Intersectionpoint in Triangle?

Unity Engine
1

Hi,
pleace excuse my english.
i try to figure out, if Intersectionpoint (Vector3 Q) is in a Triangle ( Vector3 A, B, C).
for example:
Q = “(0.5, 1.0, 0.5)”
A = “(0.5, -0.5, 0.5)”
B = “(-0.5, 0.5, 0.5)”
C = “(-0.5, -0.5, 0.5)”
In this case is Q not in the Triangle, but my code says it is Triangle.
Does any one see the issue and can explain me what I am doing wrong?

private void addToListIfIntersectionIsInTriangle(Vector3 Q, Vector3 A, Vector3 B, Vector3 C, Vector3 n)
    {
        n.Normalize(); // normal of Triangle

        float u = Vector3.Dot(Vector3.Cross((B - A), (Q - A)), n);
        float v = Vector3.Dot(Vector3.Cross((C - B), (Q - B)), n);
        float w = Vector3.Dot(Vector3.Cross((A - C), (Q - C)), n);

        if( u >= 0 && v >=0 && w>=0)
        {
            if (!newVertices.Contains(Q))
            {
                Debug.Log("1");
            }
        }
   }
2

This post sounds similar: Point In Triangle Code - C# - Unity Engine - Unity Discussions

From what I remember I thought at least one of your cross product values needed to be normalised but I’m probably wrong.

3

thank you for help, but normalise the cross products doesn’t change anything on the result.

i tried many things out, it seems like this function only works for non planar triangles, as soon a triangle planar (like (1,2,0),(1,2,3),(3,2,3)), this function tests if the Intersection Point is hover over the Triangle… hopefully you understand what i mean.

4

It’s fixed now.
My first failure was, that I only checked, if the intersection Point was on the line, but not on the segment.
Than I changed the algorithm for checking the intersection point in Triangle to:

private bool LineIntersectionInTriangle(Vector3 planePoint0, Vector3 planePoint1, Vector3 planePoint2, Vector3 intersection)
    { 
        Vector3 u = planePoint2 - planePoint0;
        Vector3 v = planePoint1 - planePoint0;
        Vector3 w = intersection - planePoint0;

        float s = ((Vector3.Dot(u,v) * Vector3.Dot(w,v)) - (Vector3.Dot(v,v) * Vector3.Dot(w,u))) / ((Mathf.Pow(Vector3.Dot(u,v),2)) - (Vector3.Dot(u,u)*Vector3.Dot(v,v)));
        float t = ((Vector3.Dot(u, v) * Vector3.Dot(w, u)) - (Vector3.Dot(u, u) * Vector3.Dot(w, v))) / ((Mathf.Pow(Vector3.Dot(u, v), 2)) - (Vector3.Dot(u, u) * Vector3.Dot(v, v)));
        if ((s >= 0 && t >= 0 && s + t <= 1) || ((s == 0 && t == 0) ||  s + t == 1))
            return true;
        else
            return false;       
    }

standard algorithm

So now I check first the intersection with line segment to plane:

//Get the intersection between a line and a plane.
    //If the line and plane are not parallel, the function outputs true, otherwise false.
    public static bool LinePlaneIntersection(out Vector3 intersection, Vector3 linePoint, Vector3 lineVec, float magnitude, Vector3 planeNormal, Vector3 planePoint)
    {

        float length;
        float dotNumerator;
        float dotDenominator;
        Vector3 vector;
        intersection = Vector3.zero;

        //calculate the distance between the linePoint and the line-plane intersection point
        dotNumerator = Vector3.Dot((planePoint - linePoint), planeNormal);
        dotDenominator = Vector3.Dot(lineVec, planeNormal);

        //line and plane are not parallel
        if (dotDenominator != 0.0f)
        {
            length = dotNumerator / dotDenominator;      
            if (0 <= length && length <= magnitude)
            {
                //create a vector from the linePoint to the intersection point
                vector = SetVectorLength(lineVec, length);

                //get the coordinates of the line-plane intersection point
                intersection = linePoint + vector;

                return true;
            }
            else // intersection but not in the length of magnitude
                return false;
        }

        //output not valid
        else
            return false;
    }

algorithm from http://wiki.unity3d.com/index.php/3d_Math_functions adapted by me

and than i check if the intersection point is in triangle(code is on top)