/// <summary>
/// 构造直线，为两平面的交线
/// </summary>
public Line(Face face1, Face face2)
{
Vector3Double normalFace1 = face1.PlaneNormal;
Vector3Double normalFace2 = face2.PlaneNormal;
Direction = Vector3Double.Cross(normalFace1, normalFace2);
if (!(Direction.magnitude < EqualityTolerance)) // 两平面不平行
{
//getting a line point, zero is set to a coordinate whose direction
// 获取线上一点，方向坐标设为零点
//component isn't zero (line intersecting its origin plan)
// 成员不为零（线与第一个平面相交）
var d1 = -Vector3Double.Dot(normalFace1, face1.v1.Position);
var d2 = -Vector3Double.Dot(normalFace2, face2.v1.Position);
if (Math.Abs(Direction.x) > EqualityTolerance)
{
startPoint = new Vector3Double
{
x = 0,
y = (d2 * normalFace1.z - d1 * normalFace2.z) / Direction.x,
z = (d1 * normalFace2.y - d2 * normalFace1.y) / Direction.x
};
}
else if (Math.Abs(Direction.y) > EqualityTolerance)
{
startPoint = new Vector3Double
{
x = (d1 * normalFace2.z - d2 * normalFace1.z) / Direction.y,
y = 0,
z = (d2 * normalFace1.x - d1 * normalFace2.x) / Direction.y
};
}
else
{
startPoint = new Vector3Double
{
x = (d2 * normalFace1.y - d1 * normalFace2.y) / Direction.z,
y = (d1 * normalFace2.x - d2 * normalFace1.x) / Direction.z,
z = 0
};
}
}
else
{
startPoint = default;
}
Direction.Normalize();
}
/// <summary>
/// Compute the point resulting from the intersection with a plane
/// </summary>
/// <param name="normal">the plane normal</param>
/// <param name="planePoint">a plane point.</param>
/// <returns>intersection point.If they don't intersect, return null</returns>
public Vector3Double ComputePlaneIntersection(Plane plane)
{
var distanceToStartFromOrigin = Vector3Double.Dot(plane.planeNormal, startPoint);
var distanceFromPlane = distanceToStartFromOrigin - plane.distanceToPlaneFromOrigin;
var denominator = Vector3Double.Dot(plane.planeNormal, Direction);
if (Math.Abs(denominator) < EqualityTolerance) // 射线与平面垂直
{
return(Math.Abs(distanceFromPlane) < EqualityTolerance ? startPoint : Vector3Double.PositiveInfinity);
}
else // 射线被平面拦截
{
return(StartPoint + (Direction * -distanceFromPlane / denominator));
}
}
/// <summary>
/// 为表面分类，基于光线追踪技术
/// </summary>
/// <param name="obj">计算面状态的 3D 物件</param>
public void RayTraceClassify(Object3D obj)
{
Line ray = new Line(PlaneNormal, Center); // 射线从面的几何中心发出，方向为法线方向
Face closet = default;
bool foundCloset = false;
double closestDistance;
bool success;
do
{
success = true;
closestDistance = double.MaxValue;
for (int faceIndex = 0; faceIndex < obj.GetNumFaces(); faceIndex++)
{
Face face = obj.GetFace(faceIndex);
var intersectionPoint = ray.ComputePlaneIntersection(face.Plane); // 对三角面所在的平面采样
if (intersectionPoint.x < float.PositiveInfinity) // 射线被平面拦截
{
var distance = ray.ComputePointToPointDistance(intersectionPoint);
var dot = Vector3Double.Dot(face.PlaneNormal, ray.Direction);
bool parallel = Math.Abs(dot) < epsilon; // 射线与平面平行
//if ray lies in plane...
if (Math.Abs(distance) < epsilon) // 交点是射线起点
{
if (parallel)
{
// 略微抖动光线方向以免采样到另一平面
ray.PerturbDirection();
success = false;
break;
}
else if (face.ContainsPoint(intersectionPoint))
{
// 面重合
closet = face;
foundCloset = true;
closestDistance = 0;
break;
}
}
else if (!parallel && distance > epsilon) // 射线产生交点
{
if (distance < closestDistance && face.ContainsPoint(intersectionPoint))
{
closestDistance = distance;
closet = face; // 当前的面时最近的平面
foundCloset = true;
}
}
}
}
} while (!success);
if (!foundCloset)
{
Status = Status.OUTSIDE;
} // 没有找到面，自己是外部面
else // 由离自己最近的面，检查方向
{
var dot = Vector3Double.Dot(closet.PlaneNormal, ray.Direction);
if (Math.Abs(closestDistance) < epsilon) // 距离为零，这个面和自己重合
{
if (dot > epsilon)
{
Status = Status.SAME;
}
else if (dot < -epsilon)
{
Status = Status.OPPOSITE;
}
}
else if (dot > epsilon)
{
Status = Status.INSIDE;
} // 不重合，同向，在参数物件内部
else if (dot < -epsilon)
{
Status = Status.OUTSIDE;
} // 不重合，反向，在参数物件外部
}
}
/// <summary>
/// 计算从线到另一点的距离
/// </summary>
/// <param name="otherPoint">the point to compute the distance from the line point. The point is supposed to be on the same line.</param>
/// <returns>如果射线起点到另一点的向量与射线方向相反，会得到负数的值</returns>
public double ComputePointToPointDistance(Vector3Double otherPoint)
{
var distance = (otherPoint - startPoint).magnitude;
return((Vector3Double.Dot((otherPoint - startPoint).normalized, Direction) < 0) ? -distance : distance);
}