Automatic Differentiation And Its Application In Computer Graphics

Automatic differentiation is a technique to evaluate the derivatives of a function defined by a computer program. Given the program code of a multivariate smooth function, we can easily use automatic differentiation to calculate its accurate derivative and partial derivative. Computer graphics is a kind of research based on the laws of physics, experimental methods, and cognitive theory, using a variety of mathematical algorithms that deal with two-dimensional or three-dimensional graphics data to generate visual data displayed on computers or other display devices. The main content of the research is how to represent graphics, and how to study the relevant principles and algorithms in graphics calculations, processing and display on the computer. Implicit curve is one of the plane curves used in computer graphics, and it is not easy for the traditional method to draw implicit curve and the graphic quality is not so good. This paper combines automatic differentiation technique with Taylor method and apply them into the subdivision based implicit curve plotting algorithm. A comparison of this new method with other two traditional methods is conducted which shows that the new method is more accurate.The centred form interval arithmetic is an effective method to estimate the range of a polynomial function. This article also made the traditional automatic differentiation technology new improvements. We combine automatic differentiation technique with centred form interval arithmetic and apply them into the subdivision based implicit curve plotting algorithm. Again a comparison and analysis between this new improved method and previous methods were conducted for several implicit curve examples, experimental data show that the centred form interval automatic differentiation applied in drawing implicit curve is more accurate, and has better graphic quality.