Package com.inductiveautomation.rm.graphics

Class RMCurveFit

java.lang.Object

com.inductiveautomation.rm.graphics.RMCurveFit

public class RMCurveFit
extends Object

This class creates an approximating polygon for a given RMFunction. The polygon is expressed as a series of sample points that can be interpolated between using Neville's method to quickly obtain the value of any function.

This is used for path animation, to map the complex curve which maps the arclength of the bezier path segment to the bezier parameter value.

The real function is the solution to an expression which would be prohibitively expensive to try to evaluate inside an animation loop, so instead we create a polynomial approximation and use that instead.

This code is distinct from RMPathFitCurves, which fits a set of bezier curves to a set of sample points.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	RMCurveFit.InverseFunc	A function whose value is the inverse of another function ie.
static class	RMCurveFit.NevilleFunc	A function whose value is determined by interpolating through a set of sample points using Neville's Method.
static class	RMCurveFit.Piece
static class	RMCurveFit.ScaledFunc	A function scaled such that f(1) == 1

Constructor Summary

Constructors

Constructor	Description
RMCurveFit()

Method Summary

Modifier and Type	Method	Description
static double[]	cheby(int n)
static void	main(String[] args)
static List	nevilleFit(RMMath.RMFunc func, double start, double end, List pieceList)	NevilleFit - This routine tries to fit an interpolating polygon to an arbitrary function.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

RMCurveFit

public RMCurveFit()

Method Details

cheby

public static double[] cheby(int n)

nevilleFit

public static List nevilleFit(RMMath.RMFunc func,
 double start,
 double end,
 List pieceList)

NevilleFit - This routine tries to fit an interpolating polygon to an arbitrary function. Neville's method takes a set of points and calculates new points by interpolating between the neighboring samples, and then interpolating between the interpolations, etc, etc. This method tries to create a set of points such that, when plugged into Neville's method, will approximate the curve with minimal error.

It first tries to create a linear->5th degree polynomial (corresponding to two to six sample points), and then calculates the maximum error of that polynomial to the real curve. If the error is too great, it subdivides at the maximum error point and recurses.

The final result is a piecewise list of polynomials, expressed as sample points.

main

public static void main(String[] args)