Polynom getLinearInterpolation(QPointF *p) {
Polynom result;
double a, b, c, d;
d = determinant(
p[0].x(), p[0].y(), 1,
p[1].x(), p[1].y(), 1,
p[2].x(), p[2].y(), 1
);
a = determinant(
function(p[0].x(), p[0].y()), p[0].y(), 1,
function(p[1].x(), p[1].y()), p[1].y(), 1,
function(p[2].x(), p[2].y()), p[2].y(), 1
) / d;
b = determinant(
p[0].x(), function(p[0].x(), p[0].y()), 1,
p[1].x(), function(p[1].x(), p[1].y()), 1,
p[2].x(), function(p[2].x(), p[2].y()), 1
) / d;
c = determinant(
p[0].x(), p[0].y(), function(p[0].x(), p[0].y()),
p[1].x(), p[1].y(), function(p[1].x(), p[1].y()),
p[2].x(), p[2].y(), function(p[2].x(), p[2].y())
) / d;
addToPolynom(result, 1, 0, a);
addToPolynom(result, 0, 1, b);
addToPolynom(result, 0, 0, c);
return result;
}
Polynom polynomPower(const Polynom &p, quint32 power) {
Polynom result;
if (!power) {
addToPolynom(result, 0, 0, 1);
return result;
}
result = p;
for (quint32 i = 0; i < power - 1; ++i)
result = polynomMultiply(result, p);
return result;
}
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;
}
Polynom psiFunctionPolynom(const Triangle &triangle, short n) {
double u1, u2, v1, v2;
QPointF a = triangle[0], b = triangle[1], c = triangle[2];
Polynom result;
if (n == 0) {
u1 = b.x();
v1 = b.y();
} else {
u1 = a.x();
v1 = a.y();
}
if (n == 2) {
u2 = b.x();
v2 = b.y();
} else {
u2 = c.x();
v2 = c.y();
}
addToPolynom(result, 1, 0, v2 - v1);
addToPolynom(result, 0, 1, u1 - u2);
addToPolynom(result, 0, 0, u2 * v1 - v2 * u1);
return result;
}
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;
}