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OrientationTests - Basic tools orientation tests Rodrigo...

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Rodrigo Silveira Computational Geometry Facultat d’Inform` atica de Barcelona Universitat Polit` ecnica de Catalunya Basic tools: orientation tests
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Turning right or turning left? Computational Geometry, Facultat d’Inform` atica de Barcelona, UPC Consider a sequence of 3 points: p , q , r p q r
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Turning right or turning left? Computational Geometry, Facultat d’Inform` atica de Barcelona, UPC Basic question: do they make a right turn? A left turn? Or perhaps they are colinear? Consider a sequence of 3 points: p , q , r p q r
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Turning right or turning left? Computational Geometry, Facultat d’Inform` atica de Barcelona, UPC Basic question: do they make a right turn? A left turn? Or perhaps they are colinear? Consider a sequence of 3 points: p , q , r p q r
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Turning right or turning left? Computational Geometry, Facultat d’Inform` atica de Barcelona, UPC Basic question: do they make a right turn? A left turn? Or perhaps they are colinear? Consider a sequence of 3 points: p , q , r p q r
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Turning right or turning left? Computational Geometry, Facultat d’Inform` atica de Barcelona, UPC Basic question: do they make a right turn? A left turn? Or perhaps they are colinear? Consider a sequence of 3 points: p , q , r p q r This is a fundamental basic operation in geometric algorithms. Requires a solution that is Efficient Numerically robust
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Turning right or turning left? Computational Geometry, Facultat d’Inform` atica de Barcelona, UPC Basic question: do they make a right turn? A left turn? Or perhaps they are colinear? Consider a sequence of 3 points: p , q , r p q r This is a fundamental basic operation in geometric algorithms. Requires a solution that is Efficient Numerically robust Solution: signed area of triangle 4 pqr
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Signed area of triangle Computational Geometry, Facultat d’Inform` atica de Barcelona, UPC The signed area of 4 pqr tells us the area of the triangle, and the sign gives the orientation (left-turning or right-turning) Signed area of 4 pqr p q r Can the area be zero?
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Signed area of triangle Computational Geometry, Facultat d’Inform` atica de Barcelona, UPC The signed area of 4 pqr tells us the area of the triangle, and the sign gives the orientation (left-turning or right-turning) Signed area of 4 pqr p q r A ( 4 pqr ) is twice the area of the parallelogram defined by vectors pq and w Recall: in 2-dimensions, the area of the paral- lelogram defined by two vectors is the deter- minant of a 2 × 2
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