Direction Of Normal Vector Research Articles

A New Slicing Procedure for Rapid Prototyping Systems

The current slicing rule of most rapid prototyping (RP) systems cannot ensure unilateral tolerances on the whole prototype and often results in problems of overcut and undercut on the same part. This drawback leads to unsatisfactory precision of the part in post processing. In order to reduce the above problems, a new slicing method is proposed in this paper. Based on the geometry information in a stereolithography (STL) file, an algorithm is developed. The appropriate slicing rule is selected according to the inner product of the normal vector and working direction of the part, together with the function of the part to be manufactured. The STL file is cut into 2D sections and an accurate contour is calculated. After the slicing computation, an appropriate working path is produced. The rules proposed in this paper have been verified. This work contributes to the improvement of slicing rules in existing RP systems, especially in systems using uniform thickness slicing. It also improves manufacturing efficiency and working tolerances.

Collision-free path planning for coordinate measurement machine probe

This paper focuses on the method of collision-free path of the coordinate measurement machine (CMM). In terms of the collision-free path, the cut face method is used to plan the displaced tracking along the boundary loop. In addition, the 'maximum angle between tangential vectors method' and the heuristic algorithm designated by the displacement characteristic among the feature faces are used to reduce the number of intermediary points. This can also reduce the distance of the displacement. The turning of the probe aims at the contact with the workpiece surface in the normal direction. If the contact position in the normal vector direction is impossible, the probe angle closest to the normal direction is adopted. The normal direction contact with the workpiece can, on the one hand, achieve better measuring position and, on the other hand, accompany with the cut face method and thus make a collision-free path possible.

Terrain shape recognition for celestial landing/rover missions from shade information

This paper proposes a direct geographic recognition scheme from a gray-scale image without shape reconstruction. Several geographic categories are expressed in 3x3-arrays of normal-vector directions. Only by looking up a table, observed pixel-values (intensities) in a window are transformed into indeces of conformity whether the scene in the window is due to each geographic category or not. The recognition is accomplished by multi-resolution interpretation and fuzzy-logical operations. The results of recognition has shown the feasibility and robustness of the proposed method.

Approximation and characterization of molecular surfaces

The representation and characterization of molecular surfaces are important in many areas of molecular modeling. Parametric representations of protein molecular surfaces are a compact way to describe a surface, and are useful for the evaluation of surface properties such as the normal vector, principal curvatures, and principal curvature directions. Simplified representations of molecular surfaces are useful for efficient rendering and for the display of large-scale surface features. Several techniques for representing surfaces by expansions of spherical harmonic functions have been reported, but these techniques require that the radius function is single valued, that is, each ray from an origin inside the surface intersects the surface at one and only one point. A new technique is described that removes this limitation and can be used to compute surface shape properties.

On rotational discontinuities propagating in an isotropic plasma

The relationships between the plasma parameters downstream and upstream of plane wave rotational discontinuities (RDs) are reanalyzed for the case of an isotropic plasma. The analysis is carried out in the rest frame of the RD using a Cartesian coordinate system with axes labeled n, j, and z. The NJZ system is oriented in such a way that the n axis is parallel to the RD surface normal vector and the j component of B is the same on both sides of the RD. In this NJZ system the magnitude of each of the downstream components of B, U, and E is equal to the magnitude of the respective upstream components, and the sign of Bz, Uz, and En changes across the discontinuity. In the NJZ system the angle through which the tangential component of the magnetic field (Bt) rotates is not arbitrary. It depends explicitly on the angle between the upstream Bt and the j axis. The above jump relations can be used to simplify initial conditions used in theoretical and simulation studies of RD structure. The jump relations can also be used, in principle, to provide an additional method for determining the direction of the RD surface normal vector from spacecraft data.

顔面形態（特に外鼻形態）の三次元計測法の方法と精度の検討

There are two accurate methods to measure facial configurations, especially the external nose, as three dimensional objects. One is laser-scanning which can immediately measure faces directly and without contact. The other method, which we usually use, measures plaster models, obtained from facial impressions made with dental impression materials, by means of a contact-type, high accuracy three dimensional coordinate measuring system (contact measuring system).This study was designed to assess the accuracy and stability of these two methods, an issue previously paid little attention. Four 25-year-old men without facial deformity were examined with these systems. Multiple plaster models were taken from each subject to investigate model stability. All data were integrated into three dimensional models, shown as computer graphics, and compared by the “best fit program, ” which can handle and superimpose the two sets of curved surface data to derive minimum differences in normal vector direction at every site of the surface.The two sets of curved surface data obtained from the same plaster model by each system were almost identical except for areas of the alar groove. In data derived from the laser-scanning system, more than 1.0 mm of distortion was noted around areas of overhang. Facial and plaster model data obtained by the laser-scanning system showed very good fit, with deviation between data being 0.2-0.3 mm.These results show the high accuracy of facial plaster models. The stability of plaster models was also examined with a contact measuring system and deviation between data was 0.1-0.2 mm. In conclusion, although the two systems employed in this study have different characteristics, both are highly accurate and useful for clinical measurement.