Matrix representing a conic

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Description

Build a symmetric matrix representing a quadratic polynomial in two variables.

Usage

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Arguments

v

(vector) a 6-length vector containing the coefficients of a quadratic polynomial.

Details

The v argument is a 6-length vector containing the coefficients of a quadratic polynomial of the form:

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    P(x_1,x_2) = v_1 x_1^2 + v_2 x_1 x_2 + v_3 x_2^2 + v_4 x_1 + v_5 x_2 + v_6 

The associated quadratic form is:

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    Q(x_1,x_2,x_3) = v_1 x_1^2 + v_2 x_1 x_2 + v_3 x_2^2 + v_4 x_1 x_3 + v_5 x_2 x_3 + v_6 x_3^2 

Value

Return the symmetric 3x3 matrix representing the associated quadratic form.

Author(s)

Bernard Desgraupes
bernard.desgraupes@u-paris10.fr
University of Paris Ouest - Nanterre
Lab Modal'X (EA 3454)

See Also

conicAsymptotes, conicAxes, conicCenter, conicPlot

Examples

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# Equation: 2*x_1^2 + 2*x_1*x_2 + 2*x_2^2 - 20*x_1 - 28*x_2 + 10 = 0
v <- c(2,2,2,-20,-28,10)
conicMatrix(v)