Creeping Ray Tracing Algorithm for Arbitrary NURBS Surfaces Based on Adaptive Variable Step Euler Method by Song Fu, Yun-Hua Zhang, Si-Yuan He, Xi Chen, Guo-Qiang Zhu

“…Although the uniform theory of diffraction (UTD) could be theoretically applied to arbitrarilyshaped convex objects modeled by nonuniform rational B-splines (NURBS), one of the great challenges in calculation of the UTD surface diffracted fields is the difficulty in determining the geodesic paths along which the creeping waves propagate on arbitrarilyshaped NURBS surfaces. In differential geometry, geodesic paths satisfy geodesic differential equation (GDE). …”
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Design of Face Gear Tooth Surface of Circular Arc Profile by Feng Zhanrong, Sheng Wei, Wang Lixia

“…Based on gear meshing theory and differential geometry theory,the tooth surface equation of the conjugate tooth profile of the basic tooth profile of the circular rack is modeled firstly,and then use the envelope forming theory to derive the equation of gear face machining arc face gear,and the cutter and circular arc tooth profile gear for each envelope forming work on tooth surface and the derivation of the face gear transition surface equation. …”
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Networking Method for the Structure of a Large Modular Deployable Space Antenna by Dake Tian, Xiaodong Fan, Junwei Zhang, Lu Jin, Rongqiang Liu, Yu Zhang

“…On the basis of basic theories of differential geometry, analytical geometry, and robotics, the mathematical model of an envelope circle and that of its center are established. …”
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Method for Establishing New Cycloidal Tooth Profile based on Rolling-sliding Effect by Yanhua Wang, Chaoyang Li, Ye Zhang, Bingkui Chen

“…Aiming at the sliding phenomenon between the cycloidal gear and pinwheel in the actual meshing process of the cycloid pinwheel transmission，a novel cycloid tooth profile modeling method，in which using a sliding function to represent the slide between the pinwheel and the cycloidal gear in the cycloid pinwheel transmission，is proposed. Based on the differential geometry and gear meshing theory，the tooth profile equation of the rolling-sliding cycloidal gear is derived，the meshing function is determined，the calculation method of comprehensive curvature radius and contact stress of the rolling-sliding cycloidal gear are given. …”
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Study on Modification and Tooth Tip Sharping Analysis of Orthogonal Arc Tooth Face Gears by Zhanrong Feng, Guangjin Xiong, Lingfeng Gao, Chao Luo

“…Tooth surface equations of cylindrical gears with arc teeth and face gears are derived， which are based on differential geometry calculation and principle of gear meshing. …”
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Augmented Superfield Approach to Nilpotent Symmetries of the Modified Version of 2D Proca Theory by A. Shukla, S. Krishna, R. P. Malik

“…For the sake of completeness, we also mention, very briefly, a unique bosonic symmetry, the ghost-scale symmetry, and discrete symmetries of the theory and show that the algebra of conserved charges provides a physical realization of the Hodge algebra (satisfied by the de Rham cohomological operators of differential geometry).…”
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A Coons Patch Spanning a Finite Number of Curves Tested for Variationally Minimizing Its Area by Daud Ahmad, Bilal Masud

“…Having a well-parameterized surface, we do some calculations on it that are motivated by differential geometry but give a better optimized and possibly more smooth surface. …”
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Calculation of Meshing Backlash for Cycloidal-pin Gear of RV Reducer Under the Influence of Tooth Profile Deviation by Tianxing Li, Guofeng Wang, Xiaotao An, Chunrong Xing, Meng Tian

“…According to the established contact analysis model of cycloidal-pin gear transmission, the minimum distance between the center of the pin tooth and the tooth profile of cycloidal gear is calculated by differential geometry principle. The accurate meshing backlash under the influence of tooth profile error is obtained, which provides a new idea for the transmission performance research and tooth profile modification design of cycloidal-pin gear pair of RV reducer.…”
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Almost contact metric 3-submersions by Bill Watson

“…Applications to the real differential geometry of Yarg-Milis field equations are indicated based on the fact that a principal SU(2)-bundle over a compactified realized space-time can be given the structure of an almost contact metric 3-submersion.…”
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Digital Modeling of Cone-generated Enveloping Torus Worm by Zhi Liu, Hong Lu, Xin Kuang, Liang Xia

“…The modeling frame is established firstly， and the meshing equations of the working tooth profile in different coordinate systems for the worm are deduced by applying differential geometry， kinematics， envelope theory and space coordinate transformation method， and the digital models of the working tooth profile of the worm are established， simultaneously， the generatrices equation of bottom and addendum surface are worked out. …”
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Evolution of CFD numerical methods and physical models towards a full discrete approach by Caltagirone, Jean-Paul

“…In recent decades, the emergence of methodologies based on differential geometry or exterior calculus has changed the point of view by starting with the creation of entangled polygonal and polyhedral structures where the variables are located. …”
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Optical wave features and sensitivity analysis of a coupled fractional integrable system by Jan Muhammad, Usman Younas, D.K. Almutairi, Aziz Khan, Thabet Abdeljawad

“…The Akbota equation, is a basic tool for investigating nonlinear phenomena in optics, differential geometry of curves, and magnetism. The optical wave solutions are extracted in the forms of different solitary waves as well as periodic, hyperbolic exponential function solutions. …”
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Cyclic surfaces accompanying non-ruled quadrics of rotation by K. L. Panchuk, T. M. Myasoedova, E. V. Lyubchinov

“…As a tool for shaping surfaces of non-linear rotation, the method of the accompanying Frenet trihedron, known in the differential geometry of curved lines, is used. The geometric scheme of surface shaping is based on a construction that includes: a curvilinear axis of rotation and a one-parameter set of its normal planes; a generatrix whose points describe in normal planes circular trajectories centered on a curvilinear axis. …”
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