如何通过3个点/数以指定数量的样本进行插值? (在C#中) [英] How to interpolate through 3 points/numbers with a defined number of samples? (in c#)

问题描述

例如，我们有1、5和10，并且想要在这些点之间插值12点，我们应该得到:

So for example we have 1, 5, and 10 and we want to interpolate between these with 12 points, we should get:

1.0000        
1.7273   
2.4545    
3.1818   
3.9091    
4.6364   
5.4545   
6.3636   
7.2727  
8.1818    
9.0909    
10.0000   

假设我们有5分，10分和4分，再有12分，我们应该得到:

say we have 5, 10, and 4 and again 12 points, we should get:

5.0000
5.9091
6.8182
7.7273
8.6364
9.5455
9.4545
8.3636
7.2727
6.1818
5.0909
4.0000

推荐答案

这是遵循以下原则的通用解决方案:

This is a generalized solution that works by these principles:

• 执行线性插值
• 它会计算输入数组中的浮点索引"
• 此索引用于从输入数组中选择1(如果小数部分非常接近0)或2个数字
• 此索引的整数部分是基本输入数组索引
• 小数部分表示我们应该向下一个数组元素移动多远

这应该可以与您需要的任何大小的输入数组和输出集合一起使用.

This should work with whatever size input arrays and output collections you would need.

public IEnumerable<double> Interpolate(double[] inputs, int count)
{
    double maxCountForIndexCalculation = count - 1;
    for (int index = 0; index < count; index++)
    {
        double floatingIndex = (index / maxCountForIndexCalculation) * (inputs.Length - 1);

        int baseIndex = (int)floatingIndex;
        double fraction = floatingIndex - baseIndex;

        if (Math.Abs(fraction) < 1e-5)
            yield return inputs[baseIndex];
        else
        {
            double delta = inputs[baseIndex + 1] - inputs[baseIndex];
            yield return inputs[baseIndex] + fraction * delta;
        }
    }
}

它会产生您在问题中显示的两个输出集合，但除此之外，我还没有对其进行测试.很少执行错误检查，因此您应该添加必要的位.

It produces the two collections of outputs you showed in your question but beyond that, I have not tested it. Little error checking is performed so you should add the necessary bits.

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