Difference between revisions of "TriangleCurve Command"
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;TriangleCurve( <Point P>, <Point Q>, <Point R>, <Equation in A, B, C> ) | ;TriangleCurve( <Point P>, <Point Q>, <Point R>, <Equation in 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 referred 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 referred to as ''A'', ''B'', ''C''. | ||
− | :{{Example|1=If ''P'', ''Q'', ''R'' are points, <code>TriangleCurve | + | :{{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''.}} |
:{{Example|1= | :{{Example|1= | ||
− | <code>TriangleCurve | + | <code>TriangleCurve(A, B, C, A*C = 1/8)</code> creates a hyperbola such that tangent, through ''A'' or ''C'', to this hyperbola splits triangle ''ABC'' in two parts of equal area.}} |
:{{Example|1= | :{{Example|1= | ||
− | <code>TriangleCurve | + | <code>TriangleCurve(A, B, C, A² + B² + C² - 2B C - 2C A - 2A B = 0)</code> creates the [[w:Steiner_inellipse|Steiner inellipse]] of the triangle ''ABC'', and <code>TriangleCurve(A, B, C, B C + C A + A B = 0)</code> creates the [[w:Steiner_ellipse|Steiner circumellipse]] of the triangle ''ABC''. }} |
{{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.}} |
Latest revision as of 09:44, 11 October 2017
- 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 referred 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.
- Example:
TriangleCurve(A, B, C, A*C = 1/8)
creates a hyperbola such that tangent, through A or C, to this hyperbola splits triangle ABC in two parts of equal area.
- Example:
TriangleCurve(A, B, C, A² + B² + C² - 2B C - 2C A - 2A B = 0)
creates the Steiner inellipse of the triangle ABC, andTriangleCurve(A, B, C, B C + C A + A B = 0)
creates the Steiner circumellipse of the triangle ABC.
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.