public SlaveVertex(int slaveIndex, int masterTriangleIndex, BarycentricPoint position, BarycentricPoint normal, BarycentricPoint tangent)
{
this.slaveIndex = slaveIndex;
this.masterTriangleIndex = masterTriangleIndex;
this.position = position;
this.normal = normal;
this.tangent = tangent;
}
/**
* We need to find the barycentric coordinates of point such that the interpolated normal at that point passes trough our target position.
*
* X
* \ / /
* \------/--/
*
* This is necessary to ensure curvature changes in the surface affect skinned points away from the face plane.
* To do so, we use an iterative method similar to Newton´s method for root finding:
*
* - Project the point on the triangle using an initial normal.
* - Get interpolated normal at projection.
* - Intersect line from point and interpolated normal with triangle, to find a new projection.
* - Repeat.
*/
BarycentricPoint FindSkinBarycentricCoords(MasterFace triangle,
Vector3 position,
int max_iterations,
float min_convergence)
{
BarycentricPoint barycentricPoint = BarycentricPoint.zero;
// start at center of triangle:
Vector3 trusted_bary = Vector3.one / 3.0f;
Vector3 temp_normal = ObiUtils.BarycentricInterpolation(triangle.n1,
triangle.n2,
triangle.n3,
trusted_bary);
int it = 0;
float trust = 1.0f;
float convergence = float.MaxValue;
while (it++ < max_iterations)
{
Vector3 point;
if (!Obi.ObiUtils.LinePlaneIntersection(triangle.p1, triangle.faceNormal, position, temp_normal, out point))
{
break;
}
// get bary coords at intersection:
Vector3 bary = Vector3.zero;
if (!triangle.BarycentricCoords(point, ref bary))
{
break;
}
// calculate error:
Vector3 error = bary - trusted_bary; // distance from current estimation to last trusted estimation.
convergence = Vector3.Dot(error, error); // get a single convergence value.
// weighted sum of bary coords:
trusted_bary = (1.0f - trust) * trusted_bary + trust * bary;
// update normal
temp_normal = ObiUtils.BarycentricInterpolation(triangle.n1,
triangle.n2,
triangle.n3,
trusted_bary);
if (convergence < min_convergence)
{
break;
}
trust *= 0.8f;
}
Vector3 pos_on_tri = trusted_bary[0] * triangle.p1 +
trusted_bary[1] * triangle.p2 +
trusted_bary[2] * triangle.p3;
float height = Vector3.Dot(position - pos_on_tri, temp_normal);
barycentricPoint.barycentricCoords = trusted_bary;
barycentricPoint.height = height;
return(barycentricPoint);
}
