static public Polynome2D MultiplyXYPolygones(Polynome1D xPolygon, Polynome1D yPolygon)
{
Polynome2D result = new Polynome2D();
for (int x = 0; x < xPolygon.termCount; x++)
{
Term1D xTerm = xPolygon.terms[x];
for (int y = 0; y < yPolygon.termCount; y++)
{
Term1D yTerm = yPolygon.terms[y];
Term2D xyTerm = Term2D.MultiplyXYTerms(xTerm, yTerm);
result += xyTerm;
}
result.AddXTerm(xTerm * yPolygon.constant);
}
for (int y = 0; y < yPolygon.termCount; y++)
{
Term1D yTerm = yPolygon.terms[y];
result.AddYTerm(yTerm * xPolygon.constant);
}
result.m_k = xPolygon.constant * yPolygon.constant;
return(result);
}
public static Polynome1D operator +(Polynome1D a, Polynome1D b)
{
Debug.Log("NOT IMPLEMENTED : Polynome1D.Optimize()");
Polynome1D result = new Polynome1D();
result.m_xTerms = new List <Term1D>(a.m_xTerms);
result.m_k = a.m_k + b.m_k;
foreach (Term1D xTerm in b.m_xTerms)
{
result.Add(xTerm);
}
return(result);
}
private void CalculateFunction()
{
m_polynome2D = new Polynome2D();
int xCount = m_xValues.Length;
int yCount = m_yValues.Length;
// Somme de i = 0 à n de...
for (int i = 0; i < xCount; i++)
{
// Somme de j = 0 à m de...
for (int j = 0; j < yCount; j++)
{
// f(xi,yj)
float z = m_zValues[i][j];
// * Li(x) * Lj(y)
Polynome1D lix = LagrangePolynome(m_xValues, i);
Polynome1D ljy = LagrangePolynome(m_yValues, j);
m_polynome2D += z * Polynome2D.MultiplyXYPolygones(lix, ljy);
}
}
}
public static Polynome1D operator *(Polynome1D a, Polynome1D b)
{
Polynome1D result = new Polynome1D();
foreach (Term1D aTerm in a.m_xTerms)
{
foreach (Term1D bTerm in b.m_xTerms)
{
result.Add(aTerm * bTerm);
}
result.Add(aTerm * b.m_k);
}
foreach (Term1D bTerm in b.m_xTerms)
{
result.Add(a.m_k * bTerm);
}
result.m_k = a.m_k * b.m_k;
return(result);
}
static public Polynome1D LagrangePolynome(List <float> points, int i)
{
Polynome1D result = new Polynome1D(1);
int n = points.Count;
for (int j = 0; j < n; j++)
{
if (j == i)
{
continue;
}
float denom = points[i] - points[j];
Term1D term = new Term1D(1, 1 / denom);
List <Term1D> terms = new List <Term1D>();
terms.Add(term);
Polynome1D polynome = new Polynome1D(terms, -points[j] / denom);
result *= polynome;
}
return(result);
}
