This submission facilitates working with quadratic curves (ellipse, parabola, hyperbola, etc.) and quadric surfaces (ellipsoid, elliptic paraboloid, hyperbolic paraboloid, hyperboloid, cone, elliptic cylinder, hyperbolic cylinder, parabolic cylinder, etc.) given with the general quadratic equation
Q(x) = x' * A * x + b' * x + c = 0
where a pseudo-MatLab notation has been used. A is a symmetric N-by-N matrix (N = 2 or N = 3 not necessarily invertible), b is an N-by-1 column vector, and c is a scalar. The parameter x is an N-by-1 column vector. Those points x that satisfy Q(x) = 0 comprise the quadratic curve or quadric surface.
The package comprises of two major components.
First, a set of functions is included for quadratic curves that identify the conic section and compute explicit parameters (semimajor axis, semiminor axis, rotation matrix, translation vector) of a conic section given with the general quadratic equation; or plot a conic section, returning a lineseries object (for circles, ellipses and parabolas) or a hggroup object (for hyperbolas).
Second, the package contains an algorithm for computing the distance from a point in 2D to a general quadratic curve defined implicitly by a second-degree quadratic equation in two variables or from a point in 3D to a general quadric surface defined implicitly by a second-degree quadratic equation in three variables.
Utility functions are included to manipulate matrices of symbolic variables that were used to pre-compute polynomials shipped with the package. |