====== Puzzle game conceptions ======
The goal: the interface for the user to allow him to join many pieces into one picture.

The piece -- is a shape with non-rectangle complex boundary. 

The shape -- is the closed polygon. It can be filled by the TGraphic's procedure Polygon.

The polygon -- is a line with straight segments. First point is closed with last point. 

The edge -- is the straight segment of the polygon. 

In this program internal edges made by jigsaw are used. There are complex simmetrical contours. And external edges -- not complex but simple line between two points.

===== Edge definition =====
We have special drawing procedure. It draw the line between two points using edge-pattern (see picture). 
{{   images:puzzle_game_the_edge_in_autocad.jpg?544}}

seg{jigsaw}:array[1..Nseg] of TPoint = [X:0; Y:0], [ X:3; Y:-2], [ X:12; Y:-3], [ X:19; Y:-3], [ X:31; Y:0),
(X:27; Y:2], [ X:23; Y:6], [ X:21; Y:10], [ X:21; Y:12], [ X:23; Y:16], [ X:27; Y:20], [ X:33; Y:22], [ X:41; Y:22], [ X:46; Y:20], [ X:50; Y:16], [ X:52; Y:12], [ X:52; Y:10], [ X:50; Y:6], [ X:45; Y:2], [ X:43; Y:0], [ X:55; Y:-3], [ X:62; Y:-3], [ X:71; Y:-2], [ X:74; Y:0]; \\ 
where Nseg = 18+6.

The procedure use vectoral geometric calculations. Therefore the edge as a whole could be drawn by any angle. 

And any edge could be processes. See simpler edge here --- [[frac:simple_edge]]. 

As an additional ability -- when the edge is drawn -- it insert new points into the global array, and when all 4 edges of the rectangle will be drawn by edge-draw procedure --- we'll receive the complex jigsaw polygon. This ability is used in this game.

===== Initial dividing of the picture into pieces =====
Ok. We have the picture 520 x 520 pixels and we want to divide it into 6 * 6 parts. 
Of course for rectangle pieces it's a simple task. But how to do the same with jigsaw edges? 

Ok. The definition: the neighbours are two polygons between one jigsaw edge. One of them should have sign = '+' and second -- sign '-'. Sign Plus ('+') -- means this polygon is greater because his jigsaw edge goes into the '-' polygon. Each polygon will have 4 signs -- one per each its edge. 

{{  images:puzzle_start.gif}}

Now we will set '+' signs into every even polygon. And minus -- all others. Then we will check where all edges have signs '-'/'+' in our compilation. If everything correct -- we'll received the puzzle game before of dividing and the piece random displacement. 

How to draw the piece of picture? Very simple -- a piece is the set of pixels are inside the polygon. 

So we have the function returns true if the point [X, Y] is inside the polygon.

May be this article to be continued...