Which side of the plane
in [Matlab]
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From: Tiago on 23 Jul 2010 12:23 Hello all, I have a data that have 4 parameters. A matrix with 4 columns. In each line of the matrix, I desing a point with the four numerical feats. So the points would be in a 4-D. After this, I want to design several planes that divide these points in two groups. The first plane would be developed by the four firsts point. The second plane by the first, second, third and fifth points and so on. The third plane by first, second, third and sixth. And so on... But I don't know if that's is true. A plane in 4-D can be structured by 4 non-collinear points ? And I don't know how to discover on which side of the plane the points are. I was thinking to projects them in one axe of that plane. If I know, for example, that equation plane is X=y+z+w, I'd project all points in X axe and then check if they come from above or below by seeing their X values. How can I project to discover this? Thank you very much.
From: Walter Roberson on 23 Jul 2010 15:11 Tiago wrote: > I have a data that have 4 parameters. A matrix with 4 columns. In each > line of the matrix, I desing a point with the four numerical feats. So > the points would be in a 4-D. After this, I want to design several > planes that divide these points in two groups. > > The first plane would be developed by the four firsts point. The second > plane by the first, second, third and fifth points > and so on. The third plane by first, second, third and sixth. And so on... > > But I don't know if that's is true. A plane in 4-D can be structured by > 4 non-collinear points ? Yes, an N-dimensional plane can be defined by N non-collinear points, each of which have N or more coordinates. > And I don't know how to discover on which side of the plane the points > are. I was thinking to projects them in one axe of that plane. If I > know, for example, that equation plane is X=y+z+w, I'd project all > points in X axe and then check if they come from above or below by > seeing their X values. > How can I project to discover this? I suggest you investigate normals and dot products and think about what information you might be able to derive from the cosine interpretation of dot products.
From: Matt J on 23 Jul 2010 16:06 "Tiago " <tmnascimento(a)spam.la> wrote in message <i2cfle$n7j$1(a)fred.mathworks.com>... > But I don't know if that's is true. A plane in 4-D can be structured by 4 non-collinear points ? > > And I don't know how to discover on which side of the plane the points are. I was thinking to projects them in one axe of that plane. If I know, for example, that equation plane is X=y+z+w, I'd project all points in X axe and then check if they come from above or below by seeing their X values. ======= Suppose the equation of a (hyper)plane with normal vector N is dot(N,x)=d Then x1 and x2 are on the same side of the plane if and only if dot(N,x1)-d has the same sign as dot(N,x2)-d.
From: Tiago on 10 Aug 2010 09:01 Thanks for all your helping, but I'm still confusing. In this (hyper)plane I have 4-D dots. P1=[x1;y1;z1;w1], P2=[X2;Y2;Z2;W2] and so on with P3 and P4. I can extract the vectors with a simple substraction. P1P2=P2-P1; P1P3=P3-P1 and P1P4=P4-P1; OK ? But this normal vector N is given by cross of the three vectors ? In matlab function "cross(A,B)" I can't get this N because cross only do in maximum 3-D. And with the function "dot" I have the same problem. >d=dot(N,x) > Then x1 and x2 are on the same side of the plane if and only if > dot(N,x1)-d has the same sign as dot(N,x2)-d. Another point is that I don't know the side of any dot. I didn't see how these equations above help me. Best Regards, Tiago
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