Abstract
For purpose of reconstruction and innovation of indigo patterns, this study explores modeling, reconstruction, and assembling of the pattern elements by means of mathematics. A model for indigo pattern elements is proposed based on cardinal splines, in which the rigidity of shape is conveyed by the tension coefficient, and the concavity and variety by configuration of the knots. The generalized version of this model is capable of covering any complex element. The contour tracing technique is employed to extract pattern elements from the image, and the closest model instance is selected in virtue of invariance of the improved Hu moments. The selected instances are transformed with respect to the geometric center, the coverage, and the coincidence to match the pattern elements in the image so as to reconstruct the whole pattern. The element filters are conducted on the reconstructed patterns to modify the elements and produce new innovative patterns of constant skeleton. The model is borrowed serving as a skeleton in element assembling. The skeleton properties are investigated to provide basis for skeleton embodiment in which these properties are involved into establishing the placement determiner and element determiner so as to carry out the assembling of elements. Also discussed is the extended skeleton which goes beyond the model and brings about variety and flexibility to element assembling. It is turned out that reconstruction with the model well implements a mathematical copy of the pattern, and the assembling of elements by skeletons provides rich possibilities to innovation of indigo patterns.
Highlights
The indigo patterns, which carry special cultural meanings in China, Japan, and other East Asian countries, are a unique type of patterns composed of various kinds of dots.[1]
The model proposed in this study involves four knots, based on which four cardinal splines connected head-totail are regulated to form a closed figure that is intended to serve as a template for pattern elements of indigo
Extended skeletons can benefit the element assembling in variety and flexibility. This effort models the indigo pattern element based on cardinal splines, taking advantage of the tension coefficient to convey the rigidity of shape, and achieving shape concavity and variety by introducing active knots
Summary
The indigo patterns, which carry special cultural meanings in China, Japan, and other East Asian countries, are a unique type of patterns composed of various kinds of dots.[1]. It has been urgent demand to rescue and recover the indigo pattern so as to help the traditional culture protection. There are plenty of studies focusing on cultural and artistic meaning of traditional indigo patterns. For innovation of these patterns, there exists few, if any, documented explorations. The pattern elements can be fetched and reconfigured manually with some graphic design software,[3] there is little idea in terms of automation presented by this kind of method. Some study has suggested to recognize and reconstruct weave patterns with computer-aided image analysis techniques,[4] but not purposed to invent new ones. Researchers have reported textile pattern generation by visualizing the famous fractal models, including iterated function
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