Wire frame Modeling An application of Bresenham s line drawing algorithm 3D models Simple objects from the world around us can be depicted as wire frame models We make a list of the key points usually corners on the object s outer surface and a list of all the lines that connect them The key points are called vertices The connecting lines are called edges We create a file that contains this data Example the basic barn 10 corner points vertices 15 line segments edges 3D coordinates Front vertices V0 0 5 0 5 0 5 V2 0 5 0 5 0 5 V4 0 5 0 5 0 5 V6 0 5 0 5 0 5 V8 0 0 1 0 0 5 Back vertices V1 0 5 0 5 0 5 V3 0 5 0 5 0 5 V5 0 5 0 5 0 5 V7 0 5 0 5 0 5 V9 0 0 1 0 0 5 Perspective Projection We imagine the computer display screen is located between the wireframe model and the eye of someone who s viewing it Each vertex is projected onto the screen We use Bresenham s algorithm to draw line segments that connect the projections A demo program will show this effect The projection Y axis P x y z P x y 0 X axis View plane Z axis Eye of viewer 0 0 D D distance of eye from view plane Similar Triangles Corresponding sides have proportional lengths C c A a b B a A b B c C Projection side view By similar triangles y y D D z P x y z So y y 1 z D P x y 0 y Eye Z axis D z View plane y Projection top view D z Z axis x x By similar triangles x x D D z So x x 1 z D P x y 0 P x y z The projection equations Point P x y z in 3D world is mapped to pixel P x y in the 2D viewplane x x 1 z D y y 1 z D Here D is distance of eye from viewplane Any fixups needed If the projected image is too small or too big it can be rescaled x x scaleX y y scaleY If the projected image is off center it can be shifted left or right up or down x x shiftX y y shiftY animation The wire frame model can be moved or the viewer s eye can be moved to show an object from different viewing angles By redrawing a series of different views in rapid succession the illusion of animation can be achieved But erasing and then redrawing a complex object can produce flickering that spoils the impression of smooth movements smooth wire frame animations Advanced hardware techniques can be employed to eliminate any flickering One such technique is page flipping It makes use of the extra graphics VRAM But it may require us to learn more about the Super VGA hardware designs And here we must confront the issue of graphics standards or the lack thereof SuperVGA The problem of standards for enhanced PC graphics hardware Limitations of VGA VGA s architecture was designed by IBM It was targeted for IBM s PC AT machines These used Intel s 8086 8088 80286 cpus Operating system was PC DOS MS DOS DOS was built to execute in real mode So address space was limited to 1MB VRAM was confined to 0xA0000 0xBFFFF Graphics mode VRAM was only 64KB VGA Modes 18 and 19 Design goals of VGA mode 18 higher screen resolution 640x480 4bpp and square pixels 16 colors Design goals of VGA mode 19 higher color depth 320x200 8bpp and linear addressing 256 colors Also backward compatibility with CGA EGA CGA mode 6 640x200 1bpp 2 colors CGA mode 5 320x200 2bpp 4 colors EGA mode 16 640x350 4bpp 16 colors0 IBM competitors Others sought a marketing advantage Their engineers devised ways to get more colors and or higher screen resolutions Example 800x600 with 4bpp 16 colors Offers square pixels and 64K addressing 800x600 480000 pixels planar memory But every competitor did it their own way So PC graphics software wasn t portable VESA Video Electronics Standards Association An industry consortium to setup standards Their idea provide a uniform programming interface for Super VGAs via the firmware Applications would not directly program the incompatible graphics hardware but would call standard ROM BIOS functions supplied in firmware by each manufacturer VESA Bios Extensions v3 0 Copy of the standards document is online It defines a programming interface for the essential and the most needed functions Examples setting various display modes querying the hardware s capabilities and enabling SuperVGA functionalities Reading assignment study vbe3 pdf
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