| 21. | Then, for any integer, the following equation is true in the homogeneous coordinate ring of:
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| 22. | An example of this is the systems of homogeneous coordinates for points and lines in the projective plane.
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| 23. | Homogeneous coordinates for projective spaces can also be created with elements from a division ring ( skewfield ).
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| 24. | Using transformation matrices containing homogeneous coordinates, translations can be seamlessly intermixed with all other types of transformations.
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| 25. | By using homogeneous coordinates, the intersection point of two implicitly defined lines can be determined quite easily.
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| 26. | Thus we define as the homogeneous coordinates of the point at infinity corresponding to the direction of the line.
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| 27. | In general, there is no difference either algebraically or logically between the homogeneous coordinates of points and lines.
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| 28. | This included the theory of complex projective space, the coordinates used ( homogeneous coordinates ) being complex numbers.
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| 29. | In a projective space,, a correlation is given by : points in homogeneous coordinates planes with equations.
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| 30. | We can convert 2D points to homogeneous coordinates by defining them as ( x, y, 1 ).
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