/** Closest point on the triangle \a abc to the point \a p.
* \see 'Real Time Collision Detection' by Christer Ericson, chapter 5.1, page 141
* 需要考虑溢出原因，所以平方和的单精度只放大10倍
*/
public static VInt3 ClosestPointOnTriangle(VInt3 a, VInt3 b, VInt3 c, VInt3 p)
{
// Check if p is in vertex region outside A
var ab = b - a;
var ac = c - a;
var ap = p - a;
var d1 = VInt3.DotLongSafe(ab, ap);
var d2 = VInt3.DotLongSafe(ac, ap);
// Barycentric coordinates (1,0,0)
if (d1 <= 0 && d2 <= 0)
{
return(a);
}
// Check if p is in vertex region outside B
var bp = p - b;
var d3 = VInt3.DotLongSafe(ab, bp);
var d4 = VInt3.DotLongSafe(ac, bp);
// Barycentric coordinates (0,1,0)
if (d3 >= 0 && d4 <= d3)
{
return(b);
}
/*CheckIntOverFlow(d1);
* CheckIntOverFlow(d2);
* CheckIntOverFlow(d3);
* CheckIntOverFlow(d4);*/
// Check if p is in edge region outside AB, if so return a projection of p onto AB
var vc = d1 * d4 - d3 * d2;
if (d1 >= 0 && d3 <= 0 && vc <= 0)
{
// Barycentric coordinates (1-v, v, 0)
/*var v = d1 / (d1 - d3);
* return a + ab * v;*/
//Modify
VFactor vf = new VFactor(d1, d1 - d3);
//Debug.Log("==type 1==" + (a + ab * vf));
return(a + ab * vf);
}
// Check if p is in vertex region outside C
var cp = p - c;
var d5 = VInt3.DotLongSafe(ab, cp);
var d6 = VInt3.DotLongSafe(ac, cp);
/*CheckIntOverFlow(d5);
* CheckIntOverFlow(d6);*/
// Barycentric coordinates (0,0,1)
if (d6 >= 0 && d5 <= d6)
{
return(c);
}
// Check if p is in edge region of AC, if so return a projection of p onto AC
var vb = d5 * d2 - d1 * d6;
if (d2 >= 0 && d6 <= 0 && vb <= 0)
{
// Barycentric coordinates (1-v, 0, v)
/*var v = d2 / (d2 - d6);
* return a + ac * v;*/
//Modify
VFactor vf = new VFactor(d2, d2 - d6);
//Debug.Log("==type 2==" + (a + ac * vf));
return(a + ac * vf);
}
// Check if p is in edge region of BC, if so return projection of p onto BC
var va = d3 * d6 - d5 * d4;
if ((d4 - d3) >= 0 && (d5 - d6) >= 0 && va <= 0)
{
/*var v = (d4 - d3) / ((d4 - d3) + (d5 - d6));
* return b + (c - b) * v;*/
//Modify
VFactor vf = new VFactor((d4 - d3), (d4 - d3) + (d5 - d6));
//Debug.Log("==type 3==" + (b + (c - b) * vf));
return(b + (c - b) * vf);
}
else
{
// P is inside the face region. Compute the point using its barycentric coordinates (u, v, w)
//var denom = 1f / (va + vb + vc);
//var v = vb * denom;
//var w = vc * denom;
//Modify
VFactor vf = new VFactor(1, va + vb + vc);
var v = vf * vb;
var w = vf * vc;
// This is equal to: u*a + v*b + w*c, u = va*denom = 1 - v - w;
//Debug.Log("==type 4==" + (a + ab * v + ac * w));
return(a + ab * v + ac * w);
}
}