Merge branch 'v1.1.0'

# Conflicts:
#	src/along_with.scad
#	src/path_extrude.scad
#	src/rotate_p.scad

README.md

@@ -1,4 +1,4 @@
-# dotSCAD
+# dotSCAD 1.1
 
 > Helpful modules and functions when playing OpenSCAD.
 
@@ -54,6 +54,7 @@ Too many dependencies? Because OpenSCAD doesn't provide namespace management, I
     - [along_with](https://openhome.cc/eGossip/OpenSCAD/lib-along_with.html)
 	- [hollow_out](https://openhome.cc/eGossip/OpenSCAD/lib-hollow_out.html)
 	- [bend](https://openhome.cc/eGossip/OpenSCAD/lib-bend.html)
+	- [shear](https://openhome.cc/eGossip/OpenSCAD/lib-shear.html)
 
 - Functon
 	- [rotate_p](https://openhome.cc/eGossip/OpenSCAD/lib-rotate_p.html)
@@ -102,6 +103,15 @@ Too many dependencies? Because OpenSCAD doesn't provide namespace management, I
 	- [archimedean_spiral_extrude](https://openhome.cc/eGossip/OpenSCAD/lib-archimedean_spiral_extrude.html)
 	- [sphere_spiral_extrude](https://openhome.cc/eGossip/OpenSCAD/lib-sphere_spiral_extrude.html)
 
+- Matrix
+	- [m_multiply](https://openhome.cc/eGossip/OpenSCAD/lib-m_multiply.html)
+	- [m_cumulate](https://openhome.cc/eGossip/OpenSCAD/lib-m_cumulate.html)	
+	- [m_translation](https://openhome.cc/eGossip/OpenSCAD/lib-m_translation.html)
+	- [m_rotation](https://openhome.cc/eGossip/OpenSCAD/lib-m_rotation.html)
+	- [m_scaling](https://openhome.cc/eGossip/OpenSCAD/lib-m_scaling.html)
+	- [m_mirror](https://openhome.cc/eGossip/OpenSCAD/lib-m_mirror.html)
+	- [m_shearing](https://openhome.cc/eGossip/OpenSCAD/lib-m_shearing.html)
+
 - Other
     - [turtle2d](https://openhome.cc/eGossip/OpenSCAD/lib-turtle2d.html)
     - [turtle3d](https://openhome.cc/eGossip/OpenSCAD/lib-turtle3d.html)

docs/lib-m_cumulate.md

@@ -0,0 +1,30 @@
+# m_cumulate
+
+The power of using transformation matrice is that you can cumulate all transformations in a matrix. This function multipies all transformation matrice. 
+
+**Since:** 1.1
+
+## Parameters
+
+- `matrice` : A list of 4x4 transformation matrice.
+
+## Examples
+
+	include <m_rotation.scad>;
+	include <m_scaling.scad>;
+	include <m_translation.scad>;
+	include <m_cumulate.scad>
+
+	m = m_cumulate([
+		m_translation([10, 20, 10]), m_scaling(2), m_rotation(60)]
+	);
+
+	multmatrix(m) 
+		cube(1);
+		
+	multmatrix(m)    
+		sphere(1);
+
+
+![m_cumulate](images/lib-m_cumulate-1.JPG)
+

docs/lib-m_mirror.md

@@ -0,0 +1,23 @@
+# m_mirror
+
+Generate a 4x4 transformation matrix which can pass into `multmatrix` to mirror the child element on a plane through the origin. 
+
+**Since:** 1.1
+
+## Parameters
+
+- `v` : The normal vector of a plane intersecting the origin through which to mirror the object.
+
+## Examples
+
+	include <m_mirror.scad>;
+
+	rotate([0, 0, 10]) 
+		cube([3, 2, 1]);
+		
+	multmatrix(m_mirror([1, 1, 0]))
+		rotate([0, 0, 10]) 
+			cube([3, 2, 1]);
+
+![m_mirror](images/lib-m_mirror-1.JPG)
+

docs/lib-m_multiply.md

@@ -0,0 +1,25 @@
+# m_multiply
+
+Multiply two 4x4 transformation matrice.
+
+**Since:** 1.1
+
+## Parameters
+
+- `ma`, `mb` : Two 4x4 transformation matrice.
+
+## Examples
+
+	include <m_multiply.scad>;
+	include <m_scaling.scad>;
+	include <m_rotation.scad>;
+
+	ma = m_scaling([0.5, 1, 2]);
+	mb = m_rotation([0, 0, 90]);
+
+	cube(10);
+	multmatrix(m_multiply(ma, mb))
+		translate([15, 0, 0])  cube(10);
+
+![m_multiply](images/lib-m_multiply-1.JPG)
+

docs/lib-m_rotation.md

@@ -0,0 +1,45 @@
+# m_rotation
+
+Generate a 4x4 transformation matrix which can pass into `multmatrix` to rotate the child element about the axis of the coordinate system or around an arbitrary axis. 
+
+**Since:** 1.1
+
+## Parameters
+
+- `a` : If it's `[deg_x, deg_y, deg_z]`, the rotation is applied in the order `x`, `y`, `z`. If it's `[deg_x, deg_y]`, the rotation is applied in the order `x`, `y`.  If it's`[deg_x]`, the rotation is only applied to the `x` axis. If it's an number, the rotation is only applied to the `z` axis or an arbitrary axis.
+- `v`: A vector allows you to set an arbitrary axis about which the object will be rotated. When `a` is an array, the `v` argument is ignored. 
+
+## Examples
+
+	include <m_rotation.scad>;
+
+	point = [20, 0, 0];
+	a = [0, -45, 45];
+
+	hull() {
+		sphere(1);
+		multmatrix(m_rotation(a))    
+			translate(point) 
+				sphere(1);   
+	}  
+
+![m_rotation](images/lib-m_rotation-1.JPG)
+
+	include <m_rotation.scad>;
+
+	v = [10, 10, 10];
+
+	hull() {
+		sphere(1);
+		translate(v)
+		sphere(1);   
+	}
+
+	p = [10, 10, 0];
+	for(i = [0:20:340]) {
+		multmatrix(m_rotation(a = i, v = v))
+			translate(p) 
+				sphere(1);  
+	}
+
+![m_rotation](images/lib-m_rotation-2.JPG)

docs/lib-m_scaling.md

@@ -0,0 +1,21 @@
+# m_scaling
+
+Generate a 4x4 transformation matrix which can pass into `multmatrix` to scale its child elements using the specified vector.
+
+**Since:** 1.1
+
+## Parameters
+
+- `v` : Elements will be scaled using the vector.
+
+## Examples
+
+	include <m_scaling.scad>;
+
+	cube(10);
+	translate([15, 0, 0]) 
+		multmatrix(m_scaling([0.5, 1, 2]))
+			cube(10);
+
+![m_scaling](images/lib-m_scaling-1.JPG)
+

docs/lib-m_shearing.md

@@ -0,0 +1,51 @@
+# m_shearing
+
+Generate a 4x4 transformation matrix which can pass into `multmatrix` to shear all child elements along the X-axis, Y-axis, or Z-axis in 3D.
+
+**Since:** 1.1
+
+## Parameters
+
+- `sx` : An array `[SHy, SHz]`. The new coordinates of child elements are `(x + SHy * y + SHz * z, y, z)`.
+- `sy` : An array `[SHx, SHz]`. The new coordinates of child elements are `(x, y + SHx * x + SHz * z, z)`.
+- `sz` : An array `[SHx, SHy]`. The new coordinates of child elements are `(x, y, z + SHx * x + SHy * y)`.
+
+## Examples
+
+	include <m_shearing.scad>;
+
+	color("red") {
+		multmatrix(m_shearing(sx = [1, 0]))
+			cube(1);
+			
+		translate([2, 0, 0]) multmatrix(m_shearing(sx = [0, 1]))
+			cube(1);
+			
+		translate([4, 0, 0]) multmatrix(m_shearing(sx = [1, 1]))
+			cube(1);
+	}
+
+	translate([0, -3, 0]) color("green") {
+		multmatrix(m_shearing(sy = [1, 0]))
+			cube(1);
+			
+		translate([2, 0, 0]) multmatrix(m_shearing(sy = [0, 1]))
+			cube(1);
+			
+		translate([4, 0, 0]) multmatrix(m_shearing(sy = [1, 1]))
+			cube(1);
+	}
+
+	translate([0, -5, 0]) color("blue") {
+		multmatrix(m_shearing(sz = [1, 0]))
+			cube(1);
+			
+		translate([2, 0, 0]) multmatrix(m_shearing(sz = [0, 1]))
+			cube(1);
+			
+		translate([4, 0, 0]) multmatrix(m_shearing(sz = [1, 1]))
+			cube(1);
+	}
+
+![m_shearing](images/lib-m_shearing-1.JPG)
+

docs/lib-m_translation.md

@@ -0,0 +1,20 @@
+# m_translation
+
+Generate a 4x4 transformation matrix which can pass into `multmatrix` to translates (moves) its child elements along the specified vector.
+
+**Since:** 1.1
+
+## Parameters
+
+- `v` : Elements will be translated along the vector.
+
+## Examples
+
+	include <m_translation.scad>;
+
+	cube(2, center = true); 
+	multmatrix(m_translation([5, 0, 0]))
+	    sphere(1,center = true);
+
+![m_translation](images/lib-m_translation-1.JPG)
+

docs/lib-rotate_p.md

@@ -1,11 +1,12 @@
 # rotate_p
 
-Rotates a point `a` degrees around an arbitrary axis. It behaves as the built-in `rotate` module
+Rotates a point `a` degrees about the axis of the coordinate system or around an arbitrary axis. It behaves as the built-in `rotate` module
 
 ## Parameters
 
 - `point` : A 3D point `[x, y, z]` or a 2D point `[x, y]`.
-- `a` : If it's `[deg_x, deg_y, deg_z]`, the rotation is applied in the order `x`, `y`, `z`. If it's `[deg_x, deg_y]`, the rotation is applied in the order `x`, `y`.  If it's`[deg_x]`, the rotation is only applied to the `x` axis. If it's an number, the rotation is only applied to the `z` axis.
+- `a` : If it's `[deg_x, deg_y, deg_z]`, the rotation is applied in the order `x`, `y`, `z`. If it's `[deg_x, deg_y]`, the rotation is applied in the order `x`, `y`.  If it's`[deg_x]`, the rotation is only applied to the `x` axis. If it's an number, the rotation is only applied to the `z` axis or an arbitrary axis.
+- `v`: A vector allows you to set an arbitrary axis about which the object will be rotated. When `a` is an array, the `v` argument is ignored. **Since:** 1.1.
 
 ## Examples
     
@@ -60,4 +61,22 @@ The `rotate_p` function is useful in some situations. For example, you probably
 	
 	%sphere(radius);
 
-![rotate_p](images/lib-rotate_p-2.JPG)
+![rotate_p](images/lib-rotate_p-2.JPG)
+
+	include <rotate_p.scad>;
+
+	v = [10, 10, 10];
+
+	hull() {
+		sphere(1);
+		translate(v)
+		sphere(1);   
+	}
+
+	p = [10, 10, 0];
+	for(i = [0:20:340]) {
+		translate(rotate_p(p, a = i, v = v)) 
+			sphere(1);  
+	}
+	
+![rotate_p](images/lib-rotate_p-3.JPG)

docs/lib-shear.md

@@ -0,0 +1,52 @@
+# shear
+
+Shear all child elements along the X-axis, Y-axis, or Z-axis in 3D.
+
+**Since:** 1.1
+
+
+## Parameters
+
+- `sx` : An array `[SHy, SHz]`. The new coordinates of child elements are `(x + SHy * y + SHz * z, y, z)`.
+- `sy` : An array `[SHx, SHz]`. The new coordinates of child elements are `(x, y + SHx * x + SHz * z, z)`.
+- `sz` : An array `[SHx, SHy]`. The new coordinates of child elements are `(x, y, z + SHx * x + SHy * y)`.
+
+## Examples
+
+	include <shear.scad>;
+
+	color("red") {
+		shear(sx = [1, 0])
+			cube(1);
+			
+		translate([2, 0, 0]) shear(sx = [0, 1])
+			cube(1);
+			
+		translate([4, 0, 0]) shear(sx = [1, 1])
+			cube(1);
+	}
+
+	translate([0, -3, 0]) color("green") {
+		shear(sy = [1, 0])
+			cube(1);
+			
+		translate([2, 0, 0]) shear(sy = [0, 1])
+			cube(1);
+			
+		translate([4, 0, 0]) shear(sy = [1, 1])
+			cube(1);
+	}
+
+	translate([0, -5, 0]) color("blue") {
+		shear(sz = [1, 0])
+			cube(1);
+			
+		translate([2, 0, 0]) shear(sz = [0, 1])
+			cube(1);
+			
+		translate([4, 0, 0]) shear(sz = [1, 1])
+			cube(1);
+	}
+
+![shear](images/lib-shear-1.JPG)
+

src/__private__/__length_between.scad

@@ -1,6 +0,0 @@
-function __length_between(p1, p2) =
-    let(
-        dx = p2[0] - p1[0],
-        dy = p2[1] - p1[1],
-        dz = p2[2] - p1[2]
-    ) sqrt(pow(dx, 2) + pow(dy, 2) + pow(dz, 2));

src/__private__/__m_multiply.scad

@@ -0,0 +1,13 @@
+function __m_multiply(ma, mb) = 
+    let(
+        c1 = [mb[0][0], mb[1][0], mb[2][0], mb[3][0]],
+        c2 = [mb[0][1], mb[1][1], mb[2][1], mb[3][1]],
+        c3 = [mb[0][2], mb[1][2], mb[2][2], mb[3][2]],
+        c4 = [mb[0][3], mb[1][3], mb[2][3], mb[3][3]]
+    )
+    [
+        [ma[0] * c1, ma[0] * c2, ma[0] * c3, ma[0] * c4],
+        [ma[1] * c1, ma[1] * c2, ma[1] * c3, ma[1] * c4],
+        [ma[2] * c1, ma[2] * c2, ma[2] * c3, ma[2] * c4],
+        [ma[3] * c1, ma[3] * c2, ma[3] * c3, ma[3] * c4]
+    ];

src/__private__/__m_shearing.scad

@@ -0,0 +1,15 @@
+function __m_shearing(sx, sy, sz) = 
+    let(
+        sx_along_y = sx[0],
+        sx_along_z = sx[1],
+        sy_along_x = sy[0],
+        sy_along_z = sy[1],
+        sz_along_x = sz[0],
+        sz_along_y = sz[1]   
+    ) 
+    [
+        [1, sx_along_y, sx_along_z, 0],
+        [sy_along_x, 1, sy_along_z, 0],
+        [sz_along_x, sz_along_y, 1, 0],
+        [0, 0, 0, 1]
+    ];

src/along_with.scad

@@ -1,9 +1,6 @@
 /**
 * along_with.scad
 *
-* Puts children along the given path. If there's only one child, 
-* it will put the child for each point. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *
@@ -14,6 +11,11 @@
 include <__private__/__angy_angz.scad>;
 include <__private__/__is_vector.scad>;
 include <__private__/__to3d.scad>;
+include <__private__/__m_multiply.scad>;
+
+// Becuase of improving the performance, this module requires m_rotation.scad which doesn't require in dotSCAD 1.0. 
+// For backward compatibility, I directly include m_rotation here.
+include <m_rotation.scad>;
 
 module along_with(points, angles, twist = 0, scale = 1.0) {
     leng_points = len(points);
@@ -30,7 +32,44 @@ module along_with(points, angles, twist = 0, scale = 1.0) {
             (scale[1] - 1) / leng_points_minus_one,
             scale[2] == undef ? 0 : (scale[2] - 1) / leng_points_minus_one
         ] : scale_step(); 
+
+    // get rotation matrice for sections
+
+    function local_ang_vects(j) = 
+        j == 0 ? [] : local_ang_vects_sub(j);
     
+    function local_ang_vects_sub(j) =
+        let(
+            vt0 = points[j] - points[j - 1],
+            vt1 = points[j + 1] - points[j],
+            a = acos((vt0 * vt1) / (norm(vt0) * norm(vt1))),
+            v = cross(vt0, vt1)
+        )
+        concat([[a, v]], local_ang_vects(j - 1));
+
+    function cumulated_rot_matrice(i, rot_matrice) = 
+        let(
+            leng_rot_matrice = len(rot_matrice),
+            leng_rot_matrice_minus_one = leng_rot_matrice - 1,
+            leng_rot_matrice_minus_two = leng_rot_matrice - 2
+        )
+        i == leng_rot_matrice - 2 ? 
+               [
+                   rot_matrice[leng_rot_matrice_minus_one], 
+                   __m_multiply(rot_matrice[leng_rot_matrice_minus_two], rot_matrice[leng_rot_matrice_minus_one])
+               ] 
+               : cumulated_rot_matrice_sub(i, rot_matrice);
+
+    function cumulated_rot_matrice_sub(i, rot_matrice) = 
+        let(
+            matrice = cumulated_rot_matrice(i + 1, rot_matrice),
+            curr_matrix = rot_matrice[i],
+            prev_matrix = matrice[len(matrice) - 1]
+        )
+        concat(matrice, [__m_multiply(curr_matrix, prev_matrix)]);
+
+    // align modules
+
     module align_with_pts_angles(i) {
         translate(points[i]) 
             rotate(angles[i])
@@ -48,20 +87,17 @@ module along_with(points, angles, twist = 0, scale = 1.0) {
                         children(0);
     }
     
-    module align_with_pts_local_rotate(j, init_a, init_s) {
+    module align_with_pts_local_rotate(j, init_a, init_s, cumu_rot_matrice) {
         if(j == 0) {  // first child
             align_with_pts_init(init_a, init_s) 
                 children(0);
         }
         else {
-            vt0 = points[j] - points[j - 1];
-            vt1 = points[j + 1] - points[j];
-            a = acos((vt0 * vt1) / (norm(vt0) * norm(vt1)));     
-            rotate(a, cross(vt0, vt1)) 
-                align_with_pts_local_rotate(j - 1, init_a, init_s) 
+            multmatrix(cumu_rot_matrice[j - 1])
+                align_with_pts_init(init_a, init_s) 
                     children(0);
         }
-    }
+    } 
 
     if(angles != undef) {
         if($children == 1) { 
@@ -75,23 +111,27 @@ module along_with(points, angles, twist = 0, scale = 1.0) {
         }
     }
     else {
+        cumu_rot_matrice = cumulated_rot_matrice(0, [
+            for(ang_vect = local_ang_vects(leng_points - 2)) 
+                m_rotation(ang_vect[0], ang_vect[1])
+        ]);
+
         translate(points[0])
-            align_with_pts_local_rotate(0, 0, [1, 1, 1])
+            align_with_pts_local_rotate(0, 0, [1, 1, 1], cumu_rot_matrice)
                 children(0); 
 
         if($children == 1) { 
             for(i = [0:leng_points - 2]) {
                 translate(points[i + 1])
-                    align_with_pts_local_rotate(i, i * twist_step_a, [1, 1, 1] + scale_step_vt * i)
+                    align_with_pts_local_rotate(i, i * twist_step_a, [1, 1, 1] + scale_step_vt * i, cumu_rot_matrice)
                         children(0);          
             }          
         } else {
             for(i = [0:min(leng_points, $children) - 2]) {
                 translate(points[i + 1])
-                    align_with_pts_local_rotate(i, i * twist_step_a, [1, 1, 1] + scale_step_vt * i)
+                    align_with_pts_local_rotate(i, i * twist_step_a, [1, 1, 1] + scale_step_vt * i, cumu_rot_matrice)
                         children(i + 1);   
             }
         }
     }
-
 }

src/arc.scad

@@ -1,10 +1,6 @@
 /**
 * arc.scad
 *
-* Creates an arc. You can pass a 2 element vector to define the central angle. 
-* Its $fa, $fs and $fn parameters are consistent with the circle module.
-* It depends on the circular_sector module so you have to include circular_sector.scad.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/arc_path.scad

@@ -1,10 +1,6 @@
 /**
 * arc_shape.scad
 *
-* Creates an arc. You can pass a 2 element vector to define the central angle. 
-* Its $fa, $fs and $fn parameters are consistent with the circle module.
-* It depends on the circular_sector module so you have to include circular_sector.scad.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/archimedean_spiral.scad

@@ -1,17 +1,5 @@
 /**
 * archimedean_spiral.scad
-*
-*  Gets all points and angles on the path of an archimedean spiral. The distance between two  points is almost constant. 
-* 
-*  It returns a vector of [[x, y], angle]. 
-*
-*  In polar coordinates (r, <EFBFBD>c) Archimedean spiral can be described by the equation r = b<EFBFBD>c where
-*  <EFBFBD>c is measured in radians. For being consistent with OpenSCAD, the function here use degrees.
-*
-*  An init_angle less than 180 degrees is not recommended because the function uses an approximate 
-*  approach. If you really want an init_angle less than 180 degrees, a larger arm_distance 
-*  is required. To avoid a small error value at the calculated distance between two points, you 
-*  may try a smaller point_distance.
 * 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html

src/archimedean_spiral_extrude.scad

@@ -1,8 +1,6 @@
 /**
 * archimedean_spiral_extrude.scad
 *
-* Extrudes a 2D shape along the path of a archimedean spiral.
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/bend.scad

@@ -1,7 +1,5 @@
 /**
 * bend.scad
-*
-* Bends a 3D object into an arc shape. 
 * 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html

src/bezier_curve.scad

@@ -1,10 +1,6 @@
 /**
 * bezier_curve.scad
 *
-* Given a set of control points, the bezier_curve function returns points of the Bézier path. 
-* Combined with the polyline, polyline3d or hull_polyline3d module defined in my lib-openscad, 
-* you can create a Bézier curve.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/bezier_smooth.scad

@@ -1,8 +1,6 @@
 /**
 * bezier_smooth.scad
 *
-* Given a path, the bezier_smooth function uses bazier curves to smooth all corners. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/bezier_surface.scad

@@ -1,12 +1,6 @@
 /**
 * bezier_surface.scad
 *
-* Given a set of control points, the bezier_surface function returns points of the Bézier surface. 
-* Combined with the function_grapher module defined in my lib-openscad, 
-* you can create a Bézier surface.
-*
-* It depends on the bezier_curve function so remember to include bezier_curve.scad.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/box_extrude.scad

@@ -1,8 +1,6 @@
 /**
 * box_extrude.scad
 *
-* Creates a box (container) from a 2D object.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/circle_path.scad

@@ -1,10 +1,6 @@
 /**
 * circle_path.scad
 *
-* Sometimes you need all points on the path of a circle. Here's 
-* the function. Its $fa, $fs and $fn parameters are consistent 
-* with the circle module.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/cross_sections.scad

@@ -1,9 +1,6 @@
 /**
 * cross_sections.scad
 *
-* Given a 2D shape, points and angles along the path, this function
-* will return all cross-sections.
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/crystal_ball.scad

@@ -1,8 +1,6 @@
 /**
 * crystal_ball.scad
 *
-* Uses Spherical coordinate system to create a crystal ball. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/ellipse_extrude.scad

@@ -1,9 +1,6 @@
 /**
 * ellipse_extrude.scad
 *
-* Extrudes a 2D object along the path of an ellipse from 0 to 180 degrees.
-* The semi-major axis is not necessary because it's eliminated while calculating.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/function_grapher.scad

@@ -1,13 +1,6 @@
 /**
 * function_grapher.scad
 *
-* 
-* Given a set of points `[x, y, f(x, y)]` where `f(x, y)` is a 
-* mathematics function, the `function_grapher` module can 
-* create the graph of `f(x, y)`.
-* It depends on the line3d, polyline3d, hull_polyline3d modules so you have 
-* to include "line3d.scad", "polyline3d.scad", "hull_polyline3d.scad".
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/golden_spiral.scad

@@ -1,10 +1,6 @@
 /**
 * golden_spiral.scad
 *
-*  Gets all points and angles on the path of a golden spiral. The distance between two  points is almost constant. 
-* 
-*  It returns a vector of [[x, y], angle]. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/golden_spiral_extrude.scad

@@ -1,8 +1,6 @@
 /**
 * golden_spiral_extrude.scad
 *
-* Extrudes a 2D shape along the path of a golden spiral.
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/helix.scad

@@ -1,10 +1,6 @@
 /**
 * helix.scad
 *
-* Gets all points on the path of a spiral around a cylinder. 
-* Its $fa, $fs and $fn parameters are consistent with the cylinder module.
-* It depends on the circle_path module so you have to include circle_path.scad.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/helix_extrude.scad

@@ -1,8 +1,6 @@
 /**
 * helix_extrude.scad
 *
-* Extrudes a 2D shape along a helix path.
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/hexagons.scad

@@ -1,9 +1,6 @@
 /**
 * hexagons.scad
 *
-* A hexagonal structure is useful in many situations. 
-* This module creates hexagons in a hexagon.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/hollow_out.scad

@@ -1,8 +1,6 @@
 /**
 * hollow_out.scad
 *
-* Hollows out a 2D object. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/hull_polyline2d.scad

@@ -1,10 +1,6 @@
 /**
 * hull_polyline2d.scad
 *
-* Creates a 2D polyline from a list of `[x, y]` coordinates. 
-* As the name says, it uses the built-in hull operation for each pair of points (created by the circle module). 
-* It's slow. However, it can be used to create metallic effects for a small $fn, large $fa or $fs.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/hull_polyline3d.scad

@@ -1,10 +1,6 @@
 /**
 * hull_polyline3d.scad
 *
-* Creates a 3D polyline from a list of `[x, y, z]` coordinates. 
-* As the name says, it uses the built-in hull operation for each pair of points (created by the sphere module). 
-* It's slow. However, it can be used to create metallic effects for a small $fn, large $fa or $fs.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/line2d.scad

@@ -1,8 +1,6 @@
 /**
 * line2d.scad
 *
-* Creates a line from two points.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/line3d.scad

@@ -1,8 +1,6 @@
 /**
 * line3d.scad
 *
-* Creates a 3D line from two points. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/log.scad

@@ -1,8 +1,6 @@
 /**
 * log.scad
 *
-* A log module which supports simple level configurations and color titles.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/m_cumulate.scad

@@ -0,0 +1,20 @@
+/**
+* m_cumulate.scad
+*
+* @copyright Justin Lin, 2019
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_cumulate.html
+*
+**/
+
+include <__private__/__m_multiply.scad>;
+
+function _m_cumulate(matrice, i) = 
+    i == len(matrice) - 2 ?
+        __m_multiply(matrice[i], matrice[i + 1]) :
+        __m_multiply(matrice[i], _m_cumulate(matrice, i + 1));
+
+function m_cumulate(matrice) = 
+    len(matrice) == 1 ? matrice[0] : _m_cumulate(matrice, 0);
+    

src/m_mirror.scad

@@ -0,0 +1,26 @@
+/**
+* m_mirror.scad
+*
+* @copyright Justin Lin, 2019
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_mirror.html
+*
+**/
+
+function m_mirror(v) = 
+    let(
+        nv = v / norm(v),
+        txx = -2* nv[0] * nv[0],
+        txy = -2* nv[0] * nv[1],
+        txz = -2* nv[0] * nv[2],
+        tyy = -2* nv[1] * nv[1],
+        tyz = -2* nv[1] * nv[2],
+        tzz = -2* nv[2] * nv[2]
+    )
+    [
+        [1 + txx, txy, txz, 0],
+        [txy, 1 + tyy, tyz, 0],
+        [txz, tyz, 1 + tzz, 0],
+        [0, 0, 0, 1]
+    ];

src/m_multiply.scad

@@ -0,0 +1,13 @@
+/**
+* m_multiply.scad
+*
+* @copyright Justin Lin, 2019
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_multiply.html
+*
+**/
+
+include <__private__/__m_multiply.scad>;
+
+function m_multiply(ma, mb) = __m_multiply(ma, mb);

src/m_rotation.scad

@@ -0,0 +1,87 @@
+/**
+* m_rotation.scad
+*
+* @copyright Justin Lin, 2019
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_rotation.html
+*
+**/
+
+include <__private__/__m_multiply.scad>;
+
+function _q_rotation(a, v) = 
+    let(
+        half_a = a / 2,
+        axis = v / norm(v),
+        s = sin(half_a),
+        x = s * axis[0],
+        y = s * axis[1],
+        z = s * axis[2],
+        w = cos(half_a),
+        
+        x2 = x + x,
+        y2 = y + y,
+        z2 = z + z,
+
+        xx = x * x2,
+        yx = y * x2,
+        yy = y * y2,
+        zx = z * x2,
+        zy = z * y2,
+        zz = z * z2,
+        wx = w * x2,
+        wy = w * y2,
+        wz = w * z2        
+    )
+    [
+        [1 - yy - zz, yx - wz, zx + wy, 0],
+        [yx + wz, 1 - xx - zz, zy - wx, 0],
+        [zx - wy, zy + wx, 1 - xx - yy, 0],
+        [0, 0, 0, 1]
+    ];
+
+function _m_xRotation(a) = 
+    let(c = cos(a), s = sin(a))
+    [
+        [1, 0, 0, 0],
+        [0, c, -s, 0],
+        [0, s, c, 0],
+        [0, 0, 0, 1]
+    ];
+
+function _m_yRotation(a) = 
+    let(c = cos(a), s = sin(a))
+    [
+        [c, 0, s, 0],
+        [0, 1, 0, 0],
+        [-s, 0, c, 0],
+        [0, 0, 0, 1]
+    ];    
+
+function _m_zRotation(a) = 
+    let(c = cos(a), s = sin(a))
+    [
+        [c, -s, 0, 0],
+        [s, c, 0, 0],
+        [0, 0, 1, 0],
+        [0, 0, 0, 1]
+    ];    
+
+function _to_avect(a) =
+     len(a) == 3 ? a : (
+         len(a) == 2 ? [a[0], a[1], 0] : (
+             len(a) == 1 ? [a[0], 0, 0] : [0, 0, a]
+         ) 
+     );
+
+function _xyz_rotation(a) =
+    let(ang = _to_avect(a))
+    __m_multiply(
+        _m_zRotation(ang[2]), __m_multiply(
+            _m_yRotation(ang[1]), _m_xRotation(ang[0])
+        )
+    );
+
+function m_rotation(a, v) = 
+    v == undef ? _xyz_rotation(a) : _q_rotation(a, v);

src/m_scaling.scad

@@ -0,0 +1,25 @@
+/**
+* m_scaling.scad
+*
+* @copyright Justin Lin, 2019
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_scaling.html
+*
+**/
+
+function _to_svect(s) =
+     len(s) == 3 ? s : (
+         len(s) == 2 ? [s[0], s[1], 1] : (
+             len(s) == 1 ? [s[0], 1, 1] : [s, s, s]
+         ) 
+     );
+
+function m_scaling(s) = 
+    let(v = _to_svect(s))
+    [
+        [v[0], 0, 0, 0],
+        [0, v[1], 0, 0],
+        [0, 0, v[2], 0],
+        [0, 0, 0, 1]
+    ];

src/m_shearing.scad

@@ -0,0 +1,14 @@
+/**
+* m_shearing.scad
+*
+* @copyright Justin Lin, 2019
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_shearing.html
+*
+**/
+
+include <__private__/__m_multiply.scad>;
+include <__private__/__m_shearing.scad>;
+
+function m_shearing(sx = [0, 0], sy = [0, 0], sz = [0, 0]) = __m_shearing(sx, sy, sz);

src/m_translation.scad

@@ -0,0 +1,25 @@
+/**
+* m_translation.scad
+*
+* @copyright Justin Lin, 2019
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_translation.html
+*
+**/
+
+function _to_tvect(v) =
+     len(v) == 3 ? v : (
+         len(v) == 2 ? [v[0], v[1], 0] : (
+             len(v) == 1 ? [v[0], 0, 0] : [v, 0, 0]
+         ) 
+     );
+
+function m_translation(v) = 
+    let(vt = _to_tvect(v))
+    [
+        [1, 0, 0, vt[0]],
+        [0, 1, 0, vt[1]],
+        [0, 0, 1, vt[2]],
+        [0, 0, 0, 1]
+    ];

src/multi_line_text.scad

@@ -1,8 +1,6 @@
 /**
 * multi_line_text.scad
 *
-* Creates multi-line text from a list of strings. 
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/parse_number.scad

@@ -1,10 +1,6 @@
 /**
 * parse_number.scad
 *
-* Parses the string argument as an number.
-* It depends on the split_str and the sub_str functions 
-* so remember to include split_str.scad and sub_str.scad.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/path_extrude.scad

@@ -1,11 +1,6 @@
 /**
 * path_extrude.scad
 *
-* It extrudes a 2D shape along a path. 
-* This module is suitable for a path created by a continuous function.
-* It depends on the rotate_p function and the polysections module. 
-* Remember to include "rotate_p.scad" and "polysections.scad".
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *
@@ -16,9 +11,14 @@
 include <__private__/__is_vector.scad>;
 include <__private__/__to3d.scad>;
 include <__private__/__angy_angz.scad>;
-include <__private__/__length_between.scad>;
+include <__private__/__m_multiply.scad>;
+
+// Becuase of improving the performance, this module requires m_rotation.scad which doesn't require in dotSCAD 1.0. 
+// For backward compatibility, I directly include m_rotation here.
+include <m_rotation.scad>;
 
 module path_extrude(shape_pts, path_pts, triangles = "SOLID", twist = 0, scale = 1.0, closed = false) {
+    // pre-process parameters
     function scale_pts(pts, s) = [
         for(p = pts) [p[0] * s[0], p[1] * s[1], p[2] * s[2]]
     ];
@@ -45,8 +45,51 @@ module path_extrude(shape_pts, path_pts, triangles = "SOLID", twist = 0, scale =
             (scale[0] - 1) / len_path_pts_minus_one, 
             (scale[1] - 1) / len_path_pts_minus_one,
             scale[2] == undef ? 0 : (scale[2] - 1) / len_path_pts_minus_one
-        ] : scale_step();         
+        ] : scale_step();   
+
+    // get rotation matrice for sections
+
+    function local_ang_vects(j) = 
+        j == 0 ? [] : local_ang_vects_sub(j);
     
+    function local_ang_vects_sub(j) =
+        let(
+            vt0 = pth_pts[j] - pth_pts[j - 1],
+            vt1 = pth_pts[j + 1] - pth_pts[j],
+            a = acos((vt0 * vt1) / (norm(vt0) * norm(vt1))),
+            v = cross(vt0, vt1)
+        )
+        concat([[a, v]], local_ang_vects(j - 1));
+
+    rot_matrice = [
+        for(ang_vect = local_ang_vects(len_path_pts - 2)) 
+            m_rotation(ang_vect[0], ang_vect[1])
+    ];
+
+    leng_rot_matrice = len(rot_matrice);
+    leng_rot_matrice_minus_one = leng_rot_matrice - 1;
+    leng_rot_matrice_minus_two= leng_rot_matrice - 2;
+
+    function cumulated_rot_matrice(i) = 
+        i == leng_rot_matrice - 2 ? 
+               [
+                   rot_matrice[leng_rot_matrice_minus_one], 
+                   __m_multiply(rot_matrice[leng_rot_matrice_minus_two], rot_matrice[leng_rot_matrice_minus_one])
+               ] 
+               : cumulated_rot_matrice_sub(i);
+
+    function cumulated_rot_matrice_sub(i) = 
+        let(
+            matrice = cumulated_rot_matrice(i + 1),
+            curr_matrix = rot_matrice[i],
+            prev_matrix = matrice[len(matrice) - 1]
+        )
+        concat(matrice, [__m_multiply(curr_matrix, prev_matrix)]);
+
+    cumu_rot_matrice = cumulated_rot_matrice(0);
+
+    // get all sections
+
     function init_section(a, s) =
         let(angleyz = __angy_angz(pth_pts[0], pth_pts[1]))
         rotate_pts(
@@ -66,14 +109,17 @@ module path_extrude(shape_pts, path_pts, triangles = "SOLID", twist = 0, scale =
         let(
             vt0 = pth_pts[j] - pth_pts[j - 1],
             vt1 = pth_pts[j + 1] - pth_pts[j],
-            a = acos((vt0 * vt1) / (norm(vt0) * norm(vt1)))      
+            ms = cumu_rot_matrice[j - 1]
         )
-        rotate_pts(
-                local_rotate_section(j - 1, init_a, init_s),
-                a,
-                cross(vt0, vt1)
-        );
-        
+        [
+            for(p = init_section(init_a, init_s)) 
+                [
+                    [ms[0][0], ms[0][1], ms[0][2]] * p,
+                    [ms[1][0], ms[1][1], ms[1][2]] * p,
+                    [ms[2][0], ms[2][1], ms[2][2]] * p
+                ]
+        ];        
+
     function sections() =
         let(
             fst_section = 
@@ -93,7 +139,7 @@ module path_extrude(shape_pts, path_pts, triangles = "SOLID", twist = 0, scale =
     sects = sections();
 
     function calculated_sections() =
-        closed && pth_pts[0] == pth_pts[len_path_pts - 1] ?
+        closed && pth_pts[0] == pth_pts[len_path_pts_minus_one] ?
             concat(sects, [sects[0]]) : // round-robin
             sects;
      

src/paths2sections.scad

@@ -1,8 +1,6 @@
 /**
 * paths2sections.scad
 *
-* Given a list of paths, this function will return all cross-sections described by those paths.
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/pie.scad

@@ -1,8 +1,6 @@
 /**
 * pie.scad
 *
-* Creates a pie (circular sector). You can pass a 2 element vector to define the central angle. Its $fa, $fs and $fn parameters are consistent with the circle module.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/polyline2d.scad

@@ -1,10 +1,6 @@
 /**
 * polyline2d.scad
 *
-* Creates a polyline from a list of x, y coordinates. When the end points are CAP_ROUND, 
-* you can use $fa, $fs or $fn to controll the circle module used internally. 
-* It depends on the line2d module so you have to include line2d.scad.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/polyline3d.scad

@@ -1,9 +1,6 @@
 /**
 * polyline3d.scad
 *
-* Creates a 3D polyline from a list of `[x, y, z]` coordinates. 
-* It depends on the line3d module so you have to include line3d.scad.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/polysections.scad

@@ -1,9 +1,6 @@
 /**
 * polysections.scad
 *
-* Crosscutting a tube-like shape at different points gets several cross-sections.
-* This module can operate reversely. It uses cross-sections to construct a tube-like shape.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/polytransversals.scad

@@ -1,9 +1,6 @@
 /**
 * polytransversals.scad
 *
-* Crosscutting a polyline at different points gets several transversals.
-* This module can operate reversely. It uses transversals to construct a polyline.
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/ring_extrude.scad

@@ -1,9 +1,6 @@
 /**
 * ring_extrude.scad
 *
-* Rotational extrusion spins a 2D shape around the Z-axis.  
-* It's similar to the built-in `rotate_extrude`; however, it supports angle, twist and scale options.
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/rotate_p.scad

@@ -1,9 +1,6 @@
 /**
 * rotate_p.scad
 *
-* Rotates a point 'a' degrees around an arbitrary axis. 
-* The rotation is applied in the following order: x, y, z. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *
@@ -72,7 +69,7 @@ function _rotz(pt, a) =
 function _rotate_p_3d(point, a) =
     _rotz(_roty(_rotx(point, a[0]), a[1]), a[2]);
 
-function to_avect(a) =
+function _to_avect(a) =
      len(a) == 3 ? a : (
          len(a) == 2 ? [a[0], a[1], 0] : (
              len(a) == 1 ? [a[0], 0, 0] : [0, 0, a]
@@ -80,7 +77,7 @@ function to_avect(a) =
      );
 
 function _rotate_p(p, a) =
-    let(angle = to_avect(a))
+    let(angle = _to_avect(a))
     len(p) == 3 ? 
         _rotate_p_3d(p, angle) :
         __to2d(

src/rounded_cube.scad

@@ -1,9 +1,6 @@
 /**
 * rounded_cube.scad
 *
-* Creates a rounded cube in the first octant. 
-* When center is true, the cube is centered on the origin.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/rounded_cylinder.scad

@@ -1,8 +1,6 @@
 /**
 * rounded_cylinder.scad
 *
-* Creates a rounded cylinder. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/rounded_extrude.scad

@@ -1,8 +1,6 @@
 /**
 * rounded_extrude.scad
 *
-* Extrudes a 2D object roundly from 0 to 180 degrees.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/rounded_square.scad

@@ -1,9 +1,6 @@
 /**
 * rounded_square.scad
 *
-* Creates a rounded square or rectangle in the first quadrant. 
-* When center is true the square is centered on the origin.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/shape_arc.scad

@@ -1,10 +1,6 @@
 /**
 * shape_arc.scad
 *
-* Returns shape points of an arc shape. 
-* They can be used with xxx_extrude modules of dotSCAD.
-* The shape points can be also used with the built-in polygon module. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/shape_cyclicpolygon.scad

@@ -1,10 +1,6 @@
 /**
 * shape_cyclicpolygon.scad
 *
-* Returns shape points of a regular cyclic polygon.
-* They can be used with xxx_extrude modules of dotSCAD.
-* The shape points can be also used with the built-in polygon module.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/shape_ellipse.scad

@@ -1,10 +1,6 @@
 /**
 * shape_ellipse.scad
 *
-* Returns shape points of an ellipse.
-* They can be used with xxx_extrude modules of dotSCAD.
-* The shape points can be also used with the built-in polygon module. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/shape_glued2circles.scad

@@ -2,10 +2,6 @@
 /**
 * shape_glued2circles.scad
 *
-* Returns shape points of two glued circles. 
-* They can be used with xxx_extrude modules of dotSCAD.
-* The shape points can be also used with the built-in polygon module. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/shape_path_extend.scad

@@ -1,11 +1,6 @@
 /**
 * shape_path_extend.scad
 *
-* It extends a 2D stroke along a path. 
-* This module is suitable for a path created by a continuous function.
-* It depends on the rotate_p function and the polytransversals module. 
-* Remember to include "rotate_p.scad" and "polytransversals.scad".
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *
@@ -14,7 +9,6 @@
 **/
 
 include <__private__/__to3d.scad>;
-include <__private__/__length_between.scad>;
 include <__private__/__polytransversals.scad>;
 include <__private__/__reverse.scad>;
 
@@ -39,7 +33,7 @@ function _shape_path_first_stroke(stroke_pts, path_pts) =
 
 function _shape_path_extend_stroke(stroke_pts, p1, p2, scale_step, i) =
     let(
-        leng = __length_between(__to3d(p1), __to3d(p2)),
+        leng = norm(__to3d(p2) - __to3d(p1)),
         a = _shape_path_extend_az(p1, p2)
     )
     [

src/shape_pentagram.scad

@@ -1,10 +1,6 @@
 /**
 * shape_pentagram.scad
 *
-* Returns shape points of a pentagram.
-* They can be used with xxx_extrude modules of dotSCAD.
-* The shape points can be also used with the built-in polygon module. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/shape_pie.scad

@@ -1,10 +1,6 @@
 /**
 * shape_pie.scad
 *
-* Returns shape points of a pie (circular sector) shape.
-* They can be used with xxx_extrude modules of dotSCAD.
-* The shape points can be also used with the built-in polygon module. 
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/shape_square.scad

@@ -1,10 +1,6 @@
 /**
 * shape_square.scad
 *
-* Returns shape points of a rounded square or rectangle.
-* They can be used with xxx_extrude modules of dotSCAD.
-* The shape points can be also used with the built-in polygon module. 
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/shape_starburst.scad

@@ -1,10 +1,6 @@
 /**
 * shape_star.scad
 *
-* Returns shape points of a starburst.
-* They can be used with xxx_extrude modules of dotSCAD.
-* The shape points can be also used with the built-in polygon module. 
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/shape_superformula.scad

@@ -1,10 +1,6 @@
 /**
 * shape_superformula.scad
 *
-* Returns shape points of a Superformula shape. 
-* They can be used with xxx_extrude modules of dotSCAD.
-* The shape points can be also used with the built-in polygon module. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/shape_taiwan.scad

@@ -1,10 +1,6 @@
 /**
 * shape_taiwan.scad
 *
-* Returns shape points of Taiwan.
-* They can be used with xxx_extrude modules of dotSCAD.
-* The shape points can be also used with the built-in polygon module. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/shape_trapezium.scad

@@ -1,10 +1,6 @@
 /**
 * shape_trapezium.scad
 *
-* Returns shape points of an isosceles trapezium.
-* They can be used with xxx_extrude modules of dotSCAD.
-* The shape points can be also used with the built-in polygon module. 
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/shear.scad

@@ -0,0 +1,16 @@
+/**
+* shear.scad
+*
+* @copyright Justin Lin, 2019
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-shear.html
+*
+**/
+
+include <__private__/__m_multiply.scad>;
+include <__private__/__m_shearing.scad>;
+
+module shear(sx = [0, 0], sy = [0, 0], sz = [0, 0]) {
+    multmatrix(__m_shearing(sx, sy, sz)) children();
+}

src/sphere_spiral.scad

@@ -1,11 +1,6 @@
 /**
 * sphere_spiral.scad
 *
-* Creates all points and angles on the path of a spiral around a sphere. 
-* It returns a vector of [[x, y, z], [ax, ay, az]]. [x, y, z] is actually
-* obtained from rotating [radius, 0, 0] by [ax, ay, az].
-* It depends on the rotate_p function. Remember to include rotate_p.scad first.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/sphere_spiral_extrude.scad

@@ -1,8 +1,6 @@
 /**
 * sphere_spiral_extrude.scad
 *
-* Extrudes a 2D shape along the path of a sphere spiral.
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/split_str.scad

@@ -1,9 +1,6 @@
 /**
 * split_str.scad
 *
-* Splits the given string around matches of the given delimiting character.
-* It depends on the sub_str function so remember to include sub_str.scad.
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/stereographic_extrude.scad

@@ -1,11 +1,6 @@
 /**
 * stereographic_extrude.scad
 *
-* Takes a 2D polygon as input and extends it onto a sphere. 
-* If you light up a lamp on the north pole of the sphere, the 
-* shadow will return to the original 2D polygon. For more 
-* information, take a look at [Stereographic projection](https://en.wikipedia.org/wiki/Stereographic_projection).
-*
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/sub_str.scad

@@ -1,8 +1,6 @@
 /**
 * sub_str.scad
 *
-* Returns a new string that is a substring of the given string.
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/turtle2d.scad

@@ -1,9 +1,6 @@
 /**
 * turtle2d.scad
 *
-* An OpenSCAD implementation of Turtle Graphics. 
-* It moves on the xy plane. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *

src/turtle3d.scad

@@ -1,8 +1,6 @@
 /**
 * turtle3d.scad
 *
-* An OpenSCAD implementation of 3D Turtle Graphics. 
-* 
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *