Wire-frame Modeling

1
Wire-frame Modeling

• An application of Bresenhams 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 objects 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 whos viewing it
• Each vertex is projected onto the screen
• We use Bresenhams algorithm to draw
  line-segments that connect the projections
• A demo program will show this effect

6
The projection
P(x,y,z)
Y-axis
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
  xshiftX y yshiftY

12
animation

• The wire-frame model can be moved (or the
  viewers 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

• VGAs architecture was designed by IBM
• It was targeted for IBMs PC/AT machines
• These used Intels 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
• 800x600480000 pixels (planar memory)
• But every competitor did it their own way!
• So PC graphics software wasnt 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 hardwares capabilities, and
  enabling SuperVGA functionalities
• Reading assignment study vbe3.pdf