Difference between revisions of "TriangleCurve Command"

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:creates implicit polynomial, whose equation in [[w:Barycentric_coordinate_system_(mathematics)|barycentric coordinates]] with respect to points P, Q,R is given by the fourth parameter; the barycentric coordinates are refered to as A,B,C.
 
:creates implicit polynomial, whose equation in [[w:Barycentric_coordinate_system_(mathematics)|barycentric coordinates]] with respect to points P, Q,R is given by the fourth parameter; the barycentric coordinates are refered to as A,B,C.
  
{{Example|1=If ''P,Q,R'' are points, <code>TriangleCurve[P,Q,R,(A-B)*(B-C)*(C-A)=0]</code> gives a cubic curve consisting of perpendicular bisectors of all the segments ''PQ, QR, RP''.}}
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{{Example|1=If ''P,Q,R'' are points, <code>TriangleCurve[P,Q,R,(A-B)*(B-C)*(C-A)=0]</code> gives a cubic curve consisting of the medians of the triangle ''PQR''.}}
  
 
{{Note|The input points can be called ''A'', ''B'' or ''C'', but in this case you cannot use e.g. ''x(A)'' in the equation, because ''A'' is interpreted as the barycentric coordinate.}}
 
{{Note|The input points can be called ''A'', ''B'' or ''C'', but in this case you cannot use e.g. ''x(A)'' in the equation, because ''A'' is interpreted as the barycentric coordinate.}}

Revision as of 00:17, 18 July 2012


TriangleCurve[<Point P>,<Point Q>,<Point R>,<Equation in A,B,C>]
creates implicit polynomial, whose equation in barycentric coordinates with respect to points P, Q,R is given by the fourth parameter; the barycentric coordinates are refered to as A,B,C.
Example: If P,Q,R are points, TriangleCurve[P,Q,R,(A-B)*(B-C)*(C-A)=0] gives a cubic curve consisting of the medians of the triangle PQR.


Note: The input points can be called A, B or C, but in this case you cannot use e.g. x(A) in the equation, because A is interpreted as the barycentric coordinate.
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