We demonstrate through comprehensive analysis and empirical evidence the inherent advantages of pixel-based computing for curvilinear photomasks when using a graphics processing unit (GPU)-based platform. The Single Instruction, Multiple Data nature of GPUs enables fast pixel-based computations. We study the advantages of using GPU acceleration for pixel-based computing in various mask processing and verification steps. We highlight the natural runtime predictability of pixel-based computing, which is in the order of number of pixels, or O(p), irrespective of the complexity of the mask shapes. We also emphasize that pixel dose equivalence and information theory provide a mathematical basis for the practical accuracy of a pixel-based approach toward mask data preparation. The Nyquist limit guides the mask rules for masks written using multi-beam writers as the mask is essentially sampled into pixels. This sampling acts as a low-pass filter. We also perform a case study of smooth shapes to show how bandlimited shapes enabled by pixel-based multi-beam writers are more manufacturable. We conclude that the O(p) approach for GPU acceleration enables accurate and practical data processing for curvy masks governed by information theory as we leap into an increasingly complex curvy world.