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intersection of two polygons: window test. If one wants to determine the intersection points of two polygons, one can check the intersection of any pair of line segments of the polygons (see above). For polygons with many segments this method is rather time-consuming. In practice one accelerates the intersection algorithm by using window tests ...
Convex polygons will only have one intersecting polygon. The same algorithm can be used for merging two polygons by starting at the outbound intersections rather than the inbound ones. However this can produce counter-clockwise holes. Some polygon combinations may be difficult to resolve, especially when holes are allowed.
In computational geometry, the point-in-polygon (PIP) problem asks whether a given point in the plane lies inside, outside, or on the boundary of a polygon. It is a special case of point location problems and finds applications in areas that deal with processing geometrical data, such as computer graphics , computer vision , geographic ...
Additional vertices are inserted into both polygons at the points of intersection; an intersection vertex holds a pointer to its counterpart in the other polygon. In the second phase, each intersection is marked as either an entry intersection or an exit intersection. This is accomplished by evaluating the even–odd rule at the first vertex ...
No two line segment endpoints or crossings have the same x-coordinate; No line segment endpoint lies upon another line segment; No three line segments intersect at a single point. In such a case, L will always intersect the input line segments in a set of points whose vertical ordering changes only at a finite set of discrete events ...
Another special case is the point in polygon problem, in which one needs to determine whether a point is inside, outside, or on the boundary of a single polygon. In many applications, one needs to determine the location of several different points with respect to the same partition of the space.
One possibility to determine a polygon of points of the intersection curve of two surfaces is the marching method (see section References). It consists of two essential parts: The first part is the curve point algorithm, which determines to a starting point in the vicinity of the two surfaces a point on the intersection curve. The algorithm ...
Assume that we want to find intersection of two infinite lines in 2-dimensional space, defined as a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0. We can represent these two lines in line coordinates as U 1 = (a 1, b 1, c 1) and U 2 = (a 2, b 2, c 2). The intersection P′ of two lines is then simply given by [4]