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Wire-frame Modeling

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”

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Wire-frame Modeling

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  1. Wire-frame Modeling An application of Bresenham’s line-drawing algorithm

  2. 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”

  3. Example: the basic barn 10 corner-points (“vertices”) 15 line-segments (“edges”)

  4. 3D-coordinates Front vertices Back vertices V0=( 0.5, 0.5, 0.5 ) V1=( 0.5, 0.5, -0.5 ) V2=( 0.5, -0.5, 0.5 ) V3=( 0.5, -0.5, -0.5 ) V4=( -0.5, -0.5, 0.5 ) V5=( -0.5, -0.5, -0.5 ) V6=( -0.5, 0.5, 0.5 ) V7=( -0.5, 0.5, -0.5 ) V8=( 0.0, 1.0, 0.5 ) V9=( 0.0, 1.0, -0.5 )

  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

  6. The projection Y-axis P(x,y,z) P*(x*,y*,0) X-axis View-plane Eye of viewer (0,0,D) D = distance of eye from view-plane Z-axis

  7. Similar Triangles Corresponding sides have proportional lengths C c A a b B a / A = b / B = c / C

  8. 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 y* Eye Z-axis D z View-plane

  9. Projection: top-view D z Z-axis x* x P*( x*, y*, 0 ) By similar triangles: x* / x = D / ( D – z ) P( x, y, z ) So: x* = x / ( 1 – z / D )

  10. 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

  11. 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;

  12. 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

  13. 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)

  14. SuperVGA The problem of “standards” for enhanced PC graphics hardware

  15. 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

  16. 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

  17. 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”

  18. 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

  19. 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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