Conic

class sonic.Conic
Constructor Summary
Conic(raw_conic, varargin)

Creates a conic object.

Inputs:

  • raw_conic (1,6 double): Implicit representation of the conic. If inputs with 6 parameters, this is assumed to be the coefficients of the implicit equation [A;B;C;D;E;F] satisfying the equation Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.

OR

  • raw_conic (1,5 double): Explicit representation of the conic. If inputs with 5 parameters, this is assumed to be [xc; yc; a; b; psi] where xc and yc are the center, a and b are the semi major and minor axis, and psi is the conic rotation.

OR

  • raw_conic (3,3 double): Matrix containing either the locus or envelope representation of the conic. Must specify using varargin whether this is a locus or envelope as shown below.

  • varargin (string): “locus” for the locus representation and “envelope” for the envelope representation.

OR

  • raw_conic (1,1 sonic.Lines2): Lines2 object containing the degenerate conic representation of 2 lines. Must contain exactly two lines.

Outputs:

  • obj (1,1 sonic.Conic): conic object containing properties of the input conic.

Last revised: 11/11/24 Last author: Michela Mancini

Property Summary
degenerateLocus

representation of degenerate conics as two lines

envelope

inverse of Conic locus satisfying all lines tangent to the Conic

explicit

values for the explicit representation of a conic [xc; yc; a; b; psi]

implicit

normalized implicit coefficients [A;B;C;D;E;F] satisfying the equation Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0

locus

Conic locus of the form [A, B/2, D/2; B/2, C, E/2; D/2, E/2, F] satisfies all points lying on the conic

proper

degeneracy of conic

stable

numerical stability, where a conic is considered not stable if a proper conic is recognized as such only after origin shift

type

conic classification (ellipse, circle, parabola, etc…)

Method Summary
center(conic)

Takes a conic object and translates it by its center.

Inputs:

  • conic (sonic.Conic object): the original conic

Outputs:

  • translatedConic (sonic.Conic object): the conic

translated by its center - center (sonic.Points2 object): new origin of the coordinate system (center of the original conic)

Last revised: 11/14/2024 Last author: Michela Mancini

static locusToParameter(locus)

Determine the semi-latus rectum for a proper conic

Inputs:

  • locus (3x3 double): conic locus matrix

Outputs:

  • p (1x1 double): semi-latus rectum

Last revised: 4/19/24 Last author: Michela Mancini

static meetConicConic(locus1, locus2)

Performs the meet of two conics, the result of which are four points in P2.

Inputs:

  • locus1 (a 3x3 double array): A non-degenerate conic locus

  • locus2 (a 3x3 double array): A non-degenerate conic locus

Outputs:

  • pts (1x1 sonic.Points2): four points of intersection of the two conics

Last revised: 04/19/2024 Last author: Michela Mancini

static meetLineConic(line, locus)

Performs the meet of a line and a conic, the result of which are two points in P2

Inputs:

  • line (a sonic.Line2 object): A line in P2.

  • locus (a 3x3 double array): A conic locus

Outputs:

  • pts (1x1 sonic.Points2): two points of intersection of line and conic

Last revised: 04/22/2024 Last author: Michela Mancini

static parabolaToLocus(explicitParabola)

Determine the conic locus associated with a parabola with a specified vertex, tilt angle and semi-latus rectum

Inputs:

  • explicitParabola (4x1 double): contains a parameterization of the parabola in terms of vertex coordinates (xc,yc), tilt angle (psi) and the semi-latus rectum (p). The expected ordering is the following: explicit_parabola = [xc; yc; psi; p].

Outputs:

  • locus (3x3 double): conic locus

Last revised: 10/30/24 Last author: Michela Mancini

rotate(conic, angle)

Takes a conic object and an angle and outputs the conic object rotated about the origin by that angle (counterclock rotation)

Inputs:

  • conic (sonic.Conic object): the original conic

  • angle (double): the angle of counter clock rotation (rad)

Outputs:

  • newConic (sonic.Conic object): the conic

translated by the translation vector

Last revised: 11/17/2024 Last author: Michela Mancini

translate(conic, translation)

Takes a conic object and a translation vector and outputs the conic object shifted by the translation vector

Inputs:

  • conic (sonic.Conic object): the original conic

  • translation (sonic.Points2 object): the translation

vector (origin of the new coordinate system)

Outputs:

  • translatedConic (sonic.Conic object): the conic

translated by the translation vector

Last revised: 11/14/2024 Last author: Michela Mancini