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2.
Triangle t is oriented, i.e., its boundary has
clockwise or counterclockwise orientation. We call the side to the left
of the boundary the positive side and the side to the right of the
boundary the negative side.
The boundary of a triangle splits the plane in two open regions, a bounded one and an unbounded one.
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introduces a triangle t with vertices p, q and r.
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| Test for equality: two triangles are equal, iff there exists a cyclic permutation of the vertices of t2, such that they are equal to the vertices of t. |
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| Test for inequality. |
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| returns the i'th vertex modulo 3 of t. |
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| returns vertex(i). |
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| triangle t is degenerate, if the vertices are collinear. | ||
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| returns the orientation of t. | ||
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returns
ON_ORIENTED_BOUNDARY, or
POSITIVE_SIDE,
or the constant
ON_NEGATIVE_SIDE,
determined by the position of point p.
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returns the constant ON_BOUNDARY,
ON_BOUNDED_SIDE, or else
ON_UNBOUNDED_SIDE,
depending on where point p is.
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For convenience we provide the following Boolean functions:
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| returns a triangle where the boundary is oriented the other way round (this flips the positive and the negative side, but not the bounded and unbounded side). |
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| returns the signed area of t. |
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| returns a bounding box containing t. |
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| returns the triangle obtained by applying at on the three vertices of t. | ||