QTransform: How to iteratively map composition of transformation matrices to object?

I've tried almost everything, but I still have no idea how to map composition of three transformation matrices to a line iteratively, to get first two iterations of the Koch curve.
Let me explain my problem. I've got three input parameters:
 base object (this object will be stored in the list as "0. iteration")
 list of transformation matrices (every matrix can be composed by more basic matrices of scaling, rotation and translation)
 iteration number
Now algorithm should be following:
 initialize empty list of new objects  the size of list will be the count of transformation matrices multiplied by the count of the list of objects from the previous iteration
 loop through all matrices
 map current matrix to base object
 store transformed object in the list
 after end of the loop the list of new objects become current iteration.
 goto 1. until required iteration number is achieved
Let's take for example the Koch curve  the first three iterations:
parameters:
 base object = line
 matrices = 1: scale to one third; 2: scale to one third, rotate 60 degrees, move to one third; 3: scale to one third, rotate 120 degrees, move to two thirds; 4: scale to one third, move to 1
 iteration number = 2
And now my code. I've tried a several changes of my code, but nothing worked :(. Now I have following:
Let's assume, that:

this>currentIterationNumber = 1
IFSFractal::Iteration* IFSFractal::nextIteration() { // if following iteration is already computed, return it if ((this>currentIterationNumber + 1) < this>iterations.size()) { return this>iterations.at(++this>currentIterationNumber); } // compute following iteration else { IFSFractal::Iteration *nextIteration = new IFSFractal::Iteration(); IFSFractal::Iteration *currentIteration = this>iterations.at(this>currentIterationNumber); QList<QTransform> newIterationMatrices; // there will be so much new shapes as the count of matrices qint32 i = 0; QListIterator<QPolygonF*> iterator(currentIteration>iteration); while (iterator.hasNext()) { QPolygonF currentShape = *iterator.next(); QPointF currentPosition = currentShape.at(0); // last computed matrix (here is stored last rotation, scale, ...) QTransform lastMatrix = this>lastIterationMatrices.at(i++); // move current shape into the origin of the coordinate system QTransform toOrigin; toOrigin.translate(currentPosition.x(), currentPosition.y()); currentShape = toOrigin.map(currentShape); // go through all matrices QListIterator<QTransform> matrixIterator(this>matrices); while (matrixIterator.hasNext()) { QTransform currentMatrix = lastMatrix * matrixIterator.next(); newIterationMatrices.append(currentMatrix); // map transformation QPolygonF newShape = currentMatrix.map(currentShape); // returns new shape back into correct position QTransform toPosition; toPosition.translate(currentPosition.x(), currentPosition.y()); newShape = toPosition.map(newShape); // save transformed shape as pointer QPolygonF *p_newShape = new QPolygonF(newShape); nextIteration>iteration.append(p_newShape); } } this>lastIterationMatrices = newIterationMatrices; this>currentIterationNumber++; this>iterations.append(nextIteration); return nextIteration; } }
and here are my QTransforms:
// line segment QPolygonF *line = new QPolygonF(); line>append(QPointF(0, 0.75)); line>append(QPointF(1, 0.75)); // 0. iteration IFSFractal::Iteration *zero = new IFSFractal::Iteration(); zero>iteration.append(line); // save 0. iteration this>iterations.append(zero); // transform matrices // scaling to one third QTransform transform1; transform1.scale(1.0 / 3, 1.0 / 3); this>addMatrix(1, transform1); // scaling to 1/3, translation and rotation about 60 deg QTransform transform2; transform2.scale(1.0 / 3, 1.0 / 3) .translate(1, 0) .rotate(60); this>addMatrix(2, transform2); // scaling to 1/3, translation and rotation about 120 deg QTransform transform3; transform3.scale(1.0 / 3, 1.0 / 3) .translate(2, 0) .rotate(120); this>addMatrix(3, transform3); // scaling to 1/3 and translation to the right QTransform transform4; transform4.scale(1.0 / 3, 1.0 / 3) .translate(2, 0); this>addMatrix(4, transform4);
But it works only for the first iteration and I have no idea how to write it correct.
My result:
Help me please, I'm little bit desperate :(.
Thank you very very much.