Mathematical Optimization in Graphics and Vision - Luiz Velho - Impa

2.8. HOW TO SOLVE IT? 33
has a solution. Moreover, this solution will be close to the point A. Geometrically,
the solution is the point P , such that its image T (P ) is the closest point of the line
r to the point A (see Figure 2.4).
A
T (P )
Figure 2.4: Well-posed formulation of a problem.
2.8 How to solve it?
It is the purpose of this book to use optimization techniques to solve computer
graphics problems.
Later on we will present several examples of computer graphics problems that
can be posed, in a natural way, as optimization problems. Nevertheless we should
remind that posing a problem as an optimization problem does not mean that it is
automatically solved, at least in the sense of obtaining an exact solution.
In fact optimization problems are, in general, very difficult to solve. Some of
the difficulties are discussed below.