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 verticesBack 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 )

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

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

Projection: side-view P(x,y,z) P*(x*,y*,0) View-plane Z-axis D z y y* By similar triangles: y* / y = D / (D – z) So y* = y / ( 1 – z / D ) Eye

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

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= 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’