An object of the class Vector_2<Kernel> is a vector in the two-dimensional vector space . Geometrically spoken, a vector is the difference of two points , and denotes the direction and the distance from to .
CGAL defines a symbolic constant NULL_VECTOR. We will explicitly state where you can pass this constant as an argument instead of a vector initialized with zeros.
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introduces the vector .
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introduces the vector .
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introduces the vector having the same direction as .
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introduces the vector having the same direction as .
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introduces a null vector v.
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introduces a vector v initialized to . Precondition: hw not equal to 0
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Test for equality: two vectors are equal, iff their and coordinates are equal. You can compare a vector with the NULL_VECTOR. | ||
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Test for inequality. You can compare a vector with the NULL_VECTOR. |
There are two sets of coordinate access functions, namely to the homogeneous and to the Cartesian coordinates. They can be used independently from the chosen kernel model.
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| returns the homogeneous coordinate. |
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| returns the homogeneous coordinate. |
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| returns the homogenizing coordinate. |
Note that you do not loose information with the homogeneous representation, because the FieldNumberType is a quotient.
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| returns the x-coordinate of v, that is . |
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| returns the y-coordinate of v, that is . |
The following operations are for convenience and for compatibility with higher dimensional vectors. Again they come in a Cartesian and homogeneous flavor.
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returns the i'th homogeneous coordinate of v, starting with 0. Precondition: . | ||
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returns the i'th
Cartesian
coordinate of v, starting at 0. Precondition: . | ||
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returns cartesian(i). Precondition: . | ||
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| returns the dimension (the constant 2). |
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| returns the direction which passes through v. | |
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returns the vector obtained by applying on v. | ||
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returns the vector perpendicular to v in clockwise or counterclockwise orientation. |
The following operations can be applied to vectors:
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| Addition. |
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| Subtraction. |
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| returns the opposite vector. |
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| returns the scalar product (= inner product) of the two vectors. |
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Multiplication with a scalar from the right. | ||
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Multiplication with a scalar from the right. | ||
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Multiplication with a scalar from the left. | ||
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Multiplication with a scalar from the left. | ||
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Division by a scalar. |