Overview
Catmull-Clark subdivision creates face, edge, and vertex points, then reconnects them to generate a smoother mesh each iteration.
ExtendedSource checked
Catmull-Clark Subdivision
Refines polygon meshes into smoother subdivision surfaces.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Geometry
- Difficulty
- Advanced
- Family
- Subdivision Surface
- Tier
- Extended
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 3
- Code example
- Ready
- Visualization
- Ready
Core Concepts
face pointedge pointvertex rulesubdivision surface
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(faces)
Average
O(iterations * faces)
Worst
O(iterations * faces)
Space
O(faces)
When to Use
- Use when collision and intersection tests needs face point.
- Use when the input matches the assumptions behind subdivision Surface.
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
- Refines polygon meshes into smoother subdivision surfaces
- Uses face point and edge point 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)
Face point
F = average(vertices of face)
F = average(vertices of face)Computes the new point at the center of each face.
Pseudocode
- 1.Prepare the inputs and state needed for Catmull-Clark Subdivision.
- 2.Apply the face point 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
- Catmull-Clark Subdivision input with a small representative case
- Output
- Geometric relation, simplified shape, or constructed geometry
- Explanation
- Catmull-Clark Subdivision applies face point to produce geometric relation, simplified shape, or constructed geometry.
Implementation Notes
- Use robust orientation and tolerance checks for boundary cases.
- Keep the face point 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 Catmull-Clark Subdivision 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 Catmull-Clark Subdivision.
geometry-mechanismNotes
Catmull-Clark Subdivision should be used with the assumptions and tradeoffs of subdivision Surface in mind.
Sources (1)
What each reference supports for this entry.
Catmull-Clark Subdivision
PaperOriginal reference for recursively refining polygon meshes into smooth subdivision surfaces.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageAlternative toLaplacian Mesh Smoothing
Subdivision refines surfaces while smoothing adjusts existing geometry.
Conceptual neighborQuadric Error Mesh Simplification
Subdivision increases mesh detail while simplification reduces it.
Tags
Computational GeometryMesh ProcessingSurface ExtractionSmoothing