{'fraction_non_alphanumeric': 0.011510791366906475, 'fraction_numerical': 0.0, 'mean_word_length': 6.03030303030303, '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}}
Deforming objects via exponential homotopy: A first approach

This work presents a novel alternative to conventional linear homotopy with suboptimal settings for applications on object deformation. Proposed approach extends the linear mapping to exponential representations that provides smooth transitions when deforming objects while homotopy conditions are fulfilled. As well, we introduce a quality indicator based on the ratio between the coefficients curve of resultant homotopy and those of a non-realistic, reference homotopy. Experimental results are promising and show the applicability of exponential homotopy to interpolating images with soft changes and homotopic geometric objects.