TriangleCurve Command

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, and TriangleCurve(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.