This OpenSCAD script will generate a 2D shape based on two partially overlapping ellipses The radii of both ellipses are controlled by specifying the final width and height of the created shape as well of the ratio of the depths of each side there is also an option for rounding the shape while preserving it's dimensions with controllable radius

Author: Mark Gaffney Version: 1.3 Date: 2013-03-19

Todo:

Warning: If band_depth > band_width the alignments might not work correctly If rounding_rad is large compared to band_depth or band_width the shape may just generate as a circle

Changes from previous versions:

v1-3

• added abilty to optionally create 3d lienar/rotate extrusion v1-2
• Some more control over centre and rounding in preparation for integration into ring creation script
• Fixed some alignment issues
• Made compatible with "Customizer" v1-1
• uses formula for an arc taken from here http://www.mathopenref.com/arcradius.html

v1-0

• uses intersection of somewhat arbitrarily sized circles minkowski using a smaller circle for rounding off to prove concept

Modify using Customizer OR download script and modify following variables: //Band Width: How wide you would like the created shape to be in the X-direction band_width=4.4;//[0:100] //Band Depth: How deep you would like the created shape to be in the Y-direction band_depth=2.5;//[0:100] //Rounding: Radius of the circle used to smooth the connection between the 2 sides rounding_rad=0.5;//[0:10] //Percent of depth of the inside overlapping ellipse part to band width inner_depth_ratio_percent=20;//[0:100] //where on the shape will be aligned to (0,0) default is along the line connecting the two points of overlap of the ellipses centre_type="default";//[half_depth, inner, outer, default] //Extrude Thickness: How thick the extrusion of the 2d shape will be (this is just to aid viewing in customiser) extrude_thickness=1;//[0:100]

if imported the module calls are as follows: ellipse_intersection_centred (band_width, band_depth, rounding_rad, inner_depth_ratio, centre_type);

ellipse_intersection_rounded (band_width, band_depth, rounding_rad, inner_depth_ratio);

ellipse_intersection (band_width, band_depth, inner_depth_ratio);