Overview
Axis-aligned bounding box intersection compares interval overlap independently on each axis. Two boxes intersect only if their projections overlap on all axes.
FoundationSource checked
Axis-Aligned Bounding Box Intersection
Tests whether two axis-aligned boxes overlap on every coordinate axis.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Geometry
- Difficulty
- Beginner
- Family
- Intersection Test
- Tier
- Foundation
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 6
- Code example
- Ready
- Visualization
- Ready
Core Concepts
axis projectioninterval overlapbroad phaseboundary convention
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(dimensions)
Average
O(dimensions)
Worst
O(dimensions)
Space
O(1)
When to Use
- Use it for fast broad-phase collision checks.
- Use it for rectangle, box, viewport, and spatial-index overlap tests.
- Use it before more expensive exact geometry tests.
When Not to Use
- Avoid it for rotated boxes unless they have first been converted to an axis-aligned bound.
- Avoid it when contact at a boundary should be treated differently from overlap without defining the convention.
- Avoid it as a precise shape-intersection test for complex geometry.
What It Does
- Tests whether two boxes aligned to coordinate axes overlap
- Uses axis projection and interval overlap 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)
AABB overlap
amin x ≤ bmax x and bmin x ≤ amax x for every axis
a_min_x <= b_max_x and b_min_x <= a_max_x for every axisRequires interval overlap on all axes.
Pseudocode
- 1.Prepare the inputs and state needed for Axis-Aligned Bounding Box Intersection.
- 2.Apply the axis projection 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
- box A = [0,0]-[2,2], box B = [1,1]-[3,3]
- Output
- intersects = true
- Explanation
- The x-intervals overlap and the y-intervals overlap.
Implementation Notes
- Normalize each box so min coordinates are less than or equal to max coordinates.
- Test overlap per axis and combine the results with AND.
- Decide whether touching edges count as intersection.
Common Pitfalls
- Mixing inclusive and exclusive boundary conventions.
- Letting min and max coordinates become inverted.
- Using AABBs as exact collision shapes when they are only broad bounds.
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 Axis-Aligned Bounding Box Intersection.
geometry-mechanismNotes
AABB tests are cheap filters; narrow-phase geometry may still be required.
Sources (1)
What each reference supports for this entry.
Real-Time Collision Detection
BookCollision detection reference for the geometric or broad-phase/narrow-phase behavior of Axis-Aligned Bounding Box Intersection.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Alternative toOriented Bounding Box Intersection
Geometry · Core
AABB tests are cheaper but less tightly fit rotated objects.
Compare with thisUsed byBroad Phase Collision Detection
Simulation · Core
Broad-phase collision detection commonly uses AABB overlap tests.
Compare with thisRelationships
View full relationship pageBroad-phase collision detection commonly uses AABB overlap tests.
Alternative toOriented Bounding Box Intersection
AABB tests are cheaper but less tightly fit rotated objects.
Tags
Computational GeometryBounding VolumeCollision DetectionGeometry