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stafu
Australia1196 Posts
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DeathByMonkeys
United States742 Posts
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Tex
United States126 Posts
Proooojections. By the looks of it, yeah, H is the projection of C onto the plane that is shared by A, B, and H. | ||
DeathByMonkeys
United States742 Posts
Then you use the same method for finding the distance from A to B. From there you have everything you need, and can simply use the Scalar Projection formula: comp of BC onto AB = ((A vector) (dot product) (B vector)) / (magnitude of A vector) | ||
stafu
Australia1196 Posts
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Antimage
Canada1293 Posts
Excuse me for being vague, I'm an accounting student and haven't done real math for 3+ years =/ | ||
stafu
Australia1196 Posts
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MER
Bulgaria125 Posts
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Tex
United States126 Posts
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EtherealDeath
United States8366 Posts
A most trivial case is where A = (0,0,0), B = (1,0,0), C = (0.5,1,1). There can be no explicit solution for H in terms of A,B,C since in this case there is no H closest to C, because we can arbitrarily change the angle between the xy axis and the plane to have the plane approach C. Could be full of shit though, at first I thought it was a trivial projection problem :/ back to foods. | ||
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Chill
Calgary25969 Posts
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DeathByMonkeys
United States742 Posts
On April 21 2010 05:59 stafu wrote: Thanks DeathByMonkeys, now to see if I can get my head around this hehe. Life saver. Actually I messed up. You don't need to know the distance between AB and BC, just the vectors. So disregard the distance formula part. AB will simply be = (Bx - Ax, By - Ay, Bz - Az) BC will simply be = (Cx - Bx, Cy - By, Cz - Bz) Now you can use the projection formula I provided earlier where you project BC onto AB. So... comp of BC onto AB = ((AB vector) (dot product) (BC vector)) / (magnitude of AB vector) This resultant scalar is the distance from B to H. | ||
Oracle
Canada411 Posts
On April 21 2010 06:08 Chill wrote: Just using common sense I don't see any reason C can't be 0.00000000000000000000000001 units away from H. Seems like a retarded question. The "Shortest distance to point C" statements implies that H and C are perpendicular. C can be epsilon units away from H but that doesn't mean anything. | ||
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]343[
United States10328 Posts
On April 21 2010 06:08 Chill wrote: Just using common sense I don't see any reason C can't be 0.00000000000000000000000001 units away from H. Seems like a retarded question. they're asking what the projection of C onto AB is, for general A, B, C which is ... dot product specifically, the length of (C-A) projected onto (B-A) is [(C-A) . (B-A)] so we multiply this by unit vector in direction of (B-A) and then add A | ||
EtherealDeath
United States8366 Posts
On April 21 2010 06:17 ]343[ wrote: Show nested quote + On April 21 2010 06:08 Chill wrote: Just using common sense I don't see any reason C can't be 0.00000000000000000000000001 units away from H. Seems like a retarded question. they're asking what the projection of C onto AB is, for general A, B, C which is ... dot product specifically, the length of (C-A) projected onto (B-A) is [(C-A) . (B-A)] so we multiply this by unit vector in direction of (B-A) and then add A That's not what they ask for. If you pick H along the projection of C onto AB, then A,B,C,H will be on the same plane, which they mentioned C is NOT on the same plane as A,B,H. | ||
Severedevil
United States4832 Posts
The unknown point H is located at the shortest distance from Point C. The shortest distance from point C to what? If it's the shortest distance from point C to line AB, this is trivial as a lot of people have pointed out. Project C onto AB and you have H. (As has also been pointed out, all four points would be coplanar.) If it's the shortest distance from point C to the plane containing AB, well... that's a problem, because the plane isn't specified in the problem. | ||
QuickStriker
United States3694 Posts
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Chill
Calgary25969 Posts
On April 21 2010 06:17 ]343[ wrote: Show nested quote + On April 21 2010 06:08 Chill wrote: Just using common sense I don't see any reason C can't be 0.00000000000000000000000001 units away from H. Seems like a retarded question. they're asking what the projection of C onto AB is, for general A, B, C which is ... dot product specifically, the length of (C-A) projected onto (B-A) is [(C-A) . (B-A)] so we multiply this by unit vector in direction of (B-A) and then add A I guess I don't understand but I'd like to have it explained for my own sake. ABH is a triangle (or line) in a plane. C is not in that plane but is the closest distance to H possible. To me, the closest distance possible is like right beside it but not in the other plane so it would be 0.00000000000000000_1 units perpendicular from the plane ABC lies in. I feel like there's a line missing or I'm misunderstanding the question entirely. | ||
Kentor
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United States5784 Posts
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stafu
Australia1196 Posts
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