#### Re: Point hit in a circuit

Hello, watchmaker, you wrote: SVZ>> If all of us still about Vatti there it is used sweep line. And in it there is a sorting. If about something another specify, about what. W> I about that is unimportant as am arranged inside Vatti and that he there demands is not related algorithm. Not clearly what for it  to the determination task the point in a circuit lies-whether. You resulted a picture which "works" inside Vatti. Therefore and talk about it. SVZ>> As far as I understand, at first it is necessary to calculate winding from each side of an edge (i.e. already additional procedure turns out), and then, sorting out edges, to define, to what area we get. W> it is not necessary to invent anything is it is not necessary. W> Do as in Wikipedia it is written or as already in an adjacent branch told: let out from a point a ray in any direction and consider number of its intersections with a circuit, considering a circuit direction (i.e. +1 or-1 for directions against and clockwise, accordingly). This number also answers about an accessory of a point to a polygon. SVZ>> count that check if the point is outside of a circuit returns: SVZ>> If the ray is launched, as nearby it is offered, from (-inf, py) in (px, py) check returns hit in a circuit. W> s = 0 - that is the point is out of a circuit in any interpretation from above-stated (odd, nonzero etc.). Everything, you understood about what. It is necessary to consider only a direction of an input of an edge in a ray. Confused a mention winding'. I thought that depth a circuit enclosure (0,1,2 is considered... On a picture). Yes, such method looks , than couples/ODD NUMBERS.

#### Re: Point hit in a circuit

Hello, V. Zudin, you wrote: SVZ> Confused a mention winding'. I thought that depth a circuit enclosure (0,1,2 is considered... On a picture). . So depth actually also is considered. Produced algorithm value s = 0 - the point means does not belong to a polygon. Produced value s = 1 - means belongs. Produced value s = 2 - means does not belong by rule ODD, but belongs by rule POSITIVE. And so on. Actually, the algorithm only also does that calculates depth of an enclosure. What here can confuse?

#### Re: Point hit in a circuit

Look at this decision, it denies classical geometry (the corner does not exist, there is a direction change). http://files.rsdn.org/125374/sg.png

#### Re: Point hit in a circuit

through it the challenging task dared more - the intersection (superimposing of figures), there the decision was reduced to a difference of vectors. Well and a classical rational way such tasks do not dare.

#### Re: Point hit in a circuit

Hello, Indy, you wrote: I> Look at this decision, it denies classical geometry (the corner does not exist, there is a direction change). I> http://files.rsdn.org/125374/sg.png 1. How many peaks are required for the description of such polygon? 2. How search of points on a surface on which the accessory of a point to a polygon is defined is fulfilled?

#### Re: Point hit in a circuit

Hello, V. Zudin, you wrote: SVZ> Hello, Indy, you wrote: I>> Look at this decision, it denies classical geometry (the corner does not exist, there is a direction change). I>> http://files.rsdn.org/125374/sg.png SVZ> 1. How many peaks are required for the description of such polygon? SVZ> 2. How search of points on a surface on which the accessory of a point to a polygon is defined is fulfilled? 1. The figure is described in the vectorial form, there is no concept of peaks and this concept is not used. As there is no concept of a corner for the arbitrary curve. The corner is concept from ancient geometry which is not real also to which there is no even an accurate determination - on sense this increment of a vector at the curve description, simplified to one point. 2. Such surface is described elementarily - by sampling of the following point on the basis of a current vector. The problem can be only standard - selection of noise on the image, join of parts and ; these are recognition problems. On the basis of this idea very much for a long time has been implemented  fillings of figures. More precisely so it is not correct to name, this selection of all integer parts (circuits) within considered region.

#### Re: Point hit in a circuit

Hello, Indy, you wrote: I> Look at this decision, it denies classical geometry (the corner does not exist, there is a direction change). I> http://files.rsdn.org/125374/sg.png Specify in which place it denies classical geometry?