Projection by a vector to a plane
Hi
That's a pure algorithmic question, nothing here related to Autodesk APIs. The source code of this method is not public, you should be able to find detailed elements of answer from mathematical resources on the web looking for projection matrices, unless somebody on this forum has custom code to share with you:
http://en.wikipedia.org/wiki/Projection_%28linear_algebra%29
I hope it helps.
Regards,
Philippe.
Philippe Leefsma
Developer Technical Services
Autodesk Developer Network
Accepted solution
Hi,
Inspired by this (old) LISP routine from my library (AutoLISP does not provide functions to deal with vectors and matrices),
;; Multiply a vector by a scalar
(defun vxs (v s)
(mapcar (function (lambda (x) (* x s))) v)
)
;; Return the dot product of two vectors
(defun vxv (v1 v2)
(apply '+ (mapcar '* v1 v2))
)
;; Apply a transformation matrix to a vector -Vladimir Nesterovsky-
(defun mxv (m v)
(mapcar (function (lambda (r) (vxv r v))) m)
)
;; Return the transformation matrix (4x4) describing the projection
;; to the plane defined by its origin and normal along the direction vector
(defun projMat (org norm dir / mat)
(append
(mapcar
(function (lambda (v x) (append v (list x))))
(setq mat
(mapcar
(function (lambda (v1 v2) (mapcar '- v1 v2)))
'((1. 0. 0.) (0. 1. 0.) (0. 0. 1.))
(mapcar
(function (lambda (x) (vxs norm x)))
(vxs dir (/ 1. (vxv norm dir)))
)
)
)
(mapcar '- org (mxv mat org))
)
'((0. 0. 0. 1.))
)
) here's a C# adaptation. It returns the same matrix as the built-in Matrix3d.Projection() method.
I overloaded the method so that it's possible to pass a Plane instance or a Point3d (origin) and a Vector3d (normal) as arguments.
public Matrix3d ProjectionMatrix(Plane projectionPlane, Vector3d projectDir)
{
return ProjectionMatrix(projectionPlane.PointOnPlane, projectionPlane.Normal, projectDir);
}
public Matrix3d ProjectionMatrix(Point3d origin, Vector3d normal, Vector3d projectDir)
{
double scale = normal.DotProduct(projectDir);
Vector3d dir = projectDir / scale;
Vector3d xVec = Vector3d.XAxis - normal * dir.X;
Vector3d yVec = Vector3d.YAxis - normal * dir.Y;
Vector3d zVec = Vector3d.ZAxis - normal * dir.Z;
Vector3d orgVec = origin.GetAsVector();
return new Matrix3d(new double[16]
{
xVec.X, xVec.Y, xVec.Z, origin.X - xVec.DotProduct(orgVec),
yVec.X, yVec.Y, yVec.Z, origin.Y - yVec.DotProduct(orgVec),
zVec.X, zVec.Y, zVec.Z, origin.Z - zVec.DotProduct(orgVec),
0.0, 0.0, 0.0, 1.0
});
}
Here's a (may be) more explainatory version (decomposed and commented).
public Matrix3d ProjectionMatrix(Point3d origin, Vector3d normal, Vector3d projectDir)
{
// Calculate a scale factor
// If scale = 0 (normal is perpendicular to projectDir) this won't throw
// an exception but return an unusable matrix :
// ((NaN,NaN,-Infinity,NaN),(NaN,NaN,NaN,NaN),(NaN,NaN,NaN,NaN),(0,0,0,1))
double scale = normal.DotProduct(projectDir);
// apply the scale factor to projectDir
Vector3d dir = projectDir / scale;
// Build the row vectors of the 'linear part' of the matrix (3x3 matrix)
Vector3d xVec = Vector3d.XAxis - normal * dir.X;
Vector3d yVec = Vector3d.YAxis - normal * dir.Y;
Vector3d zVec = Vector3d.ZAxis - normal * dir.Z;
// Build the 'translational part' of the matrix (column vector)
Vector3d orgVec = origin.GetAsVector();
// Apply the 'linear part' matrix to the origin
Point3d transformedOrigin = new Point3d(
xVec.DotProduct(orgVec), yVec.DotProduct(orgVec), zVec.DotProduct(orgVec));
// The displacement vector is the vector from tranformedOrigin to origin
Vector3d disp = origin - transformedOrigin;
// Assemble the 4x4 transformation matrix
return new Matrix3d(new double[16]
{
xVec.X, xVec.Y, xVec.Z, disp.X,
yVec.X, yVec.Y, yVec.Z, disp.Y,
zVec.X, zVec.Y, zVec.Z, disp.Z,
0.0, 0.0, 0.0, 1.0
});
}
Hi Tony,
This is what I understood too.
The reasons why I posted some code are the ability to test in AutoCAD if the returned matrix is the same as the one returned by Matrix3d.Projection(), and the fact it's easier for me to post some commented code than to try an explanation in English.
I hope the OP would be able to adapt it with the corresponding types to Point3d, Vector3d and the DotProduct() method.