Lol! Great stuff! Wow, that movie was RIDICULOUS stupid funny!!! :)
So glad this made sense and if you or anyone else has any questions, please feel free to shout out! Smiles, Cara :) --- View my Online Portfolio at: http://www.onemodelplace.com/CaraQuinn Follow me on Twitter! https://twitter.com/ModelCara On May 3, 2013, at 2:45 PM, Raul A. Gallegos <[email protected]> wrote: Hey Kara, this is super. I can actually follow this without getting too lost. It makes me think of what some games, like Lone Wolf may go through when David programmed it. However the first thing i thought of when I read the message from you was the following. What's your vector Victor. This is Captain Over over. Roger Roger, huh? What? Take care. -- Raul A. Gallegos I didn't slap you, I simply high fived your face. - Sheldon Cooper Twitter and Facebook user ID: rau47 On 5/3/2013 11:28 AM, Cara Quinn wrote: > Hi all, > > Well I'm done responding to list craziness and since you get what you focus > on, I'm focusing on cool game mechanics! :) > > I'd like to take my earlier notes on vectors and such, a step further to a > process called projection. > > When you project a vector on to another vector, you're simply adding the > components of one vector to the components of another. As in: > > 0,2,0 + 1,0,0 = 1,2,0 > > So this process is just adding the x, y, and z components of each vector > separately as in: > > 0 + 1 = 1 > > 2 + 0 = 2 > > 0 + 0 = 0 > > So this is great but why would we want to do this? > > Let's think of the first vector above (0,2,0) as perhaps a boat on an ocean. > This boat is traveling north in our game world, at 2 units per some amount of > time. > > Let's think of the second vector as a wind blowing toward the east at 1 unit > per some amount of time. You can see where I'm going with this. ;) > > If we apply the wind to the boat's motion, we end up with the boat traveling > to the coordinates 1,2,0 at the end of our given amount of time. > > If the boat captain continues to steer the boat due north at the same speed > (0,2,0) the wind will still be blowing due east (1,0,0) and thus again blow > the boat to the ending coordinates of (1,2,0) again as the next unit of time > passes. > > We can actually use projection to simulate various forces acting on entities > in our game world; wind, thrust, gravity, drag, friction. etc. > > Let's look at the above projection in a different way now. Instead of the > boat captain steering the boat against the wind, perhaps the captain is > asleep and the boat is adrift. Don't worry, we won't let him go very far. :) > > So we have our boat starting out moving north at (0,2,0). > > We have our wind steadily blowing at (1,0,0). > > Project the wind on to the boat's motion and you end up with the boat at > (1,2,0) > > What happens if the boat simply keeps moving in its new direction? > > 1,2,0 + 1,0,0 = 2,2,0 > > Our boat is now moving northeast. -And the wind keeps blowing. > > 2,2,0 + 1,0,0 = 3,2,0 > > Our boat is now traveling east-northeast. > > This looks right at a glance, but let's look at what's really happening here. > If you notice, our boat is actually speeding up and our calculations are off. > > Even though the above looks like physics, we haven't really taken any physics > into account here. -And, rather than go into a lot of physics in this note, > let's stay with a simple aspect of this boat's travel. > > In an earlier note I gave the example of a runner continuously accelerating > and we illustrated this with an ever-increasing vector length. Well if you > notice, our boat's vector of travel keeps getting longer as the wind keeps > blowing. If we kept projecting the wind vector on to the boat's travel > vector, the x coordinate would just keep in creasing and increasing and > increasing until our boat would basically be traveling faster than any other > boat I know of! :) -And it still wouldn't stop there! :) > > Obviously a wind of only 1 unit over time shouldn't be causing another object > to go faster and faster and faster. > > So what have we missed? We haven't been taking the length or magnitude of our > vector into account. > > So how does this help us? > > We know that our boat originally traveled at 2 units over time. So our boat;s > vector of travel has a magnitude of 2 units. When we project the wind vector > on to it, we are adding magnitude to the vector. > > Remember we ended up with 1,2,0 > > So rather than leave it there, let's check the magnitude of this vector. > > We do this with the Pythagoras theorem. > > > > 1 * 1 is 1 > > 2 * 2 is 4 > > 0 * 0 is 0 > > 1 + 4 + 0 is 5 > > the square root of 5 is 2.23606797749979 > > 2.24 for our uses… > > So our boat is now traveling faster than it's usual 2 units. As I said, we > can take quite a lot into account here but for now let's just go with the > idea that we really only want our boat ever traveling at 2 units over a given > time. > > We can magnify our current vector so its length (the boat's velocity) is > still 2 units but traveling in its new direction. > > Remember, we do this by dividing our vector by it's current length and then > multiplying by the length we want it to have. > > So this would look like: > > 1 / 2.24 * 2 = 0.8928 > > 2 / 2.24 * 2 = 1.7857 > > 0 / 2.24 * 2 = 0 > > So the vector of travel we end up with is: > > 0.8928,1.7857,0 > > > Okay, so it's just not as pretty as our earlier vectors but the computer > doesn't care. it will still be able to work with it just as effectively in a > gaming situation. > > So this is actually the new direction and speed of our boat as the wind blows > it. > > NOw we can do more with physics to take into account the energy being > imparted to the boat from the wind as well as the drag on the boat from the > sea and such, but for now this should be a fun start!… > > Vector projection is a really simple, useful and pretty interesting process > to play with with your game entities. > > Hope this makes sense and is something y'all may be interested in… :) > > Have a great weekend and talk with y'all soon!… > > Smiles, > > Cara :) > --- > View my Online Portfolio at: > > http://www.onemodelplace.com/CaraQuinn > > Follow me on Twitter! > > https://twitter.com/ModelCara > > > --- > Gamers mailing list __ [email protected] > If you want to leave the list, send E-mail to [email protected]. > You can make changes or update your subscription via the web, at > http://audyssey.org/mailman/listinfo/gamers_audyssey.org. > All messages are archived and can be searched and read at > http://www.mail-archive.com/[email protected]. > If you have any questions or concerns regarding the management of the list, > please send E-mail to [email protected]. > --- Gamers mailing list __ [email protected] If you want to leave the list, send E-mail to [email protected]. You can make changes or update your subscription via the web, at http://audyssey.org/mailman/listinfo/gamers_audyssey.org. All messages are archived and can be searched and read at http://www.mail-archive.com/[email protected]. If you have any questions or concerns regarding the management of the list, please send E-mail to [email protected]. --- Gamers mailing list __ [email protected] If you want to leave the list, send E-mail to [email protected]. You can make changes or update your subscription via the web, at http://audyssey.org/mailman/listinfo/gamers_audyssey.org. All messages are archived and can be searched and read at http://www.mail-archive.com/[email protected]. If you have any questions or concerns regarding the management of the list, please send E-mail to [email protected].
