Solid shape
A new approach to the surface intersection problem
Computer Aided Geometric Design
Theories of contact specified by connection matrices
Computer Aided Geometric Design - Special issue: in memory of John Gregory
Efficiency of Multi-Axis NC Machining of Sculpted Part Surfaces
SSM '98 Proceedings of the IFIP TC5 WG5.3 International Conference on Sculptured Surface Machining
The Gaussian and mean curvature criteria for curvature continuity between surfaces
Computer Aided Geometric Design
Mathematical and Computer Modelling: An International Journal
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The topic of the paper is in the area of mathematical modeling of the contact of two smooth regular surfaces in the first order of tangency. The paper is aiming to develop an approach for the mathematical description of the geometry of tangency of two smooth regular surfaces, which share a common point, and in such way to describe geometry of contact of two surfaces not only qualitatively, but quantitatively as well. Various approaches of the first-, second-, and higher-order approximation are discussed. To resolve the problem under consideration, a characteristic curve of new kind is introduced. We refer to this characteristic curve as the so-called indicatrix of conformity of two surfaces, which are tangent to each other at a point. Application of the indicatrix of conformity enables one developing an appropriate quantitative and qualitative description of the geometry of contact of two smooth regular surfaces in the first order of tangency. The results presented in the paper will have many practical applications in science and engineering: 1.(i) for optimal tool-path generating in machining sculptured surfaces on multiaxis CNC milling machine, from which the problem arose; 2.(ii) for developing a perfect TCA (tooth contact analysis) computer programs for gear pairs and for gear trains; 3.(iii) for improving accuracy of solving the problem of two rigid bodies contact; 4.(iv) for fitting two surfaces while designing blend surfaces; 5.(v) when performing elastohydrodynamic film thickness calculations, etc .