Question

请帮忙修改一下，论文标题、摘要及关键词的翻译，（计算机专业）。有意者可修改中文部分。

平面分形图形绘制技术及其改进

【摘要】本文主要研究了计算机分形图形的绘制算法，特别是运用计算机图形绘制技术实现各种经典分形图形。在了解分形理论的基本知识和分形几何的维数的基础上，对分形图形的算法作了总结，以VC++作为软件开发的工具，实现了对一些经典分形图形的绘制，在计算机上实现了Cantor集、Koch曲线、Sierpinski垫片等经典分形图形；接着提出了一种Julia和Mandelbrot集分形改进绘制技术，生成了具有很好艺术效果的彩色拟3D分形图。

【关键词】分形；Julia集；Mandelbrot集

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The Rendering methods of Plane Fractals and Its Modification

【Abstract】This paper analyze the rendering algorithm in fractal images, especially in some classical fractals by computer rendering methods. Based on the fundamental of fractal theory and the dimension in fractal geometry, we summmarize the fractal algorithms. Moreover, we use the VC++ as the tool for software development, to show the rendering of some classical fractals including the Cantor set, the Koch curve, and the Sierpinski triangles. Finally, we put foward a modified method of plotting the Julia set and the Mandelbrot set, which is appled to drawing a chromatic pseudo three-dimentional distribution graph with a good performance.

【Key Words】Fractal, Julia set, Mandelbrot set.

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有意者可修改中文标题、摘要和关键词。谢谢！
应为analyzes 。

Answer 1

平面分形图形绘制技术及其改进
摘要：本文主要研究了计算机分形图形的绘制算法，特别是运用计算机图形绘制技术实现各种经典分形图形。在了解分形理论的基本知识和分形几何的维数的基础上，对分形图形的算法作了总结，以VC++作为软件开发的工具，实现了对一些经典分形图形的绘制，在计算机上实现了Cantor集、Koch曲线、Sierpinski垫片等经典分形图形；接着提出了一种Julia和Mandelbrot集分形改进绘制技术，生成了具有很好艺术效果的彩色拟3D分形图。
关键词：分形；Julia集；Mandelbrot集

Drawing Technology and Improvement on Fractal Graph of Plane

Abstract

This paper mainly analyzes the drawing algorithm on fractal graph of computer, especially applying the drawing technology of computer graph to achieve various fractal graphs of classics. On the basis of understanding the basic knowledge of fractal theory and the dimension of fractal geometry, this paper sums up the algorithm of fractal graph, achieves the drawing of some fractal graphs of classics by vc + + as a tool of software development, and some fractal graphs of classics such as the Cantor sets, the Koch curve, and Sierpinski filling pieces. Then this paper puts forward a drawing technology of fractal improvement on Julia sets and Mandelbrot sets, and generates pseudo-3D fractal graph with color, which has a excellent effect on art.

Keywords: fractal Julia sets Mandelbrot sets

Answer 2

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Answer 3

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