametrized by the distanceλto the viewpoint.For any point x in space,color is emitted according to the function c(x)and absorbed according to the function e(x).Then the volume rendering integral is

I=

D

c(x(λ))exp

?

λ

e(x(t))dt

dλ(1)

where D is the maximum distance,in other words no color is emitted forλgreater than D.

For visualization of a continuous scalar?eld this integral is not useful since calculation of emitted colors and absorption coef?cients is not speci?ed.Therefore in direct volume rendering,the scalar value given at a sample point is mapped to physical quantities that describe the emission and absorption of light at that point.This mapping is called classi?cation(classi?cation will be discussed in detail in Sections3.2and3.3).This is usually performed by introducing transfer functions for color emission and opacity(absorption).For each scalar value s=s(x) the transfer function maps data values to color c(s)and opacityτ(s)values.Additionally other parameters can in?uence the color emission or opacity, e.g.,ambient, diffuse and specular lighting conditions or the gradient of the scalar?eld(e.g.in[7]).

Calculating the color contribution of a point in space with respect to the color value(through transfer function) and all other parameters is called shading.Applying simple shading(color and opacity are de?ned simply

through classi?cation)the volume rendering integral can be written as

I=

D

0c(s(x(λ)))exp

?

λ

τ(s(x(t)))dt

dλ.(2)

Usually an analytical evaluation of the volume integral is not possible.Therefore usually a numerical approxima-tion of the integral is calculated using a Riemann sum for n equal ray segments of length d=D/n(see Section IV.A in[11]).This technique results in the common approxima-tion of the volume rendering integral

I≈

n

i=0

αi C i

i?1

j=0

(1?αj)(3)

which can be adapted for back-to-front compositing result-ing in the following equation

C i=αi C i+(1?αi)C i+1(4) where nowαi C i corresponds to c(s(x))from the volume rendering integral.The pre-multiplied colorαC is also called associated color([1]).

Due to the fact that a discrete approximation of the vol-ume rendering integral is performed,according to the sam-pling theorem,a correct reconstruction is only possible with sampling rates larger than the Nyquist frequency.Be-cause of the non-linearity of transfer functions(increases Nyquist frequency for the sampling),it is not suf?cient to sample a volume with the Nyquist frequency of the scalar?eld.This undersampling results in visual artifacts that can only be avoided by very smooth transfer func-tions.Section3.3gives a brief overview on a classi?ca-tion method realizing an improved approximation of the volume rendering.

3.2Pre-and Post-Classi?cation

As mentioned in the previous section classi?cation has an important part in direct volume rendering.Thus there are different techniques to perform the computation of c(s(x)) andτ(s(x)).In fact,volume data is presented by a3D array of sample points.According to sampling theory,a continuous signal can be reconstructed from these sam-pling points by convolution with an appropriate?lter ker-nel.The order of the reconstruction and the application of the transfer function de?nes the difference between pre-and post-classi?cation,which leads to remarkable differ-ent visual results.

Pre-classi?cation denotes the application of the transfer function to the discrete sample points before the data in-terpolation step.In other words the color and absorption are calculated in a pre-processing step for each sampling point and then used to interpolate c(s(x))andτ(s(x))for the computation of the volume rendering integral.

On the other side post-classi?cation reverses the order of operations.This type of classi?cation is characterized

by Figure1:Direct volume rendering without illumina-tion,pre-classi?ed(left),post-classi?ed(middle)and pre-integrated(right)

the application of the transfer function after the interpola-tion of s(x)from the scalar values of the discrete sampling points.With respect to the graphics pipeline the advantage of pre-classi?cation is,that an ef?cient implementation of this concept is possible on almost every graphics hard-ware.However the results achieved by this approach are not very convincing.Post-classi?cation is usually more complex to implement but achieves superior image qual-ity.The results of both pre-and post-classi?cation can be compared in Figure1.

3.3Pre-Integrated Classi?cation

As discussed at the end of Section3.1to gather better vi-sual results,the approximation of the volume rendering integral has to be improved.R¨o ttger et al.[14]used a pre-integrated classi?cation method to enhance cell-based volume reconstruction.This algorithm has been adapted for hardware accelerated direct volume rendering by En-gel et al.[3].The main idea of pre-integrated classi?ca-tion is to split the numerical integration process.Separate integration of the continuous scalar?eld and the transfer functions is performed to cope with the problematic of the Nyquist frequency.

In more detail,for each linear segment one table lookup is executed,where each segment is de?ned by the scalar value at the start of the segment s f,the scalar value at the end of the segment s b and the length of the segment d.The opacityαi of the i-th line segment is approximated by αi=1?exp

?

(i+1)d

id

τ(s(x(λ)))dλ

≈1?exp

?

1

τ((1?ω)s f+ωs b)d dω

.(5)

Analogously the associated color?Cτi(based on a non-associated color transfer function)is computed through

?Cτ

i

≈

1

τ((1?ω)s f+ωs b)c((1?ω)s f+ωs b)(6)×exp

?

ω

τ((1?ω )s f+ω s b)d dω

d dω.

Figure2:Alignment of texture slices for3D texturing on the left,and2D texturing on the right(image from Rezk-Salama et al.[13])

Both functions are dependent on s f,s b,and d(only if lengths of the segments are not equal).As usual the vol-ume rendering integral is approximated by evaluation of Equation(3).Because pre-integrated classi?cation always computes associated colors,αi C i in Equation(3)has to be substituted by?Cτi.

Through this principle the sampling rate does not depend anymore on the non-linearity of transfer functions,re-sulting in less undersampling artifacts.Therefore,pre-integrated classi?cation has two advantages,?rst it im-proves the accuracy of the visual results,and second fewer samples are required to achieve equal results regarding to the other presented classi?cation methods.

The major drawback of this approach is that the lookup ta-bles must be recomputed every time the transfer function changes.That strongly limits the interactivity of appli-cations employing this classi?cation approach.Therefore, the pre-integration step should be very fast.Engel et al.[3] proposes to assume a constant length of the segments,thus the dimensionality of the lookup table is reduced to two. By employing integral functions forτ(s)andτ(s)c(s)the evaluation of the integrals in Equations(5)and(6)can be greatly accelerated.Adapting this idea results in the following approximation of the opacity and the associated color

α(s f,s b,d)≈1?exp

?

d

s b?s f

(T(s b)?T(s f))

?Cτ(s

f ,s b,d)≈

d

s b?s f

(Kτ(s b)?Kτ(s f))(7)

with the integral functions T(s)= s

τ(s)ds and

Kτ(s)= s

τ(s)c(s)ds.This precalculation can eas-

ily performed since scalar values s are usually discrete. Thus,the numerical computing for producing the lookup tables can be minimized by only calculating the integral functions T(s)and Kτ(s).Afterwards computing the colors and opacities according to Equations(7)can be done without any further integration.This pre-calculation can be done in very short time,so providing interactivity in transfer-functions changes.The quality enhancement of pre-integrated classi?cation in comparison to pre-and post-classi?cation can be seen in Figure1.

How the presented classi?cation methods can be adapted for hardware-based volume rendering will be discussed in Section4.3.4Texture Based Volume Rendering Basically there are two different approaches how hardware acceleration can be used to perform volume rendering.

3D texture-mapped volume rendering

If3D-textures are supported by the hardware it is possible to download the whole volume data set as one single three-dimensional texture to hardware.Because hardware capable of3D-texturing is able to perform trilinear interpolation within the volume,it is possible to render a stack of polygon slices parallel to the image plane with respect to the current viewing direction(see Figure2,left).

This viewport-aligned slice stack has to be recomputed every time,the viewing position changes.Finally,in the compositing step,the textured polygons are blended onto the image-plane in a back-to-front order.This is done by using the alpha-blending capability of computer graphics hardware which usually results in a semitransparent view of the volume.Since slice polygons can be positioned arbitrarily,as many slices as required can be rendered, resulting in an image enhancement.However,in order to obtain equivalent representations while changing the number of slices,opacity values have to be adapted according to the slice distance.But rendering too many polygons results in even worse visualizations showing severe artifacts,because the frame buffer precision limits the number of slices,that can improve image quality further.

Since it is nearly a standard that3D texture mapping capabilities are now available on consumer-oriented graphics adapters(like the ATI-Radeon family[15]or the NVIDIA GeForce3and4[17])this approach is suitable for hardware accelerated volume rending on standard PC-platforms.

2D texture-mapped volume rendering

If hardware does not support3D texturing,2D texture mapping capabilities can be used for volume rendering. In this case,the polygon slices are set orthogonal to the principal viewing axes of the rectilinear data grid. Therefore if the the viewing direction changes by more than90degrees,the orientation of the slice normal has to be changed.This requires that the volume has to be represented through three stacks of slices,one for each slicing direction respectively,so the slice direction is object-aligned(see Figure2,right).

2D texturing hardware does not have the ability to perform trilinear interpolation.Because of that the slice polygons cannot be positioned arbitrarily within the volume.So the alignment of the slices with respect to the viewport is not possible.The trilinear interpolation(as performed by3D texturing hardware)is substituted by bilinear interpolation within each slice,which is although supported by hard-

ware.This results in strong visual artifacts due to the fact of the missing spatial interpolation.Another major draw-back of this approach in contrast to the previous one is the high memory requirements,because3instances of the volume data set have to be hold in memory.As in the3D texturing approach,to obtain equivalent representations, the opacity values have to be adopted.But now according to the slice distance between adjacent slices in direction of the viewing ray.

To enhance the image quality of2D texture based volume rendering,multitexturing capabilities can be used.To avoid the artifacts caused by the lack of spatial interpola-tion Rezk-Salama at al.[13]has introduced an approach to produce intermediate slices on the?y.To enable real trilinear interpolation the missing third interpolation step is performed within the rasterization hardware.Two?xed adjacent textured slices are combined using a component-wise weighted sum,exploiting the register combiners OpenGL extension by NVIDIA(see Section4).Thus linear interpolation between neighboring slices that are bilinearly?ltered in themselves produces again trilinear interpolation.A closer look on the implementation of these approaches is covered by Section4.1.

3.5High-Quality Filtering

Commodity graphics hardware can also be exploited to achieve hardware-accelerated high-quality?ltering with arbitrary?lter kernels,as introduced by Hadwiger et al.

[5].In this approach?ltering of input data is done by con-volving it with an arbitrary?lter kernel stored in multiple texture maps.As usual,the base is the evaluation of the well-known?lter convolution sum

g(x)=(f?h)(x)=

x +m

i= x ?m+1

f[i]h(x?i)(8)

this equation describes a convolution of the discrete in-put samples f[i]with a reconstruction?ler h(x)of(?nite) half-width m.

To be able to exploit standard graphics hardware to per-form this computation,the standard evaluation order(as used in software-based?ltering)has to be reordered.In-stead of gathering all input sample contributions within the kernel width neighborhood of a single input sample,this method distributes all single input sample contributions to all relevant output samples.The input sample function is stored in a single texture and the?lter kernel in multiple textures.Kernel textures are scaled to cover exactly the contributing samples.The number of contributing sam-ples is equal to the kernel width.To be able to perform the same operation for all samples at one time,the kernel has to be divided into several parts,to cover always only one input sample width.Such parts are called?lter tiles. Instead of imagining the?lter kernel being centered at the ”current”output sample location,an identical mapping of input samples to?lter values can be achieved by replicat-ing a single?lter tile mirrored in all dimensions repeatedly over the output sample grid.The scale of this mapping is chosen,so that the size of a single tile corresponds to the width from one input sample to the next.

The calculation of the contribution of a single speci?c?l-ter tile to all output samples is done in a single rendering pass.So the number of passes necessary is equal to the number of?lter tiles the?lter kernel used consists of.Due to the fact that only a single?lter tile is needed during a single rendering pass,all tiles are stored and downloaded to the graphics hardware as separate textures.If a given hardware architecture is able to support2n textures at the same time,the number of passes can be reduced by n. This method can be applied for volume rendering purposes by switching between two rendering contexts.One for the ?ltering and one for the rendering algorithm,whereas?rst a textured slice is?ltered according to the just described method,and afterwards the?ltered output is then used in the standard volume rendering pipeline.This is not as easy as it sounds,thus implementation dif?culties are described in more detail in section4.2.For results see Figure

3. Figure3:Pre-integrated classi?cation without pre-?ltered slices(left)and applying hardware-accelerated?ltering (right).

4Implementation

Our current implementation is based on a graphical user interface programmed in java,and a rendering library written in c++.For proper usage of the c++library in java, e.g for parameter passing,we exploit the functionality of the java native interface[16],which describes how to integrate native code within programs written in java. Due to the fact that our implementation is based on the OpenGL API[18],we need a library that maps the whole functionality of the native OpenGL library of the underlying operating system to java.Therefore we use the GL4Java library[4].The following detailed implementa-tion description will only cover the structure of the c++ rendering library,because all rendering functionality is encapsulated there.

On startup of the framework,the graphics adapter cur-

rently installed in the system is detected automatically. Regarding to the OpenGL extensions that are supported by the actual hardware the rendering modes that are not possible are disabled.Through this procedure,the framework is able to support a lot of different types of graphics adapters without changing the implementation. Anyway the framework is primarily based on graphics chips from NVidia and from ATI,because the OpenGL-extensions provided by these two vendors are very powerful features,which can be exploited very well for diverse direct volume rendering techniques.Minimum requirements for our application are multi-texturing capabilities.Full functionality includes the exploitation of the so called texture shader OpenGL extension and the register combiners provided by NVidia as well as the fragment shader extension,provided by ATI.

Basically the texture based volume rendering process can be split up into several principal subtasks.Each of these tasks is realized in one or more modules,to provide easy reuse possibilities.Therefore the implementation of new algorithms and the support of new hardware-features (OpenGL-extensions)is very simple by only extending these modules with additional functionality.The overall rendering implementation need to be changed to achieve support of new techniques or new graphics chips. Texture de?nition

As described in section 3.4,in the beginning of the rendering process the scalar volume data must be down-loaded to the hardware.According to the selected rendering mode,this is either be done as one single three-dimensional texture or as three stacks of two-dimensional textures.

The selected rendering mode additionally speci?es the texture format.In our context texture format means, what values are presented in a texture.Normally,RGBA (Red,green,blue and alpha component)color values are stored in a texture,but in volume rendering,other information as the volume gradient or the density value have to be accessed during the rasterization stage.For gradient vector reconstruction,we have implemented a central-difference?lter and additionally a sobel-operator, which results in a great quality enhancement in contrast to the central-difference method,avoiding severe shading artifacts(see Figure4).

When performing shading calculations,RGBA textures are usually employed,that contain the volume gradient in the RGB components and the volume scalar in the ALPHA component.As in pre-integrated rendering modes the scalar data has to be available in the?rst three components of the color vector,it is stored in the RED component.The?rst gradient component is stored in the ALPHA component in return.Another exception occurs for rendering modes,which are based on gradient-weighted opacity scaling,where the gradient magnitude is stored in the ALPHA component.Through the limitation of only four available color components, it is trivial that for the combination of some rendering modes it is not possible to store all the required values for a single slice in only one

texture.

Figure4:Gradient reconstruction using a central-difference?lter(left)and avoiding the shading artifacts (black holes)by using a sobel-operator(right) Projection

The geometry used for direct volume rendering,in contrast to other methods,e.g.iso-surface extraction,is usually very simple.Due to the fact that texture-based volume rendering algorithms usually perform slicing through a volume,the geometry only consists of a small number of primitives,one quadrilateral polygon for each slice,respectively.To obtain correct volume information for each slice,each polygon has to be bound to the corresponding textures that are required for the actual rendering mode.In addition,the texture coordinates have to be calculated https://www.sodocs.net/doc/9b6027389.html,ually this is a very simple task.

Just for2D-texture based pre-integrated classi?cation modes,it is a little bit more complex.Instead of the general slice-by-slice approach,this algorithm renders slab-by-slab(see Figure5)from back to front into the frame buffer.A single polygon is rendered for each slab with the front and the back texture as texture maps.To have texels along all viewing rays projected upon each other for the texel fetch operation,the back slice must be projected onto the front slice.This projection is per-formed by adapting texture coordinates for the projected texture slice,which always depends on the actual viewing transformation.

Compositing

Usually in hardware accelerated direct volume ren-dering approaches,the approximation of the volume rendering integral is done by back-to-front compositing of the rendered quadriliteral polygon slices.This should be performed according to Equation(4).In general this is achieved by blending the slices into the frame

Figure5:A slab of the volume between two slices.The scalar values on the front and on the back slice for a par-ticular viewing ray are called s f and s b(image from Engel et al.[3])

buffer with the OpenGL blending function glBlend-Func(GL ONE,GL ONE MINUS SRC ALPHA).

This is a correct evaluation only,if the color-values computed by the rasterization stage are associated colors.If they are not pre-multiplied(e.g.gradient-weighted opacity modes produce non-associated colors),then the blending function must be glBlend-Func(GL SRC ALPHA,GL ONE MINUS SRC ALPHA).

Iso-surface reconstruction in hardware is in general accomplished by storing the intensity value in the alpha-component of the fragment’s color.The volume is then rendered into the frame buffer using the OpenGL alpha-test to display the speci?ed isovalues only.

These two techniques can be combined for rendering semi-transparent iso-surfaces(see Figure6,left),where the alpha-test is used for rejecting all fragments not belonging to an iso-surface,and afterwards the slices are blended into the frame buffer,as described above. All fragments not belonging to an iso-surface are as-signed a special alpha-value of zero and the alpha test is then con?gured with the OpenGL function glAlpha-Func(GL GREATER,0.0),letting pass each fragment with an alpha value greater then zero.

Register settings

Depending on the selected rendering mode,during the rasterization process,the actual performed rendering technique often needs more input data than available through the slice textures(in general hold gradient and/or density information).For shading calculations the direc-tion of the light source must be known.When modelling specular re?ection the rasterization stage requires not only the light direction,but also the direction to the viewer’s eye,because a halfway vector is used to approximate the intensity of specular re?ection.Additionally some rendering modes need to access speci?c constant vectors, to perform dot-products for gradient reconstruction for example.This information has to be stored at a proper place.Therefore NVidia and ATI provide some special registers which can be accessed during rasterization process when using the register combiners extension or the fragment shader extension.

The register combiners extension,as described in[13],is able to access two constant color registers(in addition to the primary and secondary color),which is not suf?cient for complex rendering algorithms.In the GeForce3 graphics chip,NVidia has extended the register han-dling by introducing the register combiners2extension, providing per-combiner constant color registers.This means that each combiner-stage has access to its own two constant registers,so the maximum number of additional information,provided by RGBA vectors,is the number of combiner stages multiplied by two,respectively sixteen on GeForce3.In contrast all ATI graphics chips(e.g. Radeon8500,...),that support the OpenGL fragment shader extension provide access to an equal number of constant registers,namely eight.

Due to the fact that miscellaneous rendering modes need different information contained in the constant registers, the process of packing the required data into the correct registers is more complex than it sounds.In addition these constant settings intensely in?uence the programming of the rasterization stage,where each different register setting requires a new implementation of the rasterization process.

4.1NVIDIA vs.ATI

As mentioned above our current implementation supports several graphics chips from NVidia as well as several graphics chips from ATI.In this section we discuss the differences between realizations of several rendering algorithms according to the hardware-features supported by NVidia and ATI.The main focus is set on the pro-gramming of the?exible rasterization hardware,enabling advanced rendering techniques like per pixel-lighting or advanced texture-fetch methods.The differences will be discussed in detail by showing some implementation details for some concrete rendering modes after giving an short overview of rasterization hardware differences in OpenGL.

In general the?exible rasterization hardware consists of multi-texturing capabilities(allowing one polygon to be textured with image information obtained from multiple textures),multi-stage rasterization(allowing to explicitly control how color-,opacity-and texture-components are combined to form the resulting fragment,per-pixel shading)and dependent texture address modi?cation (allowing to perform diverse mathematical operations on texture coordinates and to use these results for another texture lookup).

NVidia

On graphics hardware with an NVidia chip,this ?exibility is provided through several OpenGL ex-tensions,mainly GL REGISTER COMBINERS NV and GL TEXTURE SHADER NV.When the register combiners extension is enabled,the standard OpenGL texturing units are completely bypassed and substituted by a register-based rasterization unit.This unit consists of two (eight on GeForce3,4)general combiner stages and one ?nal combiner stage.

Per-fragment information is stored in a set of input registers,and these can be combined,i.e.by dot product or component-wise weighted sum,the results are scaled and biased and?nally written to arbitrary output registers. The output registers of the?rst combiner stage are then input registers for the next stage,and so on.

When the per-stage-constants extension is enabled (GL PER STAGE CONSTANTS NV),for each combiner stage two additional registers are available,that can hold arbitrary data,otherwise two additional registers are available too,but with equal contents for every stage. The texture shader extension provides a superset of conventional OpenGL texture addressing.It provides a number of operations that can be used to compute texture coordinates per-fragment rather than using simple interpolated per-vertex coordinates.The shader opera-tions include for example standard texture access modes, dependent texture lookup(using the result from a previous texture stage to affect the lookup of the current stages), dot product texture access(performing dot products from texture coordinates and a vector derived from a previous stage)and several special modes.

The implementation of these extensions results in a lot of code,because the stages have to be con?gured properly, and an assembler like programming is not provided.

ATI

On graphics hardware with an ATI Radeon chip, this?exibility is provided through one OpenGL extension, GL FRAGMENT SHADER ATI.Generally this extension is very similar to the the extensions described before,but encapsulates the whole functionality in a single extension. The fragment shader extension inserts a?exible per-pixel programming model into the graphics pipeline in place of the traditional multi-texture pipeline.It provides a very general means of expressing fragment color blending and dependent texture address modi?cation.

The programming model is a register-based model and the number of instructions,texture lookups,read/write registers and constants is queryable. E.g.on the ATI Radeon8500there are six texture fetch operations and eight instructions possible,both two times during one rendering pass,yielding maximum of sixteen instructions in

total.Figure6:Semi-transparent iso-surface rendering(left)and pre-integrated volume rendering(right)of different human head data sets.

One advantageous property of the model is a uni?ed in-struction set used throughout the shader.That is,the same instructions are provided when operating on address or color data.Additionally,this uni?ed approach simpli?es programming(in contrast to the above presented NVidia extensions),because only a single instruction set has to be used and the fragment shader can be programmed comparable to an assembler language.

This tremendously reduces the amount of produced code and therefore accelerates and simpli?es debugging.For these reasons and because up to six textures are supported by the multi-texturing environment,ATI graphics chips provide powerful hardware features to perform hardware-accelerated high-quality volume rendering.

Pre-and Post-classi?cation

As described in detail in Section3.2,pre-and post-classi?cation differ in the order of the reconstruction step and the application of the transfer function.

Since most NVidia graphics chips sup-port paletted textures(OpenGL extension GL SHARED TEXTURE PALETTE EXT),pre-classi?ed volume rendering is easy to implement.Paletted textures means that instead of RGBA or luminance,the internal format of a texture is an index to a color-palette,repre-senting the mapping of a scalar value to a color(de?ned by transfer-function).This lookup is performed before the texture fetch operation(before the interpolation),thus pre-classi?ed volume rendering is performed.Since there is no similar OpenGL-extension supported by ATI graph-ics chips,rendering modes,based on pre-classi?cation are not available on ATI hardware.

Post-classi?cation is available on graphics-chips from both vendors,in case that advanced texture-fetch possi-bilities are available.As described in the beginning of this section when using the texture-and fragment-shader, dependent texture lookups can be performed.This feature is exploited for post-classi?cation purposes.The transfer function is downloaded as a one-dimensional texture

Figure7:Register combiner setup for gradient reconstruc-tion and interpolation with interpolation values stored in alpha(image from Engel et al.[3])

and for each texel,fetched by the given per-fragment texture coordinates,the scalar value is used as a lookup coordinate into the dependent1D transfer-function texture.Thus post-classi?cation is available,because the scalar value obtained from the?rst texture fetch has been bi-or trilinearly?ltered,dependent on whether 2D or3D volume-data textures are employed,and the transfer-function is applied afterwards.

Pre-integration

As post-classi?cation,pre-integrated classi?cation can also be performed on graphics-chips from both vendors if texture shading is available.The pre-integrated transfer-function,since dependent on two scalar values (s f from the front and s b from the back slice,see Figure 5and Section3.3for details)is downloaded as a two-dimensional texture,containing pre-integrated values for each of the possible combinations of front and back scalar values.

For each fragment,texels of two adjacent slices along each ray through the volume are projected onto each other. Then the two fetched texels are used as texture coordinates for a dependent texture lookup into the2D pre-integration texture.To extract the scalar values,usually stored in the red component of the texture,the dot product with a constant vector v=(1,0,0)T is applied.These values are then used for the lookup.

Pre-integrated volume rendering can also be employed to render multiple isosurfaces.The basic idea is to color each ray segment according to the?rst isosurface intersected by the ray segment.So the dependent texture contains color,transparency,and interpolation values (IP=(s iso?s f)/(s b?s f))for each combination of back and front scalar.For lighting purposes the gradient of the front and back slice has to be rebuilt in the RGB components and the two gradients have to be interpolated depending on the given isovalue.The implementation of this reconstruction using register combiners is shown in Figure7.

4.2Problems

As mentioned in the previous sections,the integration of different rendering techniques in one framework support-ing varying graphics chips requires a lot of care when im-plementing the varying methods.In addition to that im-plementation dif?culties,we encountered other problems as well.

When applying the hardware accelerated high quality?l-tering method(see Section3.5)in combination with an arbitrary rendering mode,we have to cope with different rendering contexts.One context for the rendering algo-rithm and one for the high quality?ltering.A single slice is rendered into a buffer,this result is then used in the?l-tering context to apply the speci?ed?ltering method(e.g. bi-cubic),and this result is then moved back into the ren-dering context,to perform i.e.the compositing step.More dif?cult is the case of combining the?ltering with preinte-gration,where two slices have to be switched between the rendering contexts.Through different contexts the geom-etry and the OpenGL state handling is varying depending on whether?ltering is applied or not.It is a challenge to de?ne and provide the correct data in the right context and not mixing up the complex state handling.Although the performance is not so high,the resulting visualizations are very convincing(see Figure1).

Another problem that occurs when realizing such a large framework is that the performance that usually is achieved by the varying algorithms can not be guaranteed.Further-more when performing shading,rendering datasets with dimensions over2563results in a heavy performance loss, caused by the memory bottle neck.Which means that not the whole data set can be downloaded to the graph-ics adapter memory,instead of,the textures are transferred between the main and the graphics memory.

5Conclusions and Future Work On the basis of standard2D-and3D-texture based vol-ume rendering and several high quality rendering tech-niques,we have presented a?exible framework,which in-tegrates several different direct volume rendering and iso-surface reconstruction techniques that exploit rasterization hardware of PC graphics boards in order to signi?cantly improve both performance and image quality.Addition-ally the framework can easily be extended with respect to support of new OpenGL extensions and implementa-tion of new rendering algorithms,by only expanding the proper modules.The framework supports most current low-cost graphics hardware and provides comparison pos-

sibilities for several hardware-accelerated volume visual-izations with regard to performance and quality.

In the future we plan the integration of non-photorealistic rendering techniques to enhance actual volume visual-izations as well as support of upcoming new graphics adapters.To overcome the problem that different graph-ics chips require different implementations,we will try the usage of a high-level shading language.

6Acknowledgements

This work was carried out as part of the basic research on visualization(http://www.VRVis.at/vis)at the VRVis Research Center Vienna,Austria(http://www.VRVis.at/), which is funded by an Austrian governmental research project called Kplus.

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4.对本研究课题有创造性见解，并取得显著的科研成果。 5.学位论文必须是作者本人独立完成，与他人合作的只能提出本人完成的部分。 6.论文字数不少于5万字，中、英摘要3000字；详细中文摘要(单行本)1万字左右。 （四）临床专业学位博士论文要求 1.要求论文课题紧密结合中医临床或中西结合临床实际，研究结果对临床工作具有一定的应用价值。 2.论文表明研究生具有运用所学知识解决临床实际问题和从事临床科学研究的能力。 3.论文字数一般不少于3万字，中、英文摘要2000字；详细中文摘要(单行本)5000字左右。 二、学位论文的格式要求 （一）学位论文的组成 博士、硕士学位论文一般应由以下几部分组成，依次为：1.论文封面；2. 原创性声明及关于学位论文使用授权的声明；3.中文摘要；4.英文摘要；5.目录； 6.引言； 7.论文正文； 8.结语； 9.参考文献；10.附录；11.致谢。 1.论文封面：采用研究生处统一设计的封面。论文题目应以恰当、简明、引人注目的词语概括论文中最主要的内容。避免使用不常见的缩略词、缩写字，题名一般不超过30个汉字。论文封面“指导教师”栏只写入学当年招生简章注明、经正式遴选的指导教师1人，协助导师名字不得出现在论文封面。 2．原创性声明及关于学位论文使用授权的声明（后附）。 3.中文摘要：要说明研究工作目的、方法、成果和结论。并写出论文关键词3～5个。 4.英文摘要：应有题目、专业名称、研究生姓名和指导教师姓名，内容与中文提要一致，语句要通顺，语法正确。并列出与中文对应的论文关键词3～5个。 5.目录：将论文各组成部分(1～3级)标题依次列出，标题应简明扼要，逐项标明页码，目录各级标题对齐排。 6.引言：在论文正文之前，简要说明研究工作的目的、范围、相关领域前人所做的工作和研究空白，本研究理论基础、研究方法、预期结果和意义。应言简

公文写作毕业论文写作要求和格式规范

（公文写作）毕业论文写作要求和格式规范

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3．摘要：论文摘要的字数壹般为300字左右。摘要是对论文的内容不加注释和评论的简短陈述，是文章内容的高度概括。主要内容包括：该项研究工作的内容、目的及其重要性；所使用的实验方法；总结研究成果，突出作者的新见解；研究结论及其意义。摘要中不列举例证，不描述研究过程，不做自我评价。 论文摘要后另起壹行注明本文的关键词，关键词是供检索用的主题词条，应采用能够覆盖论文内容的通用专业术语，符合学科分类，壹般为3～5个，按照词条的外延层次从大到小排列。 4．目录（目录示例见附件3）：独立成页，包括论文中的壹级、二级标题、后记、参考文献、和附录以及各项所于的页码。 5．正文：包括前言、论文主体和结论 前言：为正文第壹部分内容，简单介绍本项研究的背景和国内外研究成果、研究现状，明确研究目的、意义以及要解决的问题。 论文主体：是全文的核心部分，于正文中应将调查、研究中所得的材料和数据加工整理和分析研究，提出论点，突出创新。内容可根据学科特点和研究内容的性质而不同。壹般包括：理论分析、计算方法、实验装置和测试方法、对实验结果或调研结果的分析和讨论，本研究方法和已有研究方法的比较等方面。内容要求论点正确，推理严谨，数据可靠，文字精炼，条理分明，重点突出。 结论：为正文最后壹部分，是对主要成果的归纳和总结，要突出创新点，且以简练的文字对所做的主要工作进行评价。 6．后记：对整个毕业论文工作进行简单的回顾总结，对给予毕业论文工作提供帮助的组织或个人表示感谢。内容应尽量简单明了，壹般为200字左右。 7．参考文献：是论文不可或缺的组成部分。它既可反映毕业论文工作中取材广博程度，又可反映文稿的科学依据和作者尊重他人研究成果的严肃态度，仍能够向读者提供有关

配合前面的ntheorem宏包产生各种定理结构

%=== 配合前面的ntheorem宏包产生各种定理结构,重定义一些正文相关标题===% \theoremstyle{plain} \theoremheaderfont{\normalfont\rmfamily\CJKfamily{hei}} \theorembodyfont{\normalfont\rm\CJKfamily{song}} \theoremindent0em \theoremseparator{\hspace{1em}} \theoremnumbering{arabic} %\theoremsymbol{} %定理结束时自动添加的标志 \newtheorem{definition}{\hspace{2em}定义}[chapter] %\newtheorem{definition}{\hei 定义}[section] %!!!注意当section为中国数字时，[sction]不可用！ \newtheorem{proposition}{\hspace{2em}命题}[chapter] \newtheorem{property}{\hspace{2em}性质}[chapter] \newtheorem{lemma}{\hspace{2em}引理}[chapter] %\newtheorem{lemma}[definition]{引理} \newtheorem{theorem}{\hspace{2em}定理}[chapter] \newtheorem{axiom}{\hspace{2em}公理}[chapter] \newtheorem{corollary}{\hspace{2em}推论}[chapter] \newtheorem{exercise}{\hspace{2em}习题}[chapter] \theoremsymbol{$\blacksquare$} \newtheorem{example}{\hspace{2em}例}[chapter] \theoremstyle{nonumberplain} \theoremheaderfont{\CJKfamily{hei}\rmfamily} \theorembodyfont{\normalfont \rm \CJKfamily{song}} \theoremindent0em \theoremseparator{\hspace{1em}} \theoremsymbol{$\blacksquare$} \newtheorem{proof}{\hspace{2em}证明} \usepackage{amsmath}%数学 \usepackage[amsmath,thmmarks,hyperref]{ntheorem} \theoremstyle{break} \newtheorem{example}{Example}[section]

论文写作格式规范与要求(完整资料).doc

【最新整理，下载后即可编辑】 广东工业大学成人高等教育 本科生毕业论文格式规范（摘录整理） 一、毕业论文完成后应提交的资料 最终提交的毕业论文资料应由以下部分构成： （一）毕业论文任务书（一式两份，与论文正稿装订在一起）（二）毕业论文考核评议表（一式三份，学生填写表头后发电子版给老师） （三）毕业论文答辩记录（一份, 学生填写表头后打印出来，答辩时使用） （四）毕业论文正稿（一式两份，与论文任务书装订在一起），包括以下内容： 1、封面 2、论文任务书 3、中、英文摘要（先中文摘要，后英文摘要，分开两页排版） 4、目录 5、正文（包括：绪论、正文主体、结论） 6、参考文献 7、致谢 8、附录（如果有的话） （五）论文任务书和论文正稿的光盘

二、毕业论文资料的填写与装订 毕业论文须用计算机打印，一律使用A4打印纸，单面打印。 毕业论文任务书、毕业论文考核评议表、毕业论文正稿、答辩纪录纸须用计算机打印，一律使用A4打印纸。答辩提问记录一律用黑色或蓝黑色墨水手写，要求字体工整，卷面整洁；任务书由指导教师填写并签字，经主管院领导签字后发出。 毕业论文使用统一的封面，资料装订顺序为：毕业论文封面、论文任务书、考核评议表、答辩记录、中文摘要、英文摘要、目录、正文、参考文献、致谢、附录（如果有的话）。论文封面要求用A3纸包边。 三、毕业论文撰写的内容与要求 一份完整的毕业论文正稿应包括以下几个方面： （一）封面（见封面模版） （二）论文题目（填写在封面上，题目使用2号隶书，写作格式见封面模版） 题目应简短、明确，主标题不宜超过20字；可以设副标题。（三）论文摘要（写作格式要求见《摘要、绪论、结论、参考文献写作式样》P1～P2） 1、中文“摘要”字体居中，独占一页

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使用Groff 生成独立于设备的文档开始之前 了解本教程中包含的内容和如何最好地利用本教程，以及在使用本教程的过程中您需要完成的工作。 关于本教程 本教程提供了使用Groff(GNU Troff)文档准备系统的简介。其中介绍了这个系统的工作原理、如何使用Groff命令语言为其编写输入、以及如何从该输入生成各种格式的独立于设备的排版文档。 本教程所涉及的主题包括： 文档准备过程 输入文件格式 语言语法 基本的格式化操作 生成输出 目标 本教程的主要目标是介绍Groff，一种用于文档准备的开放源码系统。如果您需要在应用程序中构建文档或帮助文件、或为客户和内部使用生成任何类型的打印或屏幕文档(如订单列表、故障单、收据或报表)，那么本教程将向您介绍如何开始使用Groff以实现这些任务。 在学习了本教程之后，您应该完全了解Groff的基本知识，包括如何编写和处理基本的Groff输入文件、以及如何从这些文件生成各种输出。

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论文的写作格式及规范

论文的写作格式及规范

附件9： 科学技术论文的写作格式及规范 用非公知公用的缩写词、字符、代号，尽量不出现数学式和化学式。 2作者署名和工作单位标引和检索，根据国家有关标准、数据规范为了提高技师、高级技师论文的学术质量，实现论文写的科学化、程序化和规范化，以利于科技信息的传递和科技情报的作评定工作，特制定本技术论文的写作格式及规范。望各位学员在注重科学研究的同时，做好科技论文撰写规范化工作。 1 题名 题名应以简明、确切的词语反映文章中最重要的特定内容，要符合编制题录、索引和检索的有关原则，并有助于选定关键词。 中文题名一般不宜超过20 个字，必要时可加副题名。英文题名应与中文题名含义一致。 题名应避免使作者署名是文责自负和拥有著作权的标志。作者姓名署于题名下方，团体作者的执笔人也可标注于篇首页地脚或文末，简讯等短文的作者可标注于文末。 英文摘要中的中国人名和地名应采用《中国人名汉语拼音字母拼写法》的有关规定；人名姓前名后分写，姓、名的首字母大写，名字中间不加连字符；地名中的专名和通名分写，每分写部分的首字母大写。 作者应标明其工作单位全称、省及城市名、邮编( 如“齐齐哈尔电业局黑龙江省齐齐哈尔市(161000) ”)，同时，在篇首页地脚标注第一作者的作者简介，内容包括姓名，姓别，出生年月，学位，职称，研究成果及方向。

3摘要 论文都应有摘要（3000 字以下的文章可以略去）。摘要的：写作应符合GB6447-86的规定。摘要的内容包括研究的目的、方法、结果和结论。一般应写成报道性文摘，也可以写成指示性或报道-指示性文摘。摘要应具有独立性和自明性，应是一篇完整的短文。一般不分段，不用图表和非公知公用的符号或术语，不得引用图、表、公式和参考文献的序号。中文摘要的篇幅：报道性的300字左右，指示性的100 字左右，报道指示性的200字左右。英文摘要一般与中文摘要内容相对应。 4关键词 关键词是为了便于作文献索引和检索而选取的能反映论文主题概念的词或词组，一般每篇文章标注3?8个。关键词应尽量从《汉语主题词表》等词表中选用规范词——叙词。未被词表收录的新学科、新技术中的重要术语和地区、人物、文献、产品及重要数据名称，也可作为关键词标出。中、英文关键词应一一对应。 5引言 引言的内容可包括研究的目的、意义、主要方法、范围和背景等。 应开门见山，言简意赅，不要与摘要雷同或成为摘要的注释，避免公式推导和一般性的方法介绍。引言的序号可以不写，也可以写为“ 0”，不写序号时“引言”二字可以省略。 6论文的正文部分 论文的正文部分系指引言之后，结论之前的部分，是论文的核心， 应按GB7713--87 的规定格式编写。 6.1层次标题