Realistic computer graphics (a) - simulation of natural scenery: Tian Jingcheng Published: 2001/02/07
Thesis:
Seeking to accurately describe the math models of the objective world and the landscape, and reappearly reproduce these phenomena and landscapes, and is an important research topic of graphics. Many natural scenes are difficult to describe geometric models such as smoke, plants, water waves, flames, etc. Several modeling and drawing techniques discussed herein beyond the limitations of geometric models, which can describe complex natural scenery with a simple model.
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Realistic Computer Graphics (1) - Natural Scenery Simulation Implements the four basic tasks that must be completed on the computer's graphics equipment. 1. Description of the three-dimensional scene. Three-dimensional modeling. 2. Convert 3D geometric description into two-dimensional perspectives. Perspective transformation. 3. Determine all the visible faces in the scene. Film algorithm, visible detection algorithm. 4. Calculate the color of the visible in the scene. The light brightness and color composition of the observed eye is calculated based on the optical physics based illumination model. Among them, three-dimensional styling technology is divided into three categories according to the shape of the model: · Surface shape: Research on how to describe a surface in the computer, how to interact with its shape. The curved shape is divided into regular curved shapes (such as plane, cylindrical surface, etc.) and irregular curved surfaces. The irregular surface modeling method mainly has a Bezier curve surface, a B-spline curve surface and a Conveus surface. · Three-dimensional shape. Studying how to define within a computer to represent a three-dimensional object. These methods are mainly voxel structural methods, boundary representation, top forgotation, and so on. Surface shape and stereoscopic modeling are known as geometric model styles. · Natural scene simulation. Studies how to simulate natural scenery in your computer, such as clouds, water flows, trees, and so on. This article will focus mainly introduce related methods about natural scenery simulation. Seeking to accurately describe the math models of the objective world and the landscape, and reappearly reproduce these phenomena and landscapes, and is an important research topic of graphics. Many natural scenes are difficult to describe geometric models such as smoke, plants, water waves, flames, etc. Several modeling and drawing techniques discussed herein beyond the limitations of geometric models, which can describe complex natural scenery with a simple model. 1.1 Fractal and IFS 1.1.1 Fractal Geometric Figure 1 "Snowflake) Curve Fractal refers to a mathematical geometric body, which has complex and fine structures on any scale. Generally, fractal geometry is self-similar, that is, each part of the graphic can be seen as a reduced copy of the overall graphic. For example, the snowflake curve is a typical fractal pattern, and the generation method is as follows: Take an equilateral triangle, and a small equilateral triangle is generated at the middle of each side, and the above process can be formed. Figure 2.1 The curve shown. In theory, the result of unlimited recursive is a limited region, and the circumference of the region is unlimited, and has an unlimited number of vertices. Such curves are inaccurate in mathematics. As early as the 19th century, some fractal graphics with self-similar characteristics were there, but they were originally just as a strange phenomenon. In the 1970s, Benoit B. Mandelbrot was first systematically studied by fractal and founded the new mathematical branch of fractal geometry. Mandelbrot extends the dimensions in the classic European miles, proposes the concept of fractional dimensionality. For example, the dimension of the above snowflake curve is 1.2618. Fractal geometry is not just an abstract mathematical theory. For example, the contour of the coastline also has an unlimited length if it is irregular. Mandelbrot believes that the coast, mountains, clouds, and many other natural phenomena have fractal characteristics. Therefore, the fractal geometry has become a very rapid development of scientific branches, especially in computer graphics, becoming an important means to describe natural scenery and computer art creation. In addition, fractal also has broad application prospects in image compression. 1.1.2 Sollation Transform and Iterative Function Iterative Function System IFS (Iteration Function System) was first proposed by Hutchinson in 1981, which has become one of the important research contents in fractal geometry. The IFS is based on the vanity transformation into a frame, and is generated by iteration depending on the integral structure of the geometric object. The affine transformation is an operation of rotation, proportional amplification, and translation of the graphic.
Define the affine transformation in the secondary O'. space to ω: R2 → R2, (x, y) a point in the two-dimensional space, its affine transformation image is (x ', y'), affine transformation The formula can be written as: affine transformation allows the graphic to generate a copy, each portion of the fractal graphic can be considered as a replica under different affine transformations. This decomposition is independent of the scale, that is, the original map can still be similarly decomposed after the emoction transform. This overall and local similar properties are the basic characteristics of fractal. An iterative function system consists of a limited compression factor {S1, S2, ..., SN}, respectively, composed of ω1, ω2, ..., ωn}, recorded as {ωn, n = 1, 2, ... , N}, where n is the number of integral partitions; the compressed factor Sn corresponding to the overall compression mapping set ωn, there is S = Max {Sn, N = 1, 2, ..., n} satisfying 0 ≤ S <1 . There is a companion probability 0 <1, and σPn = 1 is corresponding to each ωn. The compressed mapping set ωn and the corresponding accompanying probability Pn determine the IFS code. The compressed mapping theorem is known from the fractal space, for a given graphic IFS code, using a random iteration, the attraction of the graph can be drawn, that is, if the IFS code is modeled, it can be drawn with a very small amount of code. Complex graphics effect. The inverse process of this process is also very meaningful, from a graphic to obtain an IFS code, which is equivalent to the highly compressed compression of the original graphics, and is also a hot topic of the current fractal fractal research. 1.1.3 Fractal-based scene generation The fractal pattern plotted by the IFS code has an infinite self-similar structure, which can be accurately reflected in many objective things. This structure is difficult to describe with a classic mathematical model. As long as the change is selected, the graphics effect of any precision can be generated using IFS, which is also difficult to do other drawings. 1.2 Scientist Aristid LindenMayer proposed a description of plant morphology and growth in 1969, named L-grammars. In 1984, a. R. Smith applies the L system to computer graphics. The L system is actually a set of form languages, described by specific syntax, which consists of a series of generated, and all generated types are directly matched. For example, a typical L system syntax includes four letters {A, B, [,]} and two generated rules: 1. A → AA 2. B → a [b] AA [B] starting from letter A It can generate alphanumeric sequences such as A, AA, AAAA; starting from letter B, the first few steps are as follows: B A [b] AA [B] AA [A [B] AA [B]] AAAA [A [ B] AA [B]] ... If we regard the vocabulary formed by the generated iteration of this grammar rules as part of a certain diagram structure, treat the content in square brackets as the branch of the previous symbol, then The three iteration results of the above grammar are shown in Figure 2.2. On this basis, appropriately change the direction of the branch, join the random factors and draw details of the leaves, flowers, fruits in the end of the branch, and can impair the plants in the world. Of course, the above L system itself does not record any geometric information, so the L system's modeling language must be capable of supporting grammar description and geometric description; how to control the growth (iteration) process of the L system is also a problem that needs to be studied. . In this regard, refffye, prusinkiewicz, etc., respectively, respectively. In summary, the simulation of the plant growth process is very successful for the simulation of the plant growth process, providing another powerful tool for the computer's true graphics.
