Broken line

Broken line

A broken line refers to a sequence of segments of straight lines, usually in a two-dimensional plane, that are connected but not extended in a straight path. Each segment in a broken line connects two points, and these points are called vertices. The line segments are called edges. Broken lines are fundamental concepts in geometry and are widely used in various fields such as mathematics, engineering, art, and computer graphics.

Definition

A broken line is defined as a series of connected line segments where each segment starts where the previous one ends, but the direction of the line changes at least once. In mathematical terms, a broken line is a piecewise linear continuous function. In a more general sense, broken lines can be used to represent a path or a boundary that changes direction at certain points.

Properties

Broken lines have several important properties:

• Vertices: The points at which the line segments meet. The first and last points are called the endpoints.
• Edges: The line segments themselves.
• Length: The total length of a broken line can be found by summing the lengths of its individual segments.
• Angles: The angles at which the direction changes at the vertices. These angles can be used to describe the shape and direction of the broken line.

Applications

Broken lines are used in various applications:

• In geometry, they are used to construct polygons and complex shapes.
• In cartography, broken lines represent borders, roads, or paths that are not straight.
• In computer graphics, they are used to model objects and environments, especially in vector graphics where shapes are defined by paths rather than pixels.
• In engineering, broken lines can represent the path of mechanical parts, electrical circuits, or architectural plans.

Types of Broken Lines

There are several types of broken lines, including:

• Open broken lines: Where the first and last vertices are not the same, and the line does not form a closed shape.
• Closed broken lines: Where the first and last vertices are the same, forming a closed loop. This type is often used to define polygons.
• Simple broken lines: Where none of the line segments cross each other.
• Complex broken lines: Where some of the line segments may cross each other, forming more complex shapes.

See Also

• Line segment
• Vertex (geometry)
• Polygon
• Vector graphics