decided to keep the scene as simple as possible, but still be
able to convey what needs to get across. These scenes have been
done in Houdini.
I have started with reflections since it
seems to be easier to understand than refractions. We see relfections
in the real world every day. Everytime you look in the mirror,
an exact duplicate of your image is being reflected back at you.
The Law of Reflection states:
A light ray and its reflection make equal angles with the
normal to the reflecting surface.
So that you get this diagram of the rays:
Where theta1 = theta2.
So with this in mind I looked into the code on Malcom's website
and came up with a suitable surface shader that has full reflection.
The first image it in grey tones just to show that the reflection
is working, the second image is the surface shader with the ability
to change the basic surface color. I also put together a short
clip showing the spheres in motion to get an idea of how the shader
looks in an animation.
With a good start on the reflection surface
shader. I turned to refractions. As with reflections, we see refracted
images everyday, mostly through glass. Anytime you look through
a non-opaque object there will be refraction, however slight it
might be. Refractions are much more difficult to calculate since
the Incident Ray is not "bouncing" off the object but
passing through the object and being "bent" at the same
The Law of Refraction, or Snell's Law (named
for Willobrord Snell, who discovered the law in 1621.), states:
The angles that the incident ray and the refracted ray make
with the normal to the surface at the point of refraction are
based on the media through which the light rays are travelling.
With this we get this diagram:
Where n1(sin(theta1) = n2(sin(theta2)
The constants n are the indices of refraction for the corresponding
This is a basic table of a few indices of refraction:
Air at STP
Water at 20 C
By pluging these refractive indices into
our refract() in the shader we are able to control the amount
of refraction in the surface shader.
Taking all of this into consideration.
I set forth to write a shader so that the artist could "swap"
between the reflective or refractive properties. To be able to
do this I relied on a basic IF statement that states: If swap
= 0 then reflect, if not, then refract. I set up the same scene
as above with a texture map on the environment sphere to show
the refractive properties. These are the images that I got using
The refraction in the above image is based on the refractive
index of crown glass, which is 1.52. I did include into the shader
the ability of the artist to enter their own refractive index
for the shader.
With "swap" surface shader in good condition I went
to the "blend".
The idea of blending these wasn't as clear as the "swap".
I decided to base the blend on the idea we explored in the first
project on this website. By using the mix() function along with
the reflect() and refract() function I was able to get some interesting
results. I did find that the "blend" really didn't start
to show until the blend was above 50%, I conclude that this is
from the full reflective property of the reflective surface shader.
The images below and the corresponding movie shows the ability
of the artist to control and "blend" reflection and
Once again, I have based the refractive index on crown glass,
but as in the swap shader, the artist has control which index
One problem that I did run into with Houdini was the use of normalize(I).
For some reason Houdini tends to give better results for refraction
if (I) is not normalized. So in all of the examples above, I have
omitted normalize(I) for the standard (I). This is reflected also
in both of the codes below.
click here for the swap
click here for the