Geometry in Plan (Math) - math

Question

My problem is to know whether or not a point is contained in a polygon (sets of points) on the same surface.
Simple example in my favorite language DART
Point myPoint = new Point(10, 12);
List<Point> myPolygon = [ // The Polygon, for example is simple rect
new Point(2, 7),
new Point(15,7),
new Point(15, 18),
new Point(2, 18)
];
bool pointIsContainedInPolygon(List Polygon){
// .. data processing ...
}
I need to know what is the function: pointIsContainedInPolygon(myPolygon)

Answer 1

I have resumed the code data in the How can I determine whether a 2D Point is within a Polygon? post in dart, here is the result (tested)
bool pnpoly(Point point, List<Point> polygon){
// Step 1: Cut and detail
int nvert = polygon.length;
List<int> vertx = [];
List<int> verty = [];
for(Point vert in polygon){ // Listing x and y pos of all vertices
vertx.add(vert.x);
verty.add(vert.y);
}
// Step 2: Calcul..
bool c = false;
int j = nvert-1;
for (int i = 0; i < nvert; j = i++){
if( ((verty[i]>point.y) != (verty[j]>point.y)) && (point.x < (vertx[j]-vertx[i]) * (point.y-verty[i]) / (verty[j]-verty[i]) + vertx[i]) ){
c = !c;
}
}
return c;
}
Here is my test
List<Point> myPolygon = [ // classic rectangle
new Point(2,2),
new Point(52,2),
new Point(52,41),
new Point(2,41)
];
Point myPoint = new Point(53,40);
print( pnpoly(myPoint, myPolygon) ); // false