### 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

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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 http://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.

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 http://www.doteasy.com

> >

>

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

> 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 http://www.doteasy.com

> > >

> >

>

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

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

Good old FAQs.

— Paul

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]

If AB & CD intersect, then

A+r(B-A)=C+s(D-C), or

Ax+r(Bx-Ax)=Cx+s(Dx-Cx)

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

Solving the above for r and s yields

(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)

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

P=A+r(B-A) or

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< =r<=1 & 0<=s<=1, intersection exists

r<0 or r>1 or s<0 or s>1 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 r<0, P is located on extension of BA

–

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

–

If s<0, P is located on extension of DC

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

References:

[O’Rourke]< http://www.exaflop.org/docs/cgafaq/cga0.html#%5BO%27%20Rourke%5D>pp.

249-51

[Gems III] < http://www.exaflop.org/docs/cgafaq/cga0.html#%5BGems%20III%5D>pp.

199-202 "Faster Line Segment Intersection,"

On 6/20/07, Wesley Smith

> 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,

> > 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 http://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 square to test.

Mathieu

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.

David

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