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Butterfly Pattern Generation Method Based on Iterative Function

An iterative function and butterfly technology, applied in the field of computer image generation, can solve the problems of limited image style changes and the inability to realize the innovative design of butterfly patterns, so as to improve design efficiency and realize innovative design effects

Active Publication Date: 2018-07-06
GUIZHOU UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

However, in the digital design of batik patterns, the simulation of extremely irregular and extremely rough natural scenery, such as butterflies, cannot be simulated with pure mathematical models. The style of the image has limited changes and cannot realize the butterfly pattern innovative design

Method used

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  • Butterfly Pattern Generation Method Based on Iterative Function
  • Butterfly Pattern Generation Method Based on Iterative Function
  • Butterfly Pattern Generation Method Based on Iterative Function

Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0024] see figure 1 , an iterative function-based butterfly pattern generation method, comprising the following steps:

[0025] (1) Generation of basic elements: establish the following nonlinear functions in polar coordinates Generate primitives:

[0026] ,

[0027] in, ;

[0028] (2) Iterative generation: establish an iterative formula , and determine the number of iterations , generate a butterfly pattern;

[0029] (3) Generation of whiskers: After the iteration is completed, by establishing the following nonlinear function in polar coordinates Generate whiskers:

[0030] ,

[0031] in,

[0032] After step 3 above (see figure 2 ), convert polar coordinates into Cartesian coordinates, through the mapping function Generate a continuous butterfly pattern:

[0033]

[0034] in, is the number of iterations, n is the maximum preset number of iterations, .

Embodiment 2

[0036] An iterative function-based butterfly pattern generation method, comprising the following steps:

[0037] (1) Generation of basic elements: establish the following nonlinear functions in polar coordinates Generate primitives:

[0038] ,

[0039] in, ;

[0040] (2) Iterative generation: establish an iterative formula , and determine the number of iterations , generate a butterfly pattern;

[0041] (3) Generation of whiskers: After the iteration is completed, by establishing the following nonlinear function in polar coordinates Generate whiskers:

[0042] ,

[0043] in,

[0044] After step 3 above (see image 3 ), convert polar coordinates into Cartesian coordinates, through the mapping function Generate a continuous butterfly pattern:

[0045]

[0046] in, is the number of iterations, n is the maximum preset number of iterations, (see Figure 4 ).

Embodiment 3

[0048] A kind of butterfly pattern generation method based on iterative function of the present invention, comprises the following steps:

[0049] (1) Generation of basic elements: establish the following nonlinear functions in polar coordinates Generate primitives:

[0050] ,

[0051] in, ;

[0052] (2) Iterative generation: establish an iterative formula , and determine the number of iterations , generate a butterfly pattern;

[0053] (3) Generation of whiskers: After the iteration is completed, by establishing the following nonlinear function in polar coordinates Generate whiskers:

[0054] ,

[0055] in,

[0056] After the above step 3, convert the polar coordinates into rectangular coordinates, and use the mapping function Generate a continuous butterfly pattern:

[0057]

[0058] in, is the number of iterations, .

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Abstract

The invention discloses a method for generating butterfly patterns on the basis of iterated functions. The method includes steps of (1), establishing nonlinear functional equations at polar coordinates and generating fundamental elements; (2), generating iteration, to be more specific, establishing iteration formulas, determining iteration times and generating fundamental butterfly patterns; (3), generating whiskers, to be more specific, establishing nonlinear functional equations at polar coordinates after iteration is completed, and generating the whiskers. The polar coordinates are ultimately converted into rectangular coordinates, and the continuous butterfly patterns can be generated by the aid of the mapping functions. The method has the advantages that pattern models with fractal features can be automatically generated by the aid of mathematical models on the basis of the iterated functions; the pattern models in different styles can be conveniently and quickly obtained by the aid of the method, and innovative designs of batik patterns can be implemented.

Description

technical field [0001] The invention belongs to the technical field of computer image generation, in particular to an iterative function-based butterfly pattern generation method. Background technique [0002] Batik is an excellent intangible cultural heritage in my country. Its pattern has both artistic value and cultural connotation, and has a strong ethnic style. It is a treasure house of inspiration for modern design. The themes of traditional batik patterns can be classified into three categories: natural images, social objects and symbols. Figurative graphics are the most numerous and influential graphics in traditional decorative graphics, and their content involves flowers, plants, animals, mountains, the sun, etc. The patterns and shapes are often highly summarized by various subject images to form basic geometric elements. These elements are formed by repeated arrangement and have a strong sense of formal beauty. The composition of the pattern is suitable for pat...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/50
CPCG06F30/367
Inventor 袁庆霓吕健黄海松潘伟杰杨观赐胡耀
Owner GUIZHOU UNIV
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