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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.
Sequence of probes around the convex hull of a polygon to determine its diameter using Rotating Caliper method. In computational geometry, the method of rotating calipers is an algorithm design technique that can be used to solve optimization problems including finding the width or diameter of a set of points.
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 ...
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 ...
The x and y coordinates of the point of intersection of two non-vertical lines can easily be found using the following substitutions and rearrangements. Suppose that two lines have the equations y = ax + c and y = bx + d where a and b are the slopes (gradients) of the lines and where c and d are the y-intercepts of the lines.
First, find out if the line produced by the ray intersects with the plane that the triangle is on, and if it does, find the coordinates of that intersection. The only way that the line will not intersect the plane is if the ray's direction vector is parallel to the plane. [3]