Customisable bezier low-poly vase

#Summary:
I like low-poly vases and bowls.
Printing in vase mode on a delta printer is quite a nice thing to see.

Unfortunately finding one that matched exactly what I needed was tedious.
I therefore decided to learn openscad in order to build my own general customisable low-poly vase file according to bezier curves.

For more information about bezier curves what they look like, how they are calculated (https://javascript.info/bezier-curve).

In order to allow the full power of vase mode slicing, the stl output if off course full.

This customisable allows you to generate vases / bowls of

• any size
• low-poly / not
• twisted / flat sided (accoding to shape chosen)
• straight / one point of inflexion / two points of inflexion

#Parameters:

• base_sides (3 -->100): the number of sides of the polygon used for the geometrical shape of the extrusion
• 3 --> triangle
• 4 --> square
• 100 --> 100 sided approximation of a circle
• base diameter (0 --> 100) : the size of the bottom of the vase / bowl
• top diameter (0 --> 100) : the size of the top of the vase / bowl
• poly height (1 --> 200) : the height of the finished polygon.
• figure twist (0° --> 360°) : the rotation given to the geometrical shape from bottom to top.
• bezier points (2 --> 4): choose the number of control points to shape the outline of the vase / bowl
• 2 bezier control points : it will generate a straight line from bottom width to the top width.
• 3 bezier control points : takes into account the bezier control point 2 (defined below) in order to shape the vase according to a 3 point bezier curve (the first point is [base_diameter, 0] the 3rd beeing [top_diameter, poly_height]
• 4 bezier control points : takes into account the bezier control point 2 and 3 (defined below) in order to shape the vase according to a 4 point bezier curve (the first point is [base_diameter, 0] the 4th beeing [top_diameter, poly_height]
• level of interpolation (2 --> 100) : these are the number of intervals at which each bezier coordinates are going to be evaluated
• a higher level of interpolation implies that the vase / bowl follows more closely the bezier curve (but it is less low-poly like).
• subdivision by level (1 --> 20) : for each level of interpolation, it will generate one level of low_poly. This parameter allows you to split each level in x sub_levels.
• height bezier point 2 (1 --> 200) : the height at wich the 2nd control point of the bezier interpolation is going to be.
• diameter bezier point 2 (1--> 200) : the width at wich the 2nd control point of the bezier interpolation is going to be.
• height bezier point 3 (1 --> 200) : the height at wich the 3rd control point of the bezier interpolation is going to be.
• diameter bezier point 3 (1--> 200) : the width at wich the 3rd control point of the bezier interpolation is going to be.

#Disclaimer:

• some bezier curves are very strange (loops, non-smooth), not all combinaisons have been tested and some might give you strange designs.