Point Clipping

🎯 Introduction

Clipping algorithms, or simply clipping, refer to the procedure that identifies portions of a picture that lie either inside or outside a specified region of space. The region being used for clipping is known as the clip window. Clipping has various applications, such as extracting a part of a defined scene for viewing, identifying visible surfaces in three-dimensional views, antialiasing line segments or object boundaries, creating objects using solid-modeling procedures, displaying a multi-window environment, and enabling drawing and painting operations that allow selecting parts of a picture for copying, moving, erasing, or duplicating. Depending on the application, the clip window can be a general polygon or have curved boundaries.

For viewing transformations, the objective is to display only those parts of the picture that lie within the window area, discarding everything outside of it. Clipping algorithms can be applied in world coordinates, where only the contents within 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, and then clipped against the viewport boundaries. World-coordinate clipping eliminates the processing required to transform primitives outside the window to device space.

Viewport clipping, on the other hand, can streamline calculations by allowing the concatenation of viewing and geometric transformation matrices. However, viewport clipping demands transforming all objects, including those outside the window area, to device coordinates. On raster systems, clipping algorithms are often combined with scan conversion.

🎯 Point Clipping

Point clipping is one of the types of clipping and is used to determine whether a point lies within the clip window. Assuming that the clip window is a rectangle in standard position, a point P = (x, y) is saved for display only if it satisfies the following inequalities:

xwmin < x < xwmax

ywmin < y < ywmax

Here, (xwmin, xwmax, ywmin, ywmax) represent the edges of the clip window, which can be either the world-coordinate window boundaries or viewport boundaries. If any of these four inequalities is not satisfied, the point is considered outside the clip window and is clipped, i.e., not saved for display.

Point clipping is applied less frequently than line or polygon clipping. However, certain applications might require a point clipping procedure. For instance, point clipping can be applied to scenes involving explosions or sea foam modeled with particles (points) distributed within a specific region of the scene.

🎯 Summary

Clipping algorithms play a crucial role in computer graphics by determining which parts of a picture are visible within a specified region, known as the clip window. Various applications, such as scene extraction, object visibility, and drawing operations, benefit from clipping techniques. Point clipping, one of the types of clipping, focuses on determining whether a point lies inside or outside the clip window. Points that satisfy specific inequalities based on the clip window boundaries are saved for display, while those outside the window are clipped.

🎯 Key Points