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- Curve_orientation abstract "In mathematics, a positively oriented curve is a planar simple closed curve (that is, a curve in the plane whose starting point is also the end point and which has no other self-intersections) such that when traveling on it one always has the curve interior to the left (and consequently, the curve exterior to the right). If in the above definition one interchanges left and right, one obtains a negatively oriented curve.Crucial to this definition is the fact that every simple closed curve admits a well-defined interior; that follows from the Jordan curve theorem.All simple closed curves can be classified as negatively oriented (clockwise), positively oriented (counterclockwise), or non-orientable. The inner loop of a beltway road in the United States (or other countries where people drive on the right side of the road) would be an example of a negatively oriented (clockwise) curve. A circle oriented counterclockwise is an example of a positively oriented curve. The same circle oriented clockwise would be a negatively oriented curve.The concept of orientation of a curve is just a particular case of the notion of orientation of a manifold (that is, besides orientation of a curve one may also speak of orientation of a surface, hypersurface, etc.). Here, the interior and the exterior of a curve both inherit the usual orientation of the plane. The positive orientation on the curve is then the orientation it inherits as the boundary of its interior; the negative orientation is inherited from the exterior.".
- Curve_orientation thumbnail Determining_orientation.png?width=300.
- Curve_orientation wikiPageExternalLink CurveOrientation.html.
- Curve_orientation wikiPageExternalLink _topology.html.
- Curve_orientation wikiPageID "3633706".
- Curve_orientation wikiPageLength "8485".
- Curve_orientation wikiPageOutDegree "50".
- Curve_orientation wikiPageRevisionID "699820237".
- Curve_orientation wikiPageWikiLink Angle.
- Curve_orientation wikiPageWikiLink Arithmetic_overflow.
- Curve_orientation wikiPageWikiLink Category:Curves.
- Curve_orientation wikiPageWikiLink Category:Orientation_(geometry).
- Curve_orientation wikiPageWikiLink Category:Polygons.
- Curve_orientation wikiPageWikiLink Circle.
- Curve_orientation wikiPageWikiLink Clockwise.
- Curve_orientation wikiPageWikiLink Collinearity.
- Curve_orientation wikiPageWikiLink Complex_polygon.
- Curve_orientation wikiPageWikiLink Computer-aided_design.
- Curve_orientation wikiPageWikiLink Computer_graphics.
- Curve_orientation wikiPageWikiLink Concave_polygon.
- Curve_orientation wikiPageWikiLink Connect_the_dots.
- Curve_orientation wikiPageWikiLink Convex_hull.
- Curve_orientation wikiPageWikiLink Convex_polygon.
- Curve_orientation wikiPageWikiLink Convex_set.
- Curve_orientation wikiPageWikiLink Cross_product.
- Curve_orientation wikiPageWikiLink Degeneracy_(mathematics).
- Curve_orientation wikiPageWikiLink Determinant.
- Curve_orientation wikiPageWikiLink Differential_geometry_of_curves.
- Curve_orientation wikiPageWikiLink File:Determining_orientation.png.
- Curve_orientation wikiPageWikiLink Flood_fill.
- Curve_orientation wikiPageWikiLink Geometry.
- Curve_orientation wikiPageWikiLink Hypersurface.
- Curve_orientation wikiPageWikiLink outer_directions.
- Curve_orientation wikiPageWikiLink Jordan_curve_theorem.
- Curve_orientation wikiPageWikiLink Laplace_expansion.
- Curve_orientation wikiPageWikiLink Line_(geometry).
- Curve_orientation wikiPageWikiLink Line_segment.
- Curve_orientation wikiPageWikiLink Manifold.
- Curve_orientation wikiPageWikiLink MathWorld.
- Curve_orientation wikiPageWikiLink Mathematics.
- Curve_orientation wikiPageWikiLink Numerical_error.
- Curve_orientation wikiPageWikiLink Orientability.
- Curve_orientation wikiPageWikiLink Orientation_(vector_space).
- Curve_orientation wikiPageWikiLink Polygon.
- Curve_orientation wikiPageWikiLink Quadrant_(plane_geometry).
- Curve_orientation wikiPageWikiLink Self-intersecting_polygon.
- Curve_orientation wikiPageWikiLink Simple_polygon.
- Curve_orientation wikiPageWikiLink Surface.
- Curve_orientation wikiPageWikiLink Vertex_(geometry).
- Curve_orientation wikiPageWikiLink Winding_number.
- Curve_orientation wikiPageWikiLinkText "Curve orientation".
- Curve_orientation wikiPageWikiLinkText "counter-clockwise".
- Curve_orientation wikiPageWikiLinkText "curve orientation".
- Curve_orientation wikiPageWikiLinkText "orientation".
- Curve_orientation wikiPageWikiLinkText "oriented".
- Curve_orientation wikiPageWikiLinkText "positively oriented".
- Curve_orientation wikiPageUsesTemplate Template:About.
- Curve_orientation wikiPageUsesTemplate Template:Reflist.
- Curve_orientation wikiPageUsesTemplate Template:Unref.
- Curve_orientation subject Category:Curves.
- Curve_orientation subject Category:Orientation_(geometry).
- Curve_orientation subject Category:Polygons.
- Curve_orientation hypernym Curve.
- Curve_orientation type Album.
- Curve_orientation type Polytope.
- Curve_orientation comment "In mathematics, a positively oriented curve is a planar simple closed curve (that is, a curve in the plane whose starting point is also the end point and which has no other self-intersections) such that when traveling on it one always has the curve interior to the left (and consequently, the curve exterior to the right).".
- Curve_orientation label "Curve orientation".
- Curve_orientation sameAs Q5196067.
- Curve_orientation sameAs m.09r7vr.
- Curve_orientation sameAs Ориентация_кривой.
- Curve_orientation sameAs Q5196067.
- Curve_orientation wasDerivedFrom Curve_orientation?oldid=699820237.
- Curve_orientation depiction Determining_orientation.png.
- Curve_orientation isPrimaryTopicOf Curve_orientation.