Masatoshi Niizeki

Some basic geometric test conditions in terms of Plücker coordinates and Plücker coefficients

We propose some basic geometric tests that are unified, projectively invariant, and do not require any auxiliary points. We include (1) linearly independent conditions of homogeneous flats and simplices; (2) coincidence, coplanarity, concurrency, and collinearity conditions of homogeneous flats; and (3) interference conditions between homogeneous simplices, defined both in projective space and in two-sided space. All the conditions are represented in terms of Plücker coordinates and Plücker coefficients.

Study on Analysis Support of Lubrication Phenomenon by Three-Dimensional CAD Development of Auxiliary Analysis Tool for CAD

Three-dimensional CAD (Computer Aided Design) software can be used to analyze phenomena related to movement such as vibration and friction. But this requires knowledge for handling material properties and uses special three-dimensional CAD functionality. For these reasons, analysis based on three-dimensional CAD of phenomena is greatly influenced by skill level in model design and enormous time if required due to processing of analysis. Therefore, it is difficult to treat as an auxiliary tool for analysis. Also, various software exist as three-dimensional CAD, but each software varies in method of use. In addition, automatically obtained finite element mesh data in analysis differs depending on software. Therefore, even with the same model, it is difficult to analyze under the same conditions and to obtain the same result [14]. In this paper, we will study the method for analyzing the lubrication phenomena. From this study we will propose a method easy even for beginners, and show that the analysis method is simple and quick and reduces the burden on the designer.

Geometric computation based on an adaptive data length computation processor

Introduces a model of a simple geometric processor on which geometric computation packages for solid modeling and computer graphics can be based. An exact integer representation and an adaptive determinant sign detection method are built into a geometric library to give a solution to the problem of accuracy and efficiency in 3D geometric programs. The computational core of this geometric library is designed so that it can be readily replaced with a simple hardware processor. The geometric computations are based on signed Plucker coordinates and the 4/spl times/4 determinant method. A method for classifying degenerate configurations of points using parallel sign detections of the Plucker coordinates of points, lines and planes using the processor is developed. A geometric computation library designed in this way has many advantages when compared to conventional geometric approaches.

4×4 行列式法によるポリゴンに対する点の内外判定アルゴリズムの比較

Point-in-Polygon Tests are basic geometric algorithms in solid modeling. The 4 × 4 Determinant Method provides a structured framework for all interference problems in the modeling process. The authors have proposed two different algorithms for Point-in-Polygon Tests based on the 4 × 4 Determinant Method, the PNZ Triangle Method and the Vertex Convexity Method. This paper compares the (1) algorithm simplicity, (2) arithmetic operations per vertex, (3) pre-calculable data, (4) accuracy in floating point arithmetic, (5) applicability in special cases, and (6) applicability in faces with curved edges, of the two algorithms. This shows which algorithm is preferable in each situation, and which algorithm is suitable for implementation in a hardware geometric processor.