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Item INTERPOLATING CURVE NETWORKS WITH NEW BLENDING PATCHES(Eurographics Association, 1990) Saitoh, Tsuyoshi; Hosaka, MamoruThis paper describes methods of c o n s t r u c t i n g s u r f a c e patches which s a t i s f y independently given boundary conditions on a l l i t s four or t h r e e s i d e s . A patch c o n s i s t s of two p a r t s : one i s a patch s a t i s f y i n g a t l e a s t p o s i t i o n a l condition of the boundary curves, and the other gives n u l l position vectors and independent i t s f i r s t and second d e r i v a t i v e vectors on t h e i r boundaries. The l a t t e r i s used for compensating d e r i v a t i v e vectors t o s a t i s f y given boundary conditions. A network o f curves whose meshes are four or t h r e e s i d e s can be i n t e r p o l a t e d smoothly with patches of t h i s type.Item Generation of High-Quality Curve and Surface with Smoothly Varying Curvature(Eurographics Association, 1988) Higashi, Masatake; Kaneko, Kohji; Hosaka, MamoruA method for generating curves and surfaces which satisfy constraints of tangent directions and curvature at arbitrary points and which have smoothly varying curvature is introduced. The method is geometrical determination of a Bezier polygon, and quite different from conventional methods such as minimizing the integral of the square of curvature value or the second derivative. This method enables following things : generation of smooth curves by explicitly indicating the characteristic properties of the curves generation of smooth surfaces having not only smooth boundaries but also cross tangent and curvature which change smoothly along the boundary curve, high accurate approximation of intersection curves of surfaces, by satisfying a tangent direction, an osculating plane. and curvature constrained by the surface equations.Item On Formulation and Display for Visualizing Features and Evaluating Quality of Free-form Surfaces(Eurographics Association, 1990) Higashi, Masatake; Kushimoto, Takuya; Hosaka, MamoruFor evaluating quality of free-form surfaces and visualizing their features, various curves on a surface, which characterize its properties, are defined and their equations are deduced. Newly introduced curves include those of equi-gradient, silhouette, highlight and a locus of points of extremum gradient on contour curves, loci of points of extremum principal curvature on lines of curvature. The objectives of these curves and their uses are described. Other curves such as contour curves, its orthogonal ones, loci of points of zero curvatures, and lines of curvature as well as umbilics are also treated. Displays of these curves are shown.