Analysis And Extraction Of Geodesic Curve In Curved Surface

The computer-aided curved surface design is the rationale and key technology in the CAD/CAM system. It has the widespread application in the machine manufacture domain. The function of curves and surfaces modeling weighs one important target of geometry modeling ability in CAD/CAM system. The curves and surfaces'description, design and analyze become the key points of the geometric modeling technology. In view of analysis and extraction of geodesic curve in the computer auxiliary surface design, several aspects work has been mainly carried on as followed.Firstly, the elementary knowledge and theory of surfaces and geodesic curve are elaborated. One kind of precise mapping relations between the simple surfaces and the plane is established. Meanwhile, the mathematical models is established. the three kind of situations of simple surfaces is discussed and solved separately. respective measured the mathematical model about geodesic distance is determined. Then it is carried on the confirmation separately through examples.Secondly, based on the solution about geodesic curve of the simple surfaces and the surfaces characteristic, the differential equation of geodesic curve is established, which can be used for all surfaces. This theory is confirmed according to examples. Make sure the geodesic distance of surfaces visualization through the programming.Thirdly, the related knowledge about MATLAB and particle swarm optimization is introduced to this paper. Particle swarm optimization used by the MATLAB is solved. the particle swarm optimization to the solution for geodesic curve on surfaces is introduced. Take some examples for solving the distance on the given surfaces and carry on the error analysis for the results.Fourthly, based on the platform of UG re-development, the trigonometric curve method is used to load the surfaces in order to make sure the result of development surfaces visualization. The error analysis for the results are carried on in order to appraise the quality of this method.Through the research on geodesic distance, the mathematical model of geodesic curve is inferred on surfaces, which would provide the theory basis for its widespread application in industrial field.