Question

how to write an algorithm in mathematics for irregular shape in co-ordinates usin graph

Answer 1

Do you want to calculate the area given a set of coordinates for each of the vertices?

Answer 2

The irregular shape has only lines? Without curves?

Answer 3

irregular shape s wit curves and irregular polygon, and set of co ordinates r given for each vertices

Answer 4

If it is an irregular shaped polygon (i.e. lines between vertices), a simple algorithm exists to calculate the area of the polygon. The polygon can have as many vertices as necessary.

If curves join the vertices, the algorithm will depend on the kind of curves. Basically we can calculate the area of the polygon joining the vertices, then adjust the difference between a straight line and the curve(s). The second part is a little more complex depending on the types of curves joining the vertices.

Answer 5

how to align ?for example if 4 diff irregular shapes has to be aligned in such a way that minimum sheet metal s to be used in a layout,and particular bounding area has to be claculated , can u give some ideas

Answer 6

That makes the question more clear!
In this case, area is not the major question. It is the optimization of the shapes within a limited space.

Mathematically, there is an optimal solution for each of such problems, but the effort required to find the optimal solution may not pay for the gain.

You can consider two cases:
1. If the shapes are repetitive, and multiplied many times, i.e. many identical shapes, then what you do will have a major impact, and it has to be done very carefully to optimize the area of the sheet(s).
2. If the shapes vary each time, and the optimization has to be done on a daily basis, then there is a trade-off between the efforts of optimization and the material saved.

A practical solution is to create a bounding polygon which contains completely the shapes, including the cutting width (flame cutting, EDM, etc.) Then these shapes can be placed, moved or rotated mathematically with much ease. An interactive program can be made to accomplish the placement and local optimization tasks.

Answer 7

the bounding polygon s the general rule all r followin,my new concept s to create a dots across the given figure and wil try to match wit t another figure, this process wil continue until perfect match s possible. i hav to write an algorithm for this step by step process, can u help me regardin this.

Answer 8

It depends a lot on the problem. The general solution for ANY shape is not going to take a long time to run, if computationally feasible at all. Some of the parameters that could render the solution more efficient could be:
1. approximate number of shapes per sheet
2. repetitions in shapes, sizes, etc.
3. are shapes convex (all, some, most, never, ...)
4. are shapes associated (in occurrence and in number)
5. how many shapes/sheets need to be processes per day.
6. cost of sheet (raw material)
...
These factors will help design a feasible algorithm, since an optimal solution is unlikely to be possible beyond a certain number of shapes. Eventually, you will have to make a compromise between savings of material and computational cost/efficiency.
Some of the above factors will also affect the algorithm for bounding polygons.

Answer 9

On the other hand, you are probably aware that there are many commercially available software for nesting (creating layouts). Do these fit your requirements? What are the objections? Normally a commercial software is MUCH better than what we would make in-house because of their experience with the real-world.
If you still would like to write your own, you can consider the following reference, among the multitude of literature available:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.22.405&rep=rep1&type=pdf
Note that the end of the document has a list of references from which you can branch out to other references.

Different algorithms are used for nesting boxes, HVAC ducts, textile, etc because of the different characteristics.
Can you tell us which industry you're in?

Answer 10

am doin my UG IN mechanical engineering

Answer 11

People spend millions of dollars to import a machine from Italy to nest and cut leather to make leather bags. If you can find an algorithm that works for everything, you will be rich!