The procedure that identifies those portions of a picture that are either inside or outside of a specified region of space is referred to as a clipping algorithm, or simply clipping. The region against which an object is to clip is called a clip window.
Applications of clipping include extracting part of a defined scene for viewing; identifying visible surfaces in three-dimensiona1 views; antialiasing line segments or object boundaries; creating objects using solid-modeling procedures; displaying a multi-window environment; and drawing and painting operations that allow parts of a picture to be selected for copying, moving, erasing, or duplicating. Depending on the application, the clip window can be a general polygon or it can even have curved boundaries.
For the viewing transformation, we want to display only those picture parts that are within the window area. Everything outside the window is discarded. Clipping algorithms can be applied in world coordinates, so that only the contents of the window interior are mapped to device coordinates. Alternatively, the complete world-coordinate picture can be mapped first to device coordinates, or normalized device coordinates, then clipped against the viewport boundaries. World-coordinate clipping removes those primitives outside the window from further consideration, thus eliminating the processing necessary to transform those primitives to device space.
Viewport clipping, on the other hand, can reduce calculations by allowing concatenation of viewing and geometric transformation matrices. But viewport clipping does require that the transformation to device coordinates be performed for all objects, including those outside the window area. On raster systems, clipping algorithms are often combined with scan conversion.
Line and polygon clipping routines are standard components of graphics packages, but many packages accommodate curved objects, particularly spline curves and conics, such as circles and ellipses. Another way to handle curved objects is to approximate them with straight-line segments and apply the line- or polygon clipping procedure.
Assuming that the clip window is a rectangle in standard position, we save a point P = (x, y) for display if the following inequalities are satisfied:
xwmin < x < xwmax
ywmin < x < ywmax
where the edges of the clip window (xwmin, xwmax, ywmin, ywmax) can be either the world-coordinate window boundaries or viewport boundaries. If any one of these four inequalities is not satisfied, the point is clipped (not saved for display). Although point clipping is applied less often than line or polygon clipping, some .applications may require a point clipping procedure. For example, point clipping can be applied to scenes involving explosions or sea foam that is modeled with particles (points) distributed in some region of the scene.
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