# NAME

GDX_ARC - Parametric Circular Arc

# GENERAL DESCRIPTION

A GDX Parametric Circular Arc (GDX Arc) represents a circle or circular arc curve. The GDX Arc is parametrically defined using a center point and radius.

The parameterization given in the sections below defines the entity in 2D standard position. The circular arc is transformed from standard position to 2D definition space by applying the translation (defined by the CENTER and Z_DEPTH fields). The circular arc is then transformed from definition space to model space by applying the transformation matrix (defined by the MATRIX field), if any. The order of applying transformations is indicated symbolically below:

[MATRIX] [translation (CENTER(X,Y),Z_DEPTH)] [x(u), y(u), 0.0]

Note that the transformations may not be applied in the order that is considered intuitive.

# DDF SPECIFICATION

    entity 2:0   GDX_ARC   "Parametric Circular Arc" {

    double
    CENTER[2];

    double
    Z_DEPTH;

    double
    RADIUS;

    double
    START_ANGLE;

    double
    END_ANGLE;

    double
    MATRIX[];

    };

# FIELD DESCRIPTIONS

CENTER

A 2D array containing the X and Y translation of the circular arc from standard position to 2D definition space.

CENTER[0]

= X translation from standard position.

CENTER[1]

= Y translation from standard position.

Z_DEPTH

Z translation from standard position.

RADIUS

The radius (R) of the circular arc.

START_ANGLE

The start angle in radians.

END_ANGLE

The end angle in radians.

MATRIX

The transformation matrix that positions the GDX Arc from definition space to model space. This matrix is a GDX_MATRIX (typedef available by including gdx_Interface.h) which is a 1D array of 12 doubles that represent a 3x4 matrix. For a detailed description of the fields corresponding to a GDX_MATRIX, see the gdx_entity_intro manual page. For efficiency considerations, this field should be set to NULL if the circular arc being represented is 2D.

# PARAMETERIZATION (STANDARD POSITION)

       x(u) = R * cos(u)
       y(u) = R * sin(u)

# PARAMETRIC RANGE

The GDX Arc is defined over the following parametric range: 0.0 <= u <= MTH_2_PI

# IMPLICIT EQUATION (STANDARD POSITION)

The GDX Arc has the following implicit equation: C(x,y,z) = x*x + y*y - R*R = 0

# RESTRICTIONS

The GDX Arc is subject to the following restrictions: R > 0.0 0.0 <= START_ANGLE < MTH_2_PI START_ANGLE < END_ANGLE <= START_ANGLE + MTH_2_PI