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A proposed framework for remeshing polygonal models employs mesh-free techniques for processing surface sample points. It's robust to input models with problematic connectivity, and the geometric processing of points runs easily in parallel on a GPU. The framework extracts visual-perception information in the image space and maps it back to the Euclidean space. On the basis of these visual cues, the framework generates a saliency field to resample the input model. A new projection operator further optimizes the distribution of resampled points. Because the downsampled points control the number of vertices on the resulting model, this framework also works for model simplification. All the algorithms in the framework can be easily parallelized to run on GPUs. In experiments, the framework remeshed diverse polygonal models to well-shaped triangular meshes with high visual fidelity.