How to seek the intersection of three corners and lines. IntersECTION function

This algorithm comes from Microsoft DirectX SDK. Lanfortic Grass Recommended. The basic algorithm wants to understand. It is why there is no negative sign. I haven't thought about it. I don't know why the result is basically correct. It should be better.

Bool Intertion (Xray & Ray, Xtriangle & Tri, XPoint & Point, Float & T, Float & U, FLOAT & T, FLOAT & U, FLOAT & V) {// Find Vector for Two Edges Sharing Vert0 / ***

The triangle is V1, V2, V3 two sides of E1 = V2-V1 E2 = V3 - V1 rays to RAY = P0 D * T triangular internal one P = V1 U * E1 V * E2 (U V < 1)

So: V1 U * E1 V * E2 = P0 D * T ===> U * E1 V * E2 - T * D = P0 - V1 ===> - T * D V * E2 U * E1 = P0 - V1 ===>

D.X D.Y D.Z | [-T, V, U] | E2.x E2.Y E2.Z | = P0 - P1 ===> | E1.X E1.Y E1.Z |

[-t, v, u] * m = p0 - p1;

[-t, v, u] = (p0 - p1) * INV (m);

T = (p0 - p1) * E1 x E2 / DET (M) = (p0 - p1) x e1 * E2 / DET (M)

v = (p0 - p1) * E1 x d / DET (m) = (p0 - p1) x e1 * D / DET (m)

u = (p0 - p1) * D x E2 / DET (M)

** / xvector3d e1 = tri.m_points [1] - tri.m_points [0]; xVector3d e2 = tri.m_points [2] - Tri.m_points [0];

/ / See the DET (M) of the matrix M. And record D x E2; XVector3D VCP_DIR_E2; ray.m_dir.cp (E2, VCP_DIR_E2);

/ / Get the value of the row of matrices float DET = E1.DP (VCP_DIR_E2);

/ / Save (P0 - P1) XVector3D V_P0_P1;

// For the sake of judgment. DET = ABS (DET) IF (DET> 0) {v_p0_p1 = ray.m_point - tri.m_points [0];} else {v_p0_p1 = tri.m_points [0] - ray.m_point; Det = -det;}

IF (DET <0.0000001F) RETURN FALSE;

// u = (p0 - p1) * D x E2 / DET (m) DET (m) will then except U = V_P0_P1.DP (VCP_DIR_E2); if (u <0.0f || u> DET) Return False;

/ / Save (P0 - P1) X E1 XVECTOR3D VCP_P0P1_E1; V_P0_P1.CP (E1, VCP_P0P1_E1); // V = ​​(P0 - P1) * E1 X D / DET (M) = (P0 - P1) X E1 * D / DET (m) // DET (m) will then except v = ray.m_dir.dp (VCP_P0P1_E1); if (V <0.0F || U V> DET) Return False;

// Calculate T, Scale parameters, ray intersects Triangle T = E2.DP (VCP_P0P1_E1); float finvdet = 1.0f / DET; T * = finvdet; u * = finvdet; v * = finvdet;

Point = ray.m_point ray.m_dir * t;

Return True;}