Overview
Rotating Calipers Width is a rotating calipers method for polygon width. It works by rotating support lines to find the minimum strip containing a convex polygon.
ExtendedSource checked
Rotating Calipers Width
Rotating Calipers Width addresses polygon width by rotating support lines to find the minimum strip containing a convex polygon.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Geometry
- Difficulty
- Intermediate
- Family
- Rotating Calipers
- Tier
- Extended
- Status
- Verified
- Review
- Source Checked
- Sources
- 3
- Formulas
- 0
- Relationships
- 5
- Code example
- Ready
- Visualization
- Ready
Core Concepts
polygon widthrotating calipersgeometric 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 Rotating Calipers Width when solving polygon width and you want to benefit from rotating support lines to find the minimum strip containing a convex polygon.
- Choose it when O(n log n) average/worst-case time and O(n) memory match your workload profile.
- Prefer it over Rotating Calipers Diameter or Rotating Calipers Antipodal Pairs when the problem structure favors polygon width.
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 polygon width within Rotating Calipers workloads (O(n log n) time, O(n) space).
- Works by rotating support lines to find the minimum strip containing a convex polygon.
- Maintains key invariants across polygon width, rotating calipers, geometric primitives.
Use Cases
- Production and research workloads requiring polygon width via rotating support lines to find the minimum strip containing a convex polygon.
- Rotating Calipers pipelines where O(n log n) time and O(n) space fit system constraints.
- Engineering comparisons against Rotating Calipers Diameter and Rotating Calipers Antipodal Pairs when tuning polygon width.
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 polygon width.
- 2.Establish the sweep event queue, hierarchy, or scale-space pyramid required by Rotating Calipers Width.
- 3.Process geometric predicates or pixel neighborhoods by rotating support lines to find the minimum strip containing a convex polygon.
- 4.Resolve boundary degeneracies, occlusions, or threshold suppressions to maintain consistency.
- 5.Output the final polygon width primitives, descriptors, or composited buffer.
Canonical Example
- Input
- Points, segments, polygons, or geometric primitives configured for a representative polygon width test case
- Output
- Geometric decision, measurement, or constructed structure satisfying Rotating Calipers Width invariants
- Explanation
- Rotating Calipers Width processes the input by rotating support lines to find the minimum strip containing a convex polygon, tracking polygon width and rotating calipers to produce the verified polygon width 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 rotating support lines to find the minimum strip containing a convex polygon on a small polygon width example.
Step 1 of 5: Normalize input coordinates, primitives, or pixel buffers and initialize spatial data structures for polygon width.
geometry-mechanismNotes
Rotating Calipers Width operates in O(n log n) time and O(n) space within the Rotating Calipers family. Often compared with Rotating Calipers Diameter and Rotating Calipers Antipodal Pairs.
Sources (3)
What each reference supports for this entry.
Computational Geometry: Algorithms and Applications
BookComputational geometry textbook support for Rotating Calipers Width's geometric model, data structures, and robustness concerns.
Open sourceThe Algorithm Design Manual
BookAlgorithm catalog support for Rotating Calipers Width's problem context, known alternatives, and practical selection tradeoffs.
Open sourceToussaint Rotating Calipers
PaperReference for rotating-calipers methods for polygon diameter, width, antipodal pairs, and related convex-polygon queries.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Conceptual neighborRotating Calipers Diameter
Geometry · Core
Rotating Calipers Width and Rotating Calipers Diameter share a concrete rotating calipers mechanism for polygon width.
Compare with thisRelationships
View full relationship pageConceptual neighborRotating Calipers Diameter
Rotating Calipers Width and Rotating Calipers Diameter share a concrete rotating calipers mechanism for polygon width.
Conceptual neighborRotating Calipers Antipodal Pairs
Rotating Calipers Width and Rotating Calipers Antipodal Pairs share a concrete rotating calipers mechanism for polygon width.
Conceptual neighborRotating Calipers
Rotating Calipers Width and Rotating Calipers share a concrete rotating calipers mechanism for polygon width.
Related Algorithms
Tags
GeometryComputational Geometry