Fundamental Geometric Primitives

Fundamental geometric primitives are the building blocks of computational geometry. They include points, lines, and shapes that help us understand spatial relationships and perform calculations in various applications, from computer graphics to data analysis.

1. Points

   • The most basic geometric primitive, representing a location in space.
   • Defined by coordinates in a given dimensional space (e.g., 2D or 3D).
   • No size, area, or volume; purely a position.

2. Lines

   • Infinite collections of points extending in both directions without end.
   • Defined by a linear equation or two distinct points.
   • Fundamental in defining relationships between points and other geometric shapes.

3. Line Segments

   • A portion of a line defined by two endpoints.
   • Has a finite length, unlike lines which are infinite.
   • Used to represent distances and connections between points.

4. Rays

   • A part of a line that starts at a point and extends infinitely in one direction.
   • Defined by an endpoint and another point indicating direction.
   • Useful in applications involving angles and directional movement.

5. Vectors

   • Represent both magnitude and direction, often visualized as arrows.
   • Can be used to describe movement, forces, and other physical quantities.
   • Essential in computational geometry for transformations and operations.

6. Planes

   • A flat, two-dimensional surface that extends infinitely in all directions.
   • Defined by three non-collinear points or a point and a normal vector.
   • Fundamental in defining spatial relationships and intersections in 3D geometry.

7. Polygons

   • Closed figures formed by a finite number of line segments (edges).
   • Can be classified as convex or concave based on their angles and vertices.
   • Important in computer graphics, modeling, and spatial partitioning.

8. Circles

   • A set of points equidistant from a central point (the center).
   • Defined by a radius and center point, crucial in defining curves and arcs.
   • Used in various applications, including collision detection and pathfinding.

9. Triangles

   • The simplest polygon, defined by three vertices and three edges.
   • Fundamental in geometry due to their properties and ability to approximate other shapes.
   • Used extensively in algorithms for mesh generation and surface representation.

10. Convex Hulls

    • The smallest convex shape that can enclose a set of points in a plane or space.
    • Useful for simplifying complex shapes and determining boundaries.
    • Key in various computational geometry algorithms, including clustering and shape analysis.