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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.

The purpose of this paper is to investigate the process parameters and optimise the machining input parameter of powder mixed electric discharge machining for high carbon high chromium alloy steel (D2 steel) for the industrial application. Grey relational analysis approach has been used to obtain the multiple performance output response.

In this experimental work, input parameters, namely, pulse on-time, discharge current, tool material and grit size, are selected. The design of the experiment has been constructed with the help of MINITAB 7 Software, in which L16 orthogonal array has been preferred for the experimentation. The effect of input parameters, namely, material removal rate, tool wear rate and surface roughness, is investigated. Grey relational analysis and analysis of variance are performed to optimise the input parameters and better output results.

In this experimentation, there is an increment of tool wear rate by 64.49 per cent, material removal rate by 47.14 per cent and surface roughness by 35.82 per cent.

A lot of practical applications have been found in many different material processing industries like metallurgy, machinery, electronics, transportation, military science, agricultural machinery, etc. These practical applications have brought forward definite and noticeable economic benefits.

The reader is given a general overview on the machining investigation and optimisation of processes parameters through the grey theory approach. It gives a new framework to investigate the problems where multiple input machining variable and various output responses are obtained in single optimised parameters.

Driven by the development of the global digital economy, knowledge management in industrial enterprises offers more possibilities for green innovation. Based on the perspective of external knowledge sources, this study aims to construct a panel regression model to explore the relationship between digital economy and industrial green innovation efficiency.

Panel data from 30 regions in China from 2011 to 2020 were selected as research samples. All data are obtained from national and provincial statistical yearbooks. Coupling coordination degree analysis, entropy method, panel regression analysis, robustness test and threshold effect test by Stata 16.0 were used to test the hypotheses.

The empirical results demonstrate the hypotheses and reveal the following findings: the digital economy is positively related to industrial green innovation efficiency and external knowledge sources, and external knowledge sources mediate the relationship between them. Moreover, based on the threshold test results, the digital economy has a double-threshold effect on industrial green innovation efficiency.

Based on the perspective of external knowledge sources, the proposed mediating mechanism between the digital economy and industrial green innovation efficiency has not been established previously, further enriching the research on the antecedents and outcomes of external knowledge sources. Moreover, this study estimated the direct influence mechanism and double-threshold effect of the digital economy on industrial green innovation efficiency from theoretical and empirical analysis, thus responding to the call of scholars and adding to existing research on how the digital economy affects the green transformation of industrial enterprises.