java - 确定 2 个直角棱镜是否接触/相交

Question

我无法确定 2 个直角棱镜是否接触或重叠。我只有两个直角棱镜的高 X、Y、Z 和低 X、Y、Z。这是我目前所拥有的:

    public boolean overlaps(AreaSelection other) {
    boolean Xs = (lowX <= other.getHighestX()) && (other.getLowestX() <= highX);
    boolean Ys = (lowY <= other.getHighestY()) && (other.getLowestY() <= highY); 
    boolean Zs = (lowZ <= other.getHighestZ()) && (other.getLowestZ() <= highZ);
    return (Xs && Ys && Zs);        
}

有谁知道这是否正确？如果没有，解决方案是什么？谢谢!

Answer 1

两个棱柱与坐标轴平行的直角棱柱重叠当且仅当坐标轴上的各自三对投影间隔全部重叠。

所以有一个“实用”方法来检查间隔的重叠是有意义的，我们调用三次来检查棱镜的重叠。我们假设此方法将在间隔端点正确排序的情况下被调用:

public boolean overlap_1d(double aLow, double aHigh, double bLow, double bHigh)
{
    if (aLow <= bLow) return (bLow <= aHigh);
    /* else aLow > bLow */
    return (aLow <= bHigh);
}

原来的代码会变成:

public boolean overlaps(AreaSelection other)
{
    boolean Xs = overlap_1D(lowX,highX,other.getLowestX(),other.getHighestX());
    boolean Ys = overlap_1D(lowY,highY,other.getLowestY(),other.getHighestY());
    boolean Zs = overlap_1D(lowZ,highZ,other.getLowestZ(),other.getHighestZ());
    return (Xs && Ys && Zs);        
}

请注意，在此方法中，重叠可能由单个交点组成(无论是一维还是三维)。