## Translation

Some applications translate (or shift) objects drawn in the client area. If your application features this capability, use the**SetWorldTransform**function to set the appropriate world-space to page-space transformation. This function receives a pointer to an

**XFORM**structure containing the appropriate values. The

**eDx**and

**eDy**members of

**XFORM**specify the horizontal and vertical translation components, respectively. When

*translation*occurs, each point in an object is shifted vertically, horizontally, or both, by a specified amount. The following illustration shows a 20- by 20-unit rectangle that was translated to the right by 10 units when copied from world coordinate space to page coordinate space. In the preceding illustration, the x-coordinate of each point in the rectangle is 10 units greater than the original x-coordinate. Horizontal translation can be represented by the following algorithm. x' = x + Dx Where

*x'*is the new x-coordinate,

*x*is the original x-coordinate, and

*Dx*is the horizontal distance moved. Vertical translation can be represented by the following algorithm. y' = y + Dy Where

*y'*is the new y-coordinate,

*y*is the original y-coordinate, and

*Dy*is the vertical distance moved. The horizontal and vertical translation transformations can be combined into a single operation by using a 3-by-3 matrix. |1 0 0| |x' y' 1| = |x y 1| * |0 1 0| |Dx Dy 1| (The rules of matrix multiplication state that the number of rows in one matrix must equal the number of columns in the other. The integer 1 in the matrix |x y 1| is a placeholder that was added to meet this requirement.) The 3-by-3 matrix that produced the illustrated translation transformation contains the following values. |1 0 0| |0 1 0| |10 0 1|

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