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LICENSE.txt

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README.md

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+# OpenSCAD Function Plotting Library
+
+<p align="center"><img alt="Thread demo image" src="./images/demo_plot_function.png"></p>
+
+This is a general purpose function plotting library for OpenSCAD which will
+render functions with Cartesian coordinates (x & y input, z output),
+polar/cylindrical coordinates (r & angle input, z output), or axial coordinates
+(z & angle input, r output). This library is sufficiently flexible that it can
+be used for more than just plotting functions. As demonstrated in the included
+demo files, this can efficiently render ordinary objects with surfaces defined
+by mathematical functions.
+
+While there are a few other function plotting libraries out there for OpenSCAD,
+this one is particularly robust, fast, and flexible. It uses list comprehension
+to generate each plot as a single polyhedron, supports multiple user-defined
+functions of each type in one design, consistently creates properly manifold
+renders, and executes as quickly as any other rendered object of comparable
+size.
+
+# Usage
+
+Since OpenSCAD does not support passing functions as parameters, this library
+resolves it by allowing the user to declare functions Func1, Func2, etc,
+PolarFunc1, PolarFunc2, etc, and AxialFunc1, AxialFunc2, etc. Then the number
+1, 2, etc is passed to the corresponding plot routine. For example, the
+following code will create a Cartesian coordinate plot of the following
+function #1 over the domain -40 through 40 in both x and y with a step size of
+0.4:
+
+```
+include <plot_function.scad>
+function Func1(x, y) = 2*(1.5 + cos(x*x + y*y/4));
+PlotFunction(1, [-40, 0.4, 40], [-40, 0.4, 40]);
+```
+
+The module call PlotFunction can occur anywhere a normal polyhedron could be
+generated, but the function definition Func1 must be declared at the top-level
+of the code so that it can be accessed from within the included plotting
+library. Note that it must "include" plot_function.scad rather than "use" it so
+that Func1 and others are accessible. A variety of usage demonstrations are in
+the demo_plot_function.scad file, and the API for the three plotting modules is
+as follows:
+
+```
+// Plots the numbered function Func1 through Func9, where FuncN is 1 through 9.
+// Each function is a function of x and y.
+// minx_stepx_maxx should be [minx, stepx, maxx], and likewise for y,
+// specifying the domain to be plotted.
+// To guarantee a properly manifold shape, the routine will only render
+// strictly positive values (z>0) of the defined function.  Add an offset if
+// needed to achieve this.
+module PlotFunction(FuncN, minx_stepx_maxx, miny_stepy_maxy)
+
+// Plots the numbered function PolarFunc1 through PolarFunc9, where
+// PolarFuncN is 1 through 9.  Each function is a function of radius and
+// angle.
+// max_r is the outer radius, and min_step is the smallest step size between
+// points.
+// To guarantee a properly manifold shape, the routine will only render
+// strictly positive values (z>0) of the defined function.  Add an offset if
+// needed to achieve this.
+module PlotPolarFunction(PolarFuncN, max_r, min_step=-1)
+
+// Plots the numbered function AxialFunc1 through AxialFunc9, where
+// AxialFuncN is 1 through 9.  Each function is a function of z-height and
+// angle, and returns the radius outward in the xy-plane.
+// max_r is the outer radius, and min_step is the smallest step size between
+// points.
+// minz_stepz_maxz should be [minz, stepz, maxz], and likewise for y,
+// specifying the domain to be plotted.
+// To guarantee a properly manifold shape, the routine will only render
+// strictly positive values (r>0) of the defined function.  Add an offset if
+// needed to achieve this.
+module PlotAxialFunction(AxialFuncN, minz_stepz_maxz, num_circle_steps=360)
+```
+
+# How it works internally
+
+This section does not need to be read or understood to use the library. The key
+step in the design relies on the PlotClosePoints module which generates an
+arbitrary polyhedron given a two-dimensional array of points defining a series
+of consecutive loops outlining the polyhedron. This provides clear guarantees
+of producing a manifold shape as long as the outlining points are kept properly
+ordered by the Plot modules. The axial plots are then defined by loops from z=0
+to the max height, with the radial distance outward of each point given by the
+provided function. The Cartesian plots are done similarly, but starting from
+the minimum y value, including 2 coordinate values for the bottom corners at
+the x max and x min, and looping across the x values. The polar plots start
+with the bottom outer ring and loop inward with consecutive rings for each
+radial value of the polar part, with the loops adopting whatever z value the
+provided function gives.
+

demo_plot_function.scad

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+// Created in 2017 by Ryan A. Colyer.
+// This work is released with CC0 into the public domain.
+// https://creativecommons.org/publicdomain/zero/1.0/
+//
+// https://www.thingiverse.com/thing:2391851
+
+
+include <plot_function.scad>
+
+
+Demo(0);
+
+// 1 -- Gravity well
+function Func1(x, y) =
+  let ( z = 50 - 50/sqrt(x*x+y*y) )
+  z < 1 ? 1 : z;
+
+// 2 -- A bowl
+function PolarFunc2(r, a) = let(z = 23-sqrt(23*23-r*r)) (z < 2 ? 2 : z);
+
+// 3 -- A rose
+function PolarFunc3(r, a) = (15+5*sin(r*10))*exp(-pow(r*cos(a)*cos(r*8)+r*sin(a)*sin(r*35),2)/300) + 1;
+
+// 4 -- A simple chalice
+function AxialFunc1(z, ang) = 5*(cos(log(z/5+1)*360) + 2);
+function AxialFunc2(z, ang) = AxialFunc1(z, ang) - 2;
+
+// 5 --
+// Plane wave
+function Func4(x, y) = 2.5*(1+cos(y*36))+2;
+// Two-slit interference
+slit_pos = 10;
+function Func5(x, y) = 1.25*(1+cos(sqrt(y*y+(x-slit_pos)*(x-slit_pos))*36)) +
+  1.25*(1+cos(sqrt(y*y+(x+slit_pos)*(x+slit_pos))*36))+2;
+
+// One-slit
+function Func6(x, y) = 2.5*(1+cos(sqrt(y*y+(x-slit_pos)*(x-slit_pos))*36))+2;
+
+module DemoNumber(n) {
+  SelectFrom(n-1) {
+
+    // 1 -- Gravity well
+    translate([10, 0, 0])
+      PlotFunction(1, [-10, 0.2, 0], [-10, 0.2, 10]);
+
+    // 2 -- A bowl
+    difference() {
+      PlotPolarFunction(2, 20, 0.8);
+      translate([0, 0, -2]) PlotPolarFunction(2, 20.1, 0.8);
+    }
+
+    // 3 -- A rose
+    PlotPolarFunction(3, 22, 0.4);
+
+    // 4 -- A simple chalice
+		difference() {
+			PlotAxialFunction(1, [0, 0.4, 50], 180);
+			PlotAxialFunction(2, [2, 0.4, 51], 180);
+		}
+
+    // 5 -- Two-slit interference
+    union() {
+      PlotFunction(4, [-25, 0.4, 25], [-25, 0.4, 0]);
+      difference() {
+        translate([-25, -1, 0]) cube([50, 2, 16]);
+        translate([slit_pos, 0, 16/2]) cube([2, 3, 16+2], center=true);
+        translate([-slit_pos, 0, 16/2]) cube([2, 3, 16+2], center=true);
+      }
+      PlotFunction(5, [-25, 0.4, 25], [0, 0.4, 30]);
+    }
+
+    // 6 -- One-slit wave
+    union() {
+      PlotFunction(4, [-25, 0.4, 25], [-25, 0.4, 0]);
+      difference() {
+        translate([-25, -1, 0]) cube([50, 2, 16]);
+        translate([slit_pos, 0, 16/2]) cube([2, 3, 16+2], center=true);
+      }
+      PlotFunction(6, [-25, 0.4, 25], [0, 0.4, 30]);
+    }
+
+  }
+}
+
+
+module SelectFrom(n) { children(n); }
+
+module Demo(n=0) {
+  demo_cnt = 5;
+  demo_cnt_sqrt = floor(sqrt(demo_cnt));
+  demo_order = [2, 3, 4, 1, 5];
+  rotate_demos = 270;
+  //rotate_demos = 180;
+  if (n == 0) {
+    for (i=[1:demo_cnt])
+      translate([((i-1)%demo_cnt_sqrt)*60, floor((i-1)/demo_cnt_sqrt)*60, 0])
+        rotate([0, 0, rotate_demos])
+        if (i-1 < len(demo_order)) {
+          DemoNumber(demo_order[i-1]);
+        }
+        else{
+          DemoNumber(i);
+        }
+  }
+  else {
+    DemoNumber(n);
+  }
+}
+
+