Overview
Topological Sweep is a line arrangements method for line arrangement traversal. It works by sweeping an arrangement by maintaining a topological ordering instead of coordinates.
SpecializedSource checked
Topological Sweep
Topological Sweep addresses line arrangement traversal by sweeping an arrangement by maintaining a topological ordering instead of coordinates.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Geometry
- Difficulty
- Advanced
- Family
- Line Arrangements
- Tier
- Specialized
- Status
- Verified
- Review
- Source Checked
- Sources
- 2
- Formulas
- 0
- Relationships
- 4
- Code example
- Not ready
- Visualization
- Ready
Core Concepts
line arrangement traversalline arrangementsgeometric primitivesgeometry
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n log n)
Worst
O(n^2)
Space
O(n)
When to Use
- Use Topological Sweep when solving line arrangement traversal and you want to benefit from sweeping an arrangement by maintaining a topological ordering instead of coordinates.
- Choose it when O(n log n) average/worst-case time and O(n) memory match your workload profile.
- Prefer it over Zone Algorithm or Incremental Line Arrangement Construction when the problem structure favors line arrangement traversal.
When Not to Use
- Avoid when coordinate precision is too low for the required geometric decisions.
- Avoid when degenerate cases dominate and the implementation has no robustness strategy.
What It Does
- Computes line arrangement traversal within Line Arrangements workloads (O(n log n) time, O(n) space).
- Works by sweeping an arrangement by maintaining a topological ordering instead of coordinates.
- Maintains key invariants across line arrangement traversal, line arrangements, geometric primitives.
Use Cases
- Production and research workloads requiring line arrangement traversal via sweeping an arrangement by maintaining a topological ordering instead of coordinates.
- Line Arrangements pipelines where O(n log n) time and O(n) space fit system constraints.
- Engineering comparisons against Zone Algorithm and Incremental Line Arrangement Construction when tuning line arrangement traversal.
Inputs
- Points, segments, polygons, or geometric primitives
- Query or construction parameters
Outputs
- Geometric decision, measurement, or constructed structure
Pseudocode
- 1.Normalize input coordinates, primitives, or pixel buffers and initialize spatial data structures for line arrangement traversal.
- 2.Establish the sweep event queue, hierarchy, or scale-space pyramid required by Topological Sweep.
- 3.Process geometric predicates or pixel neighborhoods by sweeping an arrangement by maintaining a topological ordering instead of coordinates.
- 4.Resolve boundary degeneracies, occlusions, or threshold suppressions to maintain consistency.
- 5.Output the final line arrangement traversal primitives, descriptors, or composited buffer.
Canonical Example
- Input
- Points, segments, polygons, or geometric primitives configured for a representative line arrangement traversal test case
- Output
- Geometric decision, measurement, or constructed structure satisfying Topological Sweep invariants
- Explanation
- Topological Sweep processes the input by sweeping an arrangement by maintaining a topological ordering instead of coordinates, tracking line arrangement traversal and line arrangements to produce the verified line arrangement traversal result.
Implementation Notes
- Normalize orientation and coordinate conventions at module boundaries.
- Add degenerate cases such as collinear points and touching edges.
- Use robust predicates where sign errors change topology.
Common Pitfalls
- Ignoring collinear, coincident, or nearly degenerate geometry.
- Relying on floating-point signs without a robustness strategy.
- Mixing coordinate systems or orientation conventions.
Interactive Mechanism Walkthrough
Spatial Primitive & Sweep-Line CanvasShow sweeping an arrangement by maintaining a topological ordering instead of coordinates on a small line arrangement traversal example.
Step 1 of 5: Normalize input coordinates, primitives, or pixel buffers and initialize spatial data structures for line arrangement traversal.
geometry-mechanismNotes
Topological Sweep operates in O(n log n) time and O(n) space within the Line Arrangements family. Often compared with Zone Algorithm and Incremental Line Arrangement Construction.
Sources (2)
What each reference supports for this entry.
Computational Geometry: Algorithms and Applications
BookTextbook support for Topological Sweep's computational geometry problem family, predicates, structures, or geometric construction.
Open sourceThe Algorithm Design Manual
BookAlgorithm catalog support for Topological Sweep in the computational geometry benchmark area.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageConceptual neighborZone Algorithm
Topological Sweep and Zone Algorithm share a concrete line arrangements mechanism for line arrangement traversal.
Conceptual neighborIncremental Line Arrangement Construction
Topological Sweep and Incremental Line Arrangement Construction share a concrete line arrangements mechanism for line arrangement traversal.
Related Algorithms
Tags
GeometryComputational Geometry