三角形 - 三角形交叉點檢測

Question

我正在研究使用this文章的triange-triangle檢測算法。我寫了這段代碼，但不幸的是，當三角形之間存在交集時，該方法返回false。

private boolean checkTriangleCollision(Triangle triangle1, Triangle triangle2) { 
    Vector3f n1 = getN(triangle1); 
    Vector3f n2 = getN(triangle2); 
    Vector3f v = null; 
    v = Vector3f.cross(n1, n2, v); 

    Vector3f p = new Vector3f(); 

    float pxy = n1.z * triangle1.vertex1.position.z * n1.x * n1.y; 
    float px = n1.z * triangle1.vertex1.position.z * n1.x * n1.y * triangle1.vertex1.position.y; 
    float py = n1.z * triangle1.vertex1.position.z * n1.x * triangle1.vertex1.position.x * n1.y; 
    float p0 = n1.z * triangle1.vertex1.position.z * n1.x * triangle1.vertex1.position.x * n1.y * triangle1.vertex1.position.y; 

    p.x = (p0/(px/pxy))/pxy; 
    p.y = (p0/(py/pxy))/pxy; 

    Vector3f x = null; 
    x = Vector3f.add(p, v, x); 

    Vector3f xq1 = null; 
    xq1 = Vector3f.sub(x, triangle1.vertex1.position, xq1); 
    float i1 = Vector3f.dot(xq1, n1); 

    Vector3f xq2 = null; 
    xq2 = Vector3f.sub(x, triangle2.vertex1.position, xq2); 
    float i2 = Vector3f.dot(xq2, n2); 

    if (i1 == 0 && i2 == 0) { 
     return true; 
    } 
    return false; 
} 

private Vector3f getN(Triangle triangle) { 
    Vector3f vn1 = null; 
    vn1 = Vector3f.sub(triangle.vertex2.position, triangle.vertex1.position, vn1); 
    Vector3f vn2 = null; 
    vn2 = Vector3f.sub(triangle.vertex3.position, triangle.vertex1.position, vn2); 
    Vector3f n = null; 
    n = Vector3f.cross(vn1, vn2, n); 
    return n; 
} 

我完全不知道爲什麼，但我想這個問題是在計算p。如果是的話，我怎麼能通過代碼解決這個方程？

N1·(P0-Q1) = 0 
and 
N2·(P0-R1) = 0 

Answer 1

對我來說，你做錯了點積。

試試這個：

Vector3f n1 = getN(triangle1); 
    Vector3f n2 = getN(triangle2); 
    Vector3f v = null; 
    v = Vector3f.cross(n1, n2, v); 

    Vector3f p = new Vector3f(); 

//P0 calcuiation 

    float C1 = n1.x * triangle1.vertex1.position.x + n1.y * triangle1.vertex1.position.y + n1.z * triangle1.vertex1.position.z; 

    float C2 = n2.x * triangle2.vertex1.position.x + n2.y * triangle2.vertex1.position.y + n2.z * triangle2.vertex1.position.z; 

    float Kn = n2.x/n1.x; 

    p.y = (C2 - C1 * Kn)/(n2.y - n1.y * Kn); 

    p.x = (C1 - n1.y * p.y)/n2.x; 

p.z = 0; 

//P0 calcuiation ends 

    Vector3f x = null; 
    x = Vector3f.add(p, v, x); 

這裏是我算了一筆賬： http://i.stack.imgur.com/3USpZ.png