C#中线段与轴对齐框的交点 [英] Intersection of line segment with axis-aligned box in C#

问题描述

我正在寻找一种算法来确定线段和轴对齐框之间的近远交点.

I'm looking for an algorithm that determines the near and far intersection points between a line segment and an axis-aligned box.

这是我的方法定义:

public static Point3D[] IntersectionOfLineSegmentWithAxisAlignedBox(
    Point3D rayBegin, Point3D rayEnd, Point3D boxCenter, Size3D boxSize)

如果线段不与框相交，则该方法应返回一个空的 Point3D 数组.

If the line segment doesn't intersect the box, the method should return an empty Point3D array.

从我目前的研究来看，我遇到了一些具有高度优化算法的研究论文，但它们似乎都是用 C++ 编写的，并且需要将多个长类文件转换为 C#.就我的目的而言，最好使用相当有效、易于理解点积和交叉积的人以及简单/简短的内容.

From my research so far, I've come across some research papers with highly optimized algorithms, but they all seem to be written in C++ and would require multiple long class files to be converted to C#. For my purposes, something that is reasonably efficient, easy to understand by someone who gets dot products and cross products, and simple/short would be preferred.

推荐答案

这是我最终使用的:

public static List<Point3D> IntersectionOfLineSegmentWithAxisAlignedBox(
    Point3D segmentBegin, Point3D segmentEnd, Point3D boxCenter, Size3D boxSize)
{
    var beginToEnd = segmentEnd - segmentBegin;
    var minToMax = new Vector3D(boxSize.X, boxSize.Y, boxSize.Z);
    var min = boxCenter - minToMax / 2;
    var max = boxCenter + minToMax / 2;
    var beginToMin = min - segmentBegin;
    var beginToMax = max - segmentBegin;
    var tNear = double.MinValue;
    var tFar = double.MaxValue;
    var intersections = new List<Point3D>();
    foreach (Axis axis in Enum.GetValues(typeof(Axis)))
    {
        if (beginToEnd.GetCoordinate(axis) == 0) // parallel
        {
            if (beginToMin.GetCoordinate(axis) > 0 || beginToMax.GetCoordinate(axis) < 0)
                return intersections; // segment is not between planes
        }
        else
        {
            var t1 = beginToMin.GetCoordinate(axis) / beginToEnd.GetCoordinate(axis);
            var t2 = beginToMax.GetCoordinate(axis) / beginToEnd.GetCoordinate(axis);
            var tMin = Math.Min(t1, t2);
            var tMax = Math.Max(t1, t2);
            if (tMin > tNear) tNear = tMin;
            if (tMax < tFar) tFar = tMax;
            if (tNear > tFar || tFar < 0) return intersections;

        }
    }
    if (tNear >= 0 && tNear <= 1) intersections.Add(segmentBegin + beginToEnd * tNear);
    if (tFar >= 0 && tFar <= 1) intersections.Add(segmentBegin + beginToEnd * tFar);
    return intersections;
}

<小时>

public enum Axis
{
    X,
    Y,
    Z
}

<小时>

public static double GetCoordinate(this Point3D point, Axis axis)
{
    switch (axis)
    {
        case Axis.X:
            return point.X;
        case Axis.Y:
            return point.Y;
        case Axis.Z:
            return point.Z;
        default:
            throw new ArgumentException();
    }
}

public static double GetCoordinate(this Vector3D vector, Axis axis)
{
    switch (axis)
    {
        case Axis.X:
            return vector.X;
        case Axis.Y:
            return vector.Y;
        case Axis.Z:
            return vector.Z;
        default:
            throw new ArgumentException();
    }
}

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