Jun 20 2007 | 11:44 pm

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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- Jun 20 2007 | 11:55 pmOne way you could do this is calculate the normal to the planethat is created by three points. Pick one point, this will be yourorigin. Now pick two points and draw a line from them to your origin,thisshould form a plane. Now take your fourth point and createa vector from the origin, call this the vector x. Nowyou can calcualte the angle between the plane and x,if it is zero then you know all points are in line on the axisthe plane resides on.Anthony----- Original Message -----From: David MorneauDate: Wednesday, June 20, 2007 6:46 pmSubject: [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>
- Jun 21 2007 | 12:26 amI may have been a bit vague in my explanation. Take a lookat this... http://www.geocities.com/SiliconValley/2151/math3d.htmlOnce you have calculated the normal to the plane, I think youcan take the dot product of the normal with your remainingpoint(vector), that should give you the angle between the two.Anthony----- Original Message -----From: apalomba@austin.rr.comDate: Wednesday, June 20, 2007 6:57 pmSubject: Re: [maxmsp] math questionTo: 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> >>
- Jun 21 2007 | 12:41 amYou want to look at slopes i.e.(y1-y0)/(x1-x0)if these are the same for all points, then they are colinear.wesOn 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> > >> >>
- Jun 21 2007 | 12:39 pmTake 2 points.If they are not at the same place, determine the equation of the line theydefine (for instance of the form x + a.y + b = 0, the 2 points give you asystem 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
- Jun 21 2007 | 12:42 pmCheck out the CGA FAQ, subject 1.03, http://www.exaflop.org/docs/cgafaq/.Good old FAQs.-- PaulP.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 yourapplications. If all you want is the intersection point, the followingshould 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, thenA+r(B-A)=C+s(D-C), orAx+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, thenP=A+r(B-A) orPx=Ax+r(Bx-Ax)Py=Ay+r(By-Ay)By examining the values of r & s, you can also determine some other limitingconditions: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 coincidentIf the intersection point of the 2 lines are needed (lines in this contextmean infinite lines) regardless whether the two line segments intersect,then-If r>1, P is located on extension of AB-If r -If s>1, P is located on extension of CD-If sAlso note that the denominators of eqn 1 & 2 are identical.References:[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> > > >> > >> >>------- |(*,+,#,=)(#,=,*,+)(=,#,+,*)(+,*,=,#)| -----
- Jun 21 2007 | 1:44 pm...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, segmentor square to test.Mathieuwww.maxobjects.com
- Jun 21 2007 | 1:59 pmThanks for all of the suggestions. I ended up calculating slopes and comparing, it works great and waseasy to implement.This whole thing makes me wish I'd paid more attention in my math classes instead of complainingthat I would never need this stuff since I'm in music... oh well.DavidNeed personalized email and website? Look no further. It's easywith Doteasy $0 Web Hosting! Learn more at www.doteasy.com