Computer Graphics---Beginners_Chapter1.1_E

Using computer to render the images which conforms to you for displaying or applications and making the human life being better can be called computer graphics. We can roughly divide the computer graphics into photorealistic rendering and non-photorealistic rendering.

In general:

Photorealistic rendering --- Rendering the realistic scenes by using computer.

Non-photorealistic rendering ---Rendering the artistic images by using computer.

(Non-photorealistic rendering is various and diversified, so we first understand that how to render the realistic scenes by using computer.)

All things are discrete in computer, and the final results are displaying by the screen of computer. Now Imagining that dividing your screen into a lot of squares which are same size as shown in Figure 1. When the one of they gets the instruction, it will be shaded by the color which fits your mind. Formally, we call it pixel. Consequently, when you use the computer to render some objects, the problems are appearing, For example, how the scene’s objects are represented, how many pixels of the object, where are they in the screen and how to compute the pixel’s color satisfy the human visual perception.

Fig. 1

A. Parametric Patches and Curves: We can use the mathematical formulation to create the curves by input some parameters. The shapes of the objects in two or three dimension all can be represented by using a lot of curves. The advantages are that the small memory storage and the surfaces of the objects can be easy controlled.

(Key Works: Bezier curves, B-spline representation)

B. Polygon Meshes: Objects are composed of many polygons as shown in Figure 2. The basic element of polygons for approximately constructing the surfaces of objects can be a triangle (face) or not. For example, three vertices can form three edges and three edges can form one triangle. Therefore, the more polygon meshes can construct the finer model. This method is simple and intuition. But it needs more memory.

Fig. 2, From: wiki

C. Volumetric elements : This method is a spatial subdivision technique. We can divide the scene’s space into many cubes (or call voxels) and find that how many cubes the objects occupy and where are they as shown in Figure 3. We can use octrees to organize the voxels. We also can use different volumetric elements like sphere. This method is suitable to simulate the light scattering and becomes more popular recently.Note that the different geometric component may influence the performance of rendering and the image’s quality.

Fig. 3, From:  Thiedemann et al.[2011] ,Voxel-based Global Illumination

D. CSG: We can model the objects by combining a set of geometric primitives, and then apply the Boolean operations to decide the accurate permutation and combination of the primitives as shown in Figure 4. This method is suitable to the mechanize objects. But it is difficult to the fine objects unless you have a lot of various geometric primitives.

Fig. 4, From: Textbook

In summary, which methods of objects representation can we choose? In general, it is sufficient to most application when using polygon meshes. I will introduce the practical data structure and the general document of this method.