# How do I convert from a rotation matrix to Heading, Pitch, and Roll?

3458
1
09-17-2015 07:32 PM
by
New Contributor II

Starting with a 3D rotation matrix, how do I compute the Heading, Pitch, and Roll values that the various 3D symbols desire?

More Detail:

So, given a rotation matrix that looks like this:

[ M00, M01, M02 ]

[ M10, M11, M12 ]

[ M20, M21, M22 ]

And I'm trying to create a ConeMarkerSymbol.

First I tried this computation (source:(

Heading = Math.Atan2(M10, M00) * (180 / Math.PI)

Pitch = Math.Atan2(-M20, Math.Sqrt(M21 * M21 + M22 * M22)) * (180 / Math.PI)

Roll = Math.Atan2(M21, M22) * (180 / Math.PI)

But that didn't yield the correct results.  Then I tried this computation (source:(

Heading = Math.Atan2(M20, M21) * (180 / Math.PI)

Pitch = Math.Acos(M22) * (180 / Math.PI)

Roll = -Math.Atan2(M02, M12) * (180 / Math.PI)

But that didn't get it either.  What's the correct calculation?

Even More Details:

I'm doing all of my business logic using a state planar projection and then converting it to WGS84 to display it in a SceneView.  The GraphicsLayer is using a SurfacePlacement of Absolute and I'm able to place all of the objects correctly, but getting them oriented properly is a challenge.  I am able to render the objects in an DirectX window with the correct orientation, so I think the rotation matrix is correct,

I'm using C# and the .NET runtime SDK.  Thanks in advance!

1 Solution

Accepted Solutions
by
New Contributor II

Calculation:

public class TaitBryanAngles

{

public static TaitBryanAngles FromMatrix(Matrix3D matrix)

{

double psi, theta, phi;

if (!(matrix.M02 == 1 || matrix.M02 == -1))

{

theta = -Math.Asin(matrix.M02);

psi = Math.Atan2(matrix.M12, matrix.M22);

phi = Math.Atan2(matrix.M01, matrix.M00);

}

else

{

phi = 0.0;

if (matrix.M02 == -1)

{

theta = Math.PI / 2;

psi = phi + Math.Atan2(matrix.M10, matrix.M20);

}

else

{

theta = -Math.PI / 2;

psi = -phi + Math.Atan2(-matrix.M10, -matrix.M20);

}

}

return new TaitBryanAngles(phi * 180 / Math.PI, psi * 180 / Math.PI, theta * 180 / Math.PI);

}

public TaitBryanAngles(double heading, double roll, double pitch)

{

Roll = roll;

Pitch = pitch;

}

public double Heading { get; }

public double Roll { get; }

public double Pitch { get; }

}

Explanation:

The values that are expected are the Tait-Bryan XYZ angles.  In order to derive these angles, I followed this paper here:

http://staff.city.ac.uk/~sbbh653/publications/euler.pdf

In that paper, they derive the ZYX angles.  However, the API expects the XYZ angles.  So, I followed the same procedure with a different order of the rotation matrix multiplication and arrived at the answer given above.  Hopefully this is helpful for someone else!

by
New Contributor II

Calculation:

public class TaitBryanAngles

{

public static TaitBryanAngles FromMatrix(Matrix3D matrix)

{

double psi, theta, phi;

if (!(matrix.M02 == 1 || matrix.M02 == -1))

{

theta = -Math.Asin(matrix.M02);

psi = Math.Atan2(matrix.M12, matrix.M22);

phi = Math.Atan2(matrix.M01, matrix.M00);

}

else

{

phi = 0.0;

if (matrix.M02 == -1)

{

theta = Math.PI / 2;

psi = phi + Math.Atan2(matrix.M10, matrix.M20);

}

else

{

theta = -Math.PI / 2;

psi = -phi + Math.Atan2(-matrix.M10, -matrix.M20);

}

}

return new TaitBryanAngles(phi * 180 / Math.PI, psi * 180 / Math.PI, theta * 180 / Math.PI);

}

public TaitBryanAngles(double heading, double roll, double pitch)

{

Roll = roll;

Pitch = pitch;

}

public double Heading { get; }

public double Roll { get; }

public double Pitch { get; }

}

Explanation:

The values that are expected are the Tait-Bryan XYZ angles.  In order to derive these angles, I followed this paper here:

http://staff.city.ac.uk/~sbbh653/publications/euler.pdf

In that paper, they derive the ZYX angles.  However, the API expects the XYZ angles.  So, I followed the same procedure with a different order of the rotation matrix multiplication and arrived at the answer given above.  Hopefully this is helpful for someone else!