public static Matrix4x4 GetJacobi(IIntersect obj0, IIntersect obj1, Vector2 uv0, Vector2 uv1, Vector2 uvNew0, Vector2 uvNew1)
{
var dU0 = obj0.EvaluateDU(uv0);
var dV0 = obj0.EvaluateDV(uv0);
var dU1 = obj1.EvaluateDU(uv1);
var dV1 = obj1.EvaluateDV(uv1);
var normalT = GetTNormal(dU0, dU1, dV0, dV1);
dU0 = obj0.EvaluateDU(uvNew0);
dV0 = obj0.EvaluateDV(uvNew0);
dU1 = -obj1.EvaluateDU(uvNew1);
dV1 = -obj1.EvaluateDV(uvNew1);
var dot1 = Vector3.Dot(dU0, normalT);
var dot2 = Vector3.Dot(dV0, normalT);
var jacobiMatrix = new Matrix4x4(
dU0.X, dV0.X, dU1.X, dV1.X,
dU0.Y, dV0.Y, dU1.Y, dV1.Y,
dU0.Z, dV0.Z, dU1.Z, dV1.Z,
dot1, dot2, 0, 0);
Matrix4x4.Invert(jacobiMatrix, out Matrix4x4 inv);
return(inv);
}
public static Vector4 GetF(IIntersect obj0, IIntersect obj1, Vector2 uv0, Vector2 uv1, Vector2 uvNew0, Vector2 uvNew1, float alpha)
{
var P0 = obj0.Evaluate(uv0);
var Q = obj1.Evaluate(uvNew1);
var P1 = obj0.Evaluate(uvNew0);
var dU0 = obj0.EvaluateDU(uv0);
var dV0 = obj0.EvaluateDV(uv0);
var dU1 = obj1.EvaluateDU(uv1);
var dV1 = obj1.EvaluateDV(uv1);
var normalT = GetTNormal(dU0, dU1, dV0, dV1);
var d = alpha * 10;
return(new Vector4(P1 - Q, Vector3.Dot(P1 - P0, normalT) - d));
}
private static List <Vector2> GetGradient(IIntersect obj0, IIntersect obj1, Vector2 point0, Vector2 point1)
{
var eval0 = obj0.Evaluate(point0);
var eval1 = obj1.Evaluate(point1);
var diff = eval0 - eval1;
var eval0u = obj0.EvaluateDU(point0).Normalized();
var eval0v = obj0.EvaluateDV(point0).Normalized();
var eval1u = obj1.EvaluateDU(point1).Normalized();
var eval1v = obj1.EvaluateDV(point1).Normalized();
var grad0 = new Vector2(Vector3.Dot(diff, eval0u), Vector3.Dot(diff, eval0v));
var grad1 = new Vector2(Vector3.Dot(-diff, eval1u), Vector3.Dot(-diff, eval1v));
return(new List <Vector2>()
{
grad0, grad1
});
}
