math - 线与线段之间的最短距离（3D）

Question

我发现此代码用于计算线段和线段之间的距离。我们检查线段和线是否不平行，并找到参数方程的参数，其中线段和线之间的距离将最小。但我不明白我们是如何做到这一点的。

有人解释一下吗？或任何其他关于如何找到线段和线段之间距离的解释链接。

Result operator()(Line<N, Real> const& line, Segment<N, Real> const& segment)
        {
            Result result;

            Vector<N, Real> segCenter, segDirection;
            Real segExtent;
            segment.GetCenteredForm(segCenter, segDirection, segExtent);

            Vector<N, Real> diff = line.origin - segCenter;
            Real a01 = -Dot(line.direction, segDirection);
            Real b0 = Dot(diff, line.direction);
            Real s0, s1;

            if (std::fabs(a01) < (Real)1)
            {
                // The line and segment are not parallel.
                Real det = (Real)1 - a01 * a01;
                Real extDet = segExtent * det;
                Real b1 = -Dot(diff, segDirection);
                s1 = a01 * b0 - b1;

                if (s1 >= -extDet)
                {
                    if (s1 <= extDet)
                    {
                        // Two interior points are closest, one on the line
                        // and one on the segment.
                        s0 = (a01 * b1 - b0) / det;
                        s1 /= det;
                    }
                    else
                    {
                        // The endpoint e1 of the segment and an interior
                        // point of the line are closest.
                        s1 = segExtent;
                        s0 = -(a01 * s1 + b0);
                    }
                }
                else
                {
                    // The endpoint e0 of the segment and an interior point
                    // of the line are closest.
                    s1 = -segExtent;
                    s0 = -(a01 * s1 + b0);
                }
            }
            else
            {
                // The line and segment are parallel.  Choose the closest pair
                // so that one point is at segment origin.
                s1 = (Real)0;
                s0 = -b0;
            }

            result.parameter[0] = s0;
            result.parameter[1] = s1;
            result.closestPoint[0] = line.origin + s0 * line.direction;
            result.closestPoint[1] = segCenter + s1 * segDirection;
            diff = result.closestPoint[0] - result.closestPoint[1];
            result.sqrDistance = Dot(diff, diff);
            result.distance = std::sqrt(result.sqrDistance);
            return result;
        }