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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 ...
To generate the line that bisects the angle between two given rays [clarification needed] requires a circle of arbitrary radius centered on the intersection point P of the two lines (2). The intersection points of this circle with the two given lines (5) are T1 and T2. Two circles of the same radius, centered on T1 and T2, intersect at points P ...
The intersections of circle C(r) and the new red circle D(r) are points P and Q. If the two circles are (externally) tangential then =. Internal tangency is not possible. If the two circles do not intersect then neither does the circle with the line. Points P and Q are the intersection points of circle C(r) and the line AB.
Creating the one point or two points in the intersection of a line and a circle (if they intersect) Creating the one point or two points in the intersection of two circles (if they intersect). For example, starting with just two distinct points, we can create a line or either of two circles (in turn, using each point as centre and passing ...
For any two circles in a plane, an external tangent is a line that is tangent to both circles but does not pass between them. There are two such external tangent lines for any two circles. Each such pair has a unique intersection point in the extended Euclidean plane. Monge's theorem states that the three such points given by the three pairs of ...
In geometry, a set of Johnson circles comprises three circles of equal radius r sharing one common point of intersection H.In such a configuration the circles usually have a total of four intersections (points where at least two of them meet): the common point H that they all share, and for each of the three pairs of circles one more intersection point (referred here as their 2-wise intersection).
A lens contained between two circular arcs of radius R, and centers at O 1 and O 2. In 2-dimensional geometry, a lens is a convex region bounded by two circular arcs joined to each other at their endpoints. In order for this shape to be convex, both arcs must bow outwards (convex-convex). This shape can be formed as the intersection of two ...
A circle (or line) is unchanged by inversion if and only if it is orthogonal to the reference circle at the points of intersection. [5] Additional properties include: If a circle q passes through two distinct points A and A' which are inverses with respect to a circle k, then the circles k and q are orthogonal.