- Workshop for students interested in applying to REUs
- Today (January 26)
- 5:30 PM
- South 328
- Prof. Macula
- What would be a good mathematical representation of a ray?
- Need to calculate what ray intersects, what points lie on it
- Vector (V) + Point (P) + multiples
- R = P + tV
- To figure out if ray intersects object, O
- Solve R = O for t
- Equation for a line (relevant in that above ray equation defines a line, but not something that needs to be described separately from that equation)
- Vectors vs points
- Point is a specific place in space
- Vector is a distance and direction
- So vectors can define points by reference to a known origin
- The “difference” between 2 points can also be described as a vector
- And thus it makes sense to talk about adding a vector to a
point to yield another point
- Notice that computer graphics people think about coordinate systems in 3-space differently from everyone else: Y axis points up and Z out
- Need to calculate what ray intersects, what points lie on it
- Matlab representation?
- P, V = 3-by-1 matrix/vector
- Point on ray at t = P + t * V
>> P = [ 0 1 0 ]; >> V = [ 0 -1 -1 ]; >> P + 2 * V ans = 0 -1 -2 >> ray = struct( 'origin', P, 'direction', V ) ray = origin: [0 1 0] direction: [0 -1 -1] >> ray.direction ans = 0 -1 -1 >> ray.origin + ray.direction * 2 ans = 0 -1 -2
- Simple ray-object intersections
- Start designing and writing a first ray tracer