Homework 1

Homework 1, due Wednesday, Feb 3

Send your answer by email to the grader. Also, please note that I'm asking for something slightly different than what I specified in class.

Write a ray/sphere intersection routine which has the following interface:

int raySphere(double ray[6], double sphere[4], double t[2]);

Your routine should take as arguments:

An array ray[6] which specifies v_x, v_y, v_z, w_x, w_y, w_z
An array sphere[4] which specifies c_x, c_y, c_z, R
An array t[2] in which to place the values for t of any intersections. If there are two intersections, make sure that t[0] < t[1].

Your routine should return a number between zero and two, indicating the number of times the ray intersects the sphere.

Remember that you need to convert the equation:

(w_xt + (v_x-c_x))² + (w_yt + (v_y-c_y))² + (w_zt + (v_z-c_z))² - R² = 0

into something of the form At² + Bt + C = 0, just as we did in class, and then solve using the quadratic equation t = (-B ± sqrt(B² - 4AC)) / 2A to get the two values of t.

If the value under the square root is negative, that means the ray has missed the sphere, in which case your routine should return a value of zero.