The notion of collaborative shape conceptualization emerged as a consequence of the globalization of design activities over the former organizational boundaries. Today, geographically dispersed designers and stylists can work together by forming virtual teams, and the potential customers can be involved in defining the individually customized shape of a requested product. Efficient human-computer communications—the key element of interactive shape conceptualization in virtual design environments
(VDE)—is achieved by advanced verbal, gestural, visio-spatial, physical, and other means. The emerging tools should have the potential to handle shape input from several users (designers, customers, among others) concurrently [3]. Nonetheless, the goal is to have dedicated geometric modeling techniques offering new opportunities in collaborative model building, better tolerating uncertainty, and impreciseness. Such techniques should also allow for modality in creating and manipulating concept solutions [8].
Current virtual reality (VR) systems and VDEs are based on conventional geometric representations developed for conventional CAD systems. Governed by strict mathematical rules, these systems limit the opportunities of creative design collaboration [12]. Cognitive studies show that intuitive formation of ideas is intertwined with visual, verbal, or physical representation as well as with reasoning in the natural process of shape conceptualizing (consider, say, sketching or band drawing) [10]. In addition to the rigid modeling methodology, we believe the lack of this synergy is the reason why conventional geometric modeling schemes cannot provide sufficient support for collaborative modeling in VR systems. Designers also lack a direct physical interaction with evolving shape models, which is provided naturally, for instance, by claying and carving [6]. The modeling methods dedicated to shape conceptualization must bring ideation, representation, reasoning, and processing together [4].
These facts inspired us to direct our research to the development of a new modeling technique for collaborative shape conceptualization in a VDE [2]. We intended to find theoretically well-supported methods that allow several designers to generate components of a complex shape simultaneously by using various input techniques, and to combine these components into models in a non-prescribed way. What we also wanted to implement was handling tentative, incomplete, uncertain, and imprecise specifications, representation of the domain distribution of a cluster of shapes, and intuitive generation of shape instances.
Vague Discrete Modeling
The shape conceptualization and representation technique we developed is referred to as “vague discrete modeling” (VDM). It is a constructive modeling approach that represents the shape of objects as particle clouds. A particle is a discrete modeling entity describing the nominal position of a 3D reference point together with the accompanying uncertainty. The positional uncertainty is called “metric occurrence,” and is interpreted as a finite domain of space around the nominal position of the point. Both the nominal positions and the possible domains of the metric occurrences are described as finite vector spaces.
Participating designers are represented in the virtual design space by the models of their hands. The hands, distinguished by coloring, can be individually or jointly used to generate and manipulate shape components or complete models.
A particle cloud is an arrangement of particles in a finite region of space, indicating the material side of an object. A particle cloud is derived from one or more point sets generated by gestural sweeping, scanning physical objects, converting existing CAD models, manipulating existing particle clouds, or by verbal specification. A particle cloud can be visualized on a computer screen and/or in a virtual display space. Compound objects can be created as compositions of particle clouds and represented as particle systems.
The discreteness of a VDM comes from the discrete particles, its vagueness originates in the quantified metric occurrences of the particles. The metric occurrences make it possible to represent the variation domain of shapes. The variation domain is defined by the maximum and minimum boundaries formed by the input point sets. It is computed either by superimposing component point sets or by portraying the scattering of the points in a given point set.
As far as the technical implementation of collaborative modeling is concerned, the participating designers are represented in the virtual design space by the models of their hands. The pairs of hands are distinguished by coloring. The hands can be individually or jointly used to generate and manipulate shape components or complete models. The virtual hands receive spatial data from the status detectors (gloves) on the designers’ hands. The pilot VDM system facilitates building more than one shape model simultaneously. However, it remains the task of the collaborating designers to specify which model a newly generated shape component belongs to and how it must merged into the model.
In order to make these fundamental concepts tangible, we illustrate our approach with a simple design example. It reveals how VDM can be used for collaborative shape design in a virtual environment. The task is to produce a VDM of a mug and to derive instances from this vague model whose shape resembles the form of the adjacent boundary of the variation domain.
The first modeling action is to enter the shape components describing the limits of the distribution domain of the vague model of a mug. In our example, we used two of the many possibilities to enter the components of the target VDM. The maximal boundary of the vague model of the mug is entered as a point set derived from an existing mug by 3D scanning. The minimal boundary of the mug is generated by a sequence of hand movements of a designer [9].
The individual point sets are entered and positioned, then scaled in the virtual design space (see Figure 1), and are eventually merged into a single point set. The points generated by the subsequent sweeps are different colors. The input point sets are supposed to be dense enough to show the geometric features, but not necessarily ordered. The merge of a component means finding the intersections between the point sets positioned in the model space—if intersection exists at all—and joining the common parts. The extra parts of the point sets are trimmed. Since our approach allows for incomplete vague models, the final model is not automatically validated; this task is left for the designers. They can recognize the possible gaps by visual observation more easily than any hardwired procedure. If needed, they can generate additional point sets to make the discrete model morphologically complete.
To characterize the input point sets by surface normal vectors, a triangulation is generated over the points with the a-shapes technique. The measurement errors are filtered out based on the principle of finding extreme variations of the distances between the closest neighbor points. In the case of hand movement, the status detectors provide information about the closest neighbor points and the surface normal vectors.
Typically, a finite number of shapes is combined into one vague discrete model. To create the domain of variance for a cluster of shapes, the generated point sets are placed in a common reference frame, and the maximal and minimal boundaries of the distribution domain are computed. An initial distribution domain is determined by containment and/or intersection calculations. The variance domain is described by the principal distribution trajectories of the reference points between the boundaries. The distribution trajectories are the basis of deriving the location of the boundary points of shape instances. Figure 2 illustrates the discrete domain of a mug generated from the scanned (maximal boundary) and the gestured point sets (minimal boundary). The red lines throughout the figure indicate the distribution trajectories.
Building Compound Vague Models
A particle cloud represents a materialized domain of space. The VDM makes it possible for us to manipulate and combine the virtually materialized regions into a compound object. Assigning mechanical properties to the geometric components allows us to simulate the physical behavior of the modeled object, but also to deform and change the shape by physical interaction. To support the work of designers, so-called “tools” have been developed. The simplest tools realize union or difference of vague shapes [7]. With these tools, designers can add or remove materialized parts interactively from the vague model [5].
Another virtual tool supports interactive modification of vague models, such as sculpting [1]. Mathematically, the sculpting tool executes a virtual sweeping by generating a Minkowski-sum of a trajectory and a vague model. Here, a vague shape is used as a means to generate other vague shape. The virtual sculpting tool is in use in Figure 3. The result of the virtual sculpting is the handle for the mug.
To build a compound vague model, the designer must position the available constituents in a common reference frame and specify interactively the required structural relationship among them. The positioning can be permanent or flexible. Permanent positioning of a constituent particle cloud means its relative position to one of the boundaries of shape distribution domain is not changing when instances are generated. Flexible positioning means the relative position of the particle cloud is adapted to the generated instance.
Figure 4 illustrates the difference between these two cases. The solid handle on the left side is permanently positioned (relative to the minimal boundary), that is, it will take different shape for each instance of the mug. The hollow handle on the right side is flexibly positioned, therefore, it will have constant geometry and relationship on each instance.
Extraction of Shape Instances
The novelty of VDM is it supports rule-based instancing rather than geometric parameter-based instancing. This is a significant difference from the aspect of shape conceptualization. It relieves the designers from the necessity of thinking in parameter networks, but also from the difficulty of assigning geometric parameters to free-form shapes. By applying rules in the form of pre-coded mathematical formulas, an infinite number of shape instances can be generated between the minimal and maximal boundaries of a VDM. The instance will inherit the geometric features of the variation domain as prescribed in the rules specific to a given application field. Besides specifying the shape formation rules, the user can manipulate the structure of the instance model as well.
The novelty of VDM is it supports rule-based instancing rather than geometric parameter-based instancing. This is a significant difference from the aspect of shape conceptualization.
We can clarify these ideas better by revisiting our example. Since one handle is typically enough for a mug, the unnecessary handle can be easily removed from the structure. In our case, the formation rules for shape instancing originate in aesthetic aspects. In this particular case we assumed the designers want to have a shape that resembles an existing shape. The notion “resemble” can be converted to mathematical terms as a linearly proportional setting of an instance shape in the distribution domain.
In several cases, however, designers want to generate instances with many more different constraints. An example of generic introflexed characteristics has been created by a relevant instancing tool (Figure 5a). It applies a hyperbolic mathematical function to extract a globally concave instance from the distribution domain. The designer interactively sets the arguments of the function. For all instances the metric occurrence is reduced to zero, that is, they represent crisp shapes.
If needed, the shape of the instances can be further modified. We have developed tools to modify the shape of instances by physical effects (as in virtual claying). One tool is for deforming the shape by applying physical forces. It is especially useful for creative shape conceptualization [11]. The hands representing the designers in the virtual environment can be used to exert physical effects on a shape instance. To make the calculation of deformation possible, the designer needs to assign elastic and plastic material properties to instances [8]. The results reflect real physical behavior once given these properties.
In Figure 5, we present an example of the application of physical deformation to set the final shape of an object according to the ergonomic wishes of the designers. The region to be modified is identified by the virtual hand (Figure 5a). The designer can modify the shape interactively also by means of the virtual hands. Since all designers can have direct access to the collaborative virtual design environment (CVDE), they can modify the entire model as they see fit (Figures 5b and 5c). Supported by the networking and VR facilities, they can implement what is meant to be collaborative-shape conceptualization.
Conclusion
VDM is sufficiently natural and interactive, and efficiently supports collaborative shape design. It can be adapted to various virtual environments, and the models can be converted directly to conventional CAD models. Its inherent flexibility makes it easy for designers to express their shape ideas and to combine them in an initial model that can be modified and detailed as needed.
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