Hello @HerrMay,
Is the multiplication of a matrix with a vector (mg.off = mg * p) essentially the same what mg * c4d.utils.MatrixMove(vec) does?
No, mg * p multiplies a matrix by a vector which will yield the transformed vector p'. mg * c4d.utils.MatrixMove(vec) on the other hand multiplies two matrices, yielding the combined transform of them, a new matrix.
What would be equivalent to mg * p is mg * c4d.utils.MatrixMove(p) * c4d.Vetcor(0, 0, 0). Please note that the whole subject is also out of scope of support as declared in the forum guidelines. I understand that the subject is a common barrier for the more on the artist-sided leaning users of ours, and I help where I can, but we cannot teach you vector math, linear algebra, or however you want to label this subject.
Find below a short code example.
Cheers,
Ferdinand
Output:
M = Matrix(v1: (1, 0, 0); v2: (0, 1, 0); v3: (0, 0, 1); off: (0, 100, 0)) p = Vector(100, 0, 0) M * p = Vector(100, 100, 0) M * c4d.utils.MatrixMove(c4d.Vector(100, 0, 0)) = Matrix(v1: (1, 0, 0); v2: (0, 1, 0); v3: (0, 0, 1); off: (100, 100, 0)) M * c4d.Vector(100, 0, 0) = Vector(100, 100, 0) N * c4d.Vector( 0, 0, 0) = Vector(100, 100, 0) M * c4d.utils.MatrixMove(p) * c4d.Vector(0, 0, 0) = Vector(100, 100, 0)Code:
import c4d # Let us assume #M to be the global matrix/transform of some object #op. View it as a tool to # transform a point in global space into the local coordinate system of #op. M: c4d.Matrix = c4d.Matrix(off=c4d.Vector(0, 100, 0)) # The matrix #M now has this form: # # | v1 1 0 0 | # The "x-axis" of the coordinate system defined by #M. # | v2 0 1 0 | # The "y-axis" of the coordinate system defined by #M. # | v3 0 0 1 | # The "z-axis" of the coordinate system defined by #M. # ---------------------- # | off 0 100 0 | # The origin of the coordinate system defined by #M. # # I.e., #M has the standard orientation and scale and only translates all things by 100 units # on the y-axis. So, the object #op would have the Euler angles (0°, 0°, 0°), the scale (1, 1, 1) # and the position (0, 100, 0) in world coordinates. # Define a vector #p to transform and print both #M and #p. p: c4d.Vector = c4d.Vector(100, 0, 0) print(f"{M = }") print(f"{p = }") # Transforming a point #p by a matrix #M will yield a point #q that is in the same relation to #M # as #p is to the global frame. q: c4d.Vector = M * p # #q will be the vector (100, 100, 0) because , (100, 100, 0) and #M are the same relation as #p # and the identity matrix are, a.k.a., the world frame. In a less technical way, (0, 100, 0) is the # origin of the coordinate system defined by #M. And to express #p in a manner as if #M would be # its coordinate system, we have to add (0, 100, 0), because that is the new origin. For orientation # and scale it works more or less the same, I would recommend having a look at the Matrix manual or # Wikipedia article on the subject. print (f"{M * p = }") # We can construct new transforms in many ways (again, Matrix Manual :)), one of them is by # combining multiple transforms via matrix multiplication. # We "add" the translation transform (100, 0, 0) to #M. Note that matrix multiplication is not # commutative, i.e., "M * N = N * M" does not always hold true. In this case it would because only # translations are involved. N: c4d.Matrix = M * c4d.utils.MatrixMove(c4d.Vector(100, 0, 0)) print(f"{M * c4d.utils.MatrixMove(c4d.Vector(100, 0, 0)) = }") # To get the same point as #q when multiplying a point #r with #N, we must pick the null-vector # because the origin of #N is already at where M * (100, 0, 0) is. print (f"{M * c4d.Vector(100, 0, 0) = }") print (f"{N * c4d.Vector( 0, 0, 0) = }") # We can also do it in one operation: print (f"{M * c4d.utils.MatrixMove(p) * c4d.Vector(0, 0, 0) = }")