# Software for C1 interpolation

@inproceedings{Lawson1977SoftwareFC, title={Software for C1 interpolation}, author={Charles L. Lawson}, year={1977} }

The problem of mathematically defining a smooth surface, passing through a finite set of given points is studied. Literature relating to the problem is briefly reviewed. An algorithm is described that first constructs a triangular grid in the (x,y) domain, and first partial derivatives at the modal points are estimated. Interpolation in the triangular cells using a method that gives C sup.1 continuity overall is examined. Performance of software implementing the algorithm is discussed…

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## 98 Citations

Algorithm 677 C1 surface interpolation

- MathematicsTOMS
- 1989

A method of bivariate interpolation and smooth surface fitting is developed for rapidly varying Z values given at points irregularly distributed in the x-y plane. The surface is constructed by means…

Fitting smooth surfaces to scattered 3D data using piecewise quadratic approximation

- Computer ScienceProceedings. International Conference on Image Processing
- 2002

An automatic method for constructing smooth surfaces defined as a network of curved triangular patches that starts with a coarse mesh approximating the surface through triangular elements covering the boundary of the domain, then iteratively adds new points from the data set until a specified error tolerance is achieved.

Evaluation of Algorithms for Surface Interpolation over Triangular Patch

- Mathematics

Surface interpolation over a triangulation with scattered DEM may maintain the continuity and smoothness of surface while it is contributed by a condition that two triangles in each shaded…

Function approximation on triangular grids: some numerical results using adaptive techniques

- Computer Science
- 2000

C1 surface interpolation with constraints

- Mathematics, Computer ScienceNumerical Algorithms
- 2005

The main purpose of this work is to analyse an iterative method for determining the solution of this QP problem and find such a method is very efficient and well suited for parallel implementation on a multiprocessor system.

Surface Interpolation to Scattered Data

- Computer Science

The following sections address usage for the separate usage of STGFND, STGEXT, STGC0, and STGC1, but a user could learn this from the comments in these subroutines and the code in STGFI, if desired for specialized applications.

A local shape-preserving interpolation scheme for scattered data

- Mathematics, Computer ScienceComput. Aided Geom. Des.
- 1999

Boundary correction for piecewise linear interpolation defined over data-dependent triangulations

- Mathematics, Computer Science
- 1992

A New Moving Mesh Algorithm for the Finite Element Solution of Variational Problems

- Computer Science
- 1998

A new iterative mesh optimization algorithm for the finite element solution of variational problems set in infinite-dimensional spaces is described and shown that this procedure reduces the energy functional monotonically, without the need to solve the global discrete problem at intermediate stages.

Detection of discontinuities in scattered data approximation

- Computer ScienceNumerical Algorithms
- 2004

A Detection Algorithm for the localisation of unknown fault lines of a surface from scattered data using thin plate splines is given, and it is shown that this yields approximation of second order accuracy instead of first order as in the global case.