Reflectance
I got the idea for this exercise from a conversation with Dr. Michael McCool, University of Waterloo.
Cut some ping pong balls in half. You can use a knife, a saw, an exacto blade; be very careful. Then cut an opening in each hemi-ping-pong ball for a light to shine through. I used a hole-punch for mine. A beam of light will shine at different angles toward the center of the sphere, passing somewhere through the opening.
Collect samples of at least 4 different surface materials. Possible choices include: white paper, red paper, blue paper, shiny tin foil, crumpled tin foil, glass, brushed aluminum (an anisotropic reflector), satin, high-gloss paint, flat paint. Make the sample black everywhere except for a small disk about 2mm in diameter. You can use black paint (flat black like tempera, not shiny like enamel) or black construction paper or black felt to do the job. For mine, I punched a hole in sticky-back black felt and laid it over the sample. You can get some of this felt from the Vis Lab. I had trouble making the sample be up at the same level as the felt; at low angles of the light beam, the felt casts a shadow on my sample, which is imperfect.
Glue each ping-pong hemisphere onto the sample so that the unobstructed disk of material is visible at the center. This is your target. Shine a bright penlight or laser light at the center and you will see the distribution of reflected light on the ping-pong ball.
If you have access to a digital camera, make a sequence of images showing the reflectance distributions for the different surfaces. For each surface, shine the light at several different angles. For shiny surfaces, you should see a bright region on the surface of the ping-pong ball. Put the images/animations on your Web page.
Bring your samples to class.
For at least 3 of the samples you collected, create an Inventor file that approximates the appearance of the ping-pong ball over the sample.
Here's an example I made to illustrate, using the Inventor file format. It uses a grid texture
for the base plane and a transparent cut-out texture
for the sphere; grab a copy them in order to make the scene
display properly.
Put images on your Web page and link them to VRML files (converted from iv).
Compute points on a curve in (phi, theta)-space, using a parameter s in [0, 2pi]. The curve lies on a sphere.
phi(s) = a * cos(s) + phi0 theta(s) = a * sin(s) + theta0
Choose your phi0 between 0.5 and 1.5 . Choose your a between 0.0 and phi0 . Choose your theta0 between 1.0 and 4.0 .
Print out at least 15 pairs (phi, theta). Plot them on your styrofoam sphere using colored pushpins. If you have access to a digital camera, take a picture of the sphere and put it your Web page.
Bring the sphere to class.