我目前正在尝试创建一种方法,该方法可以在 n 维空间中对未知数量的点(数量等于 2^n)进行多线性插值。
n = 1(无插值)和 n = 2(线性插值)的情况已经实现并且似乎有效。但是现在我已经在努力使双线性插值(对于 n = 4 的情况)维度不可知,我不知道从那时起我应该如何进展(n = 8,...,2^n)。
是否有解决此问题的通用方法,或者我是否应该对某些情况进行硬编码并抛出 UnsupportedOperationException ?
下面我添加了一个 SSCCE,希望能澄清我的问题。它由一个点类组成,它存储坐标和一个值,还包含一些功能,例如计算到另一个点的距离和插值方法,其中已经包含我对 n = 1 和 n = 2 的情况的实现。
代码
import java.util.ArrayList;
import java.util.List;
public class Interpolator {
public static void main(String[] args) {
Interpolator ip = new Interpolator();
Point currentPoint = new Point(new long[]{5, 5}, 0);
List<Point> neighbors = new ArrayList<Point>() {{
add(new Point(new long[]{3, 3}, 7));
add(new Point(new long[]{10, 10}, 4));
}};
System.out.println(ip.interpolate(currentPoint, neighbors));
}
public float interpolate(Point currentPoint, List<Point> neighbors) {
if (neighbors.size() == 1) {
// no interpolation necessary with only one neighbor
return neighbors.get(0).getValue();
} else if (neighbors.size() == 2) {
// distance between point and the two neighbors
float distanceOne = currentPoint.distance(neighbors.get(0));
float distanceTwo = currentPoint.distance(neighbors.get(1));
float completeDistance = distanceOne + distanceTwo;
// calculate weights
float weightOne = 1 - distanceOne / completeDistance;
float weightTwo = 1 - distanceTwo / completeDistance;
// linear interpolation
return neighbors.get(0).getValue() * weightOne
+ neighbors.get(1).getValue() * weightTwo;
} else if (neighbors.size() == 4) {
//TODO: bilinear interpolation
} else if(neighbors.size() == 8){
//TODO: trilinear interpolation
}
//TODO: quadlinear interpolation or higher?
return -1;
}
public static class Point {
private long[] m_coordinates;
private float m_value;
public Point(final long[] coordinates, float value) {
this.m_coordinates = coordinates;
this.m_value = value;
}
public long[] getCoordinates() {
return this.m_coordinates;
}
public int numDim() {
return m_coordinates.length;
}
public long dim(final int i) {
return this.m_coordinates[i];
}
public float distance(final Point otherPoint) {
if (this.numDim() != otherPoint.numDim()) {
throw new IllegalArgumentException(
"Can't measure distance between points with different dimensionality");
}
float sum = 0;
for (int i = 0; i < this.numDim(); i++) {
sum += Math.pow(this.dim(i) - otherPoint.dim(i), 2);
}
return (float) Math.sqrt(sum);
}
public float getValue() {
return m_value;
}
}
}