What do you mean by computational geometry?
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.
Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry..
What is complexity in theory of computation?
Computational complexity theory is a mathematical research area in which the goal is to quantify the resources required to solve computational problems.
It is concerned with algorithms, which are computational methods for solving problems..
What is the application of complexity theory in computer science?
Complexity theory is a central topic in theoretical computer science.
It has direct applications to computability theory and uses computation models such as Turing machines to help test complexity.
Complexity theory helps computer scientists relate and group problems together into complexity classes..
What is the complexity of a computational problem?
In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it.
Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements..
What is the difference between computation theory and complexity theory?
In turn, imposing restrictions on the available resources is what distinguishes computational complexity from computability theory: the latter theory asks what kinds of problems can, in principle, be solved algorithmically..
What is the theory of computational complexity?
Computational complexity theory is a mathematical research area in which the goal is to quantify the resources required to solve computational problems.
It is concerned with algorithms, which are computational methods for solving problems..
What is theory of computation and complexity theory?
Put succinctly, computability theory is concerned with what can be computed versus what cannot; complexity is concerned with the resources required to compute the things that are computable.
As such, the fields are somewhat disjoint..
Why is computational geometry important?
Computational geometry is a field of study devoted to the development of efficient algorithms for problems which can be stated in geometric terms.
As data sets of all sizes are routinely and naturally described geometrically as points in space, the applications of computational geometry are far reaching..
- Let's take a fairly straightforward computational geometry problem: given a point and a polygon, does the point lie inside of the polygon? (This is called the point-in-polygon, or PIP problem.) PIP does a great job of demonstrating why computational geometry can be (deceptively) tough.
