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 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 )

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-axisD 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=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’