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 , and .
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Test for equality: two triangles are equal, iff there exists a cyclic permutation of the vertices of , 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 . Precondition: t is not degenerate. | ||
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returns the constant ON_BOUNDARY,
ON_BOUNDED_SIDE, or else
ON_UNBOUNDED_SIDE,
depending on where point is. Precondition: t is not degenerate. |
For convenience we provide the following boolean functions:
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Precondition: t is not degenerate. |
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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 on the three vertices of t. |