{'fraction_non_alphanumeric': 0.02012072434607646, 'fraction_numerical': 0.0, 'mean_word_length': 6.323529411764706, '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}}
Computer graphics in its fifth decade: ferment at the foundations

Traditionally, computer graphics is based on the mathematics of projective geometry, homogeneous coordinates, and matrix algebra. Recently these mathematical foundations have been called into question by several authors. We examine some possible alternative mathematical underpinnings for computer graphics, including Grassman spaces and Grassman coordinates, tensors and tensor algebra, and Clifford spaces and Clifford algebras.