add rail_extruded_sections

docs/lib3x-path_scaling_sections.md

@@ -67,7 +67,7 @@ You can use any point as the first point of the edge path. Just remember that yo
 	use <path_scaling_sections.scad>;
 	use <sweep.scad>;
 	use <bezier_curve.scad>;
-	use <rotate_p.scad>;
+	use <ptf/ptf_rotate.scad>;
 
 	taiwan = shape_taiwan(100);
 	fst_pt = [13, 0, 0];
@@ -91,7 +91,7 @@ You can use any point as the first point of the edge path. Just remember that yo
 		for(i = [0:leng - 1]) 
 		[
 			for(p = sections[i]) 
-				rotate_p(p, twist_step * i)        
+				ptf_rotate(p, twist_step * i)        
 		]
 	];
 
@@ -103,7 +103,7 @@ You can use any point as the first point of the edge path. Just remember that yo
 	use <shape_taiwan.scad>;
 	use <path_scaling_sections.scad>;
 	use <sweep.scad>;
-    use <rotate_p.scad>;
+    use <ptf/ptf_rotate.scad>;
 
 	taiwan = shape_taiwan(100);
 
@@ -115,12 +115,12 @@ You can use any point as the first point of the edge path. Just remember that yo
     a = atan2(fst_pt[1], fst_pt[0]);
 	edge_path = [
 		fst_pt,
-		fst_pt + rotate_p([0, 0, 10], a),
+		fst_pt + ptf_rotate([0, 0, 10], a),
-		fst_pt + rotate_p([10, 0, 20], a),
+		fst_pt + ptf_rotate([10, 0, 20], a),
-		fst_pt + rotate_p([8, 0, 30], a),
+		fst_pt + ptf_rotate([8, 0, 30], a),
-		fst_pt + rotate_p([10, 0, 40], a),
+		fst_pt + ptf_rotate([10, 0, 40], a),
-		fst_pt + rotate_p([0, 0, 50], a),
+		fst_pt + ptf_rotate([0, 0, 50], a),
-		fst_pt + rotate_p([0, 0, 60], a)
+		fst_pt + ptf_rotate([0, 0, 60], a)
 	];
 
 	#hull_polyline3d(edge_path);

docs/lib3x-rail_extruded_sections.md

@@ -0,0 +1,127 @@
+# rail_extruded_sections
+
+Given a rail with the first point at the outline of a shape. This function uses the rail to extrude the shape and returns all sections in the reversed order of the rail. Combined with the `sweep` module, you can create rail extrusion. 
+
+In order to control extrusion easily, I suggest using `[x, 0, 0]` as the first point and keeping y = 0 while building the rail.
+
+**Since:** 3.2
+
+## Parameters
+
+- `shape_pts` : A list of points represent a shape.
+- `rail` : A list of points represent the edge path.
+
+## Examples
+
+	use <hull_polyline3d.scad>;
+	use <shape_taiwan.scad>;
+	use <rail_extruded_sections.scad>;
+	use <sweep.scad>;
+
+	taiwan = shape_taiwan(100);
+	fst_pt = [13, 0, 0];
+
+	rail = [
+		fst_pt,
+		fst_pt + [0, 0, 10],
+		fst_pt + [10, 0, 20],
+		fst_pt + [8, 0, 30],
+		fst_pt + [12, 0, 40],
+		fst_pt + [0, 0, 50],
+		fst_pt + [0, 0, 60]
+	];
+
+	#hull_polyline3d(rail);
+	sweep(rail_extruded_sections(taiwan, rail));
+
+![rail_extruded_sections](images/lib3x-rail_extruded_sections-1.JPG)
+
+	use <hull_polyline3d.scad>;
+	use <shape_taiwan.scad>;
+	use <rail_extruded_sections.scad>;
+	use <sweep.scad>;
+	use <bezier_curve.scad>;
+
+
+	taiwan = shape_taiwan(100);
+	fst_pt = [13, 0, 0];
+
+	rail = bezier_curve(0.05, [
+		fst_pt,
+		fst_pt + [0, 0, 10],
+		fst_pt + [10, 0, 20],
+		fst_pt + [8, 0, 30],
+		fst_pt + [12, 0, 40],
+		fst_pt + [0, 0, 50],
+		fst_pt + [0, 0, 60]
+	]);
+
+	#hull_polyline3d(rail);
+	sweep(rail_extruded_sections(taiwan, rail));
+
+![rail_extruded_sections](images/lib3x-rail_extruded_sections-2.JPG)
+
+	use <shape_taiwan.scad>;
+	use <rail_extruded_sections.scad>;
+	use <sweep.scad>;
+	use <bezier_curve.scad>;
+	use <ptf/ptf_rotate.scad>;
+
+	taiwan = shape_taiwan(100);
+	fst_pt = [13, 0, 0];
+
+	rail = bezier_curve(0.05, [
+		fst_pt,
+		fst_pt + [0, 0, 10],
+		fst_pt + [10, 0, 20],
+		fst_pt + [8, 0, 30],
+		fst_pt + [12, 0, 40],
+		fst_pt + [0, 0, 50],
+		fst_pt + [0, 0, 60]
+	]);
+
+	leng = len(rail);
+	twist = -90;
+	twist_step = twist / leng;
+	sections = rail_extruded_sections(taiwan, rail);
+
+	rotated_sections = [
+		for(i = [0:leng - 1]) 
+		[
+			for(p = sections[i]) 
+				ptf_rotate(p, twist_step * i)        
+		]
+	];
+
+	sweep(rotated_sections);
+
+![rail_extruded_sections](images/lib3x-rail_extruded_sections-3.JPG)	
+
+	use <hull_polyline3d.scad>;
+	use <shape_taiwan.scad>;
+	use <rail_extruded_sections.scad>;
+	use <sweep.scad>;
+    use <ptf/ptf_rotate.scad>;
+
+	taiwan = shape_taiwan(100);
+
+    /* 
+	    You can use any point as the first point of the edge path.
+		Just remember that your edge path radiates from the origin.
+	*/
+	fst_pt = [taiwan[0][0], taiwan[0][1], 0];//[13, 0, 0];
+    a = atan2(fst_pt[1], fst_pt[0]);
+	rail = [
+		fst_pt,
+		fst_pt + ptf_rotate([0, 0, 10], a),
+		fst_pt + ptf_rotate([10, 0, 20], a),
+		fst_pt + ptf_rotate([8, 0, 30], a),
+		fst_pt + ptf_rotate([10, 0, 40], a),
+		fst_pt + ptf_rotate([0, 0, 50], a),
+		fst_pt + ptf_rotate([0, 0, 60], a)
+	];
+
+	#hull_polyline3d(rail);
+	sweep(rail_extruded_sections(taiwan, rail));
+
+![rail_extruded_sections](images/lib3x-rail_extruded_sections-4.JPG)

examples/distorted_vase.scad

@@ -1,7 +1,7 @@
 use <shape_circle.scad>;
 use <bezier_curve.scad>;
 use <sweep.scad>;
-use <path_scaling_sections.scad>;
+use <rail_extruded_sections.scad>;
 use <bijection_offset.scad>;
 use <util/rand.scad>;
 use <noise/nz_perlin2s.scad>;
@@ -36,7 +36,7 @@ module distorted_vase(beginning_radius, thickness, fn, amplitude,curve_step, smo
 	]);
 
 
-	sections = path_scaling_sections(section, edge_path);
+	sections = rail_extruded_sections(section, edge_path);
 
     noise = perlin == 2 ? function(pts, seed) nz_perlin2s(pts, seed) : 
                           function(pts, seed) nz_perlin3s(pts, seed);

examples/dragon/spiral_dragon.scad

@@ -5,7 +5,7 @@ use <curve.scad>;
 use <sweep.scad>;
 use <shape_circle.scad>;
 use <bezier_curve.scad>;
-use <path_scaling_sections.scad>;
+use <rail_extruded_sections.scad>;
 use <noise/nz_perlin2s.scad>;
 use <dragon_head.scad>;
 use <dragon_scales.scad>;
@@ -103,7 +103,7 @@ module flame_mountain(beginning_radius, fn, amplitude,curve_step, smoothness) {
 	]);
 
 
-	sections = path_scaling_sections(section, edge_path);
+	sections = rail_extruded_sections(section, edge_path);
 
     noise = function(pts, seed) nz_perlin2s(pts, seed);
 

examples/superformula_vase.scad

@@ -1,6 +1,6 @@
 use <trim_shape.scad>;
 use <bezier_curve.scad>;
-use <path_scaling_sections.scad>;
+use <rail_extruded_sections.scad>;
 use <sweep.scad>;
 use <ptf/ptf_rotate.scad>;
 use <bijection_offset.scad>;
@@ -27,7 +27,7 @@ module superformula_vase(phi_step, m, n, n3, d, r1, r2, h1, h2, t_step, twist) {
 
     function cal_sections(shapt_pts, edge_path, twist) =
         let(
-            sects = path_scaling_sections(shapt_pts, edge_path),
+            sects = rail_extruded_sections(shapt_pts, edge_path),
             leng = len(sects),
             twist_step = twist / leng
         )
@@ -50,7 +50,7 @@ module superformula_vase(phi_step, m, n, n3, d, r1, r2, h1, h2, t_step, twist) {
         [r2, 0, h2],
     ]);
 
-    offseted = bijection_offset(superformula, d);
+    offseted = bijection_offset(superformula, d, epsilon = 0.0000001);
 
     edge_path2 = [for(p = edge_path) p + [d, 0, 0]];
     superformula2 = trim_shape(offseted, 3, len(offseted) - 1, epsilon = 0.0001);

examples/taiwan/dancing_taiwan.scad

@@ -1,7 +1,7 @@
 use <trim_shape.scad>;
 use <bezier_curve.scad>;
 use <shape_taiwan.scad>;
-use <path_scaling_sections.scad>;
+use <rail_extruded_sections.scad>;
 use <sweep.scad>;
 use <ptf/ptf_rotate.scad>;
 use <bijection_offset.scad>;
@@ -19,7 +19,7 @@ module dancing_formosan(x1, x2, x3, y1, y2, y3, twist, t_step) {
 
     function cal_sections(shapt_pts, edge_path, twist) =
         let(
-            sects = path_scaling_sections(shapt_pts, edge_path),
+            sects = rail_extruded_sections(shapt_pts, edge_path),
             leng = len(sects),
             twist_step = twist / leng
         )

src/rail_extruded_sections.scad

@@ -0,0 +1,32 @@
+/**
+* rail_extruded_sections.scad
+*
+* @copyright Justin Lin, 2019
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib3x-rail_extruded_sections.html
+*
+**/
+
+use <util/reverse.scad>;
+use <matrix/m_scaling.scad>;
+
+function rail_extruded_sections(shape_pts, rail) = 
+    let(
+        start_point = rail[0],
+        base_leng = norm(start_point),
+        scaling_matrice = [
+            for(p = rail) 
+            let(s = norm([p[0], p[1], 0]) / base_leng)
+            m_scaling([s, s, 1])
+        ],
+        leng_rail = len(rail)
+    )
+    reverse([
+        for(i = 0; i < leng_rail; i = i + 1)
+        [
+            for(p = shape_pts) 
+            let(scaled_p = scaling_matrice[i] * [p[0], p[1], rail[i][2], 1])
+            [scaled_p[0], scaled_p[1], scaled_p[2]]
+        ]
+    ]);