public static float NearestPointFloatXZ(VInt3 lineStart, VInt3 lineEnd, VInt3 point)
{
VInt2 b = new VInt2(lineEnd.x - lineStart.x, lineEnd.z - lineStart.z);
double num = (double)b.sqrMagnitude;
VInt2 a = new VInt2(point.x - lineStart.x, point.z - lineStart.z);
double num2 = (double)VInt2.Dot(a, b);
if (num != 0.0)
{
num2 /= num;
}
return((float)num2);
}
public static float NearestPointFactorXZ(VInt3 lineStart, VInt3 lineEnd, VInt3 point)
{
VInt2 b = new VInt2(lineEnd.x - lineStart.x, lineEnd.z - lineStart.z);
double sqrMagnitude = b.sqrMagnitude;
VInt2 a = new VInt2(point.x - lineStart.x, point.z - lineStart.z);
double num4 = VInt2.Dot(a, b);
if (sqrMagnitude != 0.0)
{
num4 /= sqrMagnitude;
}
return((float)num4);
}
/** Returns the closest point on the segment in the XZ plane.
* The y coordinate of the result will be the same as the y coordinate of the \a point parameter.
*
* The segment is NOT treated as infinite.
* \see ClosestPointOnSegment
* \see ClosestPointOnLine
*/
public static VInt2 ClosestPointOnSegmentXZ(VInt2 lineStart, VInt2 lineEnd, VInt2 point)
{
lineStart.y = point.y;
lineEnd.y = point.y;
VInt2 fullDirection = lineEnd - lineStart;
VInt2 fullDirection2 = fullDirection;
fullDirection2.y = 0;
int magn = fullDirection2.magnitude;
VInt2 lineDirection = magn > float.Epsilon ? fullDirection2 / magn : VInt2.zero;
int closestPoint = VInt2.Dot((point - lineStart), lineDirection);
int a = (int)Clamp(closestPoint, 0, fullDirection2.magnitude);
return(lineStart + (lineDirection * a));
}
/** 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
*/
public static VInt2 ClosestPointOnTriangle(VInt2 a, VInt2 b, VInt2 c, VInt2 p)
{
// Check if p is in vertex region outside A
var ab = b - a;
var ac = c - a;
var ap = p - a;
var d1 = VInt2.Dot(ab, ap);
var d2 = VInt2.Dot(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 = VInt2.Dot(ab, bp);
var d4 = VInt2.Dot(ac, bp);
// Barycentric coordinates (0,1,0)
if (d3 >= 0 && d4 <= d3)
{
return(b);
}
// Check if p is in edge region outside AB, if so return a projection of p onto AB
if (d1 >= 0 && d3 <= 0)
{
var vc = d1 * d4 - d3 * d2;
if (vc <= 0)
{
// Barycentric coordinates (1-v, v, 0)
var v = d1 / (d1 - d3);
return(a + ab * v);
}
}
// Check if p is in vertex region outside C
var cp = p - c;
var d5 = VInt2.Dot(ab, cp);
var d6 = VInt2.Dot(ac, cp);
// 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
if (d2 >= 0 && d6 <= 0)
{
var vb = d5 * d2 - d1 * d6;
if (vb <= 0)
{
// Barycentric coordinates (1-v, 0, v)
var v = d2 / (d2 - d6);
return(a + ac * v);
}
}
// Check if p is in edge region of BC, if so return projection of p onto BC
if ((d4 - d3) >= 0 && (d5 - d6) >= 0)
{
var va = d3 * d6 - d5 * d4;
if (va <= 0)
{
var v = (d4 - d3) / ((d4 - d3) + (d5 - d6));
return(b + (c - b) * v);
}
}
return(p);
}
/** Closest point on the triangle \a abc to the point \a p when seen from above.
* \see 'Real Time Collision Detection' by Christer Ericson, chapter 5.1, page 141
*/
public static VInt3 ClosestPointOnTriangleXZ(VInt3 a, VInt3 b, VInt3 c, VInt3 p)
{
// Check if p is in vertex region outside A
var ab = new VInt2(b.x - a.x, b.z - a.z);
var ac = new VInt2(c.x - a.x, c.z - a.z);
var ap = new VInt2(p.x - a.x, p.z - a.z);
var d1 = VInt2.Dot(ab, ap);
var d2 = VInt2.Dot(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 = new VInt2(p.x - b.x, p.z - b.z);
var d3 = VInt2.Dot(ab, bp);
var d4 = VInt2.Dot(ac, bp);
// Barycentric coordinates (0,1,0)
if (d3 >= 0 && d4 <= d3)
{
return(b);
}
// 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 * (1 - v) + b * v);
}
// Check if p is in vertex region outside C
var cp = new VInt2(p.x - c.x, p.z - c.z);
var d5 = VInt2.Dot(ab, cp);
var d6 = VInt2.Dot(ac, cp);
// 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 * (1 - v) + c * v);
}
// 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);
}
else
{
// P is inside the face region. Compute the point using its barycentric coordinates (u, v, w)
// Note that the x and z coordinates will be exactly the same as P's x and z coordinates
var denom = 1000 / (va + vb + vc);
var v = vb * denom;
var w = vc * denom;
return(new VInt3(p.x, (1 - v - w) * a.y + v * b.y + w * c.y, p.z));
}
}
