Interesting how easy that seems to be.It seems I need new "edge3()" that is able to draw edge along the 6 grey vertices positions as stereographic projection:
The center tangent through the geodesic circle (in above Wikipedia screenshot) always goes through sphere center.
So JSCAD's "plane.fromPoints(vec3.create(), ...coords)" would be helpful.
The script already had these _3D functions:
Code:
function length_3D(v) {function dist_3D(p, q) {function add_3D(p, q) {function sub_3D(p, q) {function scale_3D(v, f) {function norm_3D(v) {function map_3D(x, y) {function center_3D(p, q, r) {Only 3D vector multiplication and cross product are needed to implement new plane_3D():
Code:
+function mul_3D(p, q) { return [p[0]*q[0],p[1]*q[1],p[2]*q[2]]; }+function cross_3D(v, w) { return [v[1]*w[2]-v[2]*w[1], v[2]*w[0]-v[0]*w[2], v[0]*w[1]-v[1]*w[0]]; }+function plane_3D(u, v, w) {+ var n = norm_3D(cross_3D(sub_3D(u, v), sub_3D(v, w)));+ n.push(length_3D(mul_3D(u, n)));+ return n;+}The geodesic circle through two vertices is uniquely determined by the two vertex coordinates and any other third vertex coordinate, I took the middle mapped coordinate. Just scaling the plane normal vector with distance of plane from origin in rightmost vector entry gives geodesic circle center coordinate. A black vertex gets drawn for visual debugging right now:
Code:
+ m = [(coords2D[0][source(G, e)] + coords2D[0][target(G, e)])/2,+ (coords2D[1][source(G, e)] + coords2D[1][target(G, e)])/2];+ var M = scale_3D(map_3D(m[0], m[1]), sc);+ var V = scale_3D(map_3D(coords2D[0][source(G, e)], coords2D[1][source(G, e)]), sc);+ var W = scale_3D(map_3D(coords2D[0][target(G, e)], coords2D[1][target(G, e)]), sc);+ var pla = plane_3D(M, V, W);+ wlog("vertex(", scale_3D(pla, pla[3]), ",[0,0,0]);");The last piece missing for implementation of "edge3()" is just move to the right position and use OpenSCAD's rotate_extrude()
with the apropriate angle less than 360° ...
Statistics: Posted by HermannSW — Thu Sep 05, 2024 6:04 am