Question

3D Cubic B-Spline Interpolation and Error Estimation

Theme: Implement and study 3D Cubic Spline Interpolation

Input: a set of points in 3D space (data(x,y,z))

Output: Spline, Spline data points and error, 3D graph that shows the original points and the Spline

The major steps involved in the B-Spline Fitting and Error Estimation are as mentioned below:

1- Sample the data points from input data.

2- Interpolate to find the position of control points.

3- Use the B-Spline basis function to generate the data points of output Spline data points.

4- Error estimation via comparing the generated data points and input data.

Suggested approach: start with some points in 2D to debug and test your code, then move to 3D. test the code for different sets of 3D points.

• Project title
• Project description (2-3 paragraphs)
  • Sample questions to answer: What is the problem? Why is it important? What is your solution? Why?
• Progress report (what has been completed) (2-3 paragraphs)
  • You may include the tools and data that is being used (programming language, libraries, etc.)
• Future work (that is to be achieved by the project deadline) (1 - 3 paragraphs)

Answer 1

spline

Cubic spline data interpolatio

Syntax

s = spline(x,y,xq)

pp = spline(x,y)

Description

s = spline(x,y,xq) returns a vector of interpolated values s corresponding to the query points in xq. The values of s are determined by cubic spline interpolation of x and y.

pp = spline(x,y) returns a piecewise polynomial structure for use by ppval and the spline utility unmkpp.