Patent ID: 8878844

Claim:
A security element for security papers, value documents, or other non-transitory data carriers, the security element comprising: (A) a motif layer including a motif image that is subdivided into a plurality of cells, in each of which are arranged imaged regions of a specified three dimensional solid defined by a solid function f(x,y,z), the image regions of the specified three dimensional solid being arranged via printing, embossing, disposing, or a combination thereof, on or in at least one of the security papers, value documents, or other non-transitory data carriers, (B) a viewing grid composed of a plurality of viewing elements for depicting the specified three dimensional solid when the motif image is viewed with the aid of the viewing grid, the motif image having an image function m(x,y) that is given by ⁢ m ⁡ ( x , y ) = f ⁡ ( x K y K z K ⁡ ( x , y , x m , y m ) ) · g ⁡ ( x , y ) , ⁢ ⁢ where ⁢ ( x K y K ) = ( x y ) + V ⁡ ( x , y , x m , y m ) · ( ( ( ( x y ) + w d ⁡ ( x , y ) ) ⁢ mod ⁢ ⁢ W ) - w d ⁡ ( x , y ) - w c ⁡ ( x , y ) ) ⁢ w d = ( x , y ) = W · ( d 1 ⁡ ( x , y ) d 2 ⁡ ( x , y ) ) ⁢ ⁢ and ⁢ ⁢ w c ⁡ ( x , y ) = W · ( c 1 ⁡ ( x , y ) c 2 ⁡ ( x , y ) ) , such that the specified three dimensional solid defined is depicted when the motif image of the motif layer is viewed through the viewing grid; wherein a unit cell of the viewing grid is described by lattice cell vectors w 1 = ( w 11 w 21 ) ⁢ ⁢ and ⁢ ⁢ w 2 = ( w 11 w 21 ) and combined in the matrix W = ( w 11 w 12 w 21 w 22 ) , and x m and y m indicate lattice points of the W-lattice, the magnification term V(x,y, x m ,y m ) is either a scalar V ⁡ ( x , y , x m , y m ) = ( z K ⁡ ( x , y , x m , y m ) e - 1 ) , where e is the effective distance of the viewing grid from the motif image, or a matrix V(x,y, x m ,y m )=(A(x,y, x m ,y m )−I), the matrix A ⁡ ( x , y , x m , y m ) = ( a 11 ⁡ ( x , y , x m , y m ) a 12 ⁡ ( x , y , x m , y m ) a 21 ⁡ ( x , y , x m , y m ) a 22 ⁡ ( x , y , x m , y m ) ) describing a desired magnification and movement behavior for the specified three dimensional solid and I being the identity matrix, the vector (c 1 (x,y), c 2 (x,y)), where 0≦c 1 (x, y), c 2 (x, y)<1, indicates a position of a center of the viewing elements relative to the cells of the motif image, the vector (d 1 (x,y), d 2 (x,y)), where 0≦d 1 (x, y), d 2 (x, y)<1, represents a displacement of cell boundaries in the motif image, and g(x,y) is a mask function for adjusting visibility of the specified three dimensional solid.