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.
Solving Systems of Volterra Integral Equations with Cardinal Splines
