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Does anyone know what additional constraints I need to make this bezier g3 continuous with this arc?
caden_kim517
Member Posts: 7 ✭
https://cad.onshape.com/documents/8e3e7eaed1d227aaf953307a/w/1a390e340a38174f9c8f10e3/e/46ae94889bac6d697ef75a58?renderMode=0&uiState=67d079ade522037cb3295f82
Best Answers
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GregBrown
Member, Onshape Employees, csevp, pcbaevp Posts: 288 
There's currently no G3 sketch constraint, so you have a couple of options:
- create a G2 sketch constraint between your Deg 6 Bezier and the arc, then move the next control point (shown below) while looking at the curvature combs. You'll probably find it needs to be close to (but not exactly) collinear with the CPs defining the G1 and G2. Move it such that the curvature combs smoothly transition (rate of change of curvature = G3, and you want that rate of change to be smooth at the intersection of the arc). I did this quickly and roughly below:
- change the workflow to use a bridging curve which does support G3. This will necessitate a rethink of the sketch, but is definitely possible.
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S1mon
Member Posts: 3,232 PRO
If you are trying to make a transition between arcs or an arc and a line, or two lines, it's possible to make a fully parametric G3 Bézier with Onshape's sketcher. The third derivative of an arc is zero since they are constant curvature. Lines, of course, have no curvature.
The trick with arcs is that you need to add some construction lines and constraints to get the right relationships with the control points. You also need your Bézier curve to be degree-7 to have enough control to be G3 on both ends.
In this example, I made a transition in sketcher between two arcs. You can look at the sketch in the document or the GIF below to see some of the important constraints that are added beyond the G2 (curvature) constraints at each end. The arcs are fully constrained, and the first control polygon legs at each of the blend are dimensioned (in this case they are both set to 5). The middle 3 legs are set to be equal to one another.
G3 to a line just requires that the first 3 control polygon lines are coincident or parallel to the line.
3
Answers
There's currently no G3 sketch constraint, so you have a couple of options:
- create a G2 sketch constraint between your Deg 6 Bezier and the arc, then move the next control point (shown below) while looking at the curvature combs. You'll probably find it needs to be close to (but not exactly) collinear with the CPs defining the G1 and G2. Move it such that the curvature combs smoothly transition (rate of change of curvature = G3, and you want that rate of change to be smooth at the intersection of the arc). I did this quickly and roughly below:
Thank you! I never realized that that G2 constraint existed. Do you happen to know how I might fully constrain that CP with other constraints and (if necessary) construction lines for "perfect" G3? And so that it won't break if the other geometry changes?
Bridging curve as you suggested is probably the best solution for this but I'm curious in case I ever find the need to do it in sketch.
If you are trying to make a transition between arcs or an arc and a line, or two lines, it's possible to make a fully parametric G3 Bézier with Onshape's sketcher. The third derivative of an arc is zero since they are constant curvature. Lines, of course, have no curvature.
The trick with arcs is that you need to add some construction lines and constraints to get the right relationships with the control points. You also need your Bézier curve to be degree-7 to have enough control to be G3 on both ends.
In this example, I made a transition in sketcher between two arcs. You can look at the sketch in the document or the GIF below to see some of the important constraints that are added beyond the G2 (curvature) constraints at each end. The arcs are fully constrained, and the first control polygon legs at each of the blend are dimensioned (in this case they are both set to 5). The middle 3 legs are set to be equal to one another.
G3 to a line just requires that the first 3 control polygon lines are coincident or parallel to the line.