1、Graphics Systems and Models (I),Based on EA, Chapter 1.,姜明 北京大学数学科学学院,更新时间2018年10月16日星期二10时11分37秒,Outline,Applications of Computer Graphics A Graphic System Images: Physical and Synthetic The Human Visual System The Pin-hole Camera,Applications of Computer Graphics,Wide-ranging applications such as
2、film-making, publishing, education, flight-simulation, etc. The combination of computers, networks, and human visual system (HVS), through computer graphics, has led to dominant ways of displaying information. Computer graphics is concerned with all aspects of producing pictures or images using comp
3、uters. It was begun by Ivan Sutherland more than 40 years ago. Development driven by the needs of the user community and advances in hardware and software.,Four Major Application Areas,Display of Information Design Simulation and animation User Interfaces,Many applications span two or more of these
4、areas.,Display of Information,The human perceives 80% of information by vision. The human visual system is unrivaled both as a processor of data and as a pattern recognizer.,Examples: Maps can be developed and manipulated in real time over the Internet with GIS. Images by medical imaging systems nee
5、d to be processed with computer graphics techniques to generate images demonstrating structures. The field of scientific visualization provides graphic tools that help researchers to interpret the vast quantity of data they generated.,Original CT Images,Volume Visualization,Volume Visualization,Desi
6、gn,Professions such as engineering and architecture are concerned with design. Rarely there is a unique optimal solution to a design problem. Design is an iterative process. The power of interacting with images on the screen of CRT was recognized by Ivan Sutherland 40 years ago. CAD (computer-aided
7、design) technology. Examples: VLSI and architectural design.,Simulation and animation,Once graphics system evolved to be capable of generating sophisticate images in real time, engineers and researchers began to use them as simulators.,Examples: Training of pilots Games. Educational software. TV, Mo
8、vie by animation. Advertising industry. Virtual Reality and remote training.,User Interfaces,Our interaction with computers has become dominated by a visual paradigm that includes windows, icons, menus and a pointing device, such as a mouse. X-window system, Microsoft Windows, and Macintosh system o
9、r Apple OS X, etc. We have become so accustomed to this style of interface that we often do not realize that what we are doing is working with computer graphics.,A Graphic System,A computer graphics system is a computer system. There are five major elements. Frame buffer may not be present in some c
10、omputer system.,Input,Output,Three Specific Components,Pixels and the Frame Buffer Output Devices Input Devices,Pixels and the Frame Buffer,Almost all graphics systems are raster based. A picture is produced as an array the raster of picture elements, or pixels, within the graphics system. Each pixe
11、l corresponds to a location, or small area in the image. Collectively, the pixels are stored in a part of memory called the frame buffer.,Pixels: (a) image of Yeti the cat. (b) Detail of area around one eye showing individual pixels.,In high-end systems, the frame buffer is implemented with special
12、types of memory chips video random-access memory (VRAM) or dynamic random-access memory (DRAM) , that enable fast redisplay of the contents of the frame buffer.,The depth of the frame buffer, defined as the number of bits that are used for each pixel, determines properties such as how many colors ca
13、n be represented on a given system. Examples 1 bit frame buffer allows only two colors; 8 bit frame buffer allows 256 colors. In full-color systems, there are 24/32 bits per pixel. They are also called true-color system, RGB-color system, because individual groups of bits in each pixel are assigned
14、to each of the three primary colors, red, green and blue.,The frame buffer is the core element of the graphics system. Its resolution the number of pixels in the frame buffer determines the details in the image that can be displayed.,In a very simple system, the frame buffer holds only the colored p
15、ixels displayed on the screen. In most systems, the frame buffer hold far more information and can be looked at as consisting of multiple buffers.,In a simple system, there may be only one processor which must do the normal processing and graphical processing. Sophisticated systems are characterized
16、 by various special-purpose processors (GPU, graphics processor unit). The main graphical function of the processors is to take specifications of graphical primitives (lines, circles, polygons, etc) and convert them to pixel assignments in the frame buffer. This is called rasterization, or scan conv
17、ersion.,Output Devices,The dominant type of display is the cathode-ray tube (CRT).,When electrons strike the phosphor coating on the tube, light is emitted. The direction of the electron beam is controlled by two pairs of deflection plates. The output of the computer is converted, by digital-to-anal
18、og converters, to voltages across the x and y deflection plates. A typical CRT will emit light for only a short time usually , a few milliseconds after the phosphor is excited by the electron beam. For a human to see a steady image on most CRT displays, the same beam path must be retraced, or refres
19、hed, at least 50 times per second.,In a raster system, the graphics system takes pixels from the frame buffer and displays them as points on the surface of the display. The entire contents of the frame are displayed on the CRT at a rate high enough to avoid flicker. This rate is called the refresh r
20、ate. It is usually 50 to 85 times per second, or 50 to 85 hertz (Hz).,Color CRTs have three different colored phosphors (red, green and blue) arranged in small groups, called triads (三色荧光点组).,One common style arranges the phosphors in triangular groups called triads. Each triad consists of three pho
21、sphors, one of each primary. Most color CRTs have three electron beams, corresponding to the three types of phosphors. In the shadow mask CRT (in the last figure), a metal screen with small holes the shadow mask ensures that an electron beam excites only phosphors of the proper color.,Although CRTs
22、are still the most common display device, they are not the only type. However, most other output technologies are also raster. The LCD (liquid-crystal display) are raster displays which, depending on the particular technology, may or may not have to be refreshed. Plasma panels and digital projection
23、 systems are also raster. Most hard-copy devices, such as printers and plotters, are also raster, but cannot be refreshed.,Input Devices,Most graphics systems provide a keyboard and at least one other input device. The most common input device are the mouse, the joystick, and the data tablet. These
24、devices allow a user to indicate a particular location on the display, often called pointing device.,Images: Physical and Synthetic,We first construct a model of the image formation process that we can then use to understand and develop computer generated imaging systems, different from the usual pe
25、dagogical approach.,Objects and Viewers Light and Images Ray Tracing,Objects and Viewers,Two basic entities must be part of any image-formation process: object and viewer. The object exists in space independent of any image-formation process and of any viewer. In computer graphics, where we deal wit
26、h synthetic objects, we form objects by specifying the positions in space of various geometric primitives, such as points, lines and polygons. In most graphics systems, a set of locations in space, or of vertices, is sufficient to define or approximate most objects.,Every imaging system must provide
27、 a means of forming images from objects. To form an image, we must have someone, or something, that is viewing our objects. It is the viewer that forms the image of our objects. Examples: a human, a camera, etc.,We usually see an object from our single perspective and forget that other viewers, loca
28、ted in other places, will see the same object differently. (a) is the image as seen by viewer A, in which there are two other viewers B and C.,A camera system viewing a building. The object and viewer are in a three dimensional world. However, the image is two dimensional.,The process by which the s
29、pecification of the object is combined with the specification of the viewer to produce a two-dimensional image is the essence of image formation in computer graphics.,Light and Images,Much information is missing from the preceding description of image formation. We have not indicated light sources,
30、how colors are generated on the picture, and what are the effects of different kinds of surfaces on the object, etc.,A simple imaging system with a light source.,Light from the source strikes various surfaces of the object, and a portion of the reflected light enters the camera through the lens. The
31、 details of the interaction between light and the surfaces of the object determine how much light enters the camera.,Light is a form of electromagnetic radiation, characterized by either the wavelength or frequency.,520,The visible spectrum, which has wavelengths in the range of 350 to 780 nanometer
32、s (nm), is called light. Green (520 nm). Blue (450 nm). Red (650 nm). Fortunately, in computer graphics, we rarely need to deal with the wave nature of light in this course. We utilize geometric optics model in this course. We consider only monochromatic point sources for now. A particular source is
33、 characterized by the intensity of light that it emits at each frequency. More complex sources can be modeled by a number of carefully placed point sources.,Ray Tracing,We can start building an imaging model by following light from source. Because light travels in straight lines, we can think in ter
34、ms of rays of light emanating in all directions from our point source. A portion of these rays contributes to the image on the film plane of the camera.,Ray Tracing,Ray A goes directly through the lens. Ray B travels to infinity. Ray C bounces off a mirror and enters the camera. Ray D hits a diffuse
35、 surface and generates (infinite) new rays that can contribute to the image. Ray E hits a surface that is partially transparent, and generates a transmitted ray and a reflected ray. Ray F is reflected from a surface, but strikes another surface that absorbs it.,Ray tracing is an image-formation tech
36、nique that is based on the above ideas and can form the basis for producing computer-generated images. Although the ray-tracing model is a close approximation to the physical world, it is not suited for fast computation. We need a tractable approximation.,The Human Visual System,Our extremely comple
37、x visual system has all the components of a physical imaging system. Cornea, lens, iris, rods and cones, retina. The rods and cones are excited by electromagnetic energy in the wavelength range of 350 to 780 nm. They do not react uniformly to light energy at difference wavelengths. Whereas intensity
38、 is a physical measure of light energy, brightness is a measure of how intense we perceive the light emitted from an object to be. The human visual system does not have the same response to a monochromatic (single frequency) red light as to a monochromatic green light.,Relative brightness sensitivit
39、ies of three types of cones at different frequencies.CIE standard observer curve.,The Pin-hole Camera,The pin-hole camera provides an example of image formation: it is a box with a small hole in the center of one side; the film is placed inside the box on the side opposite the pin-hole. It needs lon
40、g exposure.,Suppose that we orient our camera along the z-axis, with the pin-hole at the origin. We assume that the hole is so small that only a single ray of light, emanating from a point, can enter it. The file plane is located a distance d from the pin-hole. We want to calculate the image of a po
41、int (x,y,z) on the film plane z = - d.,We find that,The point (x_p, y_p, -d) is called the projection of the point (x,y,z). In our idealized model, the color on the film plane at this point will be the color of the point (x,y,z). The field or angle of view (FOV) of our camera is the angle made by th
42、e largest object that our camera can image on its film plane. We can calculate the FOV.,If h is the height of the film plane, the angle of view is,The ideal pin-hole camera has an infinite depth of field: every point within its FOV is in focus. The image of a point is a point. For our purpose, at this stage, we can work with a pin-hole camera. Like a pin-hole camera, computer graphics produces images in which all objects are in focus.,http:/,
