Building polygons are buildings' contours on the digital map stored by GIS. Based on building polygons, GIS and CG integrated system automatically generates multiple-roofed 3-D building models. A 3-D urban model including 3-D building models is the important information infrastructure that can be utilized in several fields, such as landscape evaluation, urban planning, disaster prevention simulation, etc. However, to realize a 3-D urban model enormous time and labor have to be consumed to design hundreds and thousands of 3-D building models. In order to automate the labor, the system aims at creating 3-D building models automatically from building polygons. If a building polygon has right angle only, then it can be divided in rectangles. We propose the useful polygon expression where the building polygon can be expressed as a set of its edges' turning direction (RL expression) and that decides from which vertex a dividing line (DL) is drawn. In order to generate 'probable' multiple-roofed building models, we propose the scheme of prioritizing the DL that forms a branch roof, based on the length of the DL. This scheme generates probable 3-D building models whose main roofs are higher than branch roofs.

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We propose a method for interpolation of a high-dimensional rotation matrix and also demonstrate its applications in computer graphics domain and pattern recognition domain, which are interpolation of object poses in high-dimensional space and interpolation of multivariate normal distributions.

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We have developed a tool to design car body shapes. It enables any user even with no experience and skill to design car body shapes interactively and easily. We report how we synthesize car body shapes by following process. Firstly, we create a database of existing cars and analyze all shapes in the database using Principal Component Analysis (PCA). Secondly we extract attributes that indicate the geometrical features of those car body shapes. The attributes are then mapped onto the Eigen space obtained as a result of analysis. We construct a GUI in which the distribution of the attributes on the Eigen space is visualized. By manipulating the weight of each attribute on our GUI, we can synthesize car body shapes which nobody has ever seen.

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For aesthetic evaluation of curved surfaces, we construct a unified theory for analyzing the distortion of reflected images of a set of parallel lines from a certain viewpoint. We assume both the set of parallel lines and the viewpoint are placed at infinity. For each point on the surface, the curvature of the reflected image (curve) of each straight line in 3D is computed. Among all reflected curves, we can find the curves whose curvature is 0 at the point on the surface. By computing the changes of curvature of them, which are related to the third derivatives of the reflected curves, we can compute the “degree” of distortion.

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The aesthetic curves include the logarithmic (equiangular) spiral, clothoid, and involute curves. Although most of them are expressed only by an integral form of the tangent vector, it is possible to interactively generate and deform them and they are expected to be utilized for practical use of industrial and graphical design. However, their input method proposed so far by use of three so-called control points can generate only an aesthetic curve segment with monotonic curvature variation and can not create a curve with the curvature-extremal point or the inflection point. Hence at first we propose a technique to input an aesthetic curve segment with an inflection point at its end. Then we propose a method to generate an aesthetic curve with G² continuity from a sequence of 2D points input with, for example, a liquid cristal pen tablet.

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