The ‘globe.cpp’ demo
An introduction to the application
of basic raytracing principles
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 table’s edges (side = 670)
Positioning the screen-image
• Graphics display-mode is 259 (= 0x103)
– int
hres = 800,
vres = 600;
– unsigned char
*vram;
(256 colors)
• Move coordinate-origin to screen’s 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
Illumination coefficients
• 8bpp color: allows 64 different intensities
• We apportioned these as follows:
– Iambient = 16.0
– Idiffuse = 24 .0
– Ispecular = 24.0
(= 1/4 of range 64)
(= 3/8 of range 64)
(= 3/8 of range 64)
• We decided proportions by “trial-and-error”
ambient
diffuse
specular
Maximum of 64 distinct intensity-levels
Front view
light-source
y-axis
globe
x-axis
table
Top view
light
globe
x-axis
table
eye
z-axis
Light-beam hits table
light
eye
table
screen-pixel
view-plane
Light-beam hits globe
light
screen-pixel
eye
table
view-plane
shadow
Ambient intensity
• The idea of ‘ambient light’ is that it’s a low
level of background illumination, traveling
in all directions with equal intensity
• We model this component as a constant
Diffuse reradiation
• The idea is that the light rays which aren’t
absorbed when they hit a matte surface
are redirected away from that surface in a
manner which obeys Lambert’s Law:
• Intensity is proportional to area subtended
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)
Area proportional to cosine
surface-normal
ray-direction
pixel-area
vector-angle
A bigger vector-angle would have a smaller cosine
Diffuse reflectivity
Fewer rays are incident with a given surface-area if the surface
is tilted at an angle with respect to the incoming light’s direction
A
Ө A cos Ө
So where there is less light-energy that reaches a surface,
there will be less light-energy for this surface to reradiate
Specular reflection
• The idea is that a surface that’s “shiny” will
reflect light-rays in roughly the same way
as a mirror does, obeying Fermat’s Law
(but also allowing for some “scallering”)
• Angle-of-incidence = Angle-of-reflection
mirror-like surface
angle-of-incidence
angle-of-reflection
“Reflecting” a vector
r + s = 2p
n
surface-normal
vector toward
light-source
s
p
r
vector reflected
off shiny surface
surface
p is projection of s along n
Vector-projection
• From elementary linear algebra:
p = projn( s ) = ( s•n / n•n )n
• So we can compute r from s and n :
r = -s + 2( s•n / n•n )n
“Scattering”
semi-shiny surface
very shiny suface
Use a power of the cosine
• Remember that (for acute angles) we have
0 < cos(θ) < 1
• So powers of cos(θ) 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
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: s•n)
• specular: (proportional to cos5(θ)=(rr•se)5)
In-class experimentation
• The ‘globe.cpp’ demo-program produces a
monochromatic (i.e., gray-scale) image
• A range of the DAC controller’s 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