add fourier_vase

examples/fourier_vase.scad

@@ -0,0 +1,77 @@
+use <util/degrees.scad>
+use <polyline_join.scad>
+use <bezier_curve.scad>
+use <util/reverse.scad>
+
+radius = 10;
+thickness = .5;
+model_scale = 5;
+
+stop = 50;
+sample_rate = 250;
+number_of_waves = 1; // n harmonically related number_of_waves 
+
+freq = .1;
+amplitude = 2;
+harmonic_fn = function(x, n) amplitude * sin(degrees((2 * n + 1) * freq * 2 * PI * x)) / (2 * n + 1);
+
+main_curve = reverse(
+    bezier_curve(
+        1 / sample_rate, 
+        [[0, 0], [15, 8], [10, 15], [-5, 20], [5, stop]]
+    )
+);
+    
+for(i = [1:3]) {
+    $fn = 2 * i + 2;
+    translate([i * radius * 25, 0]) 
+    scale(model_scale)
+        fourier_vase(
+            radius, 
+            thickness, 
+            stop, 
+            sample_rate, 
+            number_of_waves * i, 
+            harmonic_fn, 
+            main_curve
+        );
+}
+
+module fourier_vase(radius, thickness, stop, sample_rate, number_of_waves, harmonic_fn, main_curve) {
+    function x(y, n = 0) =
+        n == number_of_waves ? 0 : harmonic_fn(y, n) + x(y, n + 1);
+
+    wave_pts = [
+        for(y = [0:stop / sample_rate:stop]) 
+        [x(y), y]
+    ];
+    
+    pts = [
+        [0, 0],
+        each is_undef(main_curve) ? [
+            for(i = [0:len(wave_pts) - 1]) 
+            [radius + wave_pts[i].x, wave_pts[i].y]
+        ] : [
+            for(i = [0:len(wave_pts) - 1]) 
+            [radius + wave_pts[i].x + main_curve[i].x, wave_pts[i].y]],
+        [0, stop]
+    ];
+
+    translate([0, 0, stop])
+    mirror([0, 0, 1])
+    difference() {
+        rotate_extrude()
+            polygon(pts);
+
+        rotate_extrude()
+            offset(-thickness)
+                polygon(pts);
+        
+        translate([0, 0, -1])
+        linear_extrude(thickness + 1.001)
+            circle(radius * 2);
+
+        linear_extrude(stop - thickness)
+            circle(thickness * 2);
+    }
+}