3D中两个矩形之间的交点

Question

为了获得3D中两个矩形之间的交线,我将它们转换为平面,然后使用它们法线的叉积得到交线,然后我尝试使线与矩形的每个线段相交.

问题是线条平行于三个线段,并且只与NAN,NAN,NAN中的一个相交,这是完全错误的.你能告诉我我的代码有什么问题吗？

我使用此链接中的vector3 http://www.koders.com/csharp/fidCA8558A72AF7D3E654FDAFA402A168B8BC23C22A.aspx

并创建了我的飞机课程如下

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace referenceLineAlgorithm
{
struct Line
{

    public Vector3 direction;
    public Vector3 point;

}

struct lineSegment
{

    public Vector3 firstPoint;
    public Vector3 secondPoint;

}

class plane_test
{
    public enum Line3DResult
    {
        Line3DResult_Parallel = 0,
        Line3DResult_SkewNoCross = 1,
        Line3DResult_SkewCross = 2
    };

    #region Fields

    public Vector3 Normal;
    public float D;
    public Vector3[] cornersArray;
    public Vector3 FirstPoint;
    public Vector3 SecondPoint;
    public Vector3 temp;
    public Vector3 normalBeforeNormalization;


    #endregion

    #region constructors

    public plane_test(Vector3 point0, Vector3 point1, Vector3 point2, Vector3 point3)
    {
        Vector3 edge1 = point1 - point0;
        Vector3 edge2 = point2 - point0;
        Normal = edge1.Cross(edge2);
        normalBeforeNormalization = Normal;

        Normal.Normalize();
        D = -Normal.Dot(point0);

        ///// Set the Rectangle corners 
        cornersArray = new Vector3[] { point0, point1, point2, point3 };

    }

    #endregion

    #region Methods
    /// <summary>
    /// This is a pseudodistance. The sign of the return value is
    /// positive if the point is on the positive side of the plane,
    /// negative if the point is on the negative side, and zero if the
    ///  point is on the plane.
    /// The absolute value of the return value is the true distance only
    /// when the plane normal is a unit length vector.
    /// </summary>
    /// <param name="point"></param>
    /// <returns></returns>
    public float GetDistance(Vector3 point)
    {
        return Normal.Dot(point) + D;
    }

    public void Intersection(plane_test SecondOne)
    {
        ///////////////////////////// Get the parallel to the line of interrsection (Direction )
        Vector3 LineDirection = Normal.Cross(SecondOne.Normal);

        float d1 = this.GetDistance(LineDirection);
        float d2 = SecondOne.GetDistance(LineDirection);

        temp = (LineDirection - (this.Normal * d1) - (SecondOne.Normal * d2));

        temp.x = Math.Abs((float)Math.Round((decimal)FirstPoint.x, 2));
        temp.y = Math.Abs((float)Math.Round((decimal)FirstPoint.y, 2));

        Line line;
        line.direction = LineDirection;
        line.point = temp;

        ////////// Line segments 

        lineSegment AB, BC, CD, DA;

        AB.firstPoint = cornersArray[0]; AB.secondPoint = cornersArray[1];
        BC.firstPoint = cornersArray[1]; BC.secondPoint = cornersArray[2];
        CD.firstPoint = cornersArray[2]; CD.secondPoint = cornersArray[3];
        DA.firstPoint = cornersArray[3]; DA.secondPoint = cornersArray[0];

        Vector3 r1 = new Vector3(-1, -1, -1);
        Vector3 r2 = new Vector3(-1, -1, -1);
        Vector3 r3 = new Vector3(-1, -1, -1);
        Vector3 r4 = new Vector3(-1, -1, -1);

        /*
        0,0 |----------------| w,0
            |                |
            |                |
        0,h |________________|  w,h


         */

        IntersectionPointBetweenLines(AB, line, ref r1);
        IntersectionPointBetweenLines(BC, line, ref r2);
        IntersectionPointBetweenLines(CD, line, ref r3);
        IntersectionPointBetweenLines(DA, line, ref r4);

        List<Vector3> points = new List<Vector3>();
        points.Add(r1);
        points.Add(r2);
        points.Add(r3);
        points.Add(r4);
        points.RemoveAll(

           t => ((t.x == -1) && (t.y == -1) && (t.z == -1))


           );

        if (points.Count == 2)
        {
            FirstPoint = points[0];
            SecondPoint = points[1];


        }




    }

    public Line3DResult IntersectionPointBetweenLines(lineSegment first, Line aSecondLine, ref Vector3 result)
    {
        Vector3 p1 = first.firstPoint;
        Vector3 n1 = first.secondPoint - first.firstPoint;


        Vector3 p2 = aSecondLine.point;
        Vector3 n2 = aSecondLine.direction;

        bool parallel = AreLinesParallel(first, aSecondLine);
        if (parallel)
        {

            return Line3DResult.Line3DResult_Parallel;
        }
        else
        {
            float d = 0, dt = 0, dk = 0;
            float t = 0, k = 0;

            if (Math.Abs(n1.x * n2.y - n2.x * n1.y) > float.Epsilon)
            {
                d = n1.x * (-n2.y) - (-n2.x) * n1.y;
                dt = (p2.x - p1.x) * (-n2.y) - (p2.y - p1.y) * (-n2.x);
                dk = n1.x * (p2.x - p1.x) - n1.y * (p2.y - p1.y);
            }
            else if (Math.Abs(n1.z * n2.y - n2.z * n1.y) > float.Epsilon)
            {
                d = n1.z * (-n2.y) - (-n2.z) * n1.y;
                dt = (p2.z - p1.z) * (-n2.y) - (p2.y - p1.y) * (-n2.z);
                dk = n1.z * (p2.z - p1.z) - n1.y * (p2.y - p1.y);
            }
            else if (Math.Abs(n1.x * n2.z - n2.x * n1.z) > float.Epsilon)
            {
                d = n1.x * (-n2.z) - (-n2.x) * n1.z;
                dt = (p2.x - p1.x) * (-n2.z) - (p2.z - p1.z) * (-n2.x);
                dk = n1.x * (p2.x - p1.x) - n1.z * (p2.z - p1.z);
            }

            t = dt / d;
            k = dk / d;

            result = n1 * t + p1;

            // Check if the point on the segmaent or not 
           // if (! isPointOnSegment(first, result))
            //{
               // result = new Vector3(-1,-1,-1);


           // }

            return Line3DResult.Line3DResult_SkewCross;

        }



    }
    private bool AreLinesParallel(lineSegment first, Line aSecondLine)
    {
        Vector3 vector = (first.secondPoint - first.firstPoint);
        vector.Normalize();

        float kl = 0, km = 0, kn = 0;
        if (vector.x != aSecondLine.direction.x)
        {
            if (vector.x != 0 && aSecondLine.direction.x != 0)
            {
                kl = vector.x / aSecondLine.direction.x;
            }
        }
        if (vector.y != aSecondLine.direction.y)
        {
            if (vector.y != 0 && aSecondLine.direction.y != 0)
            {
                km = vector.y / aSecondLine.direction.y;
            }
        }
        if (vector.z != aSecondLine.direction.z)
        {
            if (vector.z != 0 && aSecondLine.direction.z != 0)
            {
                kn = vector.z / aSecondLine.direction.z;
            }
        }

        // both if all are null or all are equal, the lines are parallel
        return (kl == km && km == kn);




    }

    private bool isPointOnSegment(lineSegment segment, Vector3 point)
    {
        //(x - x1) / (x2 - x1) = (y - y1) / (y2 - y1) = (z - z1) / (z2 - z1)
        float component1 = (point.x - segment.firstPoint.x) / (segment.secondPoint.x  - segment.firstPoint.x);
        float component2 = (point.y - segment.firstPoint.y) / (segment.secondPoint.y - segment.firstPoint.y);
        float component3 = (point.z - segment.firstPoint.z) / (segment.secondPoint.z - segment.firstPoint.z); 

        if ((component1 == component2) && (component2 == component3))
        {
            return true;


        }
        else
        {
            return false;

        }

    }

    #endregion
}
}

static void Main(string[] args)
    {

        //// create the first plane points 
        Vector3 point11 =new Vector3(-255.5f, -160.0f,-1.5f) ;    //0,0
        Vector3 point21 = new Vector3(256.5f, -160.0f, -1.5f);   //0,w
        Vector3 point31 = new Vector3(256.5f, -160.0f, -513.5f); //h,0
        Vector3 point41 = new Vector3(-255.5f, -160.0f, -513.5f); //w,h 

        plane_test plane1 = new plane_test(point11, point21, point41, point31);

        //// create the Second plane points 

        Vector3 point12 = new Vector3(-201.6289f, -349.6289f, -21.5f);
        Vector3 point22 =new Vector3(310.3711f,-349.6289f,-21.5f);
        Vector3 point32 = new Vector3(310.3711f, 162.3711f, -21.5f);
        Vector3 point42 =new Vector3(-201.6289f,162.3711f,-21.5f);
        plane_test plane2 = new plane_test(point12, point22, point42, point32);


        plane2.Intersection(plane1);



    }

这是测试值最好的问候

Answer 1

您需要先指定一件事:

• 3D矩形表示3D平面上的平面矩形.(不是矩形棱镜).

假设您的矩形不是共面的,也不是平行的,因此有一条唯一的线D1代表每个矩形所描述的平面的交点.

根据这个假设,它们是2个矩形R1和R2交叉的4种可能情况:

(注意:有时D1不会与R1或R2和R1相交,R2可以稍微旋转,因此D1并不总是在平行边相交,而是连续的边)

当两个矩形之间存在交叉时,D1总是在同一交叉点上与R1和R2相交(参见第1和第2张图)

你的模型不好,因为你的线不能与同一个矩形的3个段相平行......

正如你在这个问题中提到的:3D线交叉算法一旦你得到D1(得到由两个矩形的交点定义的线段的端点)就确定与矩形的每个段的交点.(每个矩形的4个段需要被检查)

然后检查公共交叉点...如果找到一个,那么你的矩形相交.

对不起,直接检查代码非常困难,但我想通过这些和平的信息你应该能够找到错误.

希望能帮助到你.

编辑:

用点和2个向量定义一个矩形:

R2 {A ,u ,v}
R1 {B, u',v'}

定义R1和R2描述的平面:P1和P2

P1的一个正交矢量(相应的P2)是n1(相应的n2).让我们n1 = u ^ v和n2 = u' ^ v'带:

然后

P1: n1.(x-xA,y-yA,z-zA)=0
P2: n2.(x-xB,y-yB,z-zB)=0

那么如果你只是在寻找D1,那么D1的等式是:

D1: P1^2 + P2 ^2 =0 (x,y,z verify P1 =0  an P2 =0 )

D1 : n1.(x-xA,y-yA,z-zA)^2 + n2.(x-xB,y-yB,z-zB)^2 =0

(因此,只需使用矩形的表达式,您就可以得到具有闭合公式的D1的等式.)

现在让我们来看看交叉点:

R1中的4个点是:

{A,A + u,A + v,A + u + v}

如在3D线交叉算法中描述的 那样:

D1 inter [A,A+u] = I1
D1 inter [A,A+v] = I2
D1 inter [A+u,A+u+v] = I3
D1 inter [A+v,A+u+v] = I4

(I1,I2,I3,I4可以为null)

same for D2 you get I1' I2' I3' I4'

如果Ij'= Ik'!= null那么它就是一个交叉点

如果你一步一步正确地做到了这一点,你应该找到正确的解决方案; 除非我没有完全理解这个问题......