# How can I get a projection matrix?

### Question

• 1. I want to get a projection matrix which I can get from a device.Transform.Projection attribute of managed Direct3D.
Viewport3D.Transform.Value and Viewport3D.Camera.Transform.Value has a unitary matrix. How can I get it?
2. Why device of managed Direct3D changes yScale value (M22 of projection matrix) but Viewport3D (as I guess) changes xScale value  (M11 of projection matrix) when client area was changed? Can I force Viewport3D to have a scaling behavior as much as device of managed Direct3D?

Thanks
Friday, April 10, 2009 8:24 AM

### Answers

• You can get the projection matrix by mathematical calculations.

Pay attention to the type of Camera. PerspectiveCamera and OrthographicCamera has different calculation process.

For example:

private static Matrix3D GetProjectionMatrix(OrthographicCamera camera, double aspectRatio)
{
// This math is identical to what you find documented for
// D3DXMatrixOrthoRH with the exception that in WPF only
// the camera's width is specified.  Height is calculated
// from width and the aspect ratio.
double w = camera.Width;
double h = w / aspectRatio;
double zn = camera.NearPlaneDistance;
double zf = camera.FarPlaneDistance;
double m33 = 1 / (zn - zf);
double m43 = zn * m33;
return new Matrix3D(
2 / w, 0, 0, 0,
0, 2 / h, 0, 0,
0, 0, m33, 0,
0, 0, m43, 1);
}
private static Matrix3D GetProjectionMatrix(PerspectiveCamera camera, double aspectRatio)
{
// This math is identical to what you find documented for
// D3DXMatrixPerspectiveFovRH with the exception that in
// WPF the camera's horizontal rather the vertical
// field-of-view is specified.
double hFoV = MathUtils.DegreesToRadians(camera.FieldOfView);
double zn = camera.NearPlaneDistance;
double zf = camera.FarPlaneDistance;
double xScale = 1 / Math.Tan(hFoV / 2);
double yScale = aspectRatio * xScale;
double m33 = (zf == double.PositiveInfinity) ? -1 : (zf / (zn - zf));
double m43 = zn * m33;
return new Matrix3D(
xScale, 0, 0, 0,
0, yScale, 0, 0,
0, 0, m33, -1,
0, 0, m43, 0);
}
/// <summary>
///     Computes the effective projection matrix for the given
///     camera.
/// </summary>
public static Matrix3D GetProjectionMatrix(Camera camera, double aspectRatio)
{
if (camera == null)
{
throw new ArgumentNullException("camera");
}
PerspectiveCamera perspectiveCamera = camera as PerspectiveCamera;
if (perspectiveCamera != null)
{
return GetProjectionMatrix(perspectiveCamera, aspectRatio);
}
OrthographicCamera orthographicCamera = camera as OrthographicCamera;
if (orthographicCamera != null)
{
return GetProjectionMatrix(orthographicCamera, aspectRatio);
}
MatrixCamera matrixCamera = camera as MatrixCamera;
if (matrixCamera != null)
{
return matrixCamera.ProjectionMatrix;
}
throw new ArgumentException(String.Format("Unsupported camera type '{0}'.", camera.GetType().FullName), "camera");
}
• Proposed as answer by Tuesday, April 14, 2009 8:30 AM
• Marked as answer by Wednesday, April 15, 2009 1:24 AM
Tuesday, April 14, 2009 8:29 AM