Computer Graphics. Chapter 1 (Related to Introduction to Computer Graphics Using Java 2D and 3D)
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1 Computer Graphics Chapter 1 (Related to Introduction to Computer Graphics Using Java 2D and 3D) Introduction Applications of Computer Graphics: 1) Display of Information 2) Design 3) Simulation 4) User Interfaces We need to consider four major tasks when dealing with generating computer graphics: 1) Modeling 2) Geometric processing 3) Rasterization 4) Display Modeling This step will produce sets of vertices, which specify different geometric objects. If we have time, we will discuss this issue. Otherwise we will assume that the vertices are given. This is the easy case. We can also build curves, surfaces, etc.. Geometric processing This step will determine which geometric objects, from the previous step, should appear in the display. If we include color, also this step will determine the shades or colors of the objects. We break down this step into four sub steps: Normalization, clipping, hidden-surface removal and shading (the last item will be covered later, time permitting). Normalization: Change of coordinates from the user coordinates to the camera coordinates. Obtain normalized view volume. Clipping: Remove the parts of the objects that lie outside the viewing volume. Hidden-surface removal: Objects that should be removed because they are obscured by other objects.
2 Shading: Perform lighting calculations. Rasterization Here we have to transform the 2D objects into screen coordinates, to generate a set of pixel values. This process is sometimes also called scan conversion. Display This is the process of taking the image from the frame buffer onto the screen. Although this process is automatic, we will consider the case of poor quality display, and consider antialiasing algorithms, speeding algorithms for lines and circles, etc.. Graphics Hardware Graphics hardware has been evolving over the past several decades In the 60 s, 70 s, vector displays costing millions of dollars. US military was main (only) customer Raster displays started appearing in the 70 s In the 80 s, raster displays and graphics hardware cost 10 s to 100 s of thousands of dollars. Cost low enough that companies could afford the hardware. SGI won the battle of work station graphics, OpenGL became standard In the 90 s, graphics hardware started moving to PC s. DirectX is MicroSoft s challenge to OpenGL In the 00 s, PC graphics hardware has displaced work station graphics. Good, inexpensive cards for PCs Currently getting faster in excess of Moore s law Many graphics cards are more powerful than CPU A Graphics System: 1) Processor 2) Memory 3) Frame Buffer 4) Output devices 5) Input devices 1) and 2) should be known to you. New thing: Frame Buffer. A picture is built from individual points, called pixels. The pixels are controlled by the information on the frame buffer. The frame buffer is a portion of memory which contains
3 information for the displaying of each pixel (monochrome: pixel on or off => bit is 1 or 0). So there is a direct correspondence between a pixel and a 1-bit in frame memory. The host computer loads the memory of the frame buffer and the deflection circuitry scans the screen. In synchrony with the beam position, the pixel values are read from the frame buffer and the intensity values are displayed. If we want to have color, we need more that one bit per pixel. If we use n bits per pixel, we can obtain 2 n possible variations (colors) for that pixel. It is customary to talk about how many planes of memory correspond to a pixel, i.e. if we assign 6 bits/pixel, to say that we have a 6 planes frame buffer (consider the 6 bits arranged not in length but in depth) and therefore we can have 64 possible colors (2 6 = 64). Since the CRTs use RBG-color, and analog values, there is a DAC (Digital to Analog Converter), which will transform (following the 6 planes frame buffer example) the 2 bits assigned to each of the primary colors into an analog value. Some raster displays have a LUT: Look-Up-Table, which defines the working set of colors. And index identifies each color in the table and the application stores the index number. If we have a 3 bits/pixel, then we can have a table with 8 entries. Each entry on the table corresponds to a color, generated with 6 bits, or 8 bits or 24 bits, etc. So we have two different things: 1) The number of planes (bits/pixel) that you have. It will determine how many entries you can have in the look-up table. It also represents the number of different colors hat can be used at a given time displayed simultaneously. 2) The number of bits that each entry on the look-up table has. They are used to generate a color out of the palette of colors. So, if we have a frame buffer with 6 planes, and a palette of 16 million colors (2 24 ) we can only use 64 colors. Of course these colors are selected out of the 16 million. We can modify the selection by changing the values on the look-up table. On a workstation things are very similar, except that between the frame buffer and the CPU we could have a graphics subsystem, that transforms 3-D information into 2-D screen information, and places it in the frame buffer. The frame buffer, besides being multiplane, could have hidden memory screen, equivalent in size to the one being used. The display changes interactively which portion of the frame buffer is visible and which one is hidden. Also some of the planes could be use for z-buffering: In order to be sure that a more distant polygon is not drawn over a nearer one, we should keep track of the depth of each pixel, as we are computing it. Later, for the same x,y position, only the closer pixel should be displayed.
4 Alpha buffering: Takes care of keeping a transparency value for every pixel. Overlay planes: To keep track of the cursor position Control planes: To keep track of window relationships and attributes. Therefore a workstation with a 1280* 1024 pixels resolution will need a frame buffer with almost 16 MB for a color display with 16 million colors. 24 planes for the display + 24 planes for the hidden screen + 8 planes for the alpha buffer + 32 planes for the z-buffer + 4 planes for the overlay + 4 planes for control = 96 planes. 96 bits * 1280*1024 = bits => /8 = bytes = KB Output devices: Softcopy: Vector-refresh Displays. They are CRT devices that only draw lines. Normally the device has its own processor, the DPU (Display Processing Unit) that contains its own memory, to hold the display file. This file contains the instructions placed by the host CPU. These are read by the DPU, to display the information. The display file s last instruction is a jump to the beginning for refreshing the screen. They work following the same basic principles that we find in a pen plotter: Pen_Up Pen_Down Goto(X,Y) Get_Pen(i) Pros: Good for fast and highly interactive applications. Cons: Bad for filling regions. Raster Scan Displays. A picture is built from individual points, called pixels. The image has to be refreshed, i.e. the whole screen has to be redrawn at least 60 times a second. Cheaper solutions: 1) Interlaced scanning patterns Cons: Some flickering. 2) Persistent phosphor. Cons: No easy change of images Images:
5 The book tries to present a paradigm to create images. To understand where are we going, before the mathematical tools are used. Objects: They exist in the real world, physically or ideally. But they exist independently of anything. Very often we can supply a set of vertices on the real world, to assert the existence of the object. Or we using other modeling techniques. Example: A house could be given by the following set of points, A (10,20,30), B (50,20,30), C (50,40,30), D (10,40,30), E (10,20,45), F (50,20,45), G (50,40,45), H (10,40,45), I (20,30,50), J (40,30,50), K (10,28,30), L (10,28,35), M (10,32,35), N (10,32,30), O (22,20,39), P (34,20,39), Q (34,20,42), R (22,20,42). That will correspond to the following picture: Viewer: Is the one that looks at the objects, and by doing that, it will create the different images that we can have from the same object.
6 Although both the object and the viewer exist on a 3D world, the image they produce is 2D. Light and Images: We consider only point sources, following the ideas of geometric optics. Light travels in straight lines. Ray Tracing: For each pixel on the screen, we do not stop at the first visible surface, but bounce the ray around the scene, collecting intensities. We take into account the reflection and refraction properties of the different surfaces that we encounter when the ray is moving. This technique requires a lot of computational power. The Human Visual System and the Pinhole Camera: Light enters through the eye lens, and the image is formed on the retina. A simplification is the Pinhole Camera: A box with a small hole in the center of one side, and the film on the inside, on the opposite side to the hole. Using similar triangles is easy to find out the coordinates of the image, based on the coordinates of the object. We may talk in this model about: 1) Depth of field - Object in focus. Every point is in focus 2) Field or angle of view - Angle made by the largest object that the pinhole camera can make an image
7 Problems; I) One ray through the hole II) One single angle of view. Think of how the real world cameras solve these two problems. The synthetic-camera model Creating computer-generated images through a process similar to forming an image using an optical system. a) Specification of the object is independent of the specification of the viewer. (You may have the specification for the house, for instance, on a file, and have different possible views viewers, on another file(s)) b) The images can be computed using perhaps trigonometric calculations. c) The plane where the image is generated is placed in front of the pinhole. d) Because of the angle of view, we must define a window (clipping window) in the image plane, through which the viewer sees the real world. This window will correspond to a 3-D window in the real world. The Programmer s Interface We need to specify: 1) Objects 2) Viewer 3) Light sources 4) Material properties 1) Objects: Set of vertices 2) Viewer or camera: We must define a) the position of the camera, or the lens in the 3 dimensional world; b) the orientation, or assuming the center of coordinates is at the center of the lens, any rotation(s) around any of the three axis; c) the focal length, or portion of the world the camera sees; d) film plane, or position and orientation of this plane with respect to the coordinates system of the lens. All of these will require some mathematical transformations, so we can express the objects in the new coordinate system (with center of origin on the lens). We will not deal with material properties on this course. Remark: Although we have emphasized the independence of the object and the viewer, in many cases, due to earlier viewing techniques, there is a relationship between the object
8 and the viewer in order to obtain a particular image (one-point perspective projection, for instance). Graphics Architectures: Old systems : CPU DAC CRT Display Processors: CPU DPU CRT Display File Pipeline Architectures: Transformations Clipping Projection Rasterization Transformations: Of coordinates from one coordinate system to another one (real world system, to the one where the origin is at the lens of the synthetic_camera, for instance coordinate system of the camera). All these changes can be obtained by doing multiplications of matrices. The final matrix, result of all these multiplications will be found, and it is the only one we need to apply to change all the representations. Clipping: Because of the limitations of the synthetic_camera system, since not all the world can be placed into an image. This is done by placing a clipping rectangle on the plane where the image is going to be created (or alternatively a 3D truncated prism or parallelepiped, on the real world). Projection: At the end, the 3D objects have to be projected into the 2D screen. This process will generate several different types of projections. Rasterization: Setting the 2D objects information into the frame buffer. No concern to us. Performance Characteristics: Front end: Geometric processing, generally involving floating point arithmetic computations. Many pipeline operations are implemented in silicon to enhance the performance of this part of the graphics system. Back end: Direct manipulation of bits on the frame buffer. Parallel processing is best suited for enhancing performance of the graphic system.
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