david@5of4.com

I have four points [x,y] on a plane and I need to be able to determine if they are in a line at any angle. I 

know that they are in line if all of the x values are equal, or if all of the y values are equal. I do not know 

what math to use to check otherwise. Is this a vector problem? trig?

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I have four points [x,y] on a plane and I need to be able to determine if they are in a line at any angle. I 
know that they are in line if all of the x values are equal, or if all of the y values are equal. I do not know 
what math to use to check otherwise. Is this a vector problem? trig?

Need personalized email and website? Look no further. It's easy
with Doteasy $0 Web Hosting! Learn more at www.doteasy.com


math-question

One way you could do this is calculate the normal to the plane 

that is created by three points. Pick one point, this will be your

origin. Now pick two points and draw a line from them to your origin, 

should form a plane. Now take your fourth point and create 

a vector from the origin, call this the vector x. Now 

you can calcualte the angle between the plane and x, 

if it is zero then you know all points are in line on the axis 

> I have four points [x,y] on a plane and I need to be able to 

> determine if they are in a line at any angle. I 

> know that they are in line if all of the x values are equal, or if 

> all of the y values are equal. I do not know 

> what math to use to check otherwise. Is this a vector problem? trig?

> Need personalized email and website? Look no further. It's easy

> with Doteasy $0 Web Hosting! Learn more at www.doteasy.com

One way you could do this is calculate the normal to the plane 
that is created by three points. Pick one point, this will be your
origin. Now pick two points and draw a line from them to your origin, 
this 
should form a plane. Now take your fourth point and create 
a vector from the origin, call this the vector x. Now 
you can calcualte the angle between the plane and x, 
if it is zero then you know all points are in line on the axis 
the plane resides on.

----- Original Message -----
From: David Morneau 
Date: Wednesday, June 20, 2007 6:46 pm
Subject: [maxmsp] math question

> Hi List
>
> I have four points [x,y] on a plane and I need to be able to 
> determine if they are in a line at any angle. I 
> know that they are in line if all of the x values are equal, or if 
> all of the y values are equal. I do not know 
> what math to use to check otherwise. Is this a vector problem? trig?
>
> Any hints are appreciated.
>
> Thanks
> David
>
>
>
> Need personalized email and website? Look no further. It's easy
> with Doteasy $0 Web Hosting! Learn more at www.doteasy.com
>


I may have been a bit vague in my explanation. Take a look 

http://www.geocities.com/SiliconValley/2151/math3d.html

Once you have calculated the normal to the plane, I think you 

can take the dot product of the normal with your remaining 

point(vector), that should give you the angle between the two.

> One way you could do this is calculate the normal to the plane 

> that is created by three points. Pick one point, this will be your

> origin. Now pick two points and draw a line from them to your 

> should form a plane. Now take your fourth point and create 

> a vector from the origin, call this the vector x. Now 

> you can calcualte the angle between the plane and x, 

> if it is zero then you know all points are in line on the axis 

> > I have four points [x,y] on a plane and I need to be able to 

> > determine if they are in a line at any angle. I 

> > know that they are in line if all of the x values are equal, or 

> > all of the y values are equal. I do not know 

> > what math to use to check otherwise. Is this a vector problem? trig?

> > Need personalized email and website? Look no further. It's easy

> > with Doteasy $0 Web Hosting! Learn more at www.doteasy.com

I may have been a bit vague in my explanation. Take a look 
at this... http://www.geocities.com/SiliconValley/2151/math3d.html
Once you have calculated the normal to the plane, I think you 
can take the dot product of the normal with your remaining 
point(vector), that should give you the angle between the two.

----- Original Message -----
From: apalomba@austin.rr.com
Date: Wednesday, June 20, 2007 6:57 pm
Subject: Re: [maxmsp] math question
To: maxmsp@cycling74.com, david@5of4.com

> One way you could do this is calculate the normal to the plane 
> that is created by three points. Pick one point, this will be your
> origin. Now pick two points and draw a line from them to your 
> origin, 
> this 
> should form a plane. Now take your fourth point and create 
> a vector from the origin, call this the vector x. Now 
> you can calcualte the angle between the plane and x, 
> if it is zero then you know all points are in line on the axis 
> the plane resides on.
>
>
>
>
> Anthony
>
>
> ----- Original Message -----
> From: David Morneau 
> Date: Wednesday, June 20, 2007 6:46 pm
> Subject: [maxmsp] math question
>
> > Hi List
> >
> > I have four points [x,y] on a plane and I need to be able to 
> > determine if they are in a line at any angle. I 
> > know that they are in line if all of the x values are equal, or 
> if 
> > all of the y values are equal. I do not know 
> > what math to use to check otherwise. Is this a vector problem? trig?
> >
> > Any hints are appreciated.
> >
> > Thanks
> > David
> >
> >
> >
> > Need personalized email and website? Look no further. It's easy
> > with Doteasy $0 Web Hosting! Learn more at www.doteasy.com
> >
>


if these are the same for all points, then they are colinear.

On 6/20/07, apalomba@austin.rr.com wrote:

> I may have been a bit vague in my explanation. Take a look

> Once you have calculated the normal to the plane, I think you

> can take the dot product of the normal with your remaining

> point(vector), that should give you the angle between the two.

> To: maxmsp@cycling74.com, david@5of4.com

> > One way you could do this is calculate the normal to the plane

> > that is created by three points. Pick one point, this will be your

> > origin. Now pick two points and draw a line from them to your

> > should form a plane. Now take your fourth point and create

> > a vector from the origin, call this the vector x. Now

> > you can calcualte the angle between the plane and x,

> > if it is zero then you know all points are in line on the axis

> > Date: Wednesday, June 20, 2007 6:46 pm

> > > I have four points [x,y] on a plane and I need to be able to

> > > determine if they are in a line at any angle. I

> > > know that they are in line if all of the x values are equal, or

> > > all of the y values are equal. I do not know

> > > what math to use to check otherwise. Is this a vector problem? trig?

On 6/20/07, apalomba@austin.rr.com  wrote:
> I may have been a bit vague in my explanation. Take a look
> at this... http://www.geocities.com/SiliconValley/2151/math3d.html
> Once you have calculated the normal to the plane, I think you
> can take the dot product of the normal with your remaining
> point(vector), that should give you the angle between the two.
>
>
> Anthony
>
>
> ----- Original Message -----
> From: apalomba@austin.rr.com
> Date: Wednesday, June 20, 2007 6:57 pm
> Subject: Re: [maxmsp] math question
> To: maxmsp@cycling74.com, david@5of4.com
>
> > One way you could do this is calculate the normal to the plane
> > that is created by three points. Pick one point, this will be your
> > origin. Now pick two points and draw a line from them to your
> > origin,
> > this
> > should form a plane. Now take your fourth point and create
> > a vector from the origin, call this the vector x. Now
> > you can calcualte the angle between the plane and x,
> > if it is zero then you know all points are in line on the axis
> > the plane resides on.
> >
> >
> >
> >
> > Anthony
> >
> >
> > ----- Original Message -----
> > From: David Morneau 
> > Date: Wednesday, June 20, 2007 6:46 pm
> > Subject: [maxmsp] math question
> >
> > > Hi List
> > >
> > > I have four points [x,y] on a plane and I need to be able to
> > > determine if they are in a line at any angle. I
> > > know that they are in line if all of the x values are equal, or
> > if
> > > all of the y values are equal. I do not know
> > > what math to use to check otherwise. Is this a vector problem? trig?
> > >
> > > Any hints are appreciated.
> > >
> > > Thanks
> > > David
> > >
> > >
> > >
> > > Need personalized email and website? Look no further. It's easy
> > > with Doteasy $0 Web Hosting! Learn more at www.doteasy.com
> > >
> >
>


If they are not at the same place, determine the equation of the line they

define (for instance of the form x + a.y + b = 0, the 2 points give you a

system of 2 equations that you solve to find a and b).

Then check if your 3rd and 4th points satisfy the equation.

> I have four points [x,y] on a plane and I need to be able to determine if they

> know that they are in line if all of the x values are equal, or if all of the

Take 2 points.
If they are not at the same place, determine the equation of the line they
define (for instance of the form x + a.y + b = 0, the 2 points give you a
system of 2 equations that you solve to find a and b).
Then check if your 3rd and 4th points satisfy the equation.
JF.

> Hi List
>
> I have four points [x,y] on a plane and I need to be able to determine if they
> are in a line at any angle. I
> know that they are in line if all of the x values are equal, or if all of the
> y values are equal. I do not know
> what math to use to check otherwise. Is this a vector problem? trig?
>
> Any hints are appreciated.
>
> Thanks
> David

Subject 1.03: How do I find intersections of 2 2D line segments?

This problem can be extremely easy or extremely difficult depends on your

applications. If all you want is the intersection point, the following

Let A,B,C,D be 2-space position vectors. Then the directed line segments AB

Ay+r(By-Ay)=Cy+s(Dy-Cy) for some r,s in [0,1]

r = ----------------------------- (eqn 1)

s = ----------------------------- (eqn 2)

Let P be the position vector of the intersection point, then

By examining the values of r & s, you can also determine some other limiting

If the denominator in eqn 1 is zero, AB & CD are parallel

If the numerator in eqn 1 is also zero, AB & CD are coincident

If the intersection point of the 2 lines are needed (lines in this context

mean infinite lines) regardless whether the two line segments intersect,

Also note that the denominators of eqn 1 & 2 are identical.

199-202 "Faster Line Segment Intersection,"

> if these are the same for all points, then they are colinear.

> On 6/20/07, apalomba@austin.rr.com wrote:

> > I may have been a bit vague in my explanation. Take a look

> > Once you have calculated the normal to the plane, I think you

> > can take the dot product of the normal with your remaining

> > point(vector), that should give you the angle between the two.

> > Date: Wednesday, June 20, 2007 6:57 pm

> > To: maxmsp@cycling74.com, david@5of4.com

> > > One way you could do this is calculate the normal to the plane

> > > that is created by three points. Pick one point, this will be your

> > > origin. Now pick two points and draw a line from them to your

> > > should form a plane. Now take your fourth point and create

> > > a vector from the origin, call this the vector x. Now

> > > you can calcualte the angle between the plane and x,

> > > if it is zero then you know all points are in line on the axis

> > > Date: Wednesday, June 20, 2007 6:46 pm

----- |(*,+,#,=)(#,=,*,+)(=,#,+,*)(+,*,=,#)| -----

Check out the CGA FAQ, subject 1.03, http://www.exaflop.org/docs/cgafaq/.

P.S. Here's the text:
Subject 1.03: How do I find intersections of 2 2D line segments?

This problem can be extremely easy or extremely difficult depends on your
applications.  If all you want is the intersection point, the following
should work:

Let A,B,C,D be 2-space position vectors.  Then the directed line segments AB
& CD are given by:

        AB=A+r(B-A), r in [0,1]
        CD=C+s(D-C), s in [0,1]

        Ax+r(Bx-Ax)=Cx+s(Dx-Cx)
        Ay+r(By-Ay)=Cy+s(Dy-Cy)  for some r,s in [0,1]

            (Ay-Cy)(Dx-Cx)-(Ax-Cx)(Dy-Cy)
        r = -----------------------------  (eqn 1)
            (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)

            (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay)
        s = -----------------------------  (eqn 2)
            (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)

        Px=Ax+r(Bx-Ax)
        Py=Ay+r(By-Ay)

By examining the values of r & s, you can also determine some other limiting
conditions:

        If 0
            r1 or s1 line segments do not intersect

   If the denominator in eqn 1 is zero, AB & CD are parallel

   If the numerator in eqn 1 is also zero, AB & CD are coincident

If the intersection point of the 2 lines are needed (lines in this context
mean infinite lines) regardless whether the two line segments intersect,
then

   If r>1, P is located on extension of AB
   -

   If s>1, P is located on extension of CD
   -

[O'Rourke]pp.
249-51
[Gems III] pp.
199-202 "Faster Line Segment Intersection,"

On 6/20/07, Wesley Smith  wrote:
> You want to look at slopes i.e.
>
> (y1-y0)/(x1-x0)
>
> if these are the same for all points, then they are colinear.
>
> wes
>
> On 6/20/07, apalomba@austin.rr.com  wrote:
> > I may have been a bit vague in my explanation. Take a look
> > at this... http://www.geocities.com/SiliconValley/2151/math3d.html
> > Once you have calculated the normal to the plane, I think you
> > can take the dot product of the normal with your remaining
> > point(vector), that should give you the angle between the two.
> >
> >
> > Anthony
> >
> >
> > ----- Original Message -----
> > From: apalomba@austin.rr.com
> > Date: Wednesday, June 20, 2007 6:57 pm
> > Subject: Re: [maxmsp] math question
> > To: maxmsp@cycling74.com, david@5of4.com
> >
> > > One way you could do this is calculate the normal to the plane
> > > that is created by three points. Pick one point, this will be your
> > > origin. Now pick two points and draw a line from them to your
> > > origin,
> > > this
> > > should form a plane. Now take your fourth point and create
> > > a vector from the origin, call this the vector x. Now
> > > you can calcualte the angle between the plane and x,
> > > if it is zero then you know all points are in line on the axis
> > > the plane resides on.
> > >
> > >
> > >
> > >
> > > Anthony
> > >
> > >
> > > ----- Original Message -----
> > > From: David Morneau 
> > > Date: Wednesday, June 20, 2007 6:46 pm
> > > Subject: [maxmsp] math question
> > >
> > > > Hi List
> > > >
> > > > I have four points [x,y] on a plane and I need to be able to
> > > > determine if they are in a line at any angle. I
> > > > know that they are in line if all of the x values are equal, or
> > > if
> > > > all of the y values are equal. I do not know
> > > > what math to use to check otherwise. Is this a vector problem? trig?
> > > >
> > > > Any hints are appreciated.
> > > >
> > > > Thanks
> > > > David
> > > >
> > > >
> > > >
> > > > Need personalized email and website? Look no further. It's easy
> > > > with Doteasy $0 Web Hosting! Learn more at www.doteasy.com
> > > >
> > >
> >
>

-- 
-----   |(*,+,#,=)(#,=,*,+)(=,#,+,*)(+,*,=,#)|   -----

...or you can use some of the test object from the pmpd library :

http://www.maxobjects.com/?v=libraries&id_library=81

(pmpd.tLine2D, pmpd.tSeg2D, pmpd.tSquare2D... will be your friends)

send it your point position, and the cordinates of the line, segment 

...or you can use some of the test object from the pmpd library :
http://www.maxobjects.com/?v=libraries&id_library=81
(pmpd.tLine2D, pmpd.tSeg2D, pmpd.tSquare2D... will be your friends)
send it your point position, and the cordinates of the line, segment  
or square to test.

www.maxobjects.com
http://mathieu.chamagne.free.fr

Thanks for all of the suggestions. I ended up calculating slopes and comparing, it works great and was 

This whole thing makes me wish I'd paid more attention in my math classes instead of complaining 

that I would never need this stuff since I'm in music... oh well.

Thanks for all of the suggestions. I ended up calculating slopes and comparing, it works great and was 
easy to implement.

This whole thing makes me wish I'd paid more attention in my math classes instead of  complaining 
that I would never need this stuff since I'm in music... oh well.