Client Account:   Login
Home Site Statistics   Contact   About Us   Sunday, March 26, 2017

users on-line: 2 | Forum entries: 6   
j0185201- Back to Home
   Skip Navigation LinksHOME › AREAS OF EXPERTISE › Interpolation Applications › ~ Cubic Spline Method

"Interpolation Solutions"
Cubic Spline Method
X =
Y =

Array X = { , , , , }
Array Y = { , , , , }
Specify New X values = { , , }

[ Initial ArrayValues X: {0,2,4,6,8} ]
[ Initial ArrayValues Y: {0,4,16,36,64} ]
[ Initial SplineX Values specified: {3,5,7} ]

Cubic Spline Interpolation

This method provides a great deal of smoothness for interpolations with significantly varying data. It uses weight coefficients on the cubic polynomials to interpolate the data. These coefficients bend the line so that it passes through each of the data points without any erratic behavior or breaks in continuity.

Algorithm Creation

The basic idea of the cubic spline is actually based on a third degree polynomial defined by,

si(x) = ai(x - xi)3 + (x - xi)2 + ... for i=1,2,...n-1

Testing the Cubic Spline Method

In order to test the Spline method as defined above, a new TestSpline() static method has been added and executed. Supporting code and methods are not shown.

           static void TestSpline();
                 double[] xarray = new double[] { t1, t2, t3, t4, t5 };
                 double[] yarray = new double[] { t6, t7, t8, t9, t10 };
                 double[] x = new double[] { t11, t12, t13 };
                 double[] y = Interpolation.Spline(xarray, yarray, x);
                 VectorR vx = new VectorR(x);
                 VectorR vy = new VectorR(y);
                 ListBox1.Items.Add(" " + vx.ToString());
                 ListBox2.Items.Add(" " + vy.ToString());

We first defined a set of data points as xarray and yarray. We then compute the y values at the xSpline values specified. The user can manipulate all values and try variations on the arrays themselves as well as specifying new xSpline values.

Other Implementations...

Object-Oriented Implementation
Graphics and Animation
Sample Applications
Ore Extraction Optimization
Vectors and Matrices
Complex Numbers and Functions
Ordinary Differential Equations - Euler Method
Ordinary Differential Equations 2nd-Order Runge-Kutta
Ordinary Differential Equations 4th-Order Runge-Kutta
Higher Order Differential Equations
Nonlinear Systems
Numerical Integration
Numerical Differentiation
Function Evaluation

Skip Navigation Links.

Home Skip Navigation Links
   Algorithms, Graphics, Vectors,
            implementation techniques.
   Mineral Transactions info,
            sales, agreements...
   Numerical Modeling services
            mineral environment.
   Want to know about Mining?
            basic knowledge here...
   What are Mineral Commodities?
            our elementary charts.
   Math, Analysis and More...
            our expertise in the matter.


Platform Implementation

Home Algorithm Implementation
We design applications for different environments and platforms...
        Home Graphics and Animation
The graphics classes in Smalltalk were designed...
        Home Optimization Algorithms
An optimization problem is a numerical problem...
        Home Vectors and Matrices
The concise notation introduced in linear algebra for vector...

2017 © Keystone Mining Post  |   2461 E. Orangethorpe Av., Fullerton, CA 92631 USA  |