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We introduce a novel stratified sampling technique for mesh surfaces that gives the user control over sampling density and anisotropy via a tensor field. Our approach is based on sampling space-filling curves mapped onto mesh segments via parametrizations aligned with the tensor field. After a short pre-processing step, samples can be generated in real-time. Along with visual examples, we provide rigorous spectral analysis and differential domain analysis of our sampling. The sampledoi:10.1109/tvcg.2012.305 pmid:23661009 fatcat:ecjvyoadjfefxfq6jslmnoynxi