PA 2 Written: Eclipse

Due: Thursday 24 September 2015 (11:59pm)

This written portion of the assignment is to be done alone.

A group of astronauts has just left on their journey to Mars when ground control informs them that there will be a lunar eclipse back home. The astronauts are asked to take a picture of this rare event from their location in space and report back. The situation at the moment they take the picture is as follows:

Note that we use Earth-centered coordinates that match the ones for the sphere in the mesh assignment. So 1 Earth radius is the unit of measure.

• The sun is positioned 23,679 units away from the Earth (from the center, if you must ask), exactly above the point at latitude and longitude zero, at (0, 0, 23679).
• The moon is positioned at (0, 1, -10) units away from the center of the earth. It has radius 0.15.
• The spacecraft is at (15, 0, 20) and its camera is looking in the direction (-3/5, 0, -4/5) (which is the ray through the very center of the image)

Q1. In the astronauts' photo,

1. What (x, y, z) point on the Earth's surface appears exactly at the center of the image? Check your work by showing that the point is both on the ray and on the surface of the Earth (plug the point into the ray and sphere equations). See Sec. 4.4.1 of the textbook.
2. Is the point (0, .91, -9.88) on the moon in the shadow of the Earth? You can approximate the direction from the point to the sun as (0, 0, 1).

Q2. For the point on the Earth at the center of the image,

1. Let's assume for this question that colors only have one component (reflectance) instead of three RGB components. If the intensity of the sun is 100,000,000 units, and the Earth at that point has a diffuse reflectance 0.5, specular reflectance 0.9, and exponent 100, then what is the total light reflected from that point toward the camera (not taking into account ambient light or exposure)? Again, you can approximate the light direction as (0, 0, 1).

Q3. Write an xml scene file that models the above scenario.

1. The spaceship's camera is a perspective camera with the following properties: up-direction is (0, 1, 0), projectionDistance is 25 units, viewWidth and viewHeight are 10 units (Attention: Changed on 2015/9/19). The resolution of the camera is 2048 x 2048 pixels. The exposure is 3.3.
2. The Earth has diffuse color (0.5, 0.5, 0.5), specular color (0.9, 0.9, 0.9), and exponent 100. The moon has diffuse color (0.8, 0.8, 0.8). specular color (1, 1, 0). and exponent 50.
3. You can check your work once the coding assignment is finished by ray tracing this xml file. Both the Earth and moon should be visible.

What to Submit

Submit a pdf containing your solution to Q1 and Q2 together and an xml file containing your solution to Q3 to CMS.

Upload here (CMS)