Experimental Approach of the Asymptotic Computational Complexity of Shaders for Mobile Devices with OpenGL ES

Alex S. C. Lima, Edson A. C. Junior


The usage of mobile devices and increasingly realistic graphics is emerging, but the graphics performance is still a critical factor in games. There’s more hardware restriction on mobile devices than on a computer. Thus, this paper proposes an experimental approximation of the asymptotic computational complexity of miscellaneous vertex and fragment shaders for Android and iOS platforms. The asymptotic complexities of the shaders will be analyzed based on number of instructions per second and rendering time metrics, depending on the number of polygons rendered. By means of the adjusted curves is also possible to compare the performance of the devices used in this work, which are the Nexus 4, HTC One, iPhone 5s and iPad Air. Besides, an automatic tool – that plots the data and uses the method of least squares to adjust the values obtained – will be presented, being able to estimate which curve has better approximation to the sampled data. 


Android; iOS; shaders; mobile devices; computer graphics; asymptotic complexity.

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