Surface Generation Method Research Articles

Reparameterization of piecewise rational Bezier curves and its applications

. Although the curve segments are C1 continuous in three dimensions, they may be C0 continuous in four dimensions. In this case, the multiplicity of each interior knot cannot be reduced and the B-spline basis function becomes C0 continuous. Using a surface generation method, such as skinning these kinds of rational B-spline curves to construct an interpolatory surface, may generate surfaces with C0 continuity. This paper presents a reparameterization method for reducing the multiplicity of each interior knot to make the curve segments C1 continuous in four dimensions. The reparameterized rational B-spline curve has the same shape and degree as before and also has a standard form. Some applications in skinned surface and ruled surface generation based on the reparameterized curves are shown.

Aerodynamic Design of a Flying Wing Using Response Surface Methodology

The design of a subsonic e ying wing with maximized lift is considered. A novel method of surface generation, known as the partial differential equation (PDE) method, is used to parameterize the e ying wing. Because this method is able to parameterize complex geometries in terms of a small number of shape parameters, the computational costs that are normally associated with optimal aerodynamic design are dramatically reduced. The lift data, which are estimated using a low-order potential e ow panel method, are subject to numerical noise and yield, therefore, a design space that contains many spurious noise-induced local maxima. Standard methods of local optimization are severely hampered by this noise and may converge prematurely in nonoptimal plateau regions where the variation of the lift is small relative to that of the noise. To combat this inefe ciency, techniques from response surface methodology (RSM) are used to construct smooth analytic approximations of the noisy lift data, which can be optimized successfully. This combination of the PDE method and RSM results in a design approach that is both efe cient and robust. Three e ying-wing design problems areinvestigated, and the results are presented.

縮閉線に基づく曲率変化の滑らかな曲線，曲面の生成 （第５報） 滑らかなハイライト線を持つ曲面の生成

This research proposes a surface generation method which satisfies the designer's intention to the surfaces and smoothness of the reflected images on them. The method directly determines the curvature distribution of a surface, which is represented by a locus of the evolute of the generatrix moved along the directrices. In this report, the evolute surface formed by the locus is modified according to a criterion of the hilight lines which are silhouette pattern of the given surface. The criterion is the square of projected curvature of highlight lines per unit length. To obtain the surafaces which satisfy the criterion, the evolutes of their sections along the direction of highlight lines are determined to change smoothly. They are represented with two segments of the second-degree rational Bézier curves, whose parameters are determined to minimize the criterion. The method is extended to determine a surface when a highlight line is given by a designer. Some examples of boundary curves with various patterns of curvature variation are shown to be generated as smooth surfaces.

Cost-Effective Multipoint Design of a Blended High-Speed Civil Transport

The multipoint design of a high-speed civil transport (HSCT) is considered. Low computational costs are maintained by parameterizing the HSCT using a novel method of surface generation known as the partial differential equation method. This method enables a reduction in the computational costs because of its ability to describe complex surfaces using a small number of parameters. The two design points that are considered are the subsonic and supersonic (Mach 2) flight regimes with design criteria of maximized lift and minimized wave drag, respectively. Subsonic lift is estimated using Panel Method Ames Research Center, whereas supersonic wave drag is estimated using the Harris wave-drag code (which is based upon linearized potential flow theory and the supersonic area rule). An efficient quasi-Newton method of optimization is used to optimize a weighted combination of subsonic lift and supersonic wave drag subject to the constraints of a fixed wing plan area and fixed fuselage and wing volumes. A variety of test problems are considered in which the weightings of the two design criteria are varied

A surface generation method with volume preservation

With progress in medical tomography, multiple-layer images have easily been obtained. Various methods to construct three-dimensional surfaces have been proposed. The “surface rendering method,” in which the surface of an object represented by triangles or square patches is shaded with a normal line to each patch and optical interference, is a popular approach. To obtain the surface data from the volume data, “marching-cubes methods” have often been used, and many related papers have been published (e.g., compensation of triangle patches, high-speed operation, separation of cells). However, no method preserves the volume of an object correctly, since each uses linear interpolation. This paper proposes a method to preserve the volume accurately by adjusting the value of voxels (voxel value) before the marching-cubes method is applied. The proposed method uses an algorithm which adds a small value to each insufficient voxel, or subtracts a small value from each excess voxel. The method has been applied to four examples, and realistic three-dimensional images have been produced. © 1998 Scripta Technica, Syst Comp Jpn, 29(13): 28–35, 1998

A surface generation method with volume preservation

With progress in medical tomography, multiple-layer images have easily been obtained. Various methods to construct three-dimensional surfaces have been proposed. The “surface rendering method,” in which the surface of an object represented by triangles or square patches is shaded with a normal line to each patch and optical interference, is a popular approach. To obtain the surface data from the volume data, “marching-cubes methods” have often been used, and many related papers have been published (e.g., compensation of triangle patches, high-speed operation, separation of cells). However, no method preserves the volume of an object correctly, since each uses linear interpolation. This paper proposes a method to preserve the volume accurately by adjusting the value of voxels (voxel value) before the marching-cubes method is applied. The proposed method uses an algorithm which adds a small value to each insufficient voxel, or subtracts a small value from each excess voxel. The method has been applied to four examples, and realistic three-dimensional images have been produced. © 1998 Scripta Technica, Syst Comp Jpn, 29(13): 28–35, 1998

縮閉線に基づく曲率変化の滑らかな曲線,曲面の生成(第4報)

This research proposes a surface generation method which satisfies the designer's intention to the surfaces and smoothness of the reflected images on them. The method directly determines the curvature distribution of a surface, which is represented by a locus of the evolute of the generatrix moved along the directrices. In this report, the evolute surface formed by the locus is modified according to the designer's intention which is given by an intermediate shape of a generatrix. It is also determined to satisfy the given first and second derivatives such as tangential plane and principal curvature along the boundaries. The generated surfaces by the method have been confirmed to become smooth for the appropriate boundary conditions.

Generation of Smooth Surfaces by Controlling Curvature Variation

AbstractTo satisfy a designer's intention for constructing aesthetic shapes such as automotive bodies, we propose a surface generation method. In the surface design process, designers determine shapes according to their great concern for the reflected images of vehicle surroundings, shade lines and highlight lines. Since reflection and shading are affected by changes of surface normal, the curvature variation of the surface, which represents the change of the surface normal, should be smooth and distributed as designers want. The proposed method controls curvature distribution directly by determining a surface shape from an evolute, which is a locus of the curvature center of the generatrix and moves along directrices to form the surface. It first generates evolutes of boundary curves to be generatrices as rational Bezier curves, then interpolates their shapes with the Bezier polygons, and locates the interpolated shape to the corresponding position of the directrices. By applying this method, we have confirmed that a smooth shape is generated from four boundary curves.

Hourglass Worm Gears Designed to Concentrate Surface Normals. Manufacturing and Experimental Investigation on Tooth Bearing.

To avoid the influence from the small displacement of gear axes under load, the authors propose that all contact normals of a tooth surface be at right angles to the direction of the small displacement induced at each contact point under load. On the basis of this state of surface normals, a few methods for tooth surface generation have been devised for realizing this concept. In this research, an hourglass worm gear having the above geometrical characteristics was made using the conventional methods of tooth surface generation and tooth bearing of the worm gear was experimentally tested. As a result, the validity of this design concept was proven.

Spanning a C1‐Surface over a Given Wireframe

AbstractA problem of spanning a surface of C1 continuity (C1‐surface) over a given wireframe is introduced. By exploiting the concept of a super surface patch introduced in an earlier paper, we proved the existence of an approximate, yet practical solution of the problem. That is, we presented a method or a procedure, by which to span a C1‐surface over the wireframe. This technique is intended to be utilized as a flexible surface generation method for the 3D shape design in the industrial world.

Surface property variations in melt-formed thermoplastics

It has been observed that the method of polymer surface generation has a marked effect on surface properties. Most notably, changes have been observed in surface adhesiveness and on additive exudation when polymers have been molded against substrates of varying surface energy. The parameters affecting these surface differences have been investigated by several techniques, including contact angle measurements, reflectance infrared spectroscopy (FMIR), scanning electron microscopy (SEM), and electron spectroscopy (ESCA). The surface differences are marked in polar polymers. As an example of the observed effects, an ethylene acrylic acid copolymer (E/AA 80/20 by weight) containing 10% stearic acid was hot melt pressed against Teflon and Mylar. After cooling and removal of the Mylar and Teflon substrates, the Teflon pressed sample became opaque after 4 hr while the Mylar pressed sample was relatively clear after 4 wk. Initial clarity was independent of the time allowed to elapse before substrate removal. The contributions of several factors to these surface effects are suggested and discussed. These include surface roughness, surface energetics (polarity), nucleation, surface stresses, and transfer of material between polymer and coating substrate. Overriding factors appear to be variations in additive nucleation and in segregation of polar/nonpolar components at the substrate/polymer interface. The possible implications of these findings are discussed for adhesive bonding, coefficients of friction, printability and other properties.

Graphical Ray-Trace and Surface Generation Methods for Aspheric Surfaces

By means of geometric constructions, a series of solutions has been developed to perform marginal and paraxial ray-tracing on the drafting board. The methods are applicable to plano, spherical, and aspheric surfaces. Mechanical analog constructions of the ray-trace solutions are capable of generating Schmidt, parabolic, and other aspheric optical surfaces. The methods are applicable to the study of known designs, as well as to the development of curves to fit established or desired ray-traces.