Overview
Oriented bounding box intersection usually applies the separating axis theorem to the local axes of both boxes and their cross products.
CoreSource checked
Oriented Bounding Box Intersection
Tests overlap between rotated boxes using candidate separating axes.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Geometry
- Difficulty
- Advanced
- Family
- Intersection Test
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 4
- Code example
- Ready
- Visualization
- Ready
Core Concepts
oriented boxseparating axisaxis projectioninterval overlap
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(1)
Average
O(1)
Worst
O(1)
Space
O(1)
When to Use
- Use when collision and intersection tests needs oriented box.
- Use when the input matches the assumptions behind intersection Test.
When Not to Use
- Avoid when floating-point robustness is critical and no tolerance strategy is defined.
- Avoid when a simpler algorithm gives the required result with less setup.
What It Does
- Tests overlap between rotated boxes using candidate separating axes
- Uses oriented box and separating axis to guide the work.
- Produces geometric relation, simplified shape, or constructed geometry.
Use Cases
- Collision and intersection tests
- Shape analysis
- Geometry processing
Inputs
- Points, segments, polygons, or meshes
- Query shape or tolerance
Outputs
- Geometric relation, simplified shape, or constructed geometry
Key Formulas (1)
Separating axis test
overlapon axis = projectiona overlaps projectionb
overlap_on_axis = projection_a overlaps projection_bBoxes intersect only if projections overlap on every candidate axis.
Pseudocode
- 1.Prepare the inputs and state needed for Oriented Bounding Box Intersection.
- 2.Apply the oriented box step while the stopping condition has not been met.
- 3.Update intermediate state and discard invalid candidates.
- 4.Return geometric relation, simplified shape, or constructed geometry.
Canonical Example
- Input
- Oriented Bounding Box Intersection input with a small representative case
- Output
- Geometric relation, simplified shape, or constructed geometry
- Explanation
- Oriented Bounding Box Intersection applies oriented box to produce geometric relation, simplified shape, or constructed geometry.
Implementation Notes
- Use robust orientation and tolerance checks for boundary cases.
- Keep the oriented box step separate enough to test independently.
Common Pitfalls
- Degenerate cases such as collinear points or shared edges often need explicit handling.
- Forgetting to check edge cases can make Oriented Bounding Box Intersection look correct on only ideal inputs.
Interactive Mechanism Walkthrough
Spatial Primitive & Sweep-Line CanvasDraw the input shapes, active tests, and generated geometric result.
Step 1 of 4: Prepare the inputs and state needed for Oriented Bounding Box Intersection.
geometry-mechanismNotes
Oriented Bounding Box Intersection should be used with the assumptions and tradeoffs of intersection Test in mind.
Sources (1)
What each reference supports for this entry.
Real-Time Collision Detection
BookGeometric collision reference for Oriented Bounding Box Intersection's primitive tests, bounding volumes, and numerical edge cases.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageAlternative toAxis-Aligned Bounding Box Intersection
OBB tests fit rotated objects more tightly at higher cost.
OBB intersection commonly uses SAT projections.
Related Algorithms
Tags
Computational GeometryBounding VolumeCollision DetectionGeometry