The sphere is a common object in uncountable engineering problems, which not only appears in structural elements like domes but also in thousands of mechanisms normally used in diverse kinds of machines. To design, ca...The sphere is a common object in uncountable engineering problems, which not only appears in structural elements like domes but also in thousands of mechanisms normally used in diverse kinds of machines. To design, calculate and analyze the behaviour on service of spherical elements, it is essential to have a good method to create an ordered group of discrete points of the spherical surface from the parametric equations commonly used to define the sphere continuously. One of the best known and widely used in high-level programming environment is MATLAB. The programming language has thousands of functions, lots of them specially designed for engineering processes. One of these functions generates a sphere knowing a given radius and shows the result. Nevertheless, this function is really imprecise because it is based on parallels and meridians besides the obtained vertices do not keep a constant distance each other. This causes the fact that it would be appropriate to design a new function to generate accurate discrete approximations of the sphere. The objective of this paper is to create a low-level function in MATLAB to obtain a discrete sphere with high regularity and high approximation in order to provide a good base to solve sphere-based engineering problems. To ensure a perfect symmetry and high regularity platonic bodies, MATLAB will be used as a base to divide the continuous spherical surface in a finite number of regular triangles. The obtained results for the different seed bodies will be represented graphically and compared to each other. The accuracy of each method will be evaluated and compared too.展开更多
文摘The sphere is a common object in uncountable engineering problems, which not only appears in structural elements like domes but also in thousands of mechanisms normally used in diverse kinds of machines. To design, calculate and analyze the behaviour on service of spherical elements, it is essential to have a good method to create an ordered group of discrete points of the spherical surface from the parametric equations commonly used to define the sphere continuously. One of the best known and widely used in high-level programming environment is MATLAB. The programming language has thousands of functions, lots of them specially designed for engineering processes. One of these functions generates a sphere knowing a given radius and shows the result. Nevertheless, this function is really imprecise because it is based on parallels and meridians besides the obtained vertices do not keep a constant distance each other. This causes the fact that it would be appropriate to design a new function to generate accurate discrete approximations of the sphere. The objective of this paper is to create a low-level function in MATLAB to obtain a discrete sphere with high regularity and high approximation in order to provide a good base to solve sphere-based engineering problems. To ensure a perfect symmetry and high regularity platonic bodies, MATLAB will be used as a base to divide the continuous spherical surface in a finite number of regular triangles. The obtained results for the different seed bodies will be represented graphically and compared to each other. The accuracy of each method will be evaluated and compared too.
