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# Two dimensional Arcs

Only arcs, which are not longer than half of the full circumference are considered valid.

An arc is fully determined by two points of its ends and its curvature. Curvature is a real number, which defines how curved is the segment. Absolute value of curvature is an inverse of radius of the correspondent circumference:

Straight lines are considered a special case of arc. Straight lines are considered arcs with zero curvature (and infinite radius).

Distance between ends of an arc is always less or equal to double radius, otherwise the arc is considered invalid and does not have geometrical meaning. Arcs with curvature 0 (straight lines) are always valid.

When distance between its ends is equal double radius the arc is called full arc.

Ends of Arcs (and lines) are distinguished as first end the last end.

Curvature and radius can be negative. Geometrically, an arc has positive curvature and radius if the arc is located on the right-hand side while moving from the first end to the last end along a straight line. Fig 1. Positive arc. Fig 2. Negative arc.

Normally Arcs are present only as a part of a line strip. In a strip an arc and its ends are considered different elements because they can be selected independently. That is why as a geometric element arc has a single parameter - curvature or radius.

## Primary Properties

Primary properties completely and uniquely define geometry of an arc.

 Name Type Description Interface FirstEnd 2D Point The first end of the arc ILine2d_DG SecondEnd 2D Point The second end of the arc ILine2d_DG Curvature double Curvature (=1/radius) of the arc IArc_DG

### Secondary Properties

Secondary properties like center of the arc are the ones calculated via IArc_DG interface. They are uniquely defined by the primary properties.

### Normalized Natural Parameter

Points of an arc are often parameterized with ratio (length or partial arc between the first end and the point) / (length of the whole arc). This parameter always belongs to [0, 1] range, where 0 and 1 are mapped to the first and the second ends.

### Programmatic access

Primary  properties of an arc are accessed via ILine2d_DG and IArc_DG interfaces.

To create a new arc use a call similar to  IArc_DG iArc = IObjectGenerator.Create<IArc_DG>();.