问题描述
限时送ChatGPT账号..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();
}
}
这篇关于C#中线段与轴对齐框的交点的文章就介绍到这了,希望我们推荐的答案对大家有所帮助,也希望大家多多支持IT屋!
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