qreal polynomIntegral(const Polynom &p) {
// all xPow's should be zero
qreal result = 0;
for (int i = 0; i < p.size(); ++i)
result += p.at(i).c / (1 + p.at(i).yPow);
return result;
}
void addToPolynom(Polynom &p, const Monom &m) {
for (int i = 0; i < p.size(); ++i)
if (p.at(i).xPow == m.xPow && p.at(i).yPow == m.yPow) {
p[i].c += m.c;
return;
}
if (!qFuzzyIsNull(m.c))
p.append(m);
}
Polynom polynomMultiply(const Polynom &p1, const Polynom &p2) {
Polynom result;
int i, j;
Monom m;
for (i = 0; i < p1.size(); ++i)
for (j = 0; j < p2.size(); ++j) {
m.xPow = p1.at(i).xPow + p2.at(j).xPow;
m.yPow = p1.at(i).yPow + p2.at(j).yPow;
m.c = p1.at(i).c * p2.at(j).c;
addToPolynom(result, m);
}
return result;
}
void addToPolynom(Polynom &p, quint32 xPow, quint32 yPow, qreal c) {
if (qFuzzyIsNull(c))
return;
for (int i = 0; i < p.size(); ++i)
if (p.at(i).xPow == xPow && p.at(i).yPow == yPow) {
p[i].c += c;
return;
}
Monom m;
m.xPow = xPow;
m.yPow = yPow;
m.c = c;
p.append(m);
}
qreal getIntegralForGoodTriangle(QPointF * const triangle, const Polynom &polynom) {
qreal transform[4];
transformateTriangle(triangle, transform);
qreal newcx = transform[0] * triangle[2].x() + transform[2];
Polynom newPolynom, polynomPart1, polynomPart2, polynomBase;
int i, j;
for (i = 0; i < polynom.size(); ++i) {
polynomPart1.clear();
polynomBase.clear();
addToPolynom(polynomBase, 1, 0, 1 / transform[0]);
addToPolynom(polynomBase, 0, 0, -transform[2] / transform[0]);
polynomPart1 = polynomPower(polynomBase, polynom.at(i).xPow);
polynomPart2.clear();
polynomBase.clear();
addToPolynom(polynomBase, 0, 1, 1 / transform[1]);
addToPolynom(polynomBase, 0, 0, -transform[3] / transform[1]);
polynomPart2 = polynomPower(polynomBase, polynom.at(i).yPow);
for (j = 0; j < polynomPart2.size(); ++j)
polynomPart2[j].c *= polynom.at(i).c;
newPolynom = polynomAdd(newPolynom,
polynomMultiply(polynomPart1, polynomPart2));
}
qreal result = 0;
for (i = 0; i < newPolynom.size(); ++i) {
polynomBase.clear();
addToPolynom(polynomBase, 0, 0, 1);
addToPolynom(polynomBase, 0, 1, newcx - 1);
polynomBase = polynomPower(polynomBase, newPolynom.at(i).xPow + 1);
addToPolynom(polynomBase, 0,
newPolynom.at(i).xPow + 1, qPow(newcx, newPolynom.at(i).xPow + 1));
for (j = 0; j < polynomBase.size(); ++j) {
polynomBase[j].c /= newPolynom.at(i).xPow + 1;
polynomBase[j].yPow += newPolynom.at(i).yPow;
}
result += newPolynom.at(i).c * polynomIntegral(polynomBase) /
qAbs(transform[0] * transform[1]);
}
return result;
}
Polynom polynomAdd(const Polynom &p1, const Polynom &p2) {
Polynom result = p1;
for (int i = 0; i < p2.size(); ++i)
addToPolynom(result, p2.at(i));
return result;
}