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BoofCV is an open source Java library for real-time computer vision and robotics applications.
/*
* Copyright (c) 2011-2013, Peter Abeles. All Rights Reserved.
*
* This file is part of BoofCV (http://boofcv.org).
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package boofcv.alg.interpolate.array;
/**
* Langrange's formula is a straight forward way to perform polynomial interpolation. It is
* not the most computationally efficient approach and does not provide any estimate of its accuracy.
* The order of the polynomial refers to the number of points used in the interpolation minus one.
*
* @author Peter Abeles
*/
public class LagrangeFormula {
/**
* UsingLlangrange's formula it interpulates the value of a function at the specified sample
* point given discrete samples. Which samples are used and the order of the approximation are
* given by i0 and i1.
*
* @param sample Where the estimate is done.
* @param x Where the function was sampled.
* @param y The function's value at the sample points
* @param i0 The first point considered.
* @param i1 The last point considered.
* @return The estimated y value at the sample point.
*/
public static double process_F64(double sample, double x[], double y[], int i0, int i1) {
double result = 0;
for (int i = i0; i <= i1; i++) {
double numerator = 1.0;
for (int j = i0; j <= i1; j++) {
if (i != j)
numerator *= sample - x[j];
}
double denominator = 1.0;
double a = x[i];
for (int j = i0; j <= i1; j++) {
if (i != j)
denominator *= a - x[j];
}
result += (numerator / denominator) * y[i];
}
return result;
}
/**
* UsingLlangrange's formula it interpulates the value of a function at the specified sample
* point given discrete samples. Which samples are used and the order of the approximation are
* given by i0 and i1. The order is = i1-i0+1.
*
* @param sample Where the estimate is done.
* @param x Where the function was sampled.
* @param y The function's value at the sample points
* @param i0 The first point considered.
* @param i1 The last point considered.
* @return The estimated y value at the sample point.
*/
public static float process_F32(float sample, float x[], float y[], int i0, int i1) {
float result = 0;
for (int i = i0; i <= i1; i++) {
float numerator = 1.0f;
for (int j = i0; j <= i1; j++) {
if (i != j)
numerator *= sample - x[j];
}
float denominator = 1.0f;
float a = x[i];
for (int j = i0; j <= i1; j++) {
if (i != j)
denominator *= a - x[j];
}
result += (numerator / denominator) * y[i];
}
return result;
}
}
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