Calculate angle between two vectors (probably @Igor :)

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Calculate angle between two vectors (probably @Igor :)

 Hello, i probably made some embarassing mistake, but as i cannot find it, i ask you to have a look at this method. It should calculate the angle between two vectors. And vectors are instances of Point (perhaps here is already a misconception?). It is used in my flocking simulation PharoBoids (http://smalltalkhub.com/#!/~MartinWalk/Boids) Here is my version of the method: angleBetween: vector1 and: vector2 onError: aBlock         | cosinusOfAngle innerProductOfVectors productOfVectorsLengths|         innerProductOfVectors := (vector1 dotProduct: vector2).         productOfVectorsLengths := (vector1 r) * (vector2 r).         productOfVectorsLengths = 0 ifTrue: [ ^ aBlock value ].         cosinusOfAngle := innerProductOfVectors / productOfVectorsLengths.         ^ cosinusOfAngle arcCos         But my Boids behave wrong when i use it. I found another implementation of the same problem by Igor Stasenko which works and looks like this: angleBetween: p1 and: p2 ifDegenerate: aBlock " Calculate an angle (in radians) between two vectors. Evaluate a block, in case if calculation not possible because one of the vectors has zero length "         | x1 y1 x2 y2 dot2 n2 |         x1 := p1 x.         y1 := p1 y.         x2 := p2 x.         y2 := p2 y.                 dot2 := x1 * x2 + (y1 * y2).         dot2 := dot2 * dot2.                 n2 := (x1*x1 + (y1*y1)) * (x2*x2 + (y2*y2)).                 n2 = 0 ifTrue: [ ^ aBlock value ].                 ^ (dot2 / n2) arcCos         Can anybody explain the problem of my method? M.
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Re: Calculate angle between two vectors (probably @Igor :)

 Rounding error?This may be the reason, igor's version is working withcos = (a dot b)^2 / (|ab|^2)while you are usingcos = (a dot b) / |ab| 2014-03-16 17:01 GMT+01:00 MartinW : Hello, i probably made some embarassing mistake, but as i cannot find it, i ask you to have a look at this method. It should calculate the angle between two vectors. And vectors are instances of Point (perhaps here is already a misconception?). It is used in my flocking simulation PharoBoids (http://smalltalkhub.com/#!/~MartinWalk/Boids) Here is my version of the method: angleBetween: vector1 and: vector2 onError: aBlock         | cosinusOfAngle innerProductOfVectors productOfVectorsLengths|         innerProductOfVectors := (vector1 dotProduct: vector2).         productOfVectorsLengths := (vector1 r) * (vector2 r).         productOfVectorsLengths = 0 ifTrue: [ ^ aBlock value ].         cosinusOfAngle := innerProductOfVectors / productOfVectorsLengths.         ^ cosinusOfAngle arcCos But my Boids behave wrong when i use it. I found another implementation of the same problem by Igor Stasenko which works and looks like this: angleBetween: p1 and: p2 ifDegenerate: aBlock " Calculate an angle (in radians) between two vectors. Evaluate a block, in case if calculation not possible because one of the vectors has zero length "         | x1 y1 x2 y2 dot2 n2 |         x1 := p1 x.         y1 := p1 y.         x2 := p2 x.         y2 := p2 y.         dot2 := x1 * x2 + (y1 * y2).         dot2 := dot2 * dot2.         n2 := (x1*x1 + (y1*y1)) * (x2*x2 + (y2*y2)).         n2 = 0 ifTrue: [ ^ aBlock value ].         ^ (dot2 / n2) arcCos Can anybody explain the problem of my method? M. -- View this message in context: http://forum.world.st/Calculate-angle-between-two-vectors-probably-Igor-tp4749351.html Sent from the Pharo Smalltalk Users mailing list archive at Nabble.com.
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Re: Calculate angle between two vectors (probably @Igor :)

 In reply to this post by MartinW First of all, you could simplify your code with dotProduct, writingdot2 := p1 dotProduct: p2.But maybe you just need((p1 normalized) dotProduct: (p2 normalized)) arcCos         ;-) You can also explore the polar coordinates...AlainOn Sun, Mar 16, 2014 at 8:01 PM, MartinW wrote: Hello, i probably made some embarassing mistake, but as i cannot find it, i ask you to have a look at this method. It should calculate the angle between two vectors. And vectors are instances of Point (perhaps here is already a misconception?). It is used in my flocking simulation PharoBoids (http://smalltalkhub.com/#!/~MartinWalk/Boids) Here is my version of the method: angleBetween: vector1 and: vector2 onError: aBlock         | cosinusOfAngle innerProductOfVectors productOfVectorsLengths|         innerProductOfVectors := (vector1 dotProduct: vector2).         productOfVectorsLengths := (vector1 r) * (vector2 r).         productOfVectorsLengths = 0 ifTrue: [ ^ aBlock value ].         cosinusOfAngle := innerProductOfVectors / productOfVectorsLengths.         ^ cosinusOfAngle arcCos But my Boids behave wrong when i use it. I found another implementation of the same problem by Igor Stasenko which works and looks like this: angleBetween: p1 and: p2 ifDegenerate: aBlock " Calculate an angle (in radians) between two vectors. Evaluate a block, in case if calculation not possible because one of the vectors has zero length "         | x1 y1 x2 y2 dot2 n2 |         x1 := p1 x.         y1 := p1 y.         x2 := p2 x.         y2 := p2 y.         dot2 := x1 * x2 + (y1 * y2).         dot2 := dot2 * dot2.         n2 := (x1*x1 + (y1*y1)) * (x2*x2 + (y2*y2)).         n2 = 0 ifTrue: [ ^ aBlock value ].         ^ (dot2 / n2) arcCos Can anybody explain the problem of my method? M. -- View this message in context: http://forum.world.st/Calculate-angle-between-two-vectors-probably-Igor-tp4749351.html Sent from the Pharo Smalltalk Users mailing list archive at Nabble.com.
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Re: Calculate angle between two vectors (probably @Igor :)

 In reply to this post by Nicolai Hess This was of course wrong, I don't know what theother method computes, but not the angle between two vectors.Now the question is, why do you think your method is wrong / the boids  behave wrong? 2014-03-16 18:41 GMT+01:00 Nicolai Hess : Rounding error?This may be the reason, igor's version is working with cos = (a dot b)^2 / (|ab|^2)while you are usingcos = (a dot b) / |ab| 2014-03-16 17:01 GMT+01:00 MartinW : Hello, i probably made some embarassing mistake, but as i cannot find it, i ask you to have a look at this method. It should calculate the angle between two vectors. And vectors are instances of Point (perhaps here is already a misconception?). It is used in my flocking simulation PharoBoids (http://smalltalkhub.com/#!/~MartinWalk/Boids) Here is my version of the method: angleBetween: vector1 and: vector2 onError: aBlock         | cosinusOfAngle innerProductOfVectors productOfVectorsLengths|         innerProductOfVectors := (vector1 dotProduct: vector2).         productOfVectorsLengths := (vector1 r) * (vector2 r).         productOfVectorsLengths = 0 ifTrue: [ ^ aBlock value ].         cosinusOfAngle := innerProductOfVectors / productOfVectorsLengths.         ^ cosinusOfAngle arcCos But my Boids behave wrong when i use it. I found another implementation of the same problem by Igor Stasenko which works and looks like this: angleBetween: p1 and: p2 ifDegenerate: aBlock " Calculate an angle (in radians) between two vectors. Evaluate a block, in case if calculation not possible because one of the vectors has zero length "         | x1 y1 x2 y2 dot2 n2 |         x1 := p1 x.         y1 := p1 y.         x2 := p2 x.         y2 := p2 y.         dot2 := x1 * x2 + (y1 * y2).         dot2 := dot2 * dot2.         n2 := (x1*x1 + (y1*y1)) * (x2*x2 + (y2*y2)).         n2 = 0 ifTrue: [ ^ aBlock value ].         ^ (dot2 / n2) arcCos Can anybody explain the problem of my method? M. -- View this message in context: http://forum.world.st/Calculate-angle-between-two-vectors-probably-Igor-tp4749351.html Sent from the Pharo Smalltalk Users mailing list archive at Nabble.com.
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Re: Calculate angle between two vectors (probably @Igor :)

 Another observation in Boids>>isInFieldOfVision: aBoid...ownDirection := self velocity - self position.the own direction should be the same as the velocity. Consider a Boid at position 100@0 with velocity 100@0 would giveownDirection = 0@0.But of course, the steering direction is still 1@0. 2014-03-17 10:07 GMT+01:00 Nicolai Hess : This was of course wrong, I don't know what theother method computes, but not the angle between two vectors.Now the question is, why do you think your method is wrong / the boids  behave wrong? 2014-03-16 18:41 GMT+01:00 Nicolai Hess : Rounding error?This may be the reason, igor's version is working with cos = (a dot b)^2 / (|ab|^2)while you are usingcos = (a dot b) / |ab| 2014-03-16 17:01 GMT+01:00 MartinW : Hello, i probably made some embarassing mistake, but as i cannot find it, i ask you to have a look at this method. It should calculate the angle between two vectors. And vectors are instances of Point (perhaps here is already a misconception?). It is used in my flocking simulation PharoBoids (http://smalltalkhub.com/#!/~MartinWalk/Boids) Here is my version of the method: angleBetween: vector1 and: vector2 onError: aBlock         | cosinusOfAngle innerProductOfVectors productOfVectorsLengths|         innerProductOfVectors := (vector1 dotProduct: vector2).         productOfVectorsLengths := (vector1 r) * (vector2 r).         productOfVectorsLengths = 0 ifTrue: [ ^ aBlock value ].         cosinusOfAngle := innerProductOfVectors / productOfVectorsLengths.         ^ cosinusOfAngle arcCos But my Boids behave wrong when i use it. I found another implementation of the same problem by Igor Stasenko which works and looks like this: angleBetween: p1 and: p2 ifDegenerate: aBlock " Calculate an angle (in radians) between two vectors. Evaluate a block, in case if calculation not possible because one of the vectors has zero length "         | x1 y1 x2 y2 dot2 n2 |         x1 := p1 x.         y1 := p1 y.         x2 := p2 x.         y2 := p2 y.         dot2 := x1 * x2 + (y1 * y2).         dot2 := dot2 * dot2.         n2 := (x1*x1 + (y1*y1)) * (x2*x2 + (y2*y2)).         n2 = 0 ifTrue: [ ^ aBlock value ].         ^ (dot2 / n2) arcCos Can anybody explain the problem of my method? M. -- View this message in context: http://forum.world.st/Calculate-angle-between-two-vectors-probably-Igor-tp4749351.html Sent from the Pharo Smalltalk Users mailing list archive at Nabble.com.
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Re: Calculate angle between two vectors (probably @Igor :)

 > ownDirection := self velocity - self position. Taking that purely at face value, it doesn't look right mixing distance(m) & velocity(m.s^-1) in a calculation.  I guess you are integrating velocity over one unit of time... (m.s^-1)*(s)  - (m)  = (m) - (m) = (m) cheers -ben Nicolai Hess wrote: Another observation in Boids>>isInFieldOfVision: aBoid ... ownDirection := self velocity - self position. the own direction should be the same as the velocity. Consider a Boid at position 100@0 with velocity 100@0 would give ownDirection = 0@0. But of course, the steering direction is still 1@0. 2014-03-17 10:07 GMT+01:00 Nicolai Hess : This was of course wrong, I don't know what the other method computes, but not the angle between two vectors. Now the question is, why do you think your method is wrong / the boids  behave wrong? 2014-03-16 18:41 GMT+01:00 Nicolai Hess : Rounding error? This may be the reason, igor's version is working with cos = (a dot b)^2 / (|ab|^2) while you are using cos = (a dot b) / |ab| 2014-03-16 17:01 GMT+01:00 MartinW : Hello, i probably made some embarassing mistake, but as i cannot find it, i ask you to have a look at this method. It should calculate the angle between two vectors. And vectors are instances of Point (perhaps here is already a misconception?). It is used in my flocking simulation PharoBoids (http://smalltalkhub.com/#!/~MartinWalk/Boids) Here is my version of the method: angleBetween: vector1 and: vector2 onError: aBlock         | cosinusOfAngle innerProductOfVectors productOfVectorsLengths|         innerProductOfVectors := (vector1 dotProduct: vector2).         productOfVectorsLengths := (vector1 r) * (vector2 r).         productOfVectorsLengths = 0 ifTrue: [ ^ aBlock value ].         cosinusOfAngle := innerProductOfVectors / productOfVectorsLengths.         ^ cosinusOfAngle arcCos But my Boids behave wrong when i use it. I found another implementation of the same problem by Igor Stasenko which works and looks like this: angleBetween: p1 and: p2 ifDegenerate: aBlock " Calculate an angle (in radians) between two vectors. Evaluate a block, in case if calculation not possible because one of the vectors has zero length "         | x1 y1 x2 y2 dot2 n2 |         x1 := p1 x.         y1 := p1 y.         x2 := p2 x.         y2 := p2 y.         dot2 := x1 * x2 + (y1 * y2).         dot2 := dot2 * dot2.         n2 := (x1*x1 + (y1*y1)) * (x2*x2 + (y2*y2)).         n2 = 0 ifTrue: [ ^ aBlock value ].         ^ (dot2 / n2) arcCos Can anybody explain the problem of my method? M. -- View this message in context: http://forum.world.st/Calculate-angle-between-two-vectors-probably-Igor-tp4749351.html Sent from the Pharo Smalltalk Users mailing list archive at Nabble.com.
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Re: Calculate angle between two vectors (probably @Igor :)

 In reply to this post by Nicolai Hess Nicolai Hess wrote This was of course wrong, I don't know what the other method computes, but not the angle between two vectors. Yes i also wrote a test and i think my method is right. Nicolai Hess wrote Now the question is, why do you think your method is wrong / the boids behave wrong? When i use my method to calculate the field of vision the Boids always fly from top left to down right and if i turn on the circling option, they crowd in the bottom right quadrant. If i give them a 360 degree field of vision by always returning true for isInFieldOfVision they behave correctly. This means they fly in a nice circle around the center and if circling is turned off, the swarm flies in different directions each time you start the simulation. Perhaps the problem is not the calculation of the angle but is in the isInFieldOfVision: method...
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Re: Calculate angle between two vectors (probably @Igor :)

 2014-03-19 8:49 GMT+01:00 MartinW : Nicolai Hess wrote > This was of course wrong, I don't know what the > other method computes, but not the angle between two vectors. Yes i also wrote a test and i think my method is right. Nicolai Hess wrote > Now the question is, why do you think your method is wrong / the boids > behave wrong? When i use my method to calculate the field of vision the Boids always fly from top left to down right and if i turn on the circling option, they crowd in the bottom right quadrant. If i give them a 360 degree field of vision by always returning true for isInFieldOfVision they behave correctly. This means they fly in a nice circle around the center and if circling is turned off, the swarm flies in different directions each time you start the simulation. Perhaps the problem is not the calculation of the angle but is in the isInFieldOfVision: method...:) yes and I think the testcases in testIsInFieldOfVisionare wrong, or I misunderstand how the boids are moving.in testIsInFieldOfVision subject has velocity 100@0, I understand this as "moves from left to right".testobject other2 and other3 are above and below subect, and not behind andin front, both should be visible with the fieldOfView. Btw. the field of view is rather big, 0.75*Float Pi is 135 degree, but  clock *and* counterclockwise->  270 degree field of view.And it is funny to change the field of view to 0, after the boids started.   -- View this message in context: http://forum.world.st/Calculate-angle-between-two-vectors-probably-Igor-tp4749351p4749697.html Sent from the Pharo Smalltalk Users mailing list archive at Nabble.com.
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Re: Calculate angle between two vectors (probably @Igor :)

 In reply to this post by MartinW On 16 March 2014 17:01, MartinW wrote: Hello, i probably made some embarassing mistake, but as i cannot find it, i ask you to have a look at this method. It should calculate the angle between two vectors. And vectors are instances of Point (perhaps here is already a misconception?). It is used in my flocking simulation PharoBoids (http://smalltalkhub.com/#!/~MartinWalk/Boids) Here is my version of the method: angleBetween: vector1 and: vector2 onError: aBlock         | cosinusOfAngle innerProductOfVectors productOfVectorsLengths|         innerProductOfVectors := (vector1 dotProduct: vector2).         productOfVectorsLengths := (vector1 r) * (vector2 r).         productOfVectorsLengths = 0 ifTrue: [ ^ aBlock value ].         cosinusOfAngle := innerProductOfVectors / productOfVectorsLengths.         ^ cosinusOfAngle arcCos   But my Boids behave wrong when i use it. I found another implementation of the same problem by Igor Stasenko which works and looks like this: angleBetween: p1 and: p2 ifDegenerate: aBlock " Calculate an angle (in radians) between two vectors. Evaluate a block, in case if calculation not possible because one of the vectors has zero length "         | x1 y1 x2 y2 dot2 n2 |         x1 := p1 x.         y1 := p1 y.         x2 := p2 x.         y2 := p2 y.         dot2 := x1 * x2 + (y1 * y2).         dot2 := dot2 * dot2.         n2 := (x1*x1 + (y1*y1)) * (x2*x2 + (y2*y2)).         n2 = 0 ifTrue: [ ^ aBlock value ].         ^ (dot2 / n2) arcCos Can anybody explain the problem of my method? M. yours looks correct.i'm just using squares to avoid taking square roots of vector lengths.  -- View this message in context: http://forum.world.st/Calculate-angle-between-two-vectors-probably-Igor-tp4749351.html Sent from the Pharo Smalltalk Users mailing list archive at Nabble.com. -- Best regards,Igor Stasenko.
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Re: Calculate angle between two vectors (probably @Igor :)

 In reply to this post by Nicolai Hess Nicolai Hess wrote in testIsInFieldOfVision subject has velocity 100@0, I understand this as "moves from left to right". testobject other2 and other3 are above and below subect, and not behind and in front, both should be visible with the fieldOfView. Oh, thank you. I made a new testcase. Which is unfortunately passing :( So i am still looking for a solution… Nicolai Hess wrote Btw. the field of view is rather big, 0.75*Float Pi is 135 degree, but clock *and* counterclockwise ->  270 degree field of view. That's correct. Most birds have the eyes on the sides of their heads - thus they have a wide visual field. Some as wide as 360 degrees.