The visibility graph approach to the Euclidean shortest path problem may be sped up by forming a graph from the bitangents instead of using all visibility edges, since a Euclidean shortest path may only enter or leave the boundary of an obstacle along a bitangent.
12.
Each pair of two of these three inscribed circles has two bitangents, lines that touch both of the dashed circles and pass between them : one bitangent is the angle bisector, and the second bitangent is shown as the red dashed line in the figure.
13.
Each pair of two of these three inscribed circles has two bitangents, lines that touch both of the dashed circles and pass between them : one bitangent is the angle bisector, and the second bitangent is shown as the red dashed line in the figure.
14.
As a limiting case of this construction, a line tangent to both circles ( a bitangent line ) passes through one of the homothetic centers, as it forms right angles with both the corresponding diameters, which are thus parallel; see tangent lines to two circles for details.
15.
By symmetry, rotations of this plane around the " z " axis give all the bitangent planes through the center . ( There are also horizontal planes tangent to the top and bottom of the torus, each of which gives a double circle , but not Villarceau circles .)
16.
Label the three sides of the given triangle as,, and, and label the three bitangents that are not angle bisectors as,, and, where is the bitangent to the two circles that do not touch side, is the bitangent to the two circles that do not touch side, and is the bitangent to the two circles that do not touch side.
17.
Label the three sides of the given triangle as,, and, and label the three bitangents that are not angle bisectors as,, and, where is the bitangent to the two circles that do not touch side, is the bitangent to the two circles that do not touch side, and is the bitangent to the two circles that do not touch side.
18.
Label the three sides of the given triangle as,, and, and label the three bitangents that are not angle bisectors as,, and, where is the bitangent to the two circles that do not touch side, is the bitangent to the two circles that do not touch side, and is the bitangent to the two circles that do not touch side.
19.
Bitangents may be used to speed up the visibility graph approach to solving the Euclidean shortest path problem : the shortest path among a collection of polygonal obstacles may only enter or leave the boundary of an obstacle along one of its bitangents, so the shortest path can be found by applying Dijkstra's algorithm to a subgraph of the visibility graph formed by the visibility edges that lie on bitangent lines.
20.
Further, the notion of bitangent lines can be extended to circles with negative radius ( the same locus of points, x ^ 2 + y ^ 2 = (-r ) ^ 2, but considered " inside out " ), in which case if the radii have opposite sign ( one circle has negative radius and the other has positive radius ) the external and internal homothetic centers and external and internal bitangents are switched, while if the radii have the same sign ( both positive radii or both negative radii ) " external " and " internal " have the same usual sense ( switching one sign switches them, so switching both switches them back ).
How to say bitangent in Hindi and what is the meaning of bitangent in Hindi? bitangent Hindi meaning, translation, pronunciation, synonyms and example sentences are provided by Hindlish.com.
