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Manual Reference Pages  - uconic (3)

NAME
uconic(3f) - [M_drawplus] general conic sections (LICENSE:MIT)

CONTENTS

Synopsis
Description
Options
Author
License

SYNOPSIS
uconic(x,y,p,e,theta1,theta2,orientation) 

    real, intent=(in) :: x
    real, intent=(in) :: y
    real, intent=(in) :: p
    real, intent=(in) :: e
    real, intent=(in) :: theta1
    real, intent=(in) :: theta2
    real, intent=(in) :: orientation

DESCRIPTION

UCONIC() allows the user to draw a generalized conic section having a given focus, directrix, eccentricity, and starting and ending sweep positions. The conic sections that may be drawn are 

      CALL UCONIC (X,Y,P,E,THETA1,THETA2,ORIENTATION)
(X,Y) are used to specify the coordinates of the focus of the conic section; P is the distance from the focus to the directrix; E is the eccentricity, THETA1 and THETA2 represent the initial and final angles through which the conic section is to be drawn. Parameters E and P affect the generation of the conic section in the following manner:

OPTIONS
x x-coordinate of the focus of the conic section.
y y-coordinate of the focus of the conic section.
p Distance from the focus to the directrix.
o P.GT.0 Defines the position of the focus to be to the right of (or below) the directrix.
o P.LT.0 Indicates that the focus is positioned to the left of (or above) the directrix.
e eccentricity.
o E=0 Circular arc with a center at (X,Y) at radius P/2. The arc will subtend the angular range defined by THETA1 and THETA2.
o 0.LT.ABS(E).LT.1 ELLIPSE.
o ABS(E)=1 PARABOLA.
o ABS(E).GT.1 HYPERBOLA
o E.GT.0 Indicates that the major axis of the conic section is to be oriented parallel to the X-axis.
o E.LT.0 Specifies that the major axis is to be oriented along the Y-axis.
theta1 Initial sweep position in current angular units.
theta2 Terminal sweep position in current angular units.
orientation
  angle of conic axis in degrees

    COMMENTS
The basis for uconic is the generalized conic equation 

           R=(E*P)/(1-E*COS(THETA))
By suitably modifying the values of the parameters P and E, all types of conic sections can be created. The following describes the effects induced by different values of P of E. 

          P.GT.0       the focus is to the right (below the directrix).


          P.LT.0       the focus is to the left (above the directrix).


          P = 0        the conic will be a point at x,y.


          E = 0        the conic is a circular arc with center at x,y
                       and radius subtending the angular range from the
                       theta1 to theta2.


          0.LT.ABS
          (E).LT.1     the conic is an ellipse.


          ABS(E)=1     the conic is a parabola.


          ABS(E).GT.1  the conic is a hyperbola.


          E.GT.0       the conic is oriented along the x-axis


          E.LT.0       the conic is oriented along the y-axis
Conic sections may be rotated to any angle by defining a suitable user coordinate system.

The circle is a degenerate case not fully handled by the generalized conic equation. For completeness a circle with arbitrarily assigned radius of will be generated when E has a value of zero.

If an angle of orientation of the conic is specified, then the conic section will be oriented as specified around the point of intersection of the directrix and the semi-major axis.

In three dimensional applications, the conic section drawn by uconic will lie in the current xy plane.

AUTHOR
o Heavily based on a GCS routine written by Major Gabriel.
o John S. Urban

LICENSE
MIT License

uconic (3) March 11, 2021
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