Java examples for java.lang:Math Value
Performs a trilinear interpolation between eight values.
/**// ww w. ja va 2 s . com * Java Modular Image Synthesis Toolkit (JMIST) * Copyright (C) 2008-2013 Bradley W. Kimmel * * Permission is hereby granted, free of charge, to any person * obtaining a copy of this software and associated documentation * files (the "Software"), to deal in the Software without * restriction, including without limitation the rights to use, * copy, modify, merge, publish, distribute, sublicense, and/or sell * copies of the Software, and to permit persons to whom the * Software is furnished to do so, subject to the following * conditions: * * The above copyright notice and this permission notice shall be * included in all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR * OTHER DEALINGS IN THE SOFTWARE. */ import java.util.Arrays; import java.util.Collection; import java.util.Collections; import java.util.Iterator; import java.util.List; public class Main{ /** * Performs a trilinear interpolation between eight values. * @param _000 The value at <code>(t, u, v) = (0, 0, 0)</code>. * @param _100 The value at <code>(t, u, v) = (1, 0, 0)</code>. * @param _010 The value at <code>(t, u, v) = (0, 1, 0)</code>. * @param _110 The value at <code>(t, u, v) = (1, 1, 0)</code>. * @param _001 The value at <code>(t, u, v) = (0, 0, 1)</code>. * @param _101 The value at <code>(t, u, v) = (1, 0, 1)</code>. * @param _011 The value at <code>(t, u, v) = (0, 1, 1)</code>. * @param _111 The value at <code>(t, u, v) = (1, 1, 1)</code>. * @param t The first value at which to interpolate. * @param u The second value at which to interpolate. * @param v The third value at which to interpolate. * @return The interpolated value at <code>(t, u, v)</code>. */ public static double trilinearInterpolate(double _000, double _100, double _010, double _110, double _001, double _101, double _011, double _111, double t, double u, double v) { return interpolate( bilinearInterpolate(_000, _001, _010, _011, u, v), bilinearInterpolate(_100, _101, _110, _111, u, v), t); } /** * Interpolates between two end points. * @param a The end point at <code>t = 0</code>. * @param b The end point at <code>t = 1</code>. * @param t The value at which to interpolate. * @return The value that is the fraction <code>t</code> of the way from * <code>a</code> to <code>b</code>: <code>(1-t)a + tb</code>. */ public static double interpolate(double a, double b, double t) { return a + t * (b - a); } /** * Interpolates between two points on a line. * @param x0 The x-coordinate of the first point. * @param y0 The y-coordinate of the first point. * @param x1 The x-coordinate of the second point. * @param y1 The y-coordinate of the second point. * @param x The x-coordinate at which to interpolate. * @return The y-coordinate corresponding to <code>x</code>. */ public static double interpolate(double x0, double y0, double x1, double y1, double x) { double t = (x - x0) / (x1 - x0); return interpolate(y0, y1, t); } /** * Interpolates a piecewise linear curve. * @param xs An array of x-coordinates (this must be sorted in ascending * order). * @param ys An array of the y-coordinates (must be of the same length as * <code>xs</code>, or one less if <code>wrap == true</code>). * @param x The x-coordinate at which to interpolate. * @param wrap A value indicating whether the curve is periodic. * @return The y-coordinate corresponding to <code>x0</code>. */ public static double interpolate(double[] xs, double[] ys, double x, boolean wrap) { if (wrap) { return interpolateWrapped(xs, ys, x); } else { return interpolate(xs, ys, x); } } /** * Interpolates a piecewise linear curve. * @param xs An array of x-coordinates (this must be sorted in ascending * order). * @param ys An array of the y-coordinates (must be of the same length as * <code>xs</code>). * @param x The x-coordinate at which to interpolate. * @return The y-coordinate corresponding to <code>x0</code>. */ public static double interpolate(double[] xs, double[] ys, double x) { if (x <= xs[0]) { return ys[0]; } if (x >= xs[xs.length - 1]) { return ys[xs.length - 1]; } int index = Arrays.binarySearch(xs, x); if (index < 0) { index = -(index + 1); } while (index < xs.length - 1 && !(x < xs[index + 1])) { index++; } assert (index < xs.length - 1); return interpolate(xs[index - 1], ys[index - 1], xs[index], ys[index], x); } /** * Interpolates a piecewise linear curve. * @param xs An array of x-coordinates (this must be sorted in ascending * order). * @param ys An array of the y-coordinates (must be of the same length as * <code>xs</code>, or one less if <code>wrap == true</code>). * @param x The x-coordinate at which to interpolate. * @param wrap A value indicating whether the curve is periodic. * @return The y-coordinate corresponding to <code>x0</code>. */ public static double interpolate(List<Double> xs, List<Double> ys, double x, boolean wrap) { if (wrap) { return interpolateWrapped(xs, ys, x); } else { return interpolate(xs, ys, x); } } /** * Interpolates a piecewise linear curve. * @param xs An array of x-coordinates (this must be sorted in ascending * order). * @param ys An array of the y-coordinates (must of length of * <code>xs.size() - 1</code>). * @param x The x-coordinate at which to interpolate. * @return The y-coordinate corresponding to <code>x</code>. */ public static double interpolate(List<Double> xs, List<Double> ys, double x) { if (x <= xs.get(0)) { return ys.get(0); } int n = xs.size(); if (x >= xs.get(n - 1)) { return ys.get(n - 1); } int index = Collections.binarySearch(xs, x); if (index < 0) { index = -(index + 1); } while (index < n - 1 && !(x < xs.get(index + 1))) { index++; } assert (index < n - 1); return interpolate(xs.get(index - 1), ys.get(index - 1), xs.get(index), ys.get(index), x); } /** * Interpolates a piecewise linear curve. * @param x0 The minimum value in the domain. * @param x1 The maximum value in the domain (must not be less than * <code>x0</code>). * @param y An array of the y-coordinates (must have at least two elements). * @param x The x-coordinate at which to interpolate. * @param wrap A value indicating whether the curve is periodic. * @return The y-coordinate corresponding to <code>x</code>. */ public static double interpolate(double x0, double x1, double[] y, double x, boolean wrap) { if (wrap) { return interpolateWrapped(x0, x1, y, x); } else { return interpolate(x0, x1, y, x); } } /** * Interpolates a piecewise linear curve. * @param x0 The minimum value in the domain. * @param x1 The maximum value in the domain (must not be less than * <code>x0</code>). * @param y An array of the y-coordinates (must have at least two elements). * @param x The x-coordinate at which to interpolate. * @return The y-coordinate corresponding to <code>x</code>. */ public static double interpolate(double x0, double x1, double[] y, double x) { if (x <= x0) { return y[0]; } if (x >= x1) { return y[y.length - 1]; } double t = (y.length - 1) * ((x - x0) / (x1 - x0)); int i = (int) Math.floor(t); return interpolate(y[i], y[i + 1], t - i); } /** * Interpolates a piecewise linear curve. * @param x0 The minimum value in the domain. * @param x1 The maximum value in the domain (must not be less than * <code>x0</code>). * @param y An array of the y-coordinates (must have at least two elements * if <code>wrap == false</code>). * @param x The x-coordinate at which to interpolate. * @param wrap A value indicating whether the curve is periodic. * @return The y-coordinate corresponding to <code>x</code>. */ public static double interpolate(double x0, double x1, List<Double> y, double x, boolean wrap) { if (wrap) { return interpolateWrapped(x0, x1, y, x); } else { return interpolate(x0, x1, y, x); } } /** * Interpolates a piecewise linear curve. * @param x0 The minimum value in the domain. * @param x1 The maximum value in the domain (must not be less than * <code>x0</code>). * @param y An array of the y-coordinates (must have at least two elements). * @param x The x-coordinate at which to interpolate. * @return The y-coordinate corresponding to <code>x</code>. */ public static double interpolate(double x0, double x1, List<Double> y, double x) { if (x <= x0) { return y.get(0); } if (x > x1) { return y.get(y.size() - 1); } double t = (y.size() - 1) * ((x - x0) / (x1 - x0)); int i = (int) Math.floor(t); return interpolate(y.get(i), y.get(i + 1), t - i); } /** * Performs a bilinear interpolation between four values. * @param _00 The value at <code>(t, u) = (0, 0)</code>. * @param _10 The value at <code>(t, u) = (1, 0)</code>. * @param _01 The value at <code>(t, u) = (0, 1)</code>. * @param _11 The value at <code>(t, u) = (1, 1)</code>. * @param t The first value at which to interpolate. * @param u The second value at which to interpolate. * @return The interpolated value at <code>(t, u)</code>. */ public static double bilinearInterpolate(double _00, double _10, double _01, double _11, double t, double u) { return interpolate(interpolate(_00, _10, t), interpolate(_01, _11, t), u); } /** * Performs bilinear interpolation over a non-uniform grid. * @param xs The array of grid points along the x-axis (must have the same * length as the number of rows in <code>z</code>). * @param ys The array of grid points along the y-axis (must have the same * length as the number of columns in <code>z</code>). * @param z The <code>Matrix</code> of values to interpolate (must have * <code>xs.length</code> rows and <code>ys.length</code> columns). * @param x The x-coordinate at which to interpolate. * @param y The y-coordinate at which to interpolate. * @return The interpolated value at <code>(x, y)</code>. * @throws IllegalArgumentException if <code>z</code> does not have * dimensions of <code>xs.length</code> by <code>ys.length</code>. */ public static double bilinearInterpolate(double xs[], double ys[], Matrix z, double x, double y) { return bilinearInterpolate(xs, ys, z, x, y, false, false); } /** * Performs bilinear interpolation over a non-uniform grid. * @param xs The array of grid points along the x-axis (must have the same * length as the number of rows in <code>z</code>). * @param ys The array of grid points along the y-axis (must have the same * length as the number of columns in <code>z</code>). * @param z The <code>Matrix</code> of values to interpolate (must have * <code>xs.length - (wrapX ? 1 : 0)</code> rows and * <code>ys.length - (wrapY ? 1 : 0)</code> columns). * @param x The x-coordinate at which to interpolate. * @param y The y-coordinate at which to interpolate. * @param wrapX A value indicating whether to wrap in the x-direction. If * <code>true</code>, then <code>xs</code> should have an extra entry * at the end which maps to row <code>0</code>. * @param wrapY A value indicating whether to wrap in the y-direction. If * <code>true</code>, then <code>ys</code> should have an extra entry * at the end which maps to column <code>0</code>. * @return The interpolated value at <code>(x, y)</code>. * @throws IllegalArgumentException if <code>z</code> does not have * the correct dimensions. */ public static double bilinearInterpolate(double xs[], double ys[], Matrix z, double x, double y, boolean wrapX, boolean wrapY) { return bilinearInterpolate(Matrix.rowMajor(1, xs.length, xs) .elementsByRow(), Matrix.rowMajor(1, ys.length, ys) .elementsByRow(), z, x, y, wrapX, wrapY); } /** * Performs bilinear interpolation over a non-uniform grid. * @param xs The list of grid points along the x-axis (must have the same * length as the number of rows in <code>z</code>). * @param ys The list of grid points along the y-axis (must have the same * length as the number of columns in <code>z</code>). * @param z The <code>Matrix</code> of values to interpolate (must have * <code>xs.size()</code> rows and <code>ys.size()</code> columns). * @param x The x-coordinate at which to interpolate. * @param y The y-coordinate at which to interpolate. * @return The interpolated value at <code>(x, y)</code>. * @throws IllegalArgumentException if <code>z</code> does not have * dimensions of <code>xs.size()</code> by <code>ys.size()</code>. */ public static double bilinearInterpolate(List<Double> xs, List<Double> ys, Matrix z, double x, double y) { return bilinearInterpolate(xs, ys, z, x, y, false, false); } /** * Performs bilinear interpolation over a non-uniform grid. * @param xs The list of grid points along the x-axis (must have the same * length as the number of rows in <code>z</code>). * @param ys The list of grid points along the y-axis (must have the same * length as the number of columns in <code>z</code>). * @param z The <code>Matrix</code> of values to interpolate (must have * <code>xs.length - (wrapX ? 1 : 0)</code> rows and * <code>ys.length - (wrapY ? 1 : 0)</code> columns). * @param x The x-coordinate at which to interpolate. * @param y The y-coordinate at which to interpolate. * @param wrapX A value indicating whether to wrap in the x-direction. If * <code>true</code>, then <code>xs</code> should have an extra entry * at the end which maps to row <code>0</code>. * @param wrapY A value indicating whether to wrap in the y-direction. If * <code>true</code>, then <code>ys</code> should have an extra entry * at the end which maps to column <code>0</code>. * @return The interpolated value at <code>(x, y)</code>. * @throws IllegalArgumentException if <code>z</code> does not have * the correct dimensions. */ public static double bilinearInterpolate(List<Double> xs, List<Double> ys, Matrix z, double x, double y, boolean wrapX, boolean wrapY) { int nx = xs.size(); int ny = ys.size(); if (nx != z.rows() + (wrapX ? 1 : 0) || ny != z.columns() + (wrapY ? 1 : 0)) { throw new IllegalArgumentException( "Matrix z must be xs.size() by ys.size()"); } if (x <= xs.get(0)) { return interpolate(ys, z.row(0).elements(), y, wrapY); } if (x >= xs.get(nx - 1)) { return interpolate(ys, z.row(nx - 1).elements(), y, wrapY); } if (y <= ys.get(0)) { return interpolate(xs, z.column(0).elements(), x, wrapX); } if (y >= ys.get(ny - 1)) { return interpolate(xs, z.column(ny - 1).elements(), x, wrapX); } int ix = Collections.binarySearch(xs, x); if (ix < 0) { ix = -(ix + 1); } while (ix < nx - 1 && !(x < xs.get(ix + 1))) { ix++; } int iy = Collections.binarySearch(ys, y); if (iy < 0) { iy = -(iy + 1); } while (iy < ny - 1 && !(y < ys.get(iy + 1))) { iy++; } assert (ix < nx - 1 && iy < ny - 1); double x0 = xs.get(ix); double x1 = xs.get(ix + 1); double y0 = ys.get(iy); double y1 = ys.get(iy + 1); double tx = (x - x0) / (x1 - x0); double ty = (y - y0) / (y1 - y0); int jx = ix + 1; int jy = iy + 1; if (jx == z.rows()) { jx = 0; } if (jy == z.columns()) { jy = 0; } double _00 = z.at(ix, iy); double _01 = z.at(ix, jy); double _10 = z.at(jx, iy); double _11 = z.at(jx, jy); return bilinearInterpolate(_00, _10, _01, _11, tx, ty); } /** * Performs bilinear interpolation over a uniform grid. * @param x0 The minimum value along the x-axis. * @param x1 The maximum value along the x-axis. * @param y0 The minimum value along the y-axis. * @param y1 The maximum value along the y-axis. * @param z The <code>Matrix</code> of values to interpolate (must have at * least two rows and at least two columns). * @param x The x-coordinate at which to interpolate. * @param y The y-coordinate at which to interpolate. * @return The interpolated value at <code>(x, y)</code>. * @throws IllegalArgumentException if <code>z</code> has fewer than two * rows or fewer than two columns. */ public static double bilinearInterpolate(double x0, double x1, double y0, double y1, Matrix z, double x, double y) { return bilinearInterpolate(x0, x1, y0, y1, z, x, y, false, false); } /** * Performs bilinear interpolation over a uniform grid. * @param x0 The minimum value along the x-axis. * @param x1 The maximum value along the x-axis. * @param y0 The minimum value along the y-axis. * @param y1 The maximum value along the y-axis. * @param z The <code>Matrix</code> of values to interpolate. It must have * at least two rows (unless wrapping in X) and at least two columns * (unless wrapping in Y). * @param x The x-coordinate at which to interpolate. * @param y The y-coordinate at which to interpolate. * @param wrapX A value indicating whether to wrap in the x-direction. * @param wrapY A value indicating whether to wrap in the y-direction. * @return The interpolated value at <code>(x, y)</code>. * @throws IllegalArgumentException if <code>z</code> has fewer than two * rows (and does not wrap in X) or fewer than two columns (and does * not wrap in Y). */ public static double bilinearInterpolate(double x0, double x1, double y0, double y1, Matrix z, double x, double y, boolean wrapX, boolean wrapY) { if ((!wrapX && z.rows() < 2) || (!wrapY && z.columns() < 2)) { throw new IllegalArgumentException( "Matrix z must have length 2 in each non-wrapping dimension"); } if (x <= x0) { return interpolate(y0, y1, z.row(0).elements(), y, wrapY); } if (x >= x1) { int j = z.rows() - 1; return interpolate(y0, y1, z.row(j).elements(), y, wrapY); } if (y <= y0) { return interpolate(x0, x1, z.column(0).elements(), x, wrapX); } if (y >= y1) { int j = z.columns() - 1; return interpolate(x0, x1, z.column(j).elements(), x, wrapX); } int nx = z.rows(); int ny = z.columns(); double tx = (nx - (wrapX ? 0 : 1)) * ((x - x0) / (x1 - x0)); double ty = (ny - (wrapY ? 0 : 1)) * ((y - y0) / (y1 - y0)); int ix = (int) Math.floor(tx); int iy = (int) Math.floor(ty); int jx = ix + 1; int jy = iy + 1; jx = jx < nx ? jx : 0; jy = jy < ny ? jy : 0; double _00 = z.at(ix, iy); double _01 = z.at(ix, jy); double _10 = z.at(jx, iy); double _11 = z.at(jx, jy); return bilinearInterpolate(_00, _10, _01, _11, tx - ix, ty - iy); } /** * Interpolates a periodic piecewise linear curve. * @param xs An array of x-coordinates (this must be sorted in ascending * order). * @param ys An array of the y-coordinates (must have length * <code>xs.length - 1</code>). * @param x The x-coordinate at which to interpolate. * @return The y-coordinate corresponding to <code>x</code>. */ public static double interpolateWrapped(double[] xs, double[] ys, double x) { int n = xs.length; double x0 = xs[0]; double x1 = xs[n - 1]; x -= (x1 - x0) * Math.floor((x - x0) / (x1 - x0)); assert (inRangeCO(x, x0, x1)); int index = Arrays.binarySearch(xs, x); if (index < 0) { index = -(index + 1); } while (index < n - 1 && !(x < xs[index + 1])) { index++; } assert (index < n - 1); int i = index - 1; int j = index; if (j == n - 1) { j = 0; } return interpolate(xs[i], ys[i], xs[index], ys[j], x); } /** * Interpolates a piecewise linear curve. * @param xs An array of x-coordinates (this must be sorted in ascending * order). * @param ys An array of the y-coordinates (must be of the same length as * <code>xs</code>, or one less if <code>wrap == true</code>). * @param x The x-coordinate at which to interpolate. * @return The y-coordinate corresponding to <code>x</code>. */ public static double interpolateWrapped(List<Double> xs, List<Double> ys, double x) { int n = xs.size(); double x0 = xs.get(0); double x1 = xs.get(n - 1); x -= (x1 - x0) * Math.floor((x - x0) / (x1 - x0)); assert (inRangeCO(x, x0, x1)); int index = Collections.binarySearch(xs, x); if (index < 0) { index = -(index + 1); } while (index < n - 1 && !(x < xs.get(index + 1))) { index++; } assert (index < n - 1); int i = index - 1; int j = index; if (j == n - 1) { j = 0; } return interpolate(xs.get(i), ys.get(i), xs.get(index), ys.get(j), x); } /** * Interpolates a periodic piecewise linear curve. * @param x0 The minimum value in the domain. * @param x1 The maximum value in the domain (must not be less than * <code>x0</code>). * @param y An array of the y-coordinates. * @param x The x-coordinate at which to interpolate. * @param wrap A value indicating whether the curve is periodic. * @return The y-coordinate corresponding to <code>x</code>. */ public static double interpolateWrapped(double x0, double x1, double[] y, double x) { double t = (x - x0) / (x1 - x0); t -= Math.floor(t); t *= y.length; int i = (int) Math.floor(t); int j = i + 1; if (j == y.length) { j = 0; } assert (0 <= i && i < y.length); return interpolate(y[i], y[j], t - i); } /** * Interpolates a periodic piecewise linear curve. * @param x0 The minimum value in the domain. * @param x1 The maximum value in the domain (must not be less than * <code>x0</code>). * @param y An array of the y-coordinates. * @param x The x-coordinate at which to interpolate. * @return The y-coordinate corresponding to <code>x</code>. */ public static double interpolateWrapped(double x0, double x1, List<Double> y, double x) { double t = (x - x0) / (x1 - x0); t -= Math.floor(t); t *= y.size(); int i = (int) Math.floor(t); int j = i + 1; if (j == y.size()) { j = 0; } assert (0 <= i && i < y.size()); return interpolate(y.get(i), y.get(j), t - i); } /** * Determines whether {@code x} falls within the interval * {@code [minimum, maximum)}. * @param x The value to check. * @param minimum The lower bound of the interval to check against. * @param maximum The upper bound of the interval to check against. * @return A value indicating whether {@code x} is contained in the * interval {@code [minimum, maximum)}. */ public static boolean inRangeCO(double x, double minimum, double maximum) { return minimum <= x && x < maximum; } }