Overview
Shewchuk Adaptive Predicates is a robust geometry method for robust geometric predicates. It works by increasing arithmetic precision only when floating-point signs are uncertain.
SpecializedSource checked
Shewchuk Adaptive Predicates
Shewchuk Adaptive Predicates addresses robust geometric predicates by increasing arithmetic precision only when floating-point signs are uncertain.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Geometry
- Difficulty
- Advanced
- Family
- Robust Geometry
- Tier
- Specialized
- Status
- Verified
- Review
- Source Checked
- Sources
- 2
- Formulas
- 0
- Relationships
- 4
- Code example
- Not ready
- Visualization
- Ready
Core Concepts
robust geometric predicatesrobust geometrygeometric predicategeometric 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 Shewchuk Adaptive Predicates when solving robust geometric predicates and you want to benefit from increasing arithmetic precision only when floating-point signs are uncertain.
- Choose it when O(n log n) average/worst-case time and O(n) memory match your workload profile.
- Prefer it over Orientation Test or In-Circle Test when the problem structure favors robust geometric predicates.
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 robust geometric predicates within Robust Geometry workloads (O(n log n) time, O(n) space).
- Works by increasing arithmetic precision only when floating-point signs are uncertain.
- Maintains key invariants across robust geometric predicates, robust geometry, geometric predicate.
Use Cases
- Production and research workloads requiring robust geometric predicates via increasing arithmetic precision only when floating-point signs are uncertain.
- Robust Geometry pipelines where O(n log n) time and O(n) space fit system constraints.
- Engineering comparisons against Orientation Test and In-Circle Test when tuning robust geometric predicates.
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 robust geometric predicates.
- 2.Establish the sweep event queue, hierarchy, or scale-space pyramid required by Shewchuk Adaptive Predicates.
- 3.Process geometric predicates or pixel neighborhoods by increasing arithmetic precision only when floating-point signs are uncertain.
- 4.Resolve boundary degeneracies, occlusions, or threshold suppressions to maintain consistency.
- 5.Output the final robust geometric predicates primitives, descriptors, or composited buffer.
Canonical Example
- Input
- Points, segments, polygons, or geometric primitives configured for a representative robust geometric predicates test case
- Output
- Geometric decision, measurement, or constructed structure satisfying Shewchuk Adaptive Predicates invariants
- Explanation
- Shewchuk Adaptive Predicates processes the input by increasing arithmetic precision only when floating-point signs are uncertain, tracking robust geometric predicates and robust geometry to produce the verified robust geometric predicates 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 increasing arithmetic precision only when floating-point signs are uncertain on a small robust geometric predicates example.
Step 1 of 5: Normalize input coordinates, primitives, or pixel buffers and initialize spatial data structures for robust geometric predicates.
geometry-mechanismNotes
Shewchuk Adaptive Predicates operates in O(n log n) time and O(n) space within the Robust Geometry family. Often compared with Orientation Test and In-Circle Test.
Sources (2)
What each reference supports for this entry.
Shewchuk Robust Predicates
PaperSpecific reference for Shewchuk Adaptive Predicates's robust orientation, in-circle, or adaptive geometric predicate behavior.
Open sourceComputational Geometry: Algorithms and Applications
BookTextbook support for Shewchuk Adaptive Predicates's computational geometry problem family, predicates, structures, or geometric construction.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageConceptual neighborOrientation Test
Shewchuk Adaptive Predicates and Orientation Test share a concrete robust geometry mechanism for robust geometric predicates.
Conceptual neighborIn-Circle Test
Shewchuk Adaptive Predicates and In-Circle Test share a concrete robust geometry mechanism for robust geometric predicates.
Tags
GeometryComputational Geometry