Putting It Together
As far as first steps go, this one wasn’t too bad, and it’s laid the groundwork for some great things. You’ve got a working implementation of points and vectors! Those things are going to pop up everywhere. Sadly, you have no ray tracer yet to plug your code into, but you can still have some fun with it.
Try playing with this little program, firing virtual projectiles and seeing how far they go. It’ll let you exercise the vector and point routines you’ve written. Start with the following two data structures:
- A projectile has a position (a point) and a velocity (a vector).
- An environment has gravity (a vector) and wind (a vector).
Then, add a tick(environment, projectile) function which returns a new projectile, representing the given projectile after one unit of time has passed. (The actual units here don’t really matter—maybe they’re seconds, or milliseconds. Whatever. We’ll just call them “ticks.”)
In pseudocode, the tick function should do the following:
| | function tick(env, proj) |
| | position ← proj.position + proj.velocity |
| | velocity ← proj.velocity + env.gravity + env.wind |
| | return projectile(position, velocity) |
| | end function |
Now, initialize a projectile and an environment. Use whatever values you want, but these might get you started:
| | # projectile starts one unit above the origin. |
| | # velocity is normalized to 1 unit/tick. |
| | p ← projectile(point(0, 1, 0), normalize(vector(1, 1, 0))) |
| | |
| | # gravity -0.1 unit/tick, and wind is -0.01 unit/tick. |
| | e ← environment(vector(0, -0.1, 0), vector(-0.01, 0, 0)) |
Then, run tick repeatedly until the projectile’s y position is less than or equal to 0. Report the projectile’s position after each tick, and the number of ticks it takes for the projectile to hit the ground. Try multiplying the projectile’s initial velocity by larger and larger numbers to see how much farther the projectile goes!
Once you’ve had a chance to play with this virtual cannon a bit, move to the next chapter. You’re going to implement the visual side of your ray tracer, the canvas onto which everything will eventually be drawn.