The globe.cpp demo

1
The globe.cpp demo

• An introduction to the application of basic
  raytracing principles

2
Setting the scene

• Our example depicts a sphere and a plane
• A single monochromatic point light-source
• Objects are
• Globe a sphere of radius 100, center(0,0,0)
• Table a plane tangent to sphere at (0,-100,0)
• Light a point source located at (600,800,-800)
• Eye a viewer who is positioned at (0,0,-1800)
• Poly a square, for tables edges (side 670)

3
Positioning the screen-image

• Graphics display-mode is 259 ( 0x103)
• int hres 800, vres 600
• unsigned char vram (256 colors)
• Move coordinate-origin to screens center
• float transX hres/2, transY vres/2
• Magnify image by 25 (i.e., divide by 0.8)
• float scaleX 0.8, transY -0.8
• scale-factor for Y negative flips up/down

4
Illumination coefficients

• 8bpp color allows 64 different intensities
• We apportioned these as follows
• Iambient 16.0 ( 1/4 of range 64)
• Idiffuse 24 .0 ( 3/8 of range 64)
• Ispecular 24.0 ( 3/8 of range 64)
• We decided proportions by trial-and-error

ambient
diffuse
specular
Maximum of 64 distinct intensity-levels
5
Front view
light-source
y-axis
globe
x-axis
table
6
Top view
light
globe
x-axis
table
eye
z-axis
7
Light-beam hits table
light
eye
table
screen-pixel
view-plane
8
Light-beam hits globe
light
screen-pixel
eye
table
view-plane
shadow
9
Ambient intensity

• The idea of ambient light is that its a low
  level of background illumination, traveling in
  all directions with equal intensity
• We model this component as a constant

10
Diffuse reradiation

• The idea is that the light rays which arent
  absorbed when they hit a matte surface are
  redirected away from that surface in a manner
  which obeys Lamberts Law
• Intensity is proportional to area subtended

11
Illustration of Law
this angle is smaller (so less energy reaches
pixel)
light-energy radiates outward in all directions
pixels of equal area
this angle is larger (so more energy reaches
pixel)
12
Area proportional to cosine
surface-normal
ray-direction
pixel-area
vector-angle
A bigger vector-angle would have a smaller cosine
13
Diffuse reflectivity
Fewer rays are incident with a given surface-area
if the surface is tilted at an angle with respect
to the incoming lights direction
A
A cos ?
?
So where there is less light-energy that reaches
a surface, there will be less light-energy for
this surface to reradiate
14
Specular reflection

• The idea is that a surface thats shiny will
  reflect light-rays in roughly the same way as a
  mirror does, obeying Fermats Law (but also
  allowing for some scallering)
• Angle-of-incidence Angle-of-reflection

mirror-like surface
angle-of-incidence
angle-of-reflection
15
Reflecting a vector
r s 2p
n
surface-normal
vector toward light-source
vector reflected off shiny surface
s
r
p
surface
p is projection of s along n
16
Vector-projection

• From elementary linear algebra
• p projn( s ) ( sn / nn )n
• So we can compute r from s and n r -s
  2( sn / nn )n

17
Scattering
semi-shiny surface
very shiny suface
18
Use a power of the cosine

• Remember that (for acute angles) we have 0 lt
  cos(?) lt 1
• So powers of cos(?) are between 0 and 1
• But higher powers have sharper graphs!
• We can model the shinyness of surfaces by the
  power of the cosine we choose the higher the
  power, the shininer the surface

19
Summing up

• Intensity of achromatic light at a pixel is a sum
  of three illumination components intensity
  ambient diffuse specular
• ambient (this will just be a constant)
• diffuse (proportional to dot-product sn)
• specular (proportional to cos5(?)(rrse)5)

20
In-class experimentation

• The globe.cpp demo-program produces a
  monochromatic (i.e., gray-scale) image
• A range of the DAC controllers 256 color
  registers is programmed for 64 different
  intensities of white illunimation
• But we can also create varying intensities of
  some other RGB color-combinations
• Exercise Add color to the globe and table