This paper aims to provide a series of new methods for projecting a three-dimensional (3D) object onto a free-form surface. The projection algorithms presented can be divided into three types, namely, orthogonal, perspective and parallel projection.,For parametric surfaces, the computing strategy of the algorithm is to obtain an approximate solution by using a geometric algorithm, then improve the accuracy of the approximate solution using the Newton–Raphson iteration. For perspective projection and parallel projection on an implicit surface, the strategy replaces Newton–Raphson iteration by multi-segment tracing. The implementation takes two mesh objects as an example of calculating an image projected onto parametric and implicit surfaces. Moreover, a comparison is made for orthogonal projections with Hu’s and Liu’s methods.,The results show that the new method can solve the 3D objects projection problem in an effective manner. For orthogonal projection, the time taken by the new method is substantially less than that required for Hu’s method. The new method is also more accurate and faster than Liu’s approach, particularly when the 3D object has a large number of points.,The algorithms presented in this paper can be applied in many industrial applications such as computer aided design, computer graphics and computer vision.

New methods for projecting a 3D object onto a free-form surface

Current processing methods of face gear are mainly limited to gear shaping, gear hobbing, and other processes. In order to achieve high-precision and high-efficiency machining of face gear, this paper proposed the cutting technology and tool design of face gear skiving. Solving the tooth surface of the skiving cutter according to the meshing principle, and fitted by NURBS surface. Intersecting the rake and conjugate face to obtain cutting edge data, and import it into the CAD software to build the skiving cutter model, the tooth surface enveloped by the cutting edge of the skiving tool is solved according to the envelope principle. This paper proposed the machining principle and tool design method of face gear skiving and analyzed the influence of tool tooth profile error and installation error on the face gear tooth surface deviation, which provides a reference for improving the machining accuracy and efficiency of face gears and further improving the gear skiving process.

Machining principle and cutter design of face gear skiving

This article presents a method for multipoint inversion and multiray surface intersection problem on the parametric surface. By combining tracing along the surface and classical Newton iteration, it can solve point inversion and ray-surface intersection issues concerning a large number of points or rays in a stable and high-speed way. What is more, the computation result can approximate to exact solutions with arbitrary precision because of the self-correction of Newton-Raphson iteration. The main ideas are adopting a scheme tracing along the surface to obtain a good initial point, which is close to the desired point with any prescribed precision, and conducting Newton iteration process with the point as a start point to compute desired parameters. The new method enhances greatly iterative convergence rate compared with traditional Newton’s iteration related methods. In addition, it has a better performance than traditional methods, especially in dealing with multipoint inversion and multiray surface intersection problems. The result shows that the new method is superior to them in both speed and stability and can be widely applied to industrial and research field related to CAD and CG.

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An Approach to Computing Multipoint Inversion and Multiray Surface Intersection on Parametric Surface

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An Approach to Computing Multipoint Inversion and Multiray Surface Intersection on Parametric Surface