added function_grapher

README.md

@@ -31,7 +31,8 @@ Some modules may depend on other modules. For example, the `polyline2d` module d
 	- [line3d](https://openhome.cc/eGossip/OpenSCAD/lib-line3d.html)
 	- [polyline3d](https://openhome.cc/eGossip/OpenSCAD/lib-polyline3d.html)
 	- [hull_polyline3d](https://openhome.cc/eGossip/OpenSCAD/lib-hull_polyline3d.html)
-
+	- [function_grapher](https://openhome.cc/eGossip/OpenSCAD/lib-function_grapher.html)
+	
 - Transformation
 	- [hollow_out](https://openhome.cc/eGossip/OpenSCAD/lib-hollow_out.html)
 	- [bend](https://openhome.cc/eGossip/OpenSCAD/lib-bend.html)

docs/lib-function_grapher.md

@@ -0,0 +1,116 @@
+# function_grapher
+
+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` and `polyline3d` modules so you have to include "line3d.scad" and "polyline3d.scad".
+
+## Parameters
+
+- `points` : A set of points `[x, y, f(x, y)]`. See examples below.
+- `thickness` : The face or line thickness.
+- `style` : The style of the graph. It accepts `"FACES"`, `"LINES"` and `"HULL_FACES"`. The default value is `"FACES"` which simply takes `f(x, y) - thickness` for each point to build a bottom. It may cause thickness problems when slopes is high. The `"HULL_FACES"` value can solve the problem but is slow. When assigning `"LINES"`, it uses lines to connect points.
+- `slicing` : Given a rectangle, we have two ways to slice it into two triangles. Using this parameter to determine the way you want. It accepts `"SLASH"` (default) and `"BACK_SLASH"`.
+- `$fa`, `$fs`, `$fn` : Used by the `circle` or `sphere` module internally. It affects the speed of rending. For example, a large `$fn` may be very slow when rending. Check [the circle module](https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Using_the_2D_Subsystem#circle) or [the sphere module](https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Primitive_Solids#sphere) for more details. 
+
+## Examples
+
+	include <line3d.scad>;
+	include <polyline3d.scad>;
+	include <function_grapher.scad>;
+	
+	points = [
+	    [[0, 0, 1], [1, 0, 2], [2, 0, 2], [3, 0, 3]],
+	    [[0, 1, 1], [1, 1, 4], [2, 1, 0], [3, 1, 3]],
+	    [[0, 2, 1], [1, 2, 3], [2, 2, 1], [3, 2, 3]],
+	    [[0, 3, 1], [1, 3, 3], [2, 3, 1], [3, 3, 3]]
+	];
+	
+	thickness = 0.5;
+	
+	function_grapher(points, thickness);
+
+![function_grapher](images/lib-function_grapher-1.JPG)
+
+	include <line3d.scad>;
+	include <polyline3d.scad>;
+	include <function_grapher.scad>;
+	
+	function f(x, y) = 
+	   30 * (
+	       cos(sqrt(pow(x, 2) + pow(y, 2))) + 
+	       cos(3 * sqrt(pow(x, 2) + pow(y, 2)))
+	   );
+	
+	thickness = 2;
+	min_value =  -200;
+	max_value = 200;
+	resolution = 10;
+	
+	points = [
+	    for(y = [min_value:resolution:max_value])
+	        [
+	            for(x = [min_value:resolution:max_value]) 
+	                [x, y, f(x, y)]
+	        ]
+	];
+	
+	function_grapher(points, thickness);
+
+![function_grapher](images/lib-function_grapher-2.JPG)
+
+	include <line3d.scad>;
+	include <polyline3d.scad>;
+	include <function_grapher.scad>;
+
+	function f(x, y) = 
+	   30 * (
+	       cos(sqrt(pow(x, 2) + pow(y, 2))) + 
+	       cos(3 * sqrt(pow(x, 2) + pow(y, 2)))
+	   );
+	
+	thickness = 2;
+	min_value =  -200;
+	max_value = 200;
+	resolution = 10;
+	style = "LINES"; 
+	
+	points = [
+	    for(y = [min_value:resolution:max_value])
+	        [
+	            for(x = [min_value:resolution:max_value]) 
+	                [x, y, f(x, y)]
+	        ]
+	];
+	
+	function_grapher(points, thickness, style);
+
+![function_grapher](images/lib-function_grapher-3.JPG)
+
+	include <line3d.scad>;
+	include <polyline3d.scad>;
+	include <function_grapher.scad>;
+
+	function f(x, y) = 
+	   30 * (
+	       cos(sqrt(pow(x, 2) + pow(y, 2))) + 
+	       cos(3 * sqrt(pow(x, 2) + pow(y, 2)))
+	   );
+	
+	thickness = 2;
+	min_value =  -200;
+	max_value = 200;
+	resolution = 10;
+	style = "LINES"; 
+	slicing = "BACK_SLASH";
+	
+	points = [
+	    for(y = [min_value:resolution:max_value])
+	        [
+	            for(x = [min_value:resolution:max_value]) 
+	                [x, y, f(x, y)]
+	        ]
+	];
+	
+	function_grapher(points, thickness, style, slicing);
+
+![function_grapher](images/lib-function_grapher-4.JPG)

src/function_grapher.scad

@@ -0,0 +1,113 @@
+/**
+* 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 and polyline3d modules so you have 
+* to include "line3d.scad" and "polyline3d.scad".
+* 
+* @copyright Justin Lin, 2017
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-function_grapher.html
+*
+**/ 
+
+module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") {
+    // Increasing $fn will be slow when you use "LINES" or "HULL_FACES".
+     
+    function tri_shell_points(top) =
+        let(
+            z_offset = [0, 0, -thickness],
+            bottom = [
+                top[0] + z_offset, 
+                top[1] + z_offset, 
+                top[2] + z_offset
+            ],
+            faces = [
+                [0, 1, 2],
+                [3, 4, 5],
+                [0, 1, 4, 3],
+                [1, 2, 5, 4],
+                [2, 0, 3, 5]
+            ]
+        )
+        [
+            concat(top, bottom), 
+            faces
+        ];
+        
+        
+    module tri_to_faces(top_tri1, top_tri2) {
+        pts_faces1 = tri_shell_points(top_tri1);
+        pts_faces2 = tri_shell_points(top_tri2);
+        
+        hull() {
+            polyhedron(
+                points = pts_faces1[0], 
+                faces = pts_faces1[1]
+            );
+            polyhedron(
+                points = pts_faces2[0],
+                faces = pts_faces2[1]
+            );
+        }
+    }
+
+    module tri_to_lines(tri1, tri2) {
+       polyline3d(concat(tri1, [tri1[0]]), thickness);
+       polyline3d(concat(tri2, [tri2[0]]), thickness);
+    }
+    
+    module hull_pts(tri) {
+       half_thickness = thickness / 2;
+       hull() {
+           translate(tri[0]) sphere(half_thickness);
+           translate(tri[1]) sphere(half_thickness);
+           translate(tri[2]) sphere(half_thickness);
+       }    
+    }
+    
+    module tri_to_hull_faces(tri1, tri2) {
+       hull_pts(tri1);
+       hull_pts(tri2);
+    }    
+
+    module tri_to_graph(tri1, tri2) {
+        if(style == "FACES") {
+            tri_to_faces(tri1, tri2);
+        } else if(style == "LINES") {
+            tri_to_lines(tri1, tri2);
+        } else {  // Warning: May be very slow!!
+            tri_to_hull_faces(tri1, tri2);
+        }
+    }
+
+    for(yi = [0:len(points) - 2]) {
+        for(xi = [0:len(points[yi]) - 2]) {
+            if(slicing == "SLASH") {
+                tri_to_graph([
+                    points[yi][xi], 
+                    points[yi][xi + 1], 
+                    points[yi + 1][xi + 1]
+                ], [
+                    points[yi][xi], 
+                    points[yi + 1][xi + 1], 
+                    points[yi + 1][xi]
+                ]);
+            } else {                
+                tri_to_graph([
+                    points[yi][xi], 
+                    points[yi][xi + 1], 
+                    points[yi + 1][xi]
+                ], [
+                    points[yi + 1][xi], 
+                    points[yi][xi + 1], 
+                    points[yi + 1][xi + 1]
+                ]);                    
+            }        
+        }
+    }
+}