001/** 002 * Copyright (c) 2011, The University of Southampton and the individual contributors. 003 * All rights reserved. 004 * 005 * Redistribution and use in source and binary forms, with or without modification, 006 * are permitted provided that the following conditions are met: 007 * 008 * * Redistributions of source code must retain the above copyright notice, 009 * this list of conditions and the following disclaimer. 010 * 011 * * Redistributions in binary form must reproduce the above copyright notice, 012 * this list of conditions and the following disclaimer in the documentation 013 * and/or other materials provided with the distribution. 014 * 015 * * Neither the name of the University of Southampton nor the names of its 016 * contributors may be used to endorse or promote products derived from this 017 * software without specific prior written permission. 018 * 019 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND 020 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED 021 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE 022 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR 023 * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES 024 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 025 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON 026 * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 027 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 028 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 029 */ 030package org.openimaj.math.util; 031 032/** 033 * Static methods for performing interpolation 034 * 035 * @author Jonathon Hare (jsh2@ecs.soton.ac.uk) 036 */ 037public class Interpolation { 038 /** 039 * Linear interpolation of y at x given x0,y0 and x1,y1. 040 * 041 * @param x 042 * the x position 043 * @param x0 044 * the first x position 045 * @param y0 046 * the first y position 047 * @param x1 048 * the second x position 049 * @param y1 050 * the second y position 051 * @return the interpolated value (y) at x 052 */ 053 public static float lerp(float x, float x0, float y0, float x1, float y1) { 054 if (x == x0) 055 return y0; 056 return y0 + (x - x0) * ((y1 - y0) / (x1 - x0)); 057 } 058 059 /** 060 * Linear interpolation of y at x given x0,y0 and x1,y1. 061 * 062 * @param x 063 * the x position 064 * @param x0 065 * the first x position 066 * @param y0 067 * the first y position 068 * @param x1 069 * the second x position 070 * @param y1 071 * the second y position 072 * @return the interpolated value (y) at x 073 */ 074 public static double lerp(double x, double x0, double y0, double x1, double y1) { 075 if (x == x0) 076 return y0; 077 return y0 + (x - x0) * ((y1 - y0) / (x1 - x0)); 078 } 079 080 /** 081 * Cubic interpolation of y at x (in 0..1) given y at x=[-1, 0, 1, 2] 082 * 083 * @param x 084 * the x value to compute 085 * @param y0 086 * y value at x=-1 087 * @param y1 088 * y value at x=0 089 * @param y2 090 * y value at x=1 091 * @param y3 092 * y value at x=2 093 * @return the interpolated value 094 */ 095 public static double cubicInterp(double x, double y0, double y1, double y2, double y3) { 096 return y1 + 0.5 * x * (y2 - y0 + x * (2.0 * y0 - 5.0 * y1 + 4.0 * y2 - y3 + x * (3.0 * (y1 - y2) + y3 - y0))); 097 } 098 099 /** 100 * Cubic interpolation of y at x (in 0..1) given y at x=[-1, 0, 1, 2] 101 * 102 * @param x 103 * the x value to compute 104 * @param y0 105 * y value at x=-1 106 * @param y1 107 * y value at x=0 108 * @param y2 109 * y value at x=1 110 * @param y3 111 * y value at x=2 112 * @return the interpolated value 113 */ 114 public static float cubicInterp(float x, float y0, float y1, float y2, float y3) { 115 return (float) (y1 + 0.5 * x 116 * (y2 - y0 + x * (2.0 * y0 - 5.0 * y1 + 4.0 * y2 - y3 + x * (3.0 * (y1 - y2) + y3 - y0)))); 117 } 118 119 /** 120 * Cubic interpolation of y at x (in 0..1) given y at x=[-1, 0, 1, 2] 121 * 122 * @param x 123 * the x value to compute 124 * @param y 125 * an array of 4 y values at x=[-1, 0, 1, 2] 126 * @return the interpolated value 127 */ 128 public static double cubicInterp(double x, double[] y) { 129 return y[1] + 0.5 * x * (y[2] - y[0] + x 130 * (2.0 * y[0] - 5.0 * y[1] + 4.0 * y[2] - y[3] + x * (3.0 * (y[1] - y[2]) + y[3] - y[0]))); 131 } 132 133 /** 134 * Cubic interpolation of y at x (in 0..1) given y at x=[-1, 0, 1, 2] 135 * 136 * @param x 137 * the x value to compute 138 * @param y 139 * an array of 4 y values at x=[-1, 0, 1, 2] 140 * @return the interpolated value 141 */ 142 public static float cubicInterp(float x, float[] y) { 143 return (float) (y[1] + 0.5 * x * (y[2] - y[0] + x 144 * (2.0 * y[0] - 5.0 * y[1] + 4.0 * y[2] - y[3] + x * (3.0 * (y[1] - y[2]) + y[3] - y[0])))); 145 } 146 147 /** 148 * Bilinear interpolation of the value at x,y where 0<=x<=1 and 0<=y<=1 149 * given the values at (0,0), (0,1), (1,0) and (1,1). Note: This will work 150 * for other values of (x,y) but doesn't normally make sense. 151 * 152 * @param x 153 * the x position (in 0..1) 154 * @param y 155 * the y position (in 0..1) 156 * @param f00 157 * the value at (0,0) 158 * @param f01 159 * the value at (0,1) 160 * @param f10 161 * the value at (1,0) 162 * @param f11 163 * the value at (1,1) 164 * @return the interpolated value (x,y) 165 */ 166 public static double bilerp(double x, double y, double f00, double f01, double f10, double f11) { 167 return f00 * (1.0 - x) * (1.0 - y) + f10 * x * (1.0 - y) + f01 * (1.0 - x) * y + f11 * x * y; 168 } 169 170 /** 171 * Bilinear interpolation of the value at x,y where 0<=x<=1 and 0<=y<=1 172 * given the values at (0,0), (0,1), (1,0) and (1,1). Note: This will work 173 * for other values of (x,y) but doesn't normally make sense. 174 * 175 * @param x 176 * the x position (in 0..1) 177 * @param y 178 * the y position (in 0..1) 179 * @param f00 180 * the value at (0,0) 181 * @param f01 182 * the value at (0,1) 183 * @param f10 184 * the value at (1,0) 185 * @param f11 186 * the value at (1,1) 187 * @return the interpolated value (x,y) 188 */ 189 public static float bilerpf(float x, float y, float f00, float f01, float f10, float f11) { 190 return f00 * (1.0f - x) * (1.0f - y) + f10 * x * (1.0f - y) + f01 * (1.0f - x) * y + f11 * x * y; 191 } 192 193 /** 194 * Bilinear interpolation of the value at x,y where 0<=x<=1 and 0<=y<=1 195 * given the values at (0,0), (0,1), (1,0) and (1,1). Note: This will work 196 * for other values of (x,y) but doesn't normally make sense. 197 * 198 * @param x 199 * the x position (in 0..1) 200 * @param y 201 * the y position (in 0..1) 202 * @param f00 203 * the value at (0,0) 204 * @param f01 205 * the value at (0,1) 206 * @param f10 207 * the value at (1,0) 208 * @param f11 209 * the value at (1,1) 210 * @return the interpolated value (x,y) 211 */ 212 public static float bilerp(float x, float y, float f00, float f01, float f10, float f11) { 213 return f00 * (1.0f - x) * (1.0f - y) + f10 * x * (1.0f - y) + f01 * (1.0f - x) * y + f11 * x * y; 214 } 215 216 /** 217 * Bicubic interpolation of the value at x,y where 0<=x<=1 and 0<=y<=1 given 218 * the values at integer coordinates from (-1,-1) to (3,3). 219 * 220 * @param x 221 * the x position (in 0..1) 222 * @param y 223 * the y position (in 0..1) 224 * @param p 225 * a 4x4 array of known values at (-1,-1) to (3,3) 226 * 227 * @return the interpolated value (x,y) 228 */ 229 public static double bicubicInterp(double x, double y, double[][] p) { 230 final double y0 = cubicInterp(y, p[0]); 231 final double y1 = cubicInterp(y, p[1]); 232 final double y2 = cubicInterp(y, p[2]); 233 final double y3 = cubicInterp(y, p[3]); 234 return cubicInterp(x, y0, y1, y2, y3); 235 } 236 237 /** 238 * Bicubic interpolation of the value at x,y where 0<=x<=1 and 0<=y<=1 given 239 * the values at integer coordinates from (-1,-1) to (3,3). 240 * 241 * @param x 242 * the x position (in 0..1) 243 * @param y 244 * the y position (in 0..1) 245 * @param p 246 * a 4x4 array of known values at (-1,-1) to (3,3) 247 * 248 * @return the interpolated value (x,y) 249 */ 250 public static float bicubicInterp(float x, float y, float[][] p) { 251 final float y0 = cubicInterp(y, p[0]); 252 final float y1 = cubicInterp(y, p[1]); 253 final float y2 = cubicInterp(y, p[2]); 254 final float y3 = cubicInterp(y, p[3]); 255 return cubicInterp(x, y0, y1, y2, y3); 256 } 257}