Arc-to-Arc Transitions

In arc-to-arc transition mode the transitions are handled as follows.

  1. The arc with the larger radius is shortened by an arc length equal to the corner distance.
  2. Using this point, a transition move is calculated such that it is tangent to both arcs.
  3. The arc with the smaller radius is shortened to the point where it is tangent with the transition move.

The transition move that connects the two original arcs derives its velocity from the velocity transition parameter and the acceleration and deceleration values are derived from the next move.

There are six special cases for Arc-to-Arc transitions.

Transition Type Description
Zero-distance Transitions A zero-distance transition move is inserted when the corner distance is zero, which will only affect blending.
The path velocity will go to zero if the buffer mode is "Buffered". All other buffer modes may cause a large acceleration and jerkClosedIn physics, jerk is the rate of change of acceleration; more precisely, the derivative of acceleration with respect to time.
Intersection Transitions This will occur when the arcs intersect at two locations and the corner distance is equal to the arc length between the two intersections on the larger arc. The transition move will be zero distance.
The path velocity will go to zero if the buffer mode is "Buffered". All other buffer modes may cause a large acceleration and jerk.
Tangent Transitions with Opposite Direction

A portion of the arc with the larger radius will be replaced by an arc whose length is equal to the corner distance. This will not affect the path, but will affect blending. If the arcs have the same radius, the incoming arc will be treated as having a larger radius.

Line Segment Transitions For certain values of corner distance, the transition arc has an infinite radius and a line segment is used instead.
Same Circle, Same Direction Transitions A transition arc with a length of twice the corner distance will be added if both arcs lie on the same circle and are in the same direction. This will not affect the path, but will affect blending.
Same Circle, Opposite Direction Transitions The arcs will be shorted by an arc length equal to the corner distance and a zero distance transition will be inserted if both arcs lie on the same circle and are in the opposite direction.
The path velocity will go to zero if the buffer mode is "Buffered". All other buffer modes may cause a large acceleration and jerk.
Case Motion Path - Line-toArc / Arc-to-Line Key Motion Velocity Profile

n-degree, arcs in opposite direction

Blue: Incoming and outgoing circular motion

Black: "Trimmed" path

Red: Transition arc

1: Start / endpoint of arc move

n-degree, arcs in same direction

Blue: Incoming and outgoing circular motion

Black: "Trimmed" path

Red: Transition arc

1: Start / endpoint of arc move

2: Corner distance

Zero-distance

Blue: Incoming and outgoing circular motion

1: Original Start / Endpoint of arc move

user units/sec

Intersection

Blue: Incoming and outgoing circular motion

Black: "Trimmed" path

1: Intersection of the two arcs

Tangent arcs, opposite direction

Blue: Incoming and outgoing circular motion

Red: Transition arc

1: Original start / end point of moves

2: Start / Endpoint of arc move

Line segment

Blue: Incoming and outgoing circular motion

Red: Line Segment

1: Start / Endpoint of transition move

Same circle, same direction

Blue: Incoming and outgoing circular motion

Red: Transition arc

1: Start / Endpoint of arc move

2: Original start/end point

Same circle, opposite direction

Blue: Incoming and outgoing circular motion

1: Original Start / Endpoint of arc move

2: Start / Endpoint of arc move

Figure 7-10: Examples of Arc-to-Arc Transitions