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Figure from:HyperFun project: a framework for collaborative multidimensional FRep modeling. In

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Figure 1: System architecture In this paper, we present the state-of-the-art HyperFun project contributed to by the University of Aizu (Japan), the University of Warwick (UK), and the Moscow Engineering Physics Institute (Russia). The paper is structured as follows. Section 2 outlines the general scheme of the proposed system. The HyperFun language and its interpreter are described in Section 3. Sections 4-6 present modelers of different types. Applications are briefly characterized in Section 7. Conclusions and future directions described in Section 8.
Figure 1: System architecture In this paper, we present the state-of-the-art HyperFun project contributed to by the University of Aizu (Japan), the University of Warwick (UK), and the Moscow Engineering Physics Institute (Russia). The paper is structured as follows. Section 2 outlines the general scheme of the proposed system. The HyperFun language and its interpreter are described in Section 3. Sections 4-6 present modelers of different types. Applications are briefly characterized in Section 7. Conclusions and future directions described in Section 8.
Figure 2: Sample HyperFun model and its polygonized surface The proposed system architecture is shown in Fig. 1. It consists of the following basic groups of components: HyperFun models, F- rep library, modelers, interpreters/compilers, and applications. HyperFun models are text files that can be stored and transmitted over a network. The F-rep library contains definitions of primitives, operations, and relations used in HyperFun models. This library is currently implemented in C, Java, and HyperFun. The selection of the library depends on the application area and computing environment. While system libraries are written in C
Figure 2: Sample HyperFun model and its polygonized surface The proposed system architecture is shown in Fig. 1. It consists of the following basic groups of components: HyperFun models, F- rep library, modelers, interpreters/compilers, and applications. HyperFun models are text files that can be stored and transmitted over a network. The F-rep library contains definitions of primitives, operations, and relations used in HyperFun models. This library is currently implemented in C, Java, and HyperFun. The selection of the library depends on the application area and computing environment. While system libraries are written in C
Figure 3: Screenshot of the multidimensional modeler with a symbolic user interface.
Figure 3: Screenshot of the multidimensional modeler with a symbolic user interface.
Figure 4: Frame of an animated spreadsheet
Figure 4: Frame of an animated spreadsheet
Assigning a zero value to the function itself defines an isosurface as an elementary shape in the cells of the spreadsheet. The elementary shape illustrates function dependence on three variables x[1], x[2], and x[3]. Changes of isosurfaces along rows and columns of the spreadsheet illustrate function dependence on x[5] and x[6]. Changes of the entire spreadsheet in time show how the function depends on x[4]. The image in Fig. 4 is a frame of the animation corresponding to t = 2. It can be thought as an image of a 5D shape since x[4] has constant value.
Assigning a zero value to the function itself defines an isosurface as an elementary shape in the cells of the spreadsheet. The elementary shape illustrates function dependence on three variables x[1], x[2], and x[3]. Changes of isosurfaces along rows and columns of the spreadsheet illustrate function dependence on x[5] and x[6]. Changes of the entire spreadsheet in time show how the function depends on x[4]. The image in Fig. 4 is a frame of the animation corresponding to t = 2. It can be thought as an image of a 5D shape since x[4] has constant value.
Figure 5: HyperFun model tree structure. The tree on the left is a representation of the model shown in Figure 2 with the soft object represented as a single primitive.
Figure 5: HyperFun model tree structure. The tree on the left is a representation of the model shown in Figure 2 with the soft object represented as a single primitive.
Figure 6. VRML generation using HyperFun to Java translator
Figure 6. VRML generation using HyperFun to Java translator
Figure 7. Screenshot of Empirical Worlds in use. as version control, password protection and persistent storage for models. In this way, the HyperFun notation is being used to provide a lightweight transmission protocol for the collaborative exchange of geometric shape.
Figure 7. Screenshot of Empirical Worlds in use. as version control, password protection and persistent storage for models. In this way, the HyperFun notation is being used to provide a lightweight transmission protocol for the collaborative exchange of geometric shape.
Figure 8: HyperFun model of the bi-directional metamorphosis
Figure 8: HyperFun model of the bi-directional metamorphosis
Figure 9. Spreadsheet of bi-directional metamorphosis between four shapes Coordinates xj, X, X3 (types x, y, and z) continuously change inside the 3D bounding box. Coordinates x, and x; (types u and v) take five discrete values along horizontal and vertical axes respectively. Each cell of the spreadsheet contains an elementary shape corresponding to a specific point in the (x, x5) plane. Each of the key shapes is assigned a 3D texture. Four textures are also interpolated in the (x,, x5) plane (photometric types p1 and p2). Note that smooth shape and texture transformations can be observed in any linear direction in the image. On the other hand, the spreadsheet can be considered as a set of frames of animation The image was rendered using POV Ray 3.0 [18] (a freeware raytracer available on various platforms) running on Intel Pentium II Windows NT workstations. A modified version of POV Ray with “the POV-Ray isosurface patch” [25] was used to render the isosurfaces.
Figure 9. Spreadsheet of bi-directional metamorphosis between four shapes Coordinates xj, X, X3 (types x, y, and z) continuously change inside the 3D bounding box. Coordinates x, and x; (types u and v) take five discrete values along horizontal and vertical axes respectively. Each cell of the spreadsheet contains an elementary shape corresponding to a specific point in the (x, x5) plane. Each of the key shapes is assigned a 3D texture. Four textures are also interpolated in the (x,, x5) plane (photometric types p1 and p2). Note that smooth shape and texture transformations can be observed in any linear direction in the image. On the other hand, the spreadsheet can be considered as a set of frames of animation The image was rendered using POV Ray 3.0 [18] (a freeware raytracer available on various platforms) running on Intel Pentium II Windows NT workstations. A modified version of POV Ray with “the POV-Ray isosurface patch” [25] was used to render the isosurfaces.