Angle between two vectors
in [Matlab]
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From: Benjamin McCrite on 23 Feb 2010 19:41 Greg Heath <heath(a)alumni.brown.edu> wrote in message <1184052626.324470.175540(a)n2g2000hse.googlegroups.com>... > On Jul 9, 5:16 pm, "y Mehta" <mehtayogesh(a)gmail.(DOT).com> wrote: > > How do I find the angle between two unit vectors a and b? I know I > > can find cosine theta by the following formula: > > > > theta = acos(dot(a,b)); > > > > Invalid since it is possible that abs(dot(a,b)) > 1. > > costheta = dot(a,b)/(norm(a)*norm(b)); > theta = acos(costheta); > > will give you the anser in the interval [0,pi]. > > > However, how do I know whether the angle is > > actually theta, or -theta or pi-theta or pi+theta?? > > Angles between vectors only lie in the interval [0,pi]. > > > Notice that the vectors are in three dimension (3d). > > Dimensionality of the original space is irrelevant. As long as > norm(a)*norm(b) > 0, the vectors uniquely define a 2-d space when > dot(a,b) ~= 0 and a unique 1-d space otherwise. > > Hope this helps. > > Greg > Can you tell me what norm(),cross() and dot() do?
From: Nathan on 23 Feb 2010 19:46 On Feb 23, 4:41 pm, "Benjamin McCrite" <dragonmast...(a)hotmail.com> wrote: > Greg Heath <he...(a)alumni.brown.edu> wrote in message <1184052626.324470.175...(a)n2g2000hse.googlegroups.com>... > > > > > On Jul 9, 5:16 pm, "y Mehta" <mehtayogesh(a)gmail.(DOT).com> wrote: > > > How do I find the angle between two unit vectors a and b? I know I > > > can find cosine theta by the following formula: > > > > theta = acos(dot(a,b)); > > > Invalid since it is possible that abs(dot(a,b)) > 1. > > > costheta = dot(a,b)/(norm(a)*norm(b)); > > theta = acos(costheta); > > > will give you the anser in the interval [0,pi]. > > > > However, how do I know whether the angle is > > > actually theta, or -theta or pi-theta or pi+theta?? > > > Angles between vectors only lie in the interval [0,pi]. > > > > Notice that the vectors are in three dimension (3d). > > > Dimensionality of the original space is irrelevant. As long as > > norm(a)*norm(b) > 0, the vectors uniquely define a 2-d space when > > dot(a,b) ~= 0 and a unique 1-d space otherwise. > > > Hope this helps. > > > Greg > > Can you tell me what norm(),cross() and dot() do? Can you read the documentation? Norm: The norm of a matrix is a scalar that gives some measure of the magnitude of the elements of the matrix. The norm function calculates several different types of matrix norms: n = norm(A) returns the largest singular value of A, max(svd(A)). n = norm(A,p) returns a different kind of norm, depending on the value of p. .... Cross: C = cross(A,B) returns the cross product of the vectors A and B. That is, C = A x B. A and B must be 3-element vectors. If A and B are multidimensional arrays, cross returns the cross product of A and B along the first dimension of length 3. C = cross(A,B,dim) where A and B are multidimensional arrays, returns the cross product of A and B in dimension dim. A and B must have the same size, and both size(A,dim) and size(B,dim) must be 3. .... Dot: C = dot(A,B) returns the scalar product of the vectors A and B. A and B must be vectors of the same length. When A and B are both column vectors, dot(A,B) is the same as A'*B. For multidimensional arrays A and B, dot returns the scalar product along the first non-singleton dimension of A and B. A and B must have the same size. C = dot(A,B,dim) returns the scalar product of A and B in the dimension dim. .... Before asking what functions do, try to read and understand the documentation for them. To view the documentation, you can type: doc FUNCTIONNAME Where, in this case, FUNCTIONNAME is either cross, dot, or norm -Nathan
From: Jorian on 7 Mar 2010 05:53 "salih tuna" <salihtuna(a)gmail.com> wrote in message <fjlrpl$gii$1(a)fred.mathworks.com>... > Hi, > thanks a lot for your reply. yes they are in 2d, sorry i > forgot to mention. > i tried to apply the formula but i am getting wrong result. > for example i want to calculate the angle between a = [1 1] > and b = [0 -1] which is 225 degrees. with this formulae i > got 243.4. i couldn't see where i am doing the mistake. > thanks a lot in advance > salih > > http://www.musicpa.com > "Roger Stafford" <ellieandrogerxyzzy(a)mindspring.com.invalid> > wrote in message <fjk0tg$jli$1(a)fred.mathworks.com>... > > "salih tuna" <salihtuna(a)gmail.com> wrote in message > <fjj9nj$fia > > $1(a)fred.mathworks.com>... > > > hello, > > > how can i calculate the angles so that they are in the > range 0-360 degrees? > > > thanks > > > salih > > > > > > "y Mehta" <mehtayogesh(a)gmail.(DOT).com> wrote in message > > > <ef5ce9c.-1(a)webcrossing.raydaftYaTP>... > > > > How do I find the angle between two unit vectors a and > b? I know I > > > > can find cosine theta by the following formula: > > > > > > > > theta = acos(dot(a,b)); > > > > > > > > However, how do I know whether the angle is actually > theta, or -theta > > > > or pi-theta or pi+theta?? > > > > > > > > Notice that the vectors are in three dimension (3d). > > > > > > > > Thanks, > > > > -YM > > -------- > > Y Mehta's question involved angles between vectors in > three-dimensional > > space. I can think of no reasonable definition for a > canonical angle between > > such vectors which ranges from 0 to 360 degrees (0 to 2*pi > radians.) > > > > However, if you are in two-dimensional space, then you > can speak of the > > non-negative angle measured counterclockwise from vector a > to vector b, > > and this would give the range you have requested. If a = > [x1,y1] and b = > > [x2,y2], then such an angle is given in matlab by: > > > > angle = mod(atan2(y2-y1,x2-x1),2*pi); % Range: 0 to 2*pi > radians > > > > (Multiply this answer by 180/pi to get degrees.) > > > > Roger Stafford Thanks! Best regards, Jorian Seokaner! http://www.mathworks.com/matlabcentral/newsreader/author/126323 >
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