The Viewport and the Window

The Viewport and the Window

The mapping mode defines how Windows maps logical coordinates that are specified in GDI functions to device coordinates, where the particular device coordinate system depends on the function you use to obtain the device context. To continue this discussion of the mapping mode, we need some additional terminology. The mapping mode is said to define the mapping of the "window"(logical coordinates) to the "viewport"(device coordinates).
The use of these two terms is unfortunate. In other graphics interface systems, the viewport often implies a clipping region. And in Windows, the term "window"has a very specific meaning to describe the area that a program occupies on the screen. We'll have to put aside our preconceptions of these terms during this discussion.
The viewport is specified in terms of device coordinates (pixels). Most often the viewport is the same as the client area, but it can also refer to whole-window coordinates or screen coordinates if you've obtained a device context from GetWindowDC or CreateDC. The point (0, 0) is the upper left corner of the client area (or the whole window or the screen). Values of x increase to the right, and values of y increase going down.
The window is specified in terms of logical coordinates, which might be pixels, millimeters, inches, or any other unit you want. You specify logical window coordinates in the GDI drawing functions.
But in a very real sense, the viewport and the window are just mathematical constructs. For all mapping modes, Windows translates window (logical) coordinates to viewport (device) coordinates by the use of two formulas,

 xViewExt xViewport = (xWindow - xWinOrg) × ________ + xViewOrg xWinExt yViewExt yViewport = (yWindow - yWinOrg) × ________ + yViewOrg yWinExt

where (xWindow, yWindow) is a logical point to be translated and (xViewport, yViewport) is the translated point in device coordinates, most likely client-area coordinates.
These formulas use two points that specify an "origin"of the window and the viewport. The point (xWinOrg, yWinOrg) is the window origin in logical coordinates; the point (xViewOrg, yViewOrg) is the viewport origin in device coordinates. By default, these two points are set to (0, 0), but you can change them. The formulas imply that the logical point (xWinOrg, yWinOrg) is always mapped to the device point (xViewOrg, yViewOrg). If the window and viewport origins are left at their default (0, 0) values, the formulas simplify to

 xViewExt xViewport = xWindow × ________ xWinExt yViewExt yViewport = yWindow × ________ yWinExt

The formulas also include two points that specify "extents": the point (xWinExt, yWinExt) is the window extent in logical coordinates; (xViewExt, yViewExt) is the viewport extent in device coordinates. In most mapping modes, the extents are implied by the mapping mode and cannot be changed. Each extent means nothing by itself, but the ratio of the viewport extent to the window extent is a scaling factor for converting logical units to device units.
For example, when you set the MM_LOENGLISH mapping mode, Windows sets xViewExt to be a certain number of pixels and xWinExt to be the length in hundredths of an inch occupied by xViewExt pixels. The ratio gives you pixels per hundredths of an inch. The scaling factors are expressed as ratios of integers rather than floating point values for performance reasons.
The extents can be negative. This implies that values on the logical x-axis don't necessarily have to increase to the right and that values on the logical y-axis don't necessarily have to increase going down.
Windows can also translate from viewport (device) coordinates to window (logical) coordinates:

 xWinExt xWindow = (xViewport - xViewOrg) × ________ + xWinOrg xViewExt yWinExt yWindow = (yViewport - yViewOrg) × ________ + yWinOrg yViewExt

Windows provides two functions that let you convert between device points to logical points in a program. The following function converts device points to logical points:

DPtoLP (hdc, pPoints, iNumber) ;

The variable pPoints is a pointer to an array of POINT structures, and iNumber is the number of points to be converted. For example, you'll find this function useful for converting the size of the client area obtained from GetClientRect (which is always in terms of device units) to logical coordinates:

GetClientRect (hwnd, &rect) ; DPtoLP (hdc, (PPOINT) &rect, 2) ;

This function converts logical points to device points:

LPtoDP (hdc, pPoints, iNumber) ;