{'fraction_non_alphanumeric': 0.014749262536873156, 'fraction_numerical': 0.0, 'mean_word_length': 5.858585858585859, '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}}
A Unified Approach for Physical and Geometric Modeling for Graphics and Animation

We present a unified approach for geometric and physical modeling using implicit functions, for application to graphics and animation. This method extends previously proposed techniques, and allows the standard finite element method to be directly combined with geometric modeling, resulting in quick calculation of an object's mass and stiffness matrices, and its vibration modes and frequencies. Because the approach is based on an implicitfunction representation, it allows very fast collision detection and characterization. Examples of complex physical and geometric modeling are presented.