geometry - Draw a turning arc connecting 3 waypoints in Java -

let's starting @ point w, heading through point final point b.

i instead draw turning arc represents more realistic behavior, ideally constrained speed , turning rate.

i've been looking examples of this, such described in this article, struggling little bit extend information i've read.

does know of sample implementation of behavior or maybe tutorial has code samples work from? seems super common thing in game ai, of descriptions find rather high level.

i've tagged post java, because solution domain in working, example in language may sufficient well.

you can either devise mathematical formula (harder more efficient) or think of this:

imagine driving car , there turn (at point a) after straight road (point w point a). have velocity vector pointing along road before start turning. once begin turn have (increasing) velocity vector pointing along turn (from point point b) , (decreasing) velocity vector pointing along road. can calculate resulting velocity vector adding 2 together. sample algorithm this:

while(turning){     straight_vector.magnitude = straight_vector.magnitude - 1;     turn_vector.magnitude = turn_vector.magnitude + 1;      resulting_vector = straight_vector + turn_vector; //vector addition      next_point.x = prev_point.x + resulting_vector.magnitude * math.cos(resulting_vector.direction);     next_point.y = prev_point.y + resulting_vector.magnitude * math.sin(resulting_vector.direction);      plot(next_point);      prev_point = next_point; } 

you can use vector3d class in java represent vectors.