Conditions for tangent plane continuity over recursively generated B-spline surfaces
ACM Transactions on Graphics (TOG)
A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Surface interpolation on irregular networks with normal conditions
Computer Aided Geometric Design
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Analysis of Algorithms Generalizing B-Spline Subdivision
SIAM Journal on Numerical Analysis
Behaviour of recursive division surfaces near extraordinary points
Seminal graphics
On calculating normalized Powell-Sabin B-splines
Computer Aided Geometric Design
Subdivision of uniform Powell—Sabin splines
Computer Aided Geometric Design
Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Piecewise Quadratic Approximations on Triangles
ACM Transactions on Mathematical Software (TOMS)
Normal Control using N-adic Subdivision Schemes
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Tangent driven interpolative subdivision
Computers and Graphics
Quasi-hierarchical Powell--Sabin B-splines
Computer Aided Geometric Design
Modeling smooth shape using subdivision on differential coordinates
Computer-Aided Design
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In this article, we propose a new subdivision scheme based on uniform Powell-Sabin spline subdivision. It belongs to the class of vector subdivision schemes; for each vertex, we have three control points that form a control triangle tangent to the surface instead of one control point. The main advantage of this scheme is that we can choose the values of the normals in the initial vertices which results in more design possibilities. At first sight, it is an approximating scheme because the control points change each iteration. However, the point where the control triangle is tangent to the surface remains the same. Therefore, it is an interpolating scheme. In the regular regions, we use the uniform Powell-Sabin rules, and we develop additional subdivision rules for the new vertices in the neighborhood of extraordinary vertices. The scheme yields C1 continuous surfaces. We also do the convergence analysis based on the eigenproperties of the subdivision matrix and the properties of the characteristic map.