| English Abstract | 第8-9页 |
| Chinese Abstract | 第10-11页 |
| Chapter 1 Introduction | 第11-19页 |
| 1.1 Research background | 第11-15页 |
| 1.2 Preliminaries | 第15-19页 |
| 1.2.1 Iterated function system of fractal curves | 第15-16页 |
| 1.2.2 Iterated function system of fractal surfaces | 第16-17页 |
| 1.2.3 Fractal dimension | 第17-19页 |
| Chapter 2 Rational fractal curves with function scaling factors | 第19-43页 |
| 2.1 Construction of rational fractal curves | 第19-20页 |
| 2.2 Analysis properties of rational fractal curves | 第20-31页 |
| 2.2.1 Smoothness of rational fractal interpolation curves | 第20-26页 |
| 2.2.2 Convergence of rational FIFs | 第26-29页 |
| 2.2.3 Stability of rational fractal interpolation curves | 第29-31页 |
| 2.3 Box-counting dimension of rational fractal curves | 第31-37页 |
| 2.4 Numerical Examples | 第37-43页 |
| Chapter 3 Rational fractal surfaces with function scaling factors | 第43-73页 |
| 3.1 Construction of rational fractal surfaces | 第43-46页 |
| 3.1.1 A type of C~1 rational spline interpolation surfaces | 第43-45页 |
| 3.1.2 Bivariate rational fractal interpolation functions | 第45-46页 |
| 3.2 Analysis properties of rational fractal surfaces | 第46-59页 |
| 3.2.1 Smoothness of rational fractal interpolation surfaces | 第46-53页 |
| 3.2.2 Convergence of bivariate rational FIFs | 第53-57页 |
| 3.2.3 Stability of rational fractal interpolation surfaces | 第57-59页 |
| 3.3 Box-counting dimension of rational fractal surfaces | 第59-65页 |
| 3.4 Numerical Examples | 第65-73页 |
| Chapter 4 Application of rational fractal curves and surfaces | 第73-81页 |
| 4.1 Application of rational fractal interpolation curves | 第73-75页 |
| 4.1.1 Rational fractal fitting of the stock price | 第73页 |
| 4.1.2 Curve modelling based on rational fractal interpolation | 第73-75页 |
| 4.2 Application of rational fractal interpolation surfaces | 第75-81页 |
| 4.2.1 Natural object modelling | 第75-76页 |
| 4.2.2 Image interpolation based on rational fractal model | 第76-81页 |
| Chapter 5 Conclusion | 第81-83页 |
| References | 第83-89页 |
| 致谢 | 第89-90页 |
| 攻读学位期间完成的学术论文目录 | 第90-91页 |
| 学位论文评阅及答辩情况表 | 第91页 |
