Piecewise curve generation.

The piesewise curve uses 5th degree polynomial interpolation between positions. The 5th degree polynomial has 6 unknowns so in order to solve it we need 6 data values.

For a profile consisting of 2 points these are

Point 1 position, point 1 speed, point 1 acceleration

Point 2 position, point 2 speed, point 2 acceleration

For profiles consisting of more segments, interpolation is done per-segment (the above is applied for each segment).

Position, speed and acceleration values at control points are supplied by the user. Defaults for speed and acceleration are zero, but could be changed to the desired values.

In case the user would like to have part of the profile with linear motion (constant speed) he could change the point type to “Line Start” or use the “Insert Line” view mode to draw a straight line in the view. This could be achieved manually by having the same speed and acceleration values at two consecutive points, but it’s preferred to use the “Line Start” – “Line End” pair.

Please note at the below graphics the speed and acceleration curves between the second and third points- they’re constant.