Vector Plane Equation

[pithikoulis]

nice but the audio was a bit too loud

[duderseb]

Oh man thanks a lot! Finally made sense! I've been staring at letters for so long that all I really needed was a simple graphic representation, again, thank you!

[JaySmith91]

Might be worth comparing it to the vector equation of a line.

[aWizardsTail]

Thanks!

[woho000]

nice accent. if you taught my math class, id have a lot easier time paying attention.

[eternaladi1]

how would u go about finding the vector from the origin to a point on the plane in terms of x and y :S

[astrotrain101]

finally a non-american accent.

Thanks

[LAnonHubbard]

I really liked the visualisation and the distinction between position vectors and direction vectors.

[samisicycool]

thnx >>>>>really helped>>>>>>



[Nnoshah]

kooool ^^

waiting for more ^^

[YoshuaRider]

Really helpful, you should do more of these, thanks!

[333329753]

Excellent!!!

[taledarkside]

i was wondering where can i get that file for sketchpad

[jishuenkam]

nicely explained!

[deprmmuaz]

pretty good. keep it up

[sullivanseven]

Your accent is too much

[Brammers451]

It's perfectly understandable.

[TroyaE117]

Bomber :

The plane is defined by a single point on the plane, and two DIRECTION vectors PARALLEL to the plane. Remember that direction vectors have no position, they convey only direction.

They can be thought of as being ON the plane if it helps understand them, but they are not, fundamentally, "on" the plane.

This vector plane equation is not often seen.

More often you will see the classical :

Ax + By + Cz + D = 0

becoming...

x/a + y/b + z/c = 1

[Bomberofdoom]

This is what I understand:

The plane that is created by the 3 points exsits in a 3D world, but the plane itself is a plain, two axis, 2D. The vectors AB and AC are ON the plane itself. They need to touch the surface of the plane, and can be aimed anywhere along the plane, they can't go "above" or "below" the plane (prependicular to the surface of the plane).

Is what I said correct? I fear not. :P

[marsCubed]

@Bomberofdoom

For 3d models, The normal of the plane is useful, ie, the direction (3vector) the plane is facing.

This is necessary for 3d, such as calculating the angle something would bounce if something hit it.

direction = (a-b) cross (c-a)

normal = direction / length (direction)

Use Pythagorean formula for length

Use linear interpolation to get 3 point vectors around an object relative to known vertices of a mesh triangle if required.

For denser meshes you could just use 3 nearby verts

[Bomberofdoom]

Wow dude.... You went way overboard for my question at the time (which I finally understand), but what you've added is quite relevant for me to understand, 'cause I've recently just started studying Linear Algebra and I've worked on programming some 3D models for a Flight Simulator. I'm not quite sure I understand about the last topics you've mentioned, but I understand they relate to Ray Casting (which I don't entirely understand these days :) ).

[TroyaE117]

Remember that the plane is not bounded.

Superbly explained.

[whatismyusername2882]

thank you!!!

[EdgeStormcrow]

Go aussi go

[EdgeStormcrow]

nice :)

[11cardium]

riephen,

Thank you very, very much. My son was asking me for help with this and I was trying my best, but he still didn't get it. One look at this video and Voila! Thank you again for uploading.

[TsaiChengWen]

WO!! This is really clear!

Is this ISB's Mr. Armstrong's video?

(sorry, just checking; I can't decipher what rievphen means)