{'fraction_non_alphanumeric': 0.021576763485477178, 'fraction_numerical': 0.0, 'mean_word_length': 5.518918918918919, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Functional optimization for fair surface design

This paper presents a simple-to-use mechanism for the creation of complex smoothly shaped surfaces of any genus or topology. The work described here is the result of research into the fairness of curves and surfaces specified through geometric interpolarity constraints. Constraints consist of positions and, optionally, surface normals and surface curvatures. The outcome of our investigation is a recommendation for the use of nonlinear optimization techniques that minimize a fairness functional based on the variation of curvature. The approach produces very high quality surfaces with predictable, intuitive behavior, while generating, where possible, simple shapes, such as cylinders, spheres, or tori which are commonly used in geometric modeling. From a designer''s point of view, this approach allows the specification of a desired surface in the most natural way. Though computationally intense, the techniques described have now become practical because of the wide availability of very fast work stations. As the processing power available on each desk-top further increases, the techniques described here will become real-time and interactive.