Computational Geometry Questions Medium
In Computational Geometry, various data structures are used to efficiently store and manipulate geometric objects. Some of the commonly used data structures in this field include:
1. Point: The most basic data structure used in Computational Geometry is a point, which represents a single location in space. Points are typically represented by their coordinates (x, y, z) in a Cartesian coordinate system.
2. Line Segment: A line segment is a data structure that represents a straight line connecting two points. It is commonly used to represent edges in geometric objects such as polygons or polyhedra.
3. Polygon: A polygon is a closed geometric shape with straight sides. It is represented by a sequence of vertices connected by line segments. Various data structures can be used to store and manipulate polygons, such as linked lists, arrays, or doubly-connected edge lists (DCEL).
4. Quadtree: A quadtree is a tree-based data structure that partitions space into four quadrants recursively. It is commonly used for spatial indexing and efficient searching of points or objects in two-dimensional space.
5. Octree: Similar to a quadtree, an octree is a tree-based data structure that partitions three-dimensional space into eight octants recursively. It is used for spatial indexing and efficient searching of points or objects in three-dimensional space.
6. Voronoi Diagram: A Voronoi diagram is a data structure that partitions a plane into regions based on the distance to a set of input points. It is commonly used for proximity analysis, nearest neighbor search, and spatial clustering.
7. Delaunay Triangulation: A Delaunay triangulation is a data structure that connects a set of points in a way that no point is inside the circumcircle of any triangle formed by the points. It is commonly used for triangulation, interpolation, and mesh generation.
8. Binary Space Partitioning (BSP) Tree: A BSP tree is a binary tree data structure that recursively partitions space using hyperplanes. It is commonly used for efficient visibility determination, collision detection, and ray tracing in three-dimensional space.
These are just a few examples of the data structures used in Computational Geometry. Depending on the specific problem or application, other specialized data structures may also be employed to optimize geometric computations and algorithms.