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# Vector to Angle , and vice versa

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19 replies to this topic

### #1DarkScience  Members

Posted 11 June 2012 - 11:42 AM

I'm currently trying to figure out how to convert XYZ to PYR. Here are my classes.

Also i'm currently looking it up. I know of sin/cos. I'm learning what i can from online docs.

Vector:
Spoiler

Angle:
Spoiler

Edited by DarkScience, 11 June 2012 - 11:47 AM.

### #2Álvaro  Members

Posted 11 June 2012 - 11:57 AM

I didn't look at your code, but there seems to be a conceptual problem with what you are doing: XYZ describes a vector, while PYR describes a rotation. These are different things, and you can't convert one to another.

What are you really trying to do?

### #3DarkScience  Members

Posted 11 June 2012 - 12:00 PM

I didn't look at your code, but there seems to be a conceptual problem with what you are doing: XYZ describes a vector, while PYR describes a rotation. These are different things, and you can't convert one to another.

What are you really trying to do?

You don't appear to understand the Vector/Angle model. It is possible and is done in just about every game out there. PYR can be converted to a normal which is a direction represented in XYZ and vice-versa.

Also i may of just figured it out. Ensuring consistency now ...
Never mind still don't have it ....

Edited by DarkScience, 11 June 2012 - 12:11 PM.

### #4DarkScience  Members

Posted 11 June 2012 - 12:34 PM

first set
Spoiler

second set
Spoiler

this is what im using to determine the accuracy of the values, they seem to slightly off in the second set though very close to what there suppose to be. Seems to increase in inaccuracy the larger the number.
http://www.mathsisfu...Cosine, Tangent

Edited by DarkScience, 11 June 2012 - 12:45 PM.

### #5Álvaro  Members

Posted 11 June 2012 - 12:49 PM

You don't appear to understand the Vector/Angle model.

### #6DarkScience  Members

Posted 11 June 2012 - 01:02 PM

You don't appear to understand the Vector/Angle model.

Hoping you're not saying that in a sarcastic way in which your mad. I don't insult people in that way and wasn't implying anything by that comment.

Also I believe i will try a more manual way of doing what it is i desire. By converting 0 to 360 to -180 to 180 and applying some arithmetic's to convert it to x and y.

Edited by DarkScience, 11 June 2012 - 01:05 PM.

### #7Álvaro  Members

Posted 11 June 2012 - 01:15 PM

My comment was sarcastic, but I am not mad. The point of my first post is that you should probably try to explain how that vector XYZ expresses a rotation (i.e., how do you apply it to another vector?), so you can make things more clear to yourself and others. The procedure to convert PYR to the other format might become apparent once you express things precisely.

Also, giving some background about what you are trying to accomplish will generally get you much better help. Perhaps the solution to your problem would be trivial if you used some other representation for rotations, for example.

Edited by alvaro, 11 June 2012 - 01:15 PM.

### #8DarkScience  Members

Posted 11 June 2012 - 01:28 PM

I didn't look at your code, but there seems to be a conceptual problem with what you are doing: XYZ describes a vector, while PYR describes a rotation. These are different things, and you can't convert one to another.

What are you really trying to do?

Thought it was clear from the code i posted. But i shall explain further. Also Can't be done isn't asking for a better explanation nor is not reading all that i posted advised when your goal is to understand what i am after.

This is the object orientation in 3D space.
-X is Left, +X is Right
-Y is Backward , +Y is Forward
-Z is Down , +Z is Up

Now this is the view as in camera or object rotation.
-Pitch is Down, +Pitch is Up
-Yaw is Left, +Pitch is Right
-Roll is Roll Left, +Roll is Roll right // this isn't as important right now

The goal is to convert Pitch , Yaw , Roll to X , Y , Z and then back.
So Angle( 0 , 0 , 0 ) would be in XYZ ( 0 , 1 , 0 ).
So Angle( 0 , 90 , 0 ) would be in XYZ ( 1 , 0 , 0 ).
So Angle( 0 , 180 , 0 ) would be in XYZ ( 0 , -1 , 0 ).
So Angle( 0 , 270, 0 ) would be in XYZ ( -1 , -1 , 0 ).
So Angle( 0 , 360, 0 ) would be in XYZ ( 0 , 1 , 0 ).

Edited by DarkScience, 11 June 2012 - 01:29 PM.

### #9frob  Moderators

Posted 11 June 2012 - 01:28 PM

You don't appear to understand the Vector/Angle model. It is possible and is done in just about every game out there. PYR can be converted to a normal which is a direction represented in XYZ and vice-versa.

Orientation and position are related but VERY different.

To represent position in 3D space you need spatial coordinates.
To represent orientation in 3D space you need a PYR triplet, or a 3x3 matrix, or a quaternion.

The first says where you are, the second defines your orientation (which can be used to determine what directions are up and forward).

Check out my book, Game Development with Unity, aimed at beginners who want to build fun games fast.

Also check out my personal website at bryanwagstaff.com, where I occasionally write about assorted stuff.

### #10clb  Members

Posted 11 June 2012 - 01:37 PM

Alvaro is correct: a triplet of pitch, yaw and roll (Euler angles) represents a 3D orientation. An euclidean 3D vector can at most represent a direction in 3D space (plus a magnitude). That direction can be e.g. an axis of rotation, or a look-at direction, but it does not capture a full 3D orientation.

If representing an axis of rotation with a 3D euclidean vector, one needs to add in a single scalar (the angle of rotation about that axis) to make it a complete representation of a 3D orientation. This is commonly called an axis-angle representation of an orientation. If you are looking to convert an axis-angle representation to a 3D rotation matrix (and then to an Euler triplet), see e.g. MathGeoLib's float3x3::RotateAxisAngle function (boils down to Quat::SetFromAxisAngle).

If representing a look-at direction with a 3D euclidean vector, one needs to add in the concept of a 'up' vector (also called a 'world up' or a 'scene up' vector, a fixed vector specifying the upwards direction convention in the scene), or a single scalar 'roll' (being equivalent to above axis-angle) to make it a complete representation of a 3D orientation. This orientation however cannot have any roll, if the up vector is kept static. If you are looking how to turn a look-at direction vector into a 3D orientation, see e.g. MathGeoLib's float3x3::LookAt.

To convert a rotation matrix to pitch-yaw-roll components (Euler angles), see e.g. MathGeoLib's float3x3::ToEuler*** conversion functions.
Me+PC=clb.demon.fi | C++ Math and Geometry library: MathGeoLib, test it live! | C++ Game Networking: kNet | 2D Bin Packing: RectangleBinPack | Use gcc/clang/emcc from VS: vs-tool | Resume+Portfolio | gfxapi, test it live!

### #11frob  Moderators

Posted 11 June 2012 - 01:37 PM

The goal is to convert Pitch , Yaw , Roll to X , Y , Z and then back.
So Angle( 0 , 0 , 0 ) would be in XYZ ( 0 , 1 , 0 ).
So Angle( 0 , 90 , 0 ) would be in XYZ ( 1 , 0 , 0 ).
So Angle( 0 , 180 , 0 ) would be in XYZ ( 0 , -1 , 0 ).
So Angle( 0 , 270, 0 ) would be in XYZ ( -1 , -1 , 0 ).
So Angle( 0 , 360, 0 ) would be in XYZ ( 0 , 1 , 0 ).

Your numbers don't make sense. How can (0,270,0) be (-1,-1,0) ?

Perhaps it is time for to go find a primer on 3D mathematics?

As for converting between them, it looks like you want to project one unit along the forward vector of the orientation and find that position.
As for reversing it, there are infinitely many orientations that can generate the forward vector.

Check out my book, Game Development with Unity, aimed at beginners who want to build fun games fast.

Also check out my personal website at bryanwagstaff.com, where I occasionally write about assorted stuff.

### #12DarkScience  Members

Posted 11 June 2012 - 01:41 PM

The goal is to convert Pitch , Yaw , Roll to X , Y , Z and then back.
So Angle( 0 , 0 , 0 ) would be in XYZ ( 0 , 1 , 0 ).
So Angle( 0 , 90 , 0 ) would be in XYZ ( 1 , 0 , 0 ).
So Angle( 0 , 180 , 0 ) would be in XYZ ( 0 , -1 , 0 ).
So Angle( 0 , 270, 0 ) would be in XYZ ( -1 , -1 , 0 ).
So Angle( 0 , 360, 0 ) would be in XYZ ( 0 , 1 , 0 ).

Your numbers don't make sense. How can (0,270,0) be (-1,-1,0) ?

Perhaps it is time for to go find a primer on 3D mathematics?

As for converting between them, it looks like you want to project one unit along the forward vector of the orientation and find that position.
As for reversing it, there are infinitely many orientations that can generate the forward vector.

Sorry wrote that in a hurry to represent the directions in relation to x,y,z not the proper numbers.

### #13DarkScience  Members

Posted 11 June 2012 - 01:43 PM

Alvaro is correct: a triplet of pitch, yaw and roll (Euler angles) represents a 3D orientation. An euclidean 3D vector can at most represent a direction in 3D space (plus a magnitude). That direction can be e.g. an axis of rotation, or a look-at direction, but it does not capture a full 3D orientation.

If representing an axis of rotation with a 3D euclidean vector, one needs to add in a single scalar (the angle of rotation about that axis) to make it a complete representation of a 3D orientation. This is commonly called an axis-angle representation of an orientation. If you are looking to convert an axis-angle representation to a 3D rotation matrix (and then to an Euler triplet), see e.g. MathGeoLib's float3x3::RotateAxisAngle function (boils down to Quat::SetFromAxisAngle).

If representing a look-at direction with a 3D euclidean vector, one needs to add in the concept of a 'up' vector (also called a 'world up' or a 'scene up' vector, a fixed vector specifying the upwards direction convention in the scene), or a single scalar 'roll' (being equivalent to above axis-angle) to make it a complete representation of a 3D orientation. This orientation however cannot have any roll, if the up vector is kept static. If you are looking how to turn a look-at direction vector into a 3D orientation, see e.g. MathGeoLib's float3x3::LookAt.

To convert a rotation matrix to pitch-yaw-roll components (Euler angles), see e.g. MathGeoLib's float3x3::ToEuler*** conversion functions.

Alvaro is incorrect. I explained that im looking for the direction not the absolute full 3d orientation. He should of figured given the deffinition of Angle. Alvaro thanks for this stressful encounter. Go to hell.

clb thanks for an actual reply to my inquiry. Though go to hell for saying "Alvaro is correct".

Sorry i thought he would understand that i'm trying to get a Angle not a Position or Vector.

### #14DarkScience  Members

Posted 11 June 2012 - 01:46 PM

Oh and Alarvo http://en.wikipedia.org/wiki/Angle

Edited by DarkScience, 11 June 2012 - 01:46 PM.

### #15frob  Moderators

Posted 11 June 2012 - 01:47 PM

Each of your posts say you want to go back again. Only one direction makes sense.

You can project one unit along your orientation to find a 'forward' normal. That is a matter of simple trig.

The other direction, finding an orientation that generates the same forward normal, does not really make sense. There are infinitely many solutions.

Check out my book, Game Development with Unity, aimed at beginners who want to build fun games fast.

Also check out my personal website at bryanwagstaff.com, where I occasionally write about assorted stuff.

### #16clb  Members

Posted 11 June 2012 - 01:49 PM

The goal is to convert Pitch , Yaw , Roll to X , Y , Z and then back.
So Angle( 0 , 0 , 0 ) would be in XYZ ( 0 , 1 , 0 ).
So Angle( 0 , 90 , 0 ) would be in XYZ ( 1 , 0 , 0 ).
So Angle( 0 , 180 , 0 ) would be in XYZ ( 0 , -1 , 0 ).
So Angle( 0 , 270, 0 ) would be in XYZ ( -1 , -1 , 0 ).
So Angle( 0 , 360, 0 ) would be in XYZ ( 0 , 1 , 0 ).

This sounds like you're trying to define a 3D orientation based on a LookAt direction of an object. See if the functions in my previous post can help you with that (float3x3::LookAt, and then float3x3::ToEuler***).
Me+PC=clb.demon.fi | C++ Math and Geometry library: MathGeoLib, test it live! | C++ Game Networking: kNet | 2D Bin Packing: RectangleBinPack | Use gcc/clang/emcc from VS: vs-tool | Resume+Portfolio | gfxapi, test it live!

### #17DarkScience  Members

Posted 11 June 2012 - 01:51 PM

Each of your posts say you want to go back again. Only one direction makes sense.

What ???

You can project one unit along your orientation to find a 'forward' normal. That is a matter of simple trig.

Thats what i'm asking how to do. I've been getting an output which i posted here.

first set

Spoiler

second set
Spoiler

PYR are in degrees in second set...

Seems to be a slight inaccuracy. I cant get it working properly even though from what i know second set should work fine.

Ignore the Z = nonsense. Its just a placeholder.

EDIT The issue is that when X or Y is suppose to be full (-1 ,0, 1) they are but the other number is 6.E~~~ (first set)

EDIT AGAIN:

Remember that 6.12303176911189E-17 is 0.00000000000000006 (I may have even missed a zero there!) so it is a very, very small deviation.

That's the issue i was having, now that i know what it is i can fix it. So my calculations are correct. Just a issue that i must work around.

Also as to the -1 rating. Thanks. It means alot to me.

Edited by DarkScience, 11 June 2012 - 02:32 PM.

### #18DarkScience  Members

Posted 11 June 2012 - 02:42 PM

SOLUTION
private PointF DegreesToXY( float degrees , float radius , Point origin )
{
PointF xy = new PointF ( );
double radians = degrees * Math.PI / 180.0;
xy.X = (float) Math.Round ( x * 1000000 ) / 1000000;
xy.Y = (float) Math.Round ( y * 1000000 ) / 1000000;
return xy;
}


or
Spoiler

Edited by DarkScience, 11 June 2012 - 03:09 PM.

### #19Álvaro  Members

Posted 15 June 2012 - 08:30 AM

That's a solution to what exactly? I don't see a conversion from XYZ to PYR anywhere.

The strange rounding you do at the end will give you the illusion that the result is more precise, but you are actually throwing precision away in general.

### #20WiredCat  Members

Posted 17 June 2012 - 08:33 AM

float __fastcall T3DPlanet::GetLongitude(t3dpoint cpos)   //poludniki (Dlugosc)
{
float	   angle;
angle = n2dGetPolarCoordAngleA(cpos.x-pos.x,cpos.z-pos.z) / 6.2731860f;

angle = -360.0f*angle;
angle = VALIDUJ(angle)+90.0f;
angle = VALIDUJ(angle);
return angle;

}

float __fastcall T3DPlanet::GetLatitude(t3dpoint cpos)
{
t3dpoint cpn;
cpn = vectorAB(pos,cpos);
cpn = Normalize(cpn);
float t = cpn.x*cpn.x + cpn.z*cpn.z;
t = sqrt(t);
if (cpn.y == 0.0f) return 0.0f;
float tanges = t / cpn.y;
float angle;
angle = atan(tanges);
if (angle < 0) angle = -1.0f*(90.0f + angle); else
angle = 90.0f - angle;
return angle;
}
float __fastcall n2dGetPolarCoordAngleA(float x,float y)
{
if ( (x > 0) && (y >= 0) ) {  return ArcTan(y/x);		}
if ( (x > 0) && (y < 0) )  {  return ArcTan(y/x)+2.0*3.1415926535897932384626433832795;	 }
if  (x < 0)				{ return ArcTan(y/x)+3.1415926535897932384626433832795;	  }
if ( (x == 0) && (y > 0) )  {  return 3.1415926535897932384626433832795/2.0;				   }
if ( (x == 0) && (y < 0) )  {  return 3.0*3.1415926535897932384626433832795/2.0;				 }
//last versions were without .0 just simple 2 division
return - 1000.0;
}


pos is a point(0,0,0)

glop is acually heading angle! imopi =pi / 180
SUPERPOINT.x = 100000.0*(sin((glop)*imopi)*cos((heading)*imopi));


then the vector is +SUPERPOINT.x,
-SUPERPOINT.y,-SUPERPOINT.z

need more ?

Edited by ___, 17 June 2012 - 08:38 AM.

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