Scattered Points Interpolation with Globally Smooth B-Spline Surface using Iterative Knot Insertion

Xin Jiang, Bolun Wang, Guanying Huo, Cheng Su, Dong-Ming Yan, Zhiming Zheng

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We introduce a new method to interpolate scattered 3D data points with a single B-spline surface patch which is globally smooth. Given a set of scattered 3D data points and their corresponding parametrization, our method first constructs a set α of B-spline bases using a weighted strategy, and inserts knots to the knot vectors based on α. Then, the knot insertion procedure is iterated until a set β of B-spline bases exists, which indicates the existence of the interpolation surface. Finally, by applying the fairing energy minimizing with interpolation constraints, a globally smooth B-spline surface which interpolates the data points can be produced. Experimental results demonstrate that the generated B-spline surfaces often have fewer control points than those of traditional methods, while keeping the scattered data points interpolated accurately. The implementation of our algorithm and the scripts to reproduce all the results are available at
Original languageEnglish (US)
Pages (from-to)103244
JournalComputer-Aided Design
StatePublished - Mar 17 2022
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2022-10-25

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering
  • Computer Science Applications


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