Texture mapping: A new tool for molecular graphics

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Michael Teschner, Christian Henn, Horst Vollhardt, Stephan Reiling, and
Jürgen Brickmann

Journ.Mol.Biol. 1994

Abstract
The real-time texture mapping capabilities of modern graphics workstations
are explored with respect to their applications in a variety of relevant
scenarios in interactive molecular modeling techniques. The common usage of
texture mapping to reduce geometric complexity while enhancing realism is
extended, opening new ways to visualize large amounts of molecular data in
a comprehensive fashion. Thus, texture mapping may be employed to (1)
display and filter multichannel information of structural properties on
molecular surfaces, (2) improve the quality and accuracy of highly complex
isodensity contours, (3) increase the rendering speed of space-filling
atomic representations by two orders of magnitude and (4) apply
volume-rendering techniques to large, three-dimensional density
distributions in real time. Implementation of these novel techniques
requires only moderate modifications or extensions to existing molecular
modeling applications.

Introduction

The complexity of molecular systems leads to huge amounts of data generated
by experiments or simulations. For a better understanding of the structure
and function of molecular systems, more advanced computer graphics
capabilities are desirable, allowing one to go from a qualitative general
overview toward more and more detailed aspects.

With the advent of general-purpose workstations supporting the advanced
technique of texture mapping [1,2] in computer graphics hardware [3], a new
door for the visualization of molecular systems has been opened.
Integration of the texture-mapping concept in molecular graphics
applications dramatically extends existing visualization capabilities.
Moreover, solutions to unsolved problems in molecular visualization are
offered, filling a gap in the analysis of molecular scenarios.

The texture-mapping method is characterized by its simplicity and elegance
in obtaining quite complex results. The technique, which may often provide
additional physical and chemical insight to molecular problems, is
demonstrated in the following selected examples. Due to hardware support,
all visual effects may be fine-tuned to ultimately capture a complicated
three-dimensional (3D) system in a simple fashion. Furthermore,
implementation of texture-mapping capabilities is straightforward and
simple, avoiding algorithmic complexity and the loss of compute
performance.

Texture mapping has been widely used in visual simulation applications
[4,5]. In these applications, the major concern is that there is a constant
frame rate for the visual representation of 3D objects moving in real time
and represented with a high degree of realism. In visual simulations,
texture mapping is helpful, because it reduces geometric complexity and
enhances the realism of the scene. This is achieved by projecting images
onto the surfaces of a 3D objects.

At present, texture mapping is not widely used by the molecular graphics
community. Noninteractive applications of the technique, such as computer
animation, have provided a severe bias towards what texture mapping can be
used (e.g., wooden [6] or marble surfaces for the simulating solid
materials or fuzzy, stochastic patterns mapped on quadrics to visualize
clouds [4,5]).

This article demonstrates that the new potential brought about by texture
mapping may generate an enormous impact on molecular graphics by
identifying the real-time visual representation of molecular surfaces and
3D structural properties as the most important application areas. Moreover,
this article attempts to provide a new way of thinking about texture
mapping for molecular problems.

Reverting to the original, strict and formal definition of texture mapping,
the technique becomes a flexible, elegant and more general framework for
the generation and modification of visual molecular information obtained
from a variety of sources. Based on this abstract definition of texture
mapping, selected problems in molecular visualization can be elucidated in
the form of four different examples: (1) display and filtering of
multichannel structural information on molecular surfaces, (2) quality and
accuracy improvement necessary for the visualization of highly complex
isodensity contours, (3) increased speed of the rendering step of
space-filling atomic representations, and (4) application of
volume-rendering techniques to large 3D density distributions in real time.

The texture-mapping concept

Texture mapping is a technique that applies an image to an object's surface
as if the image were a decal or cellophane shrink-wrap. The image exists in
a parametric coordinate space called the texture space [7,8,9]. The
individual elements of a texture are called texels. Figure 1 shows how a
simple texture is defined in two-dimensional (2D) texture space and mapped
to 3D object space.

Figure 1. The basic principle of texture mapping. The texture (left) is
defined in a normalized coordinate system. The mapping of the texture onto
the geometry (right) is done on a per vertex basis.

At the moment, the general benefit provided by the application of texture
mapping is to add realism or reduce geometric complexity. The object
material can be shown by wrapping a wood grain pattern around a rectangular
solid to create a block of wood. By mapping an image of a house onto a few
polygons, instead of drawing a large number of polygons to represent the
house, the complexity is reduced.

Texture mapping, in a more abstract definition, can be used in a variety of
ways to enhance visual representation. Two basic components are needed for
the texture-mapping procedure - the texture, which is defined in a texture
space, and the 3D geometry, defined on a per-vertex basis in object
coordinates. 3D geometry could be a set of points and vertices, but the
real value of texture mapping emerges on drawing filled polygons, such as
triangles or higher order polygons.

Texture mapping assigns a coordinate in the texture space to each vertex of
the 3D object . The mapping describes where the texels are placed in object
space. This is not, however, a one-to-one mapping to screen pixels. It can
be magnified or reduced through interpolation. This is done during the
rendering step, where pixel information generated by lighting and coloring
is modified, based on the texture information.

Assignment of texture coordinates is often done in an explicit fashion
(i.e., specific texture values are attached to each object vertex).
Alternatively, texture coordinates can be generated automatically. One
method is based on the distance from a reference plane in world or object
space, while another method uses the object's normals to determine texture
coordinates depending on the direction in which it is viewed.

Texture space can be one-dimensional (1D), 2D or 3D (Figure 2). Analogous
to the pixel in screen space, each element in texture space is called a
texel (texture element). Current hardware implementations offer flexibility
with respect to how the information stored with each texel is interpreted.
Multichannel colors, transparency or even look-up indices, corresponding to
a color look-up table, are supported [3,10].

Figure 2. The dimensionality of the texture space is independent of the
geometry.

As a basic definition, the texture space can be regarded as a special
memory, where a variety of information can be stored and then linked to
object representations in real 3D space.

Application fields for texture-mapping techniques

Molecular surfaces
The detailed study of molecular surfaces have become important tools for
the interpretation of properties beyond the molecular structure, in terms
of atomic coordinates [11-14]. Models of molecular surfaces are either
based on a spherical probe rolled over the atomic structure [15,16] or on
isocontouring of 3D density grids [17]. Both approaches use algorithms
capable of generating 3D objects with solid surfaces composed of triangles
[18,19].

The combination of these forms of molecular representation with
texture-mapping capabilities offers a variety of new ways for visualizing
molecular properties.

Volumetric properties
Visualization of large 3D data sets has always been a challenge to
interactive computer graphics applications. This is true not only for the
field of molecular modeling, but also for other areas of scientific
visualization with potentially high demands on interactivity and visual
clarity. Two such areas can be found in medical applications: CT scanning
and MR imaging.

Two approaches are used to generate visual information out of 3D data sets:
extraction of a discrete isocontour surface [20] or voxel-based rendering
of the volume [21] using a color look-up table to attribute irrelevant
parts of the volume with transparency.

Applications

Color coding
Color coding is a popular means of displaying scalar information on a
surface [22]. In interactive molecular graphics, high-contrast color code
variation on sparsely tessellated geometry has so far been a serious
problem. While standard hardware implementations allow the specification of
an RGB color triplet per surface vertex, color interpolation on pixels in
between is performed in a linear way [23]. As a consequence, all entries in
the color code lying outside the linear color ramp joining two RGB triplets
are never taken into account. With a highly tessellated surface, this
problem can be reduced. An alignment of the surface vertices with the
expected color code change or multipass rendering may remove such artifacts
completely. However, these methods demand large numbers of polygons or
extreme algorithmic complexity, both undesired in interactive applications.

A solution to this problem is provided by representing the color ramp as a
1D texture. Mapping the calculated property into texture space instead of
color space ensures that the coloring evaluated at every pixel is taken
from information lying in between the values of the relevant vertices
(Figure 3). High contrast variation in the color code is then possible,
even on sparsely tessellated surfaces (Figure 4 and 5). It is important to
note that, although the texture is 1D, it is possible to tackle a 3D
problem, because the dimensionality of the texture space does not affect
the object space.

Figure 3. The difference between interpolation in color space (left) and in
texture space (right).

Figure 4. Isocontouring of the hydrophobic potential on the
solvent-accessible surface of Gramicidine A. Using a different scaling for
the texture space results in a different spacing of the isocontour lines.

The independence of texture and object coordinate space is well suited to
accommodate immediate changes to the meaning of the color (i.e., by
applying simple 3D transformations in texture space). Translation allows
readjustment of the zero line of the color code, while scaling of the
texture changes the range of the mapping. Such modifications may be
performed in real time.

[ ]
Figure 5: Solvent-accessible surface of ethanol, color coded against the
electrostatic potential, using the traditional color coding (left) and
using texture mapping (right). With texture mapping, the resulting sharp
transitions from one color value to the next signifixantly improve the
accuracy of rendering. In addition, the sharp transitions help to visually
understand the oject's 3D shape.

Similar to the 1D texture used as a color code on a molecular surface, the
texture space may be extended to two or even three dimensions,
incorporating additional information with each additional dimension, such
that a maximum of three independent properties can simultaneously be
visualized simultaneously. However, special care must be taken not to
overload the surface with too much information. Combining two sources of
information that together do not provide new insight into the properties of
the molecular system does not make much sense either.

A rather useful application of multiple property mapping is the
introduction of transparency. This is illustrated in analyzing the local
flexibility of a structure, according to the crystallographically
determined B-factors. The more rigid the structure is, the more opaque the
surface will be displayed. Increasing transparency indicates higher
floppiness of the domains. Such a transparency map may well be combined
with any other color-coded property, as it is of interest to study the
dynamic properties of a molecule in many different contexts.

By filtering property information on a molecular surface, one is able to
generate more insight in two different ways:

(1) The filter allows the scientist to distinguish between important and
irrelevant information.

(2) The filter puts an otherwise qualitative property into a quantitative
context (e.g., the standard deviation from a mean value may provide a hint
as to accuracy of a represented property).

Figure 6. The solvent-accessible surface of Trypsin, color coded against
the electrostatic potential, using the texture-mapping approach (left).
This needs only one dimension in texture space. With coding the electric
field in the second dimension, it is possible to filter the potential with
the strength of the field. Only those areas are color coded where the
electric field is above a given threshold.

In both cases, the information can be filtered using a delta-type function,
suppressing all information not exceeding a specific threshold, or else a
continuous filter may be used to allow for a more fine-grained
quantification (Figure 6).

Filtering may be implemented analogously to the color-coding technique
earlier, if one uses 2D or 3D texture maps. A useful application results
from the filtering of properties such as the electrostatic potential and
the electric field. Taking the absolute value of the electric field, the
filter threshold easily pinpoints the areas of the highest local field
gradient, which is often used in identifying the binding site of an
inhibitor without additional interaction of the scientist. Another
application includes filtering based on the statistical error of a
represented property, such as putting the displayed property into a
quantitative context.

Real-time Phong shading
Electron density maps are often quite complex. They can exhibit a high
degree of local curvature, which is a major challenge for accurate
visualization. This is where the simple Gouraud shading [23] approach often
fails. It destroys information in the highly curved regions of the surface
because the linear interpolation of vertex colors cannot account for the
local shadow variation due to the lighting model.

Correct perception of the curvature can only be achieved with
computationally much more demanding shading techniques (e.g., Phong
algorithms [24]). In contrast to linear interpolation of vertex colors, the
Phong shading approach interpolates the normal vectors for each pixel of a
given geometric primitive, computing the lighting equation in the
subsequent step. Attempts have been made to overcome some of the
computationally intensive steps of the procedure [25], but their
performance was insufficient to be a reasonable alternative to Gouraud
shading in real-time applications.

A much more simpler solution is possible using a special texture-mapping
technique called normal mapping. In contrast to Phong shading, the
interpolation is not performed on the normals directly. However, normals
are used to automatically generate texture coordinates based on the
orientation of the surface vertices in the world coordinate system. The
subsequent interpolation then takes place in 2D texture space, using the
image of a perfectly rendered sphere as the texture (Figure7 and 8).

The visual result compares exactly to a surface computed with the original
Phong approach. Although this trick is only applicable for infinitely
distant light sources, it is a tremendous aid for the visualization of
highly complex surfaces.

[ ]
Figure 7. Differences between Gouraud shading and texture mapping for
shaded surfaces. The tessellation in both cases is the same (left). In the
Gouraud case (middle), the tessellation influences the shading, which is
not valid for texture mapping.

Figure 8. Application of Phong shading to arbitrary surfaces. The sphere is
used as the texture. The example shown is a 3D surface reconstrution of an
electron microscopy experiment visualizing the asymmetric unit membrane of
the unrinary bladder. The difference between Gouraud shading (right) and
the texture mapping implementation of Phong shading (left) is very obvious,
looking at the close-ups.

Real-time space-filling models
The use of high-quality CPK models [26] in interactive molecular-modeling
applications is currently restricted to molecules of limited size. Spheres
that are used to represent individual atoms need to be highly tessellated,
which increases the geometric complexity of the model system. In order to
display a simple sphere with sufficient accuracy, a few hundred Gouaud
shaded triangles are required. The rendering of large molecules without
degradation of the visual quality is impossible within reasonable effort.

This problem can be solved with a special form of 2D texture mapping. Each
atom is represented by a square on which there is an image of a perfectly
rendered sphere. Areas of the square that are not covered by the actual
sphere are drawn fully transparent. However, each sphere might intersect
with other objects. To handle this problem appropriately, one can use a
special feature allows correct, hidden line removal on a per-pixel basis
[27].

Figure 9: Fast spheres using texture mapping. The 13,767 spheres of a
hydrated phospholipid bilayer (DLPE), part of a cell membrane can be
rotated in real time. The configuration is taken from a molecular dynamics
simulation performed by some of the authors [28].

This approach reduces the geometric complexity to one squared polygon per
atom, resulting in a performance at least two orders of magnitude better.
Furthermore, the visual quality of the representation is raised to an
optimum (Figure 9).

Volumetric molecular properties
Texture-oriented volumetric visualization is based on sampling a 3D texture
volume with vertex-based geometry. The final coloring of the geometry
reflects the result of the intersection with the texture.

The most simple application of this principle is that of a slice plane,
defined either in object or in world coordinates. The slicing samples the
texture to reflect the contents of the volume as if it were exposed by
cutting the object with a knife. The orientation of such a slice may be
modified interactively (Figure 10). A direct extension of the slice plane
approach leads to the complete visualization of the entire volume. A stack
of planes, oriented in parallel to the computer screen, is used to sample
the entire 3D texture. The planes are drawn starting from the slice plane
at the far end of the stack and then proceeding up to the viewer in
regular, sufficiently small intervals. Geometric transformations of the
volume are performed by manipulating the orientation of the texture,
keeping the planes in screen-parallel orientation.

Figure 10: A slice plane cutting a volumetric density distribution. The
property visualized is the probability of water being distributed around a
sugar molecule. The slice plane may be reoriented within the property
volume in real time.

This type of volume visualization technique is greatly enhanced by
interactive updates of the color look-up table used in defining the
texture. In fact a general-purpose color ramp editor may be used to vary
the look-up colors or even to vary the transparency based on the scalar
value at a given point in the 3D volume.

The concept of the slice plane can be extended to arbitrarily shaped
objects (Figure 11). The idea is to probe a volumetric property and to
display it wherever the primitive of the probing object cuts the volume.
The probing geometry can be of any shape (e.g., a sphere) that collects
information about the volumetric property at a certain distance from a
specified point or it may be extended to describe a complete molecular
surface.

The independence of the object's transformation from that of the 3D volume,
treated as a 3D texture, offers complete freedom in orienting the surface
with respect to the volume. This provides an opportunity to look at a
molecular surface and have the displayed property updated, based on the
current orientation of the object.

[ ]
Figure 11: A slice plane cutting a volumetric density distribution. This
time, a stack of slice planes is used to produce a volume-rendered
representation.

Implementation

All of the examples presented earlier can be implemented using techniques
other than texture mapping. The trade-off is either a complete loss of
performance or an high level of algorithmic complexity. Both of them are
undesirable.

Using texture mapping, it is sufficient to modify existing code fragments
or to incorporate modest extensions, such as reading in a texture and
activating texture coordinates. In other words, implementing texture
mapping in existing molecular graphics applications is extremely simple and
strongly encouraged. All examples were implemented on a Silicon Graphics
Crimson Reality Engine [3] equipped with two raster managers. The programs
were written in C, either in mixed mode GLX or pure GL. Sample code
fragments are available from the authors.

Conclusions

The potential of hardware-supported texture mapping, available on
general-purpose graphics workstations, has been demonstrated for a number
of molecular graphics applications. Its main impact may be expected where
(1) the geometric complexity must be reduced to get interactive
performance, (2) the information density needs to be increased to reflect
adequately the properties of a molecule, (3) irrelevant information has to
be filtered; and (4) an improvement of the rendering quality is required to
fully support correct perception of highly complex surfaces. It can be
expected that in the near future even more uses for real-time texture
mapping in molecular graphics will emerge.

Literature
[1] Blinn, J.F., and Newell, M.E. Texture and reflection in computer
generated images. Communications of the ACM 1976, 19, 542-547.
[2] Blinn, J.F. Simulation of wrinkled surfaces, Computer Graphics 1978,
12, 286-292.
[3] Akeley, K. Reality Engine Graphics, Computer Graphics 1993, 27,
109-116.
[4] Gardner, G.Y. Simulation of natural scenes using textured quadric
surfaces, Computer Graphics 1984, 18, 11-20.
[5] Gardner, G.Y. Visual simulations of clouds, Computer Graphics 1985, 19,
297-303.
[6] Peachey, D.R. Solid texturing of complex surfaces, Computer Graphics
1985, 19, 279-286.
[7] Catmull, E. A subdivision algorithm for computer display of curved
surfaces, Ph.D. dissertation, University of Utah, 1974.
[8] Crow, F.C. Summed area tables for texture mapping, Computer Graphics
1984, 18, 207-212.
[9] Williams, L. Pyramidal parametrics, Computer Graphics 1983, 17, 1-11.
[10] Porter, T., and Duff, T. Compositing of digital images, Computer
Graphics 1984, 18, 253-259.
[11] Langridge, R., Ferrin, T.E., Kunz, J.D., Connolly, M.L Real-time color
graphics in studies of molecular interactions, Science 1981, 211, 661.
[12] Pang, L., Lucken, E.A.C., Weber, J. and Bernardelli, G. Structural
investigations and modeling of cavities in clathrates. J. Mol.
Comput.-Aided Mol. Design 1991, 5, 285-291.
[13] Freeman, C.M., Levine, S.M., Newsam, J.M., Sauer, J., Tomlinson, S.M.,
Brickmann, J. and Bell, R.G. In "Zeolite Computer Graphics," Modelling of
Structure and Reactivity in Zeolites (C.R.A. Catlow, Ed) Academic Press,
London (1992) 133-155.
[14] Mezey, P. In "Molecular Surfaces," Reviews in Computational Chemistry
(K. Lipkowitz and D. Boyd, Eds) VCH, Weinheim, (1990) 265-294.
[15] Richards, F. Calculation of molecular volumes and areas for structures
of known geometry, Methods in Enzymology 1985, 115, 440-465.
[16] Connolly, M. Analytical molecular surface calculation, J. of Applied
Cryst. 1983, 16, 548-558.
[17] Goetze, T. The fractal dimension of molecular surfaces. Thesis,
Technische Hochschule Darmstadt, in preparation
[18] Heiden, W., Schlenkrich, M. and Brickmann, J. Triagulation algorithms
for the representation of molecular surface properties. J. Comput.-aided
Mol. Desing 1990, 4, 255-269.
[19] Heiden, W., Goetze, T. and Brickmann, J. Fast geneartion of molecular
surfaces from 3D data fields with an enhanced "marching cube" algorithm. J.
Comp. Chem. 1993, 14, 246-250.
[20] Lorensen, W.E., and Cline, H.W. Marching cubes: a high-resolution
surface construction algorithm, Computer Graphics 1987, 21, 163-169.
[21] Drebin, R., Carpenter, L., and Hanrahan, P. Volume Rendering, Computer
Graphics 1988, 22, 65-74.
[22] Dill, J.C. An application of color graphics to the display of surface
curvature, Computer Graphics 1981, 15, 153-161.
[23] Gouraud, H. Continuous shading of curved surfaces, IEEE Transactions
on Computers 1971, 20, 623-628.
[24] Phong. B.T. Illumination for computer-generated pictures,
Communications of the ACM 1987, 18, 311-317.
[25] Bishp, G., and Weimer, D.M. Fast Phong shading, Computer Graphics
1986, 20, 103-106.
[26] Corey, R.B. and Pauling, L., Molecular models of amino acids, peptides
and proteins, Rev. Sci. Instr1953, 24, 621ff.
[27] Fuchs, H, et.al. Fast spheres, shadows, textures, transparencies, and
image enhancements in pixel-plane, Computer Graphics 1985, 19, 111-120.
[28] Vollhardt, H. and Brickmann, J. Molecular dynamics simulation of
phospholipid bilayers in contact with an aqueous solution. in prepartion

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