├── LICENSE.txt ├── README.md ├── demo_plot_function.scad ├── demo_plot_function.stl ├── images └── demo_plot_function.png └── plot_function.scad /LICENSE.txt: -------------------------------------------------------------------------------- 1 | Creative Commons Legal Code 2 | 3 | CC0 1.0 Universal 4 | 5 | CREATIVE COMMONS CORPORATION IS NOT A LAW FIRM AND DOES NOT PROVIDE 6 | LEGAL SERVICES. DISTRIBUTION OF THIS DOCUMENT DOES NOT CREATE AN 7 | ATTORNEY-CLIENT RELATIONSHIP. CREATIVE COMMONS PROVIDES THIS 8 | INFORMATION ON AN "AS-IS" BASIS. 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Affirmer understands and acknowledges that Creative Commons is not a 120 | party to this document and has no duty or obligation with respect to 121 | this CC0 or use of the Work. 122 | 123 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # OpenSCAD Function Plotting Library 2 | 3 |

Demo image

4 | 5 | This is a general purpose function plotting library for OpenSCAD which will 6 | render functions with Cartesian coordinates (x & y input, z output), 7 | polar/cylindrical coordinates (r & angle input, z output), or axial coordinates 8 | (z & angle input, r output). This library is sufficiently flexible that it can 9 | be used for more than just plotting functions. As demonstrated in the included 10 | demo files, this can efficiently render ordinary objects with surfaces defined 11 | by mathematical functions. 12 | 13 | While there are a few other function plotting libraries out there for OpenSCAD, 14 | this one is particularly robust, fast, and flexible. It uses list comprehension 15 | to generate each plot as a single polyhedron, supports multiple user-defined 16 | functions of each type in one design, consistently creates properly manifold 17 | renders, and executes as quickly as any other rendered object of comparable 18 | size. 19 | 20 | # Usage 21 | 22 | Since OpenSCAD does not support passing functions as parameters, this library 23 | resolves it by allowing the user to declare functions Func1, Func2, etc, 24 | PolarFunc1, PolarFunc2, etc, and AxialFunc1, AxialFunc2, etc. Then the number 25 | 1, 2, etc is passed to the corresponding plot routine. For example, the 26 | following code will create a Cartesian coordinate plot of the following 27 | function #1 over the domain -40 through 40 in both x and y with a step size of 28 | 0.4: 29 | 30 | ``` 31 | include 32 | function Func1(x, y) = 2*(1.5 + cos(x*x + y*y/4)); 33 | PlotFunction(1, [-40, 0.4, 40], [-40, 0.4, 40]); 34 | ``` 35 | 36 | The module call PlotFunction can occur anywhere a normal polyhedron could be 37 | generated, but the function definition Func1 must be declared at the top-level 38 | of the code so that it can be accessed from within the included plotting 39 | library. Note that it must "include" plot_function.scad rather than "use" it so 40 | that Func1 and others are accessible. A variety of usage demonstrations are in 41 | the demo_plot_function.scad file, and the API for the three plotting modules is 42 | as follows: 43 | 44 | ``` 45 | // Plots the numbered function Func1 through Func9, where FuncN is 1 through 9. 46 | // Each function is a function of x and y. 47 | // minx_stepx_maxx should be [minx, stepx, maxx], and likewise for y, 48 | // specifying the domain to be plotted. 49 | // To guarantee a properly manifold shape, the routine will only render 50 | // strictly positive values (z>0) of the defined function. Add an offset if 51 | // needed to achieve this. 52 | module PlotFunction(FuncN, minx_stepx_maxx, miny_stepy_maxy) 53 | 54 | // Plots the numbered function PolarFunc1 through PolarFunc9, where 55 | // PolarFuncN is 1 through 9. Each function is a function of radius and 56 | // angle. 57 | // max_r is the outer radius, and min_step is the smallest step size between 58 | // points. 59 | // To guarantee a properly manifold shape, the routine will only render 60 | // strictly positive values (z>0) of the defined function. Add an offset if 61 | // needed to achieve this. 62 | module PlotPolarFunction(PolarFuncN, max_r, min_step=-1) 63 | 64 | // Plots the numbered function AxialFunc1 through AxialFunc9, where 65 | // AxialFuncN is 1 through 9. Each function is a function of z-height and 66 | // angle, and returns the radius outward in the xy-plane. 67 | // max_r is the outer radius, and min_step is the smallest step size between 68 | // points. 69 | // minz_stepz_maxz should be [minz, stepz, maxz], and likewise for y, 70 | // specifying the domain to be plotted. 71 | // To guarantee a properly manifold shape, the routine will only render 72 | // strictly positive values (r>0) of the defined function. Add an offset if 73 | // needed to achieve this. 74 | module PlotAxialFunction(AxialFuncN, minz_stepz_maxz, num_circle_steps=360) 75 | ``` 76 | 77 | # How it works internally 78 | 79 | This section does not need to be read or understood to use the library. The key 80 | step in the design relies on the PlotClosePoints module which generates an 81 | arbitrary polyhedron given a two-dimensional array of points defining a series 82 | of consecutive loops outlining the polyhedron. This provides clear guarantees 83 | of producing a manifold shape as long as the outlining points are kept properly 84 | ordered by the Plot modules. The axial plots are then defined by loops from z=0 85 | to the max height, with the radial distance outward of each point given by the 86 | provided function. The Cartesian plots are done similarly, but starting from 87 | the minimum y value, including 2 coordinate values for the bottom corners at 88 | the x max and x min, and looping across the x values. The polar plots start 89 | with the bottom outer ring and loop inward with consecutive rings for each 90 | radial value of the polar part, with the loops adopting whatever z value the 91 | provided function gives. 92 | 93 | -------------------------------------------------------------------------------- /demo_plot_function.scad: -------------------------------------------------------------------------------- 1 | // Created in 2017 by Ryan A. Colyer. 2 | // This work is released with CC0 into the public domain. 3 | // https://creativecommons.org/publicdomain/zero/1.0/ 4 | // 5 | // https://www.thingiverse.com/thing:2391851 6 | 7 | 8 | include 9 | 10 | 11 | Demo(0); 12 | 13 | // 1 -- Gravity well 14 | function Func1(x, y) = 15 | let ( z = 50 - 50/sqrt(x*x+y*y) ) 16 | z < 1 ? 1 : z; 17 | 18 | // 2 -- A bowl 19 | function PolarFunc2(r, a) = let(z = 23-sqrt(23*23-r*r)) (z < 2 ? 2 : z); 20 | 21 | // 3 -- A rose 22 | 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; 23 | 24 | // 4 -- A simple chalice 25 | function AxialFunc1(z, ang) = 5*(cos(log(z/5+1)*360) + 2); 26 | function AxialFunc2(z, ang) = AxialFunc1(z, ang) - 2; 27 | 28 | // 5 -- 29 | // Plane wave 30 | function Func4(x, y) = 2.5*(1+cos(y*36))+2; 31 | // Two-slit interference 32 | slit_pos = 10; 33 | function Func5(x, y) = 1.25*(1+cos(sqrt(y*y+(x-slit_pos)*(x-slit_pos))*36)) + 34 | 1.25*(1+cos(sqrt(y*y+(x+slit_pos)*(x+slit_pos))*36))+2; 35 | 36 | // One-slit 37 | function Func6(x, y) = 2.5*(1+cos(sqrt(y*y+(x-slit_pos)*(x-slit_pos))*36))+2; 38 | 39 | module DemoNumber(n) { 40 | SelectFrom(n-1) { 41 | 42 | // 1 -- Gravity well 43 | translate([10, 0, 0]) 44 | PlotFunction(1, [-10, 0.2, 0], [-10, 0.2, 10]); 45 | 46 | // 2 -- A bowl 47 | difference() { 48 | PlotPolarFunction(2, 20, 0.8); 49 | translate([0, 0, -2]) PlotPolarFunction(2, 20.1, 0.8); 50 | } 51 | 52 | // 3 -- A rose 53 | PlotPolarFunction(3, 22, 0.4); 54 | 55 | // 4 -- A simple chalice 56 | difference() { 57 | PlotAxialFunction(1, [0, 0.4, 50], 180); 58 | PlotAxialFunction(2, [2, 0.4, 51], 180); 59 | } 60 | 61 | // 5 -- Two-slit interference 62 | union() { 63 | PlotFunction(4, [-25, 0.4, 25], [-25, 0.4, 0]); 64 | difference() { 65 | translate([-25, -1, 0]) cube([50, 2, 16]); 66 | translate([slit_pos, 0, 16/2]) cube([2, 3, 16+2], center=true); 67 | translate([-slit_pos, 0, 16/2]) cube([2, 3, 16+2], center=true); 68 | } 69 | PlotFunction(5, [-25, 0.4, 25], [0, 0.4, 30]); 70 | } 71 | 72 | // 6 -- One-slit wave 73 | union() { 74 | PlotFunction(4, [-25, 0.4, 25], [-25, 0.4, 0]); 75 | difference() { 76 | translate([-25, -1, 0]) cube([50, 2, 16]); 77 | translate([slit_pos, 0, 16/2]) cube([2, 3, 16+2], center=true); 78 | } 79 | PlotFunction(6, [-25, 0.4, 25], [0, 0.4, 30]); 80 | } 81 | 82 | } 83 | } 84 | 85 | 86 | module SelectFrom(n) { children(n); } 87 | 88 | module Demo(n=0) { 89 | demo_cnt = 5; 90 | demo_cnt_sqrt = floor(sqrt(demo_cnt)); 91 | demo_order = [2, 3, 4, 1, 5]; 92 | rotate_demos = 270; 93 | //rotate_demos = 180; 94 | if (n == 0) { 95 | for (i=[1:demo_cnt]) 96 | translate([((i-1)%demo_cnt_sqrt)*60, floor((i-1)/demo_cnt_sqrt)*60, 0]) 97 | rotate([0, 0, rotate_demos]) 98 | if (i-1 < len(demo_order)) { 99 | DemoNumber(demo_order[i-1]); 100 | } 101 | else{ 102 | DemoNumber(i); 103 | } 104 | } 105 | else { 106 | DemoNumber(n); 107 | } 108 | } 109 | 110 | 111 | -------------------------------------------------------------------------------- /demo_plot_function.stl: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/rcolyer/plot-function/804086e16086548eb58a167fee7b45e63a4bdeb6/demo_plot_function.stl -------------------------------------------------------------------------------- /images/demo_plot_function.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/rcolyer/plot-function/804086e16086548eb58a167fee7b45e63a4bdeb6/images/demo_plot_function.png -------------------------------------------------------------------------------- /plot_function.scad: -------------------------------------------------------------------------------- 1 | // Created in 2017 by Ryan A. Colyer. 2 | // This work is released with CC0 into the public domain. 3 | // https://creativecommons.org/publicdomain/zero/1.0/ 4 | // 5 | // https://www.thingiverse.com/thing:2391851 6 | 7 | 8 | // Note: For use as a library this file must be included with "include", 9 | // not "use", so that it can access the functions defined in the including 10 | // scad file. 11 | 12 | 13 | //// Uncomment to try the usage examples: 14 | 15 | //// Gravity well 16 | // function Func1(x, y) = 17 | // let ( z = 30 - 10*10/(x*x+y*y) ) 18 | // z < 1 ? 1 : z; 19 | // 20 | // translate([10, 0, 0]) 21 | // PlotFunction(1, [-10, 0.4, 0], [-10, 0.4, 10]); 22 | 23 | 24 | //// A bowl 25 | // function PolarFunc2(r, a) = let(z = 23-sqrt(23*23-r*r)) (z < 2 ? 2 : z); 26 | // 27 | // difference() { 28 | // PlotPolarFunction(2, 20, 0.8); 29 | // translate([0, 0, -2]) PlotPolarFunction(2, 20.1, 0.8); 30 | // } 31 | 32 | 33 | //// A rose 34 | // 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; 35 | // 36 | // PlotPolarFunction(3, 22, 0.4); 37 | 38 | 39 | //// A simple chalice 40 | // function AxialFunc1(z, ang) = 5*(cos(log(z/5+1)*360) + 2); 41 | // function AxialFunc2(z, ang) = AxialFunc1(z, ang) - 2; 42 | // 43 | // difference() { 44 | // PlotAxialFunction(1, [0, 0.4, 50], 180); 45 | // PlotAxialFunction(2, [2, 0.4, 51], 180); 46 | // } 47 | 48 | 49 | // Plots the numbered function Func1 through Func9, where FuncN is 1 through 9. 50 | // Each function is a function of x and y. 51 | // minx_stepx_maxx should be [minx, stepx, maxx], and likewise for y, 52 | // specifying the domain to be plotted. 53 | // To guarantee a properly manifold shape, the routine will only render 54 | // strictly positive values (z>0) of the defined function. Add an offset if 55 | // needed to achieve this. 56 | module PlotFunction(FuncN, minx_stepx_maxx, miny_stepy_maxy) { 57 | minx = minx_stepx_maxx[0]; 58 | stepx = minx_stepx_maxx[1]; 59 | maxx = minx_stepx_maxx[2] + 0.001*stepx; 60 | miny = miny_stepy_maxy[0]; 61 | stepy = miny_stepy_maxy[1]; 62 | maxy = miny_stepy_maxy[2] + 0.001*stepy; 63 | minplot = 0.0005*(stepx+stepy); 64 | 65 | pointarrays = concat( 66 | [concat( // Close miny edge of plot. 67 | [[maxx, miny-0.001*stepy, 0]], 68 | [[minx, miny-0.001*stepy, 0]], 69 | [ 70 | for (x = [minx:stepx:maxx]) 71 | [x, miny-0.001*stepy, 0.0001] 72 | ] 73 | )], 74 | 75 | [ for (y = [miny:stepy:maxy]) 76 | concat( 77 | [[maxx, y, 0]], 78 | [[minx, y, 0]], 79 | [ 80 | for (x = [minx:stepx:maxx]) let( 81 | z = CallFunc(x, y, FuncN), 82 | zchecked = z < minplot ? minplot : z 83 | ) 84 | [x, y, zchecked] 85 | ] 86 | ) 87 | ], 88 | 89 | [concat( // Close maxy edge of plot. 90 | [[maxx, maxy+0.001*stepy, 0]], 91 | [[minx, maxy+0.001*stepy, 0]], 92 | [ 93 | for (x = [minx:stepx:maxx]) 94 | [x, maxy+0.001*stepy, 0.0001] 95 | ] 96 | )] 97 | ); 98 | 99 | PlotClosePoints(pointarrays); 100 | } 101 | 102 | 103 | // Plots the numbered function PolarFunc1 through PolarFunc9, where 104 | // PolarFuncN is 1 through 9. Each function is a function of radius and 105 | // angle. 106 | // max_r is the outer radius, and min_step is the smallest step size between 107 | // points. 108 | // To guarantee a properly manifold shape, the routine will only render 109 | // strictly positive values (z>0) of the defined function. Add an offset if 110 | // needed to achieve this. 111 | module PlotPolarFunction(PolarFuncN, max_r, min_step=-1) { 112 | num_circle_steps = (min_step <= 0) ? 360 : 113 | ceil((max_r * 2*PI / min_step) / 8)*8; 114 | ang_step = 360 / num_circle_steps; 115 | eff_minstep = (min_step <= 0) ? 2*PI*max_r/num_circle_steps : min_step; 116 | num_r_steps = ceil(max_r / eff_minstep); 117 | r_step = (max_r - 0.001*eff_minstep) / num_r_steps; 118 | minplot = 0.001*r_step; 119 | 120 | pointarrays = concat( 121 | [ 122 | [ for (a = [0:ang_step:359.9999]) 123 | [max_r * cos(a), max_r * sin(a), 0] 124 | ] 125 | ], 126 | 127 | [ for (r = [max_r:-r_step:0.000001*r_step]) 128 | [ for (a = [0:ang_step:359.9999]) let( 129 | z = CallPolarFunc(r, a, PolarFuncN), 130 | zchecked = z < minplot ? minplot : z 131 | ) 132 | [r * cos(a), r * sin(a), zchecked] 133 | ] 134 | ] 135 | ); 136 | 137 | PlotClosePoints(pointarrays); 138 | } 139 | 140 | 141 | // Plots the numbered function AxialFunc1 through AxialFunc9, where 142 | // AxialFuncN is 1 through 9. Each function is a function of z-height and 143 | // angle, and returns the radius outward in the xy-plane. 144 | // max_r is the outer radius, and min_step is the smallest step size between 145 | // points. 146 | // minz_stepz_maxz should be [minz, stepz, maxz], and likewise for y, 147 | // specifying the domain to be plotted. 148 | // To guarantee a properly manifold shape, the routine will only render 149 | // strictly positive values (r>0) of the defined function. Add an offset if 150 | // needed to achieve this. 151 | module PlotAxialFunction(AxialFuncN, minz_stepz_maxz, num_circle_steps=360) { 152 | ang_step = 360 / num_circle_steps; 153 | minz = minz_stepz_maxz[0]; 154 | stepz = minz_stepz_maxz[1]; 155 | maxz = minz_stepz_maxz[2] + 0.001*stepz; 156 | minplot = 0.001*stepz; 157 | 158 | pointarrays = [ 159 | for (z = [minz:stepz:maxz]) 160 | [ for (ai = [0:num_circle_steps-1]) let( 161 | a = ai * ang_step, 162 | r = CallAxialFunc(z, a, AxialFuncN), 163 | rchecked = r < minplot ? minplot : r 164 | ) 165 | [rchecked * cos(a), rchecked * sin(a), z] 166 | ] 167 | 168 | ]; 169 | 170 | PlotClosePoints(pointarrays); 171 | } 172 | 173 | 174 | // Relays function calls to Func1 through Func9 175 | function CallFunc(x, y, n) = 176 | (n == 1) ? Func1(x, y) : 177 | (n == 2) ? Func2(x, y) : 178 | (n == 3) ? Func3(x, y) : 179 | (n == 4) ? Func4(x, y) : 180 | (n == 5) ? Func5(x, y) : 181 | (n == 6) ? Func6(x, y) : 182 | (n == 7) ? Func7(x, y) : 183 | (n == 8) ? Func8(x, y) : 184 | (n == 9) ? Func9(x, y) : 185 | FunctionNumberOutOfRange; 186 | 187 | 188 | // Relays function calls to PolarFunc1 through PolarFunc9 189 | function CallPolarFunc(r, ang, n) = 190 | (n == 1) ? PolarFunc1(r, ang) : 191 | (n == 2) ? PolarFunc2(r, ang) : 192 | (n == 3) ? PolarFunc3(r, ang) : 193 | (n == 4) ? PolarFunc4(r, ang) : 194 | (n == 5) ? PolarFunc5(r, ang) : 195 | (n == 6) ? PolarFunc6(r, ang) : 196 | (n == 7) ? PolarFunc7(r, ang) : 197 | (n == 8) ? PolarFunc8(r, ang) : 198 | (n == 9) ? PolarFunc9(r, ang) : 199 | PolarFunctionNumberOutOfRange; 200 | 201 | 202 | // Relays function calls to AxialFunc1 through AxialFunc9 203 | function CallAxialFunc(z, ang, n) = 204 | (n == 1) ? AxialFunc1(z, ang) : 205 | (n == 2) ? AxialFunc2(z, ang) : 206 | (n == 3) ? AxialFunc3(z, ang) : 207 | (n == 4) ? AxialFunc4(z, ang) : 208 | (n == 5) ? AxialFunc5(z, ang) : 209 | (n == 6) ? AxialFunc6(z, ang) : 210 | (n == 7) ? AxialFunc7(z, ang) : 211 | (n == 8) ? AxialFunc8(z, ang) : 212 | (n == 9) ? AxialFunc9(z, ang) : 213 | AxialFunctionNumberOutOfRange; 214 | 215 | 216 | function isfinite(x) = (!(x!=x)) && (x<(1/0)) && (x>(-1/0)); 217 | 218 | 219 | // This generates a closed polyhedron from an array of arrays of points, 220 | // with each inner array tracing out one loop outlining the polyhedron. 221 | // pointarrays should contain an array of N arrays each of size P outlining a 222 | // closed manifold. The points must obey the right-hand rule. For example, 223 | // looking down, the P points in the inner arrays are counter-clockwise in a 224 | // loop, while the N point arrays increase in height. Points in each inner 225 | // array do not need to be equal height, but they usually should not meet or 226 | // cross the line segments from the adjacent points in the other arrays. 227 | // (N>=2, P>=3) 228 | // Core triangles: 229 | // [j][i], [j+1][i], [j+1][(i+1)%P] 230 | // [j][i], [j+1][(i+1)%P], [j][(i+1)%P] 231 | // Then triangles are formed in a loop with the middle point of the first 232 | // and last array. 233 | module PlotClosePoints(pointarrays) { 234 | function recurse_avg(arr, n=0, p=[0,0,0]) = (n>=len(arr)) ? p : 235 | recurse_avg(arr, n+1, p+(arr[n]-p)/(n+1)); 236 | 237 | N = len(pointarrays); 238 | P = len(pointarrays[0]); 239 | NP = N*P; 240 | lastarr = pointarrays[N-1]; 241 | midbot = recurse_avg(pointarrays[0]); 242 | midtop = recurse_avg(pointarrays[N-1]); 243 | 244 | faces_bot = [ 245 | for (i=[0:P-1]) 246 | [0,i+1,1+(i+1)%len(pointarrays[0])] 247 | ]; 248 | 249 | loop_offset = 1; 250 | bot_len = loop_offset + P; 251 | 252 | faces_loop = [ 253 | for (j=[0:N-2], i=[0:P-1], t=[0:1]) 254 | [loop_offset, loop_offset, loop_offset] + (t==0 ? 255 | [j*P+i, (j+1)*P+i, (j+1)*P+(i+1)%P] : 256 | [j*P+i, (j+1)*P+(i+1)%P, j*P+(i+1)%P]) 257 | ]; 258 | 259 | top_offset = loop_offset + NP - P; 260 | midtop_offset = top_offset + P; 261 | 262 | faces_top = [ 263 | for (i=[0:P-1]) 264 | [midtop_offset,top_offset+(i+1)%P,top_offset+i] 265 | ]; 266 | 267 | points = [ 268 | for (i=[-1:NP]) 269 | (i<0) ? midbot : 270 | ((i==NP) ? midtop : 271 | pointarrays[floor(i/P)][i%P]) 272 | ]; 273 | faces = concat(faces_bot, faces_loop, faces_top); 274 | 275 | polyhedron(points=points, faces=faces, convexity=8); 276 | } 277 | 278 | 279 | --------------------------------------------------------------------------------