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Any sampled point acquired from a real-world geometric object or scene represents a finite surface area and not just a single surface point. Samples therefore have an inherent scale, very valuable information that has been crucial for high quality reconstructions. We introduce a new method for surface reconstruction from oriented, scale-enabled sample points which operates on large, redundant and potentially noisy point sets. The approach draws upon a simple yet efficient mathematical formulation to construct an implicit function as the sum of compactly supported basis functions. The implicit function has spatially continuous "floating" scale and can be readily evaluated without any preprocessing. The final surface is extracted as the zero-level set of the implicit function. One of the key properties of the approach is that it is virtually parameter-free even for complex, mixed-scale datasets. In addition, our method is …