Cultural
Heritage Preservation Using
Constructive
Shape Modeling
C. Vilbrandt ^{(a)}, G. Pasko ^{(b)}, A. Pasko ^{(c,b)}, J. R. Goodwin ^{(d)}, J. M. Goodwin ^{(e)} and T. L. Kunii^{(c,b)}
^{(a)}University of Aizu, Computer Arts Lab, AizuWakamatsu,
Japan
Email: vilb@uaizu.ac.jp
^{(b)} IT Institute of Kanazawa Institute of Technology,
Tokyo, Japan
Email:
gpasko@iti.kanazawait.ac.jp
^{(c)}Hosei University, Department of Digital
Media, Tokyo, Japan
Email:{pasko,kunii}@k.hosei.ac.jp
^{(d)}Director of the Aizu History Project, Los Angeles (CA),
USA
Email: jan@pollux.csustan.edu
The issues of digital preservation of
cultural heritage are discussed. An overview of existing approaches to
computer modeling of historical objects of cultural significance is presented
and corresponding problems are considered. We propose a digital preservation
paradigm yielding more than visible surface models. Our approach is based
on constructive modeling that reflects the shapes and logical structure
of the objects that are to be digitally preserved. Constructive Solid Geometry
(CSG) and Function Representation (FRep) are examined and practically applied
as mathematical representations providing for the independent robust data
structures necessary for the digital archiving of cultural heritage objects
and sites. Examples of CSG based reconstruction of historical temples
and FRep based modeling of traditional lacquer ware are given. The
construction of FRep model of a sake pot from a cloud of points is
reviewed and shown. We discuss the critical importance of holding all of
the source code used in the digital preservation processes open to public
inspection modification and verification. We will argue that rigorous
proof of complex digital manipulations that are entrusted with the long
term digital preservation of cultural heritage is an essential key element
to the development and implementation of the digital preservation system
proposed in this paper.
Introduction
In
this paper,
we
demonstrate two methods of modeling cultural heritage objects. Our first
method, which we have used to model buildings from both archaeological
data and onsite measurements, reveals how the actual objects were constructed.
This approach could be used to parametrically augment the current "scan and mesh" approach that typically yields only visible surface models. Like most current methods of modeling, however, this approach relies on hardware and on proprietary software packages that may conceivably become obsolete and unusable even before the modeled objects themselves are destroyed.
Accordingly, we next propose and demonstrate a new paradigm for cultural heritage preservation that avoids such pitfalls. This paradigm is based on constructive modeling, which reflects the logical structure of the shapes reproduced. We illustrate this method with models of ancient Japanese temples and traditional Japanese lacquer ware.
Let us discuss and compare
different approaches to computeraided preservation of the shapes of culturally
valuable objects. In the general case, a shape can be considered a point
set in a multidimensional space. Thus, not only external boundaries, but
also internal structures of objects as well as their time and other parametric
dependencies can be subjects of digital preservation.
Measurements and drafting
Measurements and modeling
This approach is especially valuable if the real object
has been lost, destroyed or damaged, and is documented only by previous
measurements and drawings. The goals are to create a 3D model of the object
that is as complete as possible, and to represent its internal structure,
design logic (showing how components are interconnected or layered), and
history of the shape construction, as well as timedependent aspects and
other parametric dependencies.
De facto standard industrial
modeling tools are usually based on the socalled boundary representation
(BRep) of 3D objects. In particular, BRep can be based on a polygonal mesh
approximation of the object surface. This modeling scheme is only partly
appropriate for achieving the modeling goals described above. BRep data
structures do not reflect the object's internal structures (e.g., material
distribution) or design logic. Parameterization of BRep models is quite
limited. Only simple timedependent parameterization of BRep is allowed,
which does not change the object topology. A constructive modeling
approach can be an alternative. It is based on the construction of complex
objects using simple primitive elements and combining and transformation
operations. This approach is supported by the Constructive Solid Geometry
(CSG) and the Function Representation (FRep) methods discussed in the following
sections.
Scanning
There exist several welldeveloped technologies
for automatic noncontact acquisition of 3D point coordinates on the visible
surfaces of objects. These technologies are based on lasers, structured
light, sound, and stereo imagery. Archiving of the raw data (the measured
point locations) is preferable in any case to archiving shapes inferred
from this data. Moreover, the raw data itself can be the best way of actually
representing the surface, as was shown in the Digital Michelangelo project.^{2}
The authors’ dataset of range images obtained with laser rangefinders
provided 18:1 storage savings with no loss in information, if compared
with the equivalent polygonal mesh. A special viewer based on range images
was developed. The project authors claim that “if one only wants
to view a 3D model, and not perform geometric operations on it, then it
need not be represented polygonally.”
Scanning and meshing
Traditionally a polygonal mesh is generated on the basis of the rough data. This can be necessary especially if the measurement equipment does not provide point coordinates directly. For example, in the Pietà Project^{3} the scanner consisted of six blackandwhite cameras capturing images of a striped pattern projected on an object. Accompanying software computed a triangle mesh from the captured images using principles of stereo computer vision.
Scanning and modeling
Scanning can provide a set of reference control points for manual modeling or the full point cloud can be used for (semi)automatic model generation. An example of the latter case is voxel model generation from a set of range images.^{4} The potential of an automatic search of a simple model structure and parameters fitting of an implicit surface model on the base of range data was illustrated in the work of S. Muraki.^{5} In the case of unknown initial estimation of the model structure, evolution of shapes using techniques such as genetic algorithms can be applied, in the manner of the reported experiments with CSG ^{6} and analytically defined implicit surfaces.^{7} Here, the overall distance from the shape surface to the scanned points can serve as an optimization criterion. In this work, we use measurements and constructive modeling of parameterized shapes oriented towards automatic optimization of shape parameters and further genetic evolution of shape structures.
2.2 Problems of cultural heritage preservation
Most current methods of modeling, including the first approach demonstrated in this paper, rely on proprietary software packages using data formats embedded in operating systems and hardware platforms. Since it is difficult, and in many cases illegal, to access the data directly, it is impossible to verify the application's operations independently and difficult to translate or provide interoperability or migration across platforms. Thus, proprietary software violates basic scientific requirements for rigorous proof of the accuracy of data gathering methods, research procedures, and digital processes. These methods and procedures must be open to inspection and inquiry in order to assure that cultural artifacts have been accurately modeled, and it should be possible to perform independent verifiable evaluation of the results of a given study. Moreover, information must be disseminated and archived using an open and understandable data format and a stable storage medium that provides secure storage and retrieval, at a reasonable cost, for the near and distant future.
Most digital information technology presently in use fails to meet these basic requirements. Proprietary methods and processes make it impossible to know how a given process works, what it accomplishes, and whether or not the results are reproducible. This snarled and secretive situation limits the life of the data, often to a period shorter than the life of the artifact itself. It should be selfevident that concealed and unverifiable procedures are unacceptable for archiving data. Academic exchange and research are diminished, when commercial proprietary products and data formats are accepted and used in academic circles as de facto standard tools with little other choice.
Computer models of cultural heritage sites and artifacts are made with the specific purpose of preserving these objects for future generations. Thus it makes little sense to create models using software and data formats that may become obsolete, unusable, or unavailable. Accordingly, a crucial feature of our second approach discussed in this paper is its development and utilization of opensource software. This approach should contribute to the production of secure and longlasting digital archives for cultural heritage preservation.
Problems with current shape modeling systems are not limited to the issues of proprietary data formats, methods, and processes. In addition:
Data is not accurate enough to make models that are consistent at every level of detail.
On the other hand, geometric modeling procedures and the fundamental mathematical base for 3D shape modeling, volume rendering, and multidimensional modeling are not well known or understood in the digital archiving community. These are core issues in the development of digital archives. Basic geometric modeling procedures, the retention of originating data attached to these procedures, the retention of the order of constructive events, and the modeling and embedding of physical dynamic attributes of 3D models for the creation of synthetic processes and simulations will change the way we look at digital data.
3.
Shape Representations
In the following section, we describe two
major shape representations and discuss them from the practical modeling
point of view. Then, the function representation is discussed as a new
promising direction.
3.1 Boundary representation and Constructive Solid Geometry
There are several different ways to represent solids digitally. Each representation has to provide determination of point membership: given any point it must be possible to determine whether it is inside, outside, or on the surface of a solid. In this section, we describe basic representational schemes: Boundary Representation and Constructive Solid Geometry. Formal definitions and more details on solids and solid representations can be found elsewhere.^{8,9}
A solid can be represented by its boundary. To define a boundary surface one can introduce points (vertices), curves (edges), and surface patches (faces), and stitch them together (Fig. 1 upper). This boundary representation (or BRep) has two parts (Fig. 1 lower): topological information on the connectivity of vertices, edges, and faces, and geometric information embedding these boundary elements in threedimensional space. Topological information specifies incidences and adjacencies of boundary elements. Geometric information specifies coordinates of vertices or the equations of the surfaces containing the faces. The boundary of the solid is a twodimensional manifold. Each point of the boundary has a neighborhood with onetoone correspondence to a disk in the plane.
Figure 1:Boundary representation of a cube is based on surface faces (triangles and/or quadrangles), edges, and vertices.
Local modifications of the boundary are performed using tweaking operations such as moving the vertex, edge, or face. Topological modifications are performed using Euler operators, which include adding and removing vertices, edges, and faces. These operators satisfy Euler's formula and thus ensure topological validity of the resulting solids.
From
the practical modeling point of view, wire frame or BRep is used for visualization
of CSG or FRep defined objects. Currently, most commercial modeling programs
use BRep not only for visualization but also for mathematical definition
of objects. Systems based on this approach are exceedingly complex and
prone to error. The objects made in this manner may be aptly described
as polygons with holes and should not be considered archival quality digital
objects. In the practice of modeling with these systems, wire frame is
convenient for finding the center of arcs and circles and thus indispensable
to the creation and editing of entities, and BRep is helpful during the
creation and editing of entities and necessary for rendering the entities.
Hybrid systems using BRep based interaction and visualization together
with mathematically rigorous representation are needed for quintessential
digital modeling of objects.
Constructive Solid Geometry.
Figure 2: Set operations between two 2D disks: union (?), intersection (?), and subtraction (\). The result of each operation is shown as a hatched area.
Using the modeling paradigm called Constructive Solid Geometry or CSG, one can begin by selecting simple shapes (primitives), specifying their parameters and positions in space, and then using them to construct more complex shapes by applying union, intersection, or subtraction set operations (Fig. 2). Traditional CSG primitives are the block, the cylinder, the cone, the sphere, and the torus. Linear transformations (translation and rotation) can be used together with regularized set operations. A regularized set operation includes removing lower dimensional parts of the standard set operation result such as dangling surfaces, curves or points.
A CSG object is represented as a binary tree (or CSG tree) with operations at the internal nodes and primitives at the leaves (Fig. 3). The point membership classification algorithm defines whether a given point is inside, outside, or on the boundary of the solid. This algorithm recursively traverses the CSG tree starting from the root. In the nodes with linear transformations, the inverse of the transformation is applied to the current point coordinates. When the recursion reaches the leaves, the point is tested against the corresponding primitives. Then, the classification results are combined in the internal nodes with settheoretic operations.
Figure 3: Example of a CSG tree. Operations: R (rotation), \ (subtraction), ? (union).
From
the practical modeling point of view, CSG inherently provides a constructive
history, which allows interactive editing of subelements. If a complex
object is created with CSG, its constructive primitives
and the order in which they were processed can be accessed; CSG modeling
can be called bidirectional. Furthermore, CSG allows for surface calculations
of area and mass calculations of weight, volume, and centricity. The disadvantage
of CSG is its limitation in geometrical representation; it is not suitable
for producing organic shapes. Thus, though it performs well in its representation
of most architecture, it would not do for sculpture.
IGES
(Initial Graphics Exchange Standard) is the U. S. national standard for
exchange of data between dissimilar CAD systems. Over the last twenty years,
IGES has failed to include in its standards support for the translation
and exchange of CSG 3D data, whose primitives and procedures are well defined
and understood. On the other hand, STEP protocol (International Standard
for the Exchange of Product Model Data, ISO 10303 standard) supports CSG,
but this part of the protocol is quite rarely used nowadays. A suitable
protocol should, at least, support CSG.
3.2 Function representation and the HyperFun modeling language
The basic mathematical representation in digital preservation should serve several purposes. It should reflect the logic of the object's construction, support modeling of parametric families of shapes, support specific and extensible modeling operations, generate polygonal and other surface models, as well as voxelization, for visualization, animation and virtual objects presentation on the Web, and serve for direct control of rapid prototyping machines with the precision needed to reproduce the modeled objects. We propose to use socalled function representation (FRep) as our basic mathematical model.^{10} FRep is a generalization of traditional implicit surfaces ^{11} and CSG. It represents an object by a continuous function of three variables as F(x,y,z) ? 0. A point belongs to the object if the function is positive at the point. The function is zero on the entire surface (called usually an implicit surface) of the object and is negative at any point outside the object.The function can be easily parameterized to support modeling of a parametric family.
In FRep, an object is represented by a tree structure (similar to one used in CSG, see Fig. 3) reflecting the logical structure of the object construction, where leaves are arbitrary "black box" primitives and nodes are arbitrary operations. Function evaluation procedures traverse the tree and evaluate the function value in any given point. Algebraic surfaces, skeletonbased implicit surfaces, convolution surfaces, procedural objects (such as solid noise), swept objects, and volumetric (voxel) objects can be used as primitives (leaves of the construction tree).
Many modeling operations are closed on the representation, i.e., generate as a result another continuous function defining the transformed object. These modeling operations include settheoretic operations, blending, offsetting, nonlinear deformations, metamorphosis, and projection. A new operation can be included in the modeling system without changing its integrity by providing a corresponding function evaluation or space mapping procedure.
In FRep, there is no difference in processing soft objects, CSG solids, or volumetric objects. This allowed researchers to solve such long standing problems as metamorphosis between objects of different topology, sweeping by a moving solid, controlled blending for all types of settheoretic operations, collision detection and hypertexturing for arbitrary solids, and direct modeling of spacetime and multidimensional objects.
The HyperFun language ^{12,13} was introduced for teaching and practical use of FRep modeling. It is a minimalist programming language supporting all notions of FRep. The following tools are available for processing HyperFun models: a polygonizer that generates a polygonal mesh on the surface of the object and exports it in the VRML format; and a plugin for the POVRay raytracer that helps to generate highquality photorealistic images. Application software deals with HyperFun models through an interpreter, which evaluates the defining function at any given point.
FRep also naturally supports 4D (spacetime) and multidimensional modeling using functions of several variables. We are investigating approaches and tools for further utilization of multidimensional models. The main idea is to provide a mapping of such objects to a multimedia space with such coordinates as 2D/3D world space coordinates, time, color, textures and other photometric coordinates, and sounds. Deeper connections between multimedia space and geometric multidimensional spaces should be investigated in the context of computer animation, computer art, and cultural heritage preservation applications.
HyperFun was also designed to serve as a lightweight protocol for exchanging FRep models among people, software systems, and networked computers. The average size of HyperFun files is 5K. This allows for efficient implementation of a clientserver modeling system in which a client can run simple interface tasks and generate HyperFun protocols to be sent to the server. The server site can be a powerful parallel computer or a computer cluster that performs timeconsuming tasks such as raytracing, polygonization, or voxelization.
It is quite easy to learn and use HyperFun on the beginner's level. It does not require deep mathematical knowledge. Highschool level geometry and common sense in constructing and using building blocks are enough to start modeling. The authors have had the experience of teaching HyperFun to first year university, high school and even junior high school students.
The open and simple textual format of HyperFun, its clearly defined mathematical basis, its support of constructive, parameterized and multidimensional models, its support by free modeling and visualization software, and its ease of use make it a good candidate as a tool for the digital preservation of cultural heritage objects.
4. Constructive Modeling in Cultural Heritage Preservation
4.1 Constructive modeling approach
We propose the use of FRep and CSG as its subclass as the basis of constructive shape modeling procedures in cultural heritage preservation. The ultimate goal of this work is to create a synthetic CAD modeling system based on constructive modeling principles and to apply it to cultural heritage preservation purposes. The system could have a hybrid character including CSG and FRep as primary representations and BRep and voxels as auxiliary ones. The multidimensional modeling system would allow not only for the threedimensional coordinates, but for additional variables such as time, and other physical properties of an object. The proposed system would have a FRep construction tree and be capable of accurately modeling not only the shape or volume of a given object and its physical attributes, but also the dynamic relationships between objects and object processes.
Recently FRep has been applied to represent not only point set geometry, but also material distribution and other properties of arbitrary nature (optical, physical, statistical, etc.).^{14} The proposed synthetic CAD system defining a volume and describing mixed materials within that volume will allow for the support of 3D printing processes, which require a great deal of volumetric data that polygonal mesh systems cannot provide.
The synthetic CAD modeling system that uses HyperFun will be a completely free and open source software package, just as is HyperFun itself. The proposed system will meet the basic tenets of the rigorous proof of operations required by scientific study. The proposed system's data will be abstracted and the constructive processes and procedures will be embedded within the digital data structure. These constructive processes will be bidirectional and verifiable and uniquely based on materialbased procedural textures. Using this approach, the logic of hidden structural elements and the uniqueness of a historical object can be captured. The data resulting from the proposed system will have a lifetime suitable for long term archiving.
The proposed CSG and FRep based system is computationally intensive and will need to use clusters of networked computers. By comparison, presentday systems based on polygonal meshed data structures would be viewed much the same as paper data of the past. The proposed system for archiving applications steps beyond the indexing of simple and fragile paper based data structures of the past toward complex robust and active data structures of the future.
In the following, we illustrate our experience with application of CSG and FRep to practical problems of cultural heritage preservation.
4.2
Constructive modeling of historical buildings
Considering the experience of data loss, the authors specified CSG as the most likely data format for modeling historical architecture with any possibility of archival quality for the Aizu History Project.^{15} All parts of the two historical buildings, the Golden Hall at Enchiji and Sazaedô, featured in this paper were created whenever possible with only CSG based entities. However, because CSG is limited in its range of shape representation and the overall size of the models was extremely large, the thatch roof of the Golden Hall and the double helix ramp inside Sazaedô had to be represented unsatisfactorily by a polygonal mesh.
In using CSG, computational requirements dictated that sections of the model be developed in many separate files on four different PC based systems. There were significant problems in data creation and manipulation of sections of the buildings across separate files on different computers as the coordination was all manually done. When combining the files into one file, it is needless to say that this data overwhelmed even the fastest single system on several different platforms. Even now, the entire model of Sazaedô cannot be handled easily at one time in present day animation and rendering systems. The efforts the authors experienced using CSG in commercial products on single computer systems with the hope of creating digital archival data seems wasted. It is doubtful that even this CSG constructed data will live through the next several decades because of the proprietary nature of the commercial software and the unknown quality of the CSG database. It may take as much or more effort to extract the CSG data structure embedded in these proprietary programs as it would to reconstruct the buildings from original data.
The benefits of using threedimensional graphics techniques in constructing models are obvious. First of all, models can be manipulated to provide multiple viewpoints. Rotating a model can provide a better understanding of the physical relationships of the components of the actual structure, as well as the construction techniques involved. Moreover, threedimensional models can replicate the actual construction of the building itself, including features normally hidden to the eye, such as interior bracketing, and the model can be deconstructed to reveal such hidden features. Our work on two Buddhist temple buildings in the Aizu region of Japan illustrates these benefits.
Golden Hall at Enichiji
The
first structure that we modeled using the CSG system was the Golden Hall
at Enichiji, a temple located at the foot of Mt. Bandai. Although Enichiji
was the religious center of the region throughout much of the Heian period
(7941185), no buildings or images from that period are extant today. In
order to produce a model of the Heian Golden Hall, the structure that housed
the temple's most important Buddhaimages, the authors relied on data introduced
in archaeological site reports.^{16}
Figure 4: Structural view
The
construction of the Golden Hall model was a difficult task. At present
the only solid information is the existence of seven foundation stones
for pillars, demarking the north and part of the east walls. A base of
piled stones also stretches along the north and east walls, and remains
of a retaining wall abut the (surmised) southwest corner. This information
has led archaeologists at the site to conclude that the building measured
five bays from east to west and four or five from north to south. We have
constructed the Golden Hall model as a five by four building (Figs. 4 and
5).
Figure 5: Normal view
In addition to archaeological data, the model was based on standard templebuilding practices of the eighth and ninth centuries.^{17} We also took into consideration the snowy climate of the Aizu region, which dictated a steeper roof slope than is common in other areas of Japan. In addition, we consulted Yamagishi Seiji, a master miya daiku (shrine carpenter) and the scion of an 800year carpentry tradition in this region.
Sazaedô Pagoda
Recently
declared a National Important Cultural Property, Sazaedô, a pagoda
built in 1796 in AizuWakamatsu, is noted for its unique architectural
feature, a doublehelical interior walkway that takes visitors from the
front entrance to the top of the structure, then over and down to the back
entrance. The double helical walkway is part of an interior tower (Figs.
6a, b and c). (For more details on the Sazaedô construction, including
black and white reproductions of these figures and some others, see Vilbrandt,
Goodwin, and Goodwin, 1999.^{18} The drawings in Figs. 6c, 7c,
8c and 9a were adapted from engineering blueprints done in 1965 by Kobayashi
Bunji.)


Figure
6a: Interior
tower with image alcoves  wire frame

Figure
6b: Interior tower  colorized

Figure
6c: Full drawing showing

The 3D CAD model can be used to display such components separately, so that the construction may be seen and understood. Even an actual visit to the site does not enable such views.



Figure
7a: Exterior
tower with walls added  wire frame

Figure
7b: Model
of exterior tower with walls  colorized

Figure
7c: Full drawing showing the location of the exterior tower

The interior tower
is housed in an exterior tower, with a separate support structure (Figs.
7a, b and c).



Figure
8a: The
exterior tower overhang  wire frame

Figure
8b: The
exterior tower overhang  colorized view

Figure
8c: Full
drawing showing the location of the exterior overhang

The tower exterior shows helical overhangs protecting the windows from direct sunlight (Figs. 8a, b and c).


Figure
9a: Roof
 engineering drawing

Figure
9b: Roof
 wire frame 3D CAD model



Figure
9c: Roof
 false color CAD Model

Figure
9d: Roof
 Rendered 3D CAD model, from below

Fig. 9a is an engineering drawing of the roof shown from below. By using measurements from this drawing, and supplementing them with measurements taken on site, a 3D CAD model was constructed, and is displayed in the wire frame view (Fig. 9b) and the rendered views (Figs. 9c and 9d).
The entrance and its
canopy are structures which can be better understood from the model (Figs.
10b, 10c, and 10d) than from a photograph (Fig. 10a) or even from a visit
to the actual site, since they are complex objects and access and sightlines
are restricted.


Figure 10a: Entrance canopy photograph  Figure
10b: Entrance
canopy – wire frame
CAD model 


Figure 10c: Entrance canopy rendered  Figure 10d: Entrance canopy – alternate view 
It is possible to select only one section from the single CAD model of the entire structure, and display it from multiple viewpoints and with various levels of detail (Figs. 11a, b and c).
Figure 11a: Wire frame of the base  Figure 11b: Colorized CAD model of the base  Figure 11c: Base – details of the supports 
Because of the constructive approach, any part may be rendered without displaying the other components, as shown in (Fig. 11d), and an external shell may be fully rendered (Fig. 11e).


Figure
11d: Rendered
model showing helical structure

Figure
11e: Fully
rendered view

The models illustrated above are virtual constructions using virtual lumber cut, positioned and joined according to the specifications of the miya daiku. This empirically shows the value of digital preservation of cultural heritage using constructive modeling. The 3D model has recently been used to produce high quality renderings of the interior of Sazaedô, as would be seen by a person walking through the structure,^{19} and to produce QuickTime and AVI movies of the journey through the temple. We plan to enhance the current model by including 3D reproductions of the images formerly enshrined in the building. We also intend to develop VR facilities to allow the examination of these images independently, and to allow the viewing of parts of the structure that cannot be accessed in the actual building.
4.3 Constructive modeling of Japanese lacquer ware
Digital preservation of crafts heritage
As
subjects of computerbased preservation efforts, traditional crafts such
as pottery, embroidery or lacquer ware require special treatment. First
of all, any craft is a living tradition, not a fixed set of inherited items.
At the center of the tradition are masters with knowledge of essential
craft technology, which is often not presented in written form. While computers
may be used to preserve this technology or even to enhance it, computerbased
technology is sometimes considered not to support, but rather to rival
traditional crafts, giving rise to psychological and economic conflicts.
However, the decreasing number of masters, fading technologies, and economic
difficulties for crafts and their practitioners validate the necessity
of computerbased preservation. The production of traditional Japanese
lacquer ware or shikki suffers from the problems mentioned above,
as well as from additional economic pressure due to cheap production of
plastic lookalikes. In this section, we demonstrate how computers can
help to preserve traditional crafts such as shikki manufacture,
using a practical example of FRep modeling, conversion to polygonal BRep,
and Web presentation of shikki items.
Virtual
Shikki
When
making actual shikki, parts of an item are produced manually using
thin pieces of wood, which are then assembled, painted in different colors,
and covered by natural lacquer or urushi. There is a great variety
of shikki items: boxes, small drawers, stands, cups, bowls, sake
pots, chopsticks, notebooks, and even ball pens and pencils. These items
are quite different from one another in their topology, geometry, and texture.
The “Virtual Shikki” project includes the following research and development activities:
Some additional specific operationsfor example,bounded blendingwere required for adequate modeling of shikki shapes. A blending operation generates a smooth transition between two given surfaces. Blending operations for FRep were formulated by Pasko et al.^{10} for all set operations (union, intersection, difference) between two solids. However, this formulation of blending suffers from the resulting surfaces being offset (expanded or contracted) everywhere in the space. This is not acceptable in modeling lacquer ware shapes, because blending should not affect original surfaces outside the specified area of influence. To satisfy this requirement, we proposed and implemented bounded blending operations,^{20} illustrated in Fig. 12. A sake pot is shown in Fig. 12a with the circle showing the region of bounded blending. Fig. 12b shows the union of the initial pot spout and the ellipsoidal shape (the left bottom part of the pot body) which are to be blended. The cylindrical bounding solid is shown in Fig. 12c. The blended shape resulting from the bounded blending operation should completely reside inside this solid. The resulting blend satisfying this requirement is shown in Fig. 12d.
The implementation of the three first stages of the project, namely modeling shapes, digitizing textures, and presentation of virtual objects, includes the following:
We found that VRML files are too memory expensive, especially in the case of complex shapes and sets. Other and more compact Web3D formats should be considered in the future. A more radical solution would be to transfer small HyperFun models to the user’s computer and provide a browser able to unfold a polygonal or other representation suitable for interactive visualization.
Modeling specific shapes required a large amount of routine labor in measuring control points and fitting model parameters. Semiautomatic methods should be introduced based on 3D scanning of real objects for acquisition of control points and nonlinear optimization for automatic fitting of parameters.
5. Conclusion
While the approach proposed here seems laborintensive, it has several distinct advantages over methods based on automatic surface scanning and almostautomatic polygonal mesh generation. The purpose of a particular project should determine which method to use. If only a visualization animation from a distant viewpoint is needed, then polygonal mesh or other BRep models can be satisfactory. However, even a virtual walkthrough allowing close inspection of the object requires more accurate and detailed modeling. Constructive modeling helps to reveal knowledge about a shape's logical macrostructure. The representation of threedimensional surface microstructure (bumps, cracks, roughness) is also out of the range of BRep abilities, but it is possible to model it using FRep.
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a b c d
Figure
12: Bounded
blending operation: a) sake pot with the region of blending circled; b)
initial pot shape without blending; c) pot and cylindrical bounding solid;
d) resulting pot shape with bounded blending.
Figure 13: Snapshots of the “Virtual Shikki” Web site with images hyperlinked to the HyperFun and VRML models of corresponding lacquer ware items.
Figure 14: VRML model of the sake set examined using the CosmoPlayer software.