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Affirmer understands and acknowledges that Creative Commons is not a + party to this document and has no duty or obligation with respect to + this CC0 or use of the Work. + diff --git a/README.md b/README.md new file mode 100644 index 0000000..4483c8b --- /dev/null +++ b/README.md @@ -0,0 +1,94 @@ +# OpenSCAD ClosePoints Library + +

Demo image

+ +This is a general purpose OpenSCAD library for easily creating diverse shapes +by simply creating lists of points which trace out layers in an outline of the +desired shape. The library consists of modules for creating polyhedrons from +these lists of points, as well as functions to assist in specifying the points +using transformations. + +The file names starting with "demo" provide various examples of usage. + +# closepoints.scad API + +ClosePoints and CloseLoop are the two modules for creating a polyhedron. +ClosePoints is for creating a polyhedron with no holes (e.g., a ball, or a +cup), while CloseLoop is for creating a polyhedron which topologically contains +one hole (e.g., a donut). To achieve this difference, ClosePoints auto-closes +the top and bottom of the provided layer loops, while CloseLoop connects the +last layer loop to the first layer loop to close the polyhedron. + +Following these are a number of functions for working with affine +transformations, which can help significantly in tracing out the surface layers +of a desired polyhedron. + +The API is as follows: + + +``` +// This generates a closed polyhedron from an array of arrays of points, +// with each inner array tracing out one loop outlining the polyhedron. +// pointarrays should contain an array of N arrays each of size P outlining +// a closed manifold. The points must obey the right-hand rule. Point your +// right-hand thumb in the direction the N point arrays travel, and then the +// P points in the inner arrays must loop in the direction the fingers curl. +// For example, looking down, the P points in the inner arrays are +// counter-clockwise in a loop, while the N point arrays increase in height. +// Points in each inner array do not need to be equal height, but they +// usually should not meet or cross the line segments from the adjacent +// points in the other arrays. +// (N>=2, P>=3) +// Core triangles: +// [j][i], [j+1][i], [j+1][(i+1)%P] +// [j][i], [j+1][(i+1)%P], [j][(i+1)%P] +// Then triangles are formed in a loop with the middle point of the first +// and last array. To override this middle closure point, specify a +// coordinate position for close_top_pt and/or close_bot_pt. +module ClosePoints(pointarrays, close_top_pt=undef, close_bot_pt=undef) + +// This generates a looped polyhedron from an array of arrays of points, with +// each inner array tracing out one layer loop outlining the polyhedron. +// pointarrays should contain an array of N arrays each of size P outlining a +// closed manifold. The points must obey the right-hand rule. For example, +// looking down, the P points in the inner arrays are counter-clockwise in a +// loop, while the N point arrays increase in height. Points in each inner +// array do not need to be equal height, but they usually should not meet or +// cross the line segments from the adjacent points in the other arrays. The +// last layer loop should geometrically lead into the first when it is closed. +// (N>=2, P>=3) +// Core triangles: +// [j][i], [j+1][i], [j+1][(i+1)%P] +// [j][i], [j+1][(i+1)%P], [j][(i+1)%P] +module CloseLoop(pointarrays) + +// Perform an affine transformation of matrix M on coordinate v. +// +// [Scale X] [Shear X along Y] [Shear X along Z] [Translate X] +// [Shear Y along X] [Scale Y] [Shear Y along Z] [Translate Y] +// [Shear Z along X] [Shear Z along Y] [Scale Z] [Translate Z] +// or rotation matrix [[cos,-sin],[sin,cos]] in the 2 axes for a plane. +function Affine(M, v) + +// Combine a list of affine transformation matrices into one. +function AffMerge(Mlist) + +// Prepare a matrix to rotate around the x-axis. +function RotX(a) + +// Prepare a matrix to rotate around the y-axis. +function RotY(a) + +// Prepare a matrix to rotate around the z-axis. +function RotZ(a) + +// Prepare a matrix to rotate around x, then y, then z. +function Rotate(rotvec) + +// Prepare a matrix to translate by vector v. +function Translate(v) + +// Prepare a matrix to scale by vector v. +function Scale(v) +``` + diff --git a/closepoints.scad b/closepoints.scad new file mode 100644 index 0000000..fb9419d --- /dev/null +++ b/closepoints.scad @@ -0,0 +1,161 @@ +// Created 2021 by Ryan A. Colyer. +// This work is released with CC0 into the public domain. +// https://creativecommons.org/publicdomain/zero/1.0/ + + +// This generates a closed polyhedron from an array of arrays of points, +// with each inner array tracing out one loop outlining the polyhedron. +// pointarrays should contain an array of N arrays each of size P outlining +// a closed manifold. The points must obey the right-hand rule. Point your +// right-hand thumb in the direction the N point arrays travel, and then the +// P points in the inner arrays must loop in the direction the fingers curl. +// For example, looking down, the P points in the inner arrays are +// counter-clockwise in a loop, while the N point arrays increase in height. +// Points in each inner array do not need to be equal height, but they +// usually should not meet or cross the line segments from the adjacent +// points in the other arrays. +// (N>=2, P>=3) +// Core triangles: +// [j][i], [j+1][i], [j+1][(i+1)%P] +// [j][i], [j+1][(i+1)%P], [j][(i+1)%P] +// Then triangles are formed in a loop with the middle point of the first +// and last array. To override this middle closure point, specify a +// coordinate position for close_top_pt and/or close_bot_pt. +module ClosePoints(pointarrays, close_top_pt=undef, close_bot_pt=undef) { + function recurse_avg(arr, n=0, p=[0,0,0]) = (n>=len(arr)) ? p : + recurse_avg(arr, n+1, p+(arr[n]-p)/(n+1)); + + N = len(pointarrays); + P = len(pointarrays[0]); + NP = N*P; + midbot = is_undef(close_bot_pt) ? + recurse_avg(pointarrays[0]) : + close_bot_pt; + midtop = is_undef(close_top_pt) ? + recurse_avg(pointarrays[N-1]) : + close_top_pt; + + faces_bot = [ + for (i=[0:P-1]) + [0,i+1,1+(i+1)%len(pointarrays[0])] + ]; + + loop_offset = 1; + + faces_loop = [ + for (j=[0:N-2], i=[0:P-1], t=[0:1]) + [loop_offset, loop_offset, loop_offset] + (t==0 ? + [j*P+i, (j+1)*P+i, (j+1)*P+(i+1)%P] : + [j*P+i, (j+1)*P+(i+1)%P, j*P+(i+1)%P]) + ]; + + top_offset = loop_offset + NP - P; + midtop_offset = top_offset + P; + + faces_top = [ + for (i=[0:P-1]) + [midtop_offset,top_offset+(i+1)%P,top_offset+i] + ]; + + points = [ + for (i=[-1:NP]) + (i<0) ? midbot : + ((i==NP) ? midtop : + pointarrays[floor(i/P)][i%P]) + ]; + faces = concat(faces_bot, faces_loop, faces_top); + + polyhedron(points=points, faces=faces, convexity=8); +} + + +// This generates a looped polyhedron from an array of arrays of points, with +// each inner array tracing out one layer loop outlining the polyhedron. +// pointarrays should contain an array of N arrays each of size P outlining a +// closed manifold. The points must obey the right-hand rule. For example, +// looking down, the P points in the inner arrays are counter-clockwise in a +// loop, while the N point arrays increase in height. Points in each inner +// array do not need to be equal height, but they usually should not meet or +// cross the line segments from the adjacent points in the other arrays. The +// last layer loop should geometrically lead into the first when it is closed. +// (N>=2, P>=3) +// Core triangles: +// [j][i], [j+1][i], [j+1][(i+1)%P] +// [j][i], [j+1][(i+1)%P], [j][(i+1)%P] +module CloseLoop(pointarrays) { + function recurse_avg(arr, n=0, p=[0,0,0]) = (n>=len(arr)) ? p : + recurse_avg(arr, n+1, p+(arr[n]-p)/(n+1)); + + N = len(pointarrays); + P = len(pointarrays[0]); + NP = N*P; + + faces_loop = [ + for (j=[0:N-1], i=[0:P-1], t=[0:1]) + t==0 ? + [j*P+i, ((j+1)%N)*P+i, ((j+1)%N)*P+(i+1)%P] : + [j*P+i, ((j+1)%N)*P+(i+1)%P, j*P+(i+1)%P] + ]; + + points = [ + for (i=[0:NP-1]) + pointarrays[floor(i/P)][i%P] + ]; + + polyhedron(points=points, faces=faces_loop, convexity=8); +} + + +// Perform an affine transformation of matrix M on coordinate v. +// +// [Scale X] [Shear X along Y] [Shear X along Z] [Translate X] +// [Shear Y along X] [Scale Y] [Shear Y along Z] [Translate Y] +// [Shear Z along X] [Shear Z along Y] [Scale Z] [Translate Z] +// or rotation matrix [[cos,-sin],[sin,cos]] in the 2 axes for a plane. +function Affine(M, v) = M * [v[0], v[1], v[2], 1]; + + +// Combine a list of affine transformation matrices into one. +function AffMerge(Mlist, i=0) = i >= len(Mlist) ? + [[1,0,0,0],[0,1,0,0],[0,0,1,0]] : + let ( + rest = AffMerge(Mlist, i+1), + prod = Mlist[i] * [rest[0], rest[1], rest[2], [0,0,0,1]] + ) + [prod[0], prod[1], prod[2]]; + + +// Prepare a matrix to rotate around the x-axis. +function RotX(a) = + [[ 1, 0, 0, 0], + [ 0, cos(a), -sin(a), 0], + [ 0, sin(a), cos(a), 0]]; + +// Prepare a matrix to rotate around the y-axis. +function RotY(a) = + [[ cos(a), 0, sin(a), 0], + [ 0, 1, 0, 0], + [-sin(a), 0, cos(a), 0]]; + +// Prepare a matrix to rotate around the z-axis. +function RotZ(a) = + [[cos(a), -sin(a), 0, 0], + [sin(a), cos(a), 0, 0], + [ 0, 0, 1, 0]]; + +// Prepare a matrix to rotate around x, then y, then z. +function Rotate(rotvec) = + AffMerge([RotZ(rotvec[0]), RotY(rotvec[1]), RotX(rotvec[2])]); + +// Prepare a matrix to translate by vector v. +function Translate(v) = + [[1, 0, 0, v[0]], + [0, 1, 0, v[1]], + [0, 0, 1, v[2]]]; + +// Prepare a matrix to scale by vector v. +function Scale(v) = + [[v[0], 0, 0, 0], + [ 0, v[1], 0, 0], + [ 0, 0, v[2], 0]]; + diff --git a/demo_3D_art.scad b/demo_3D_art.scad new file mode 100644 index 0000000..263ae32 --- /dev/null +++ b/demo_3D_art.scad @@ -0,0 +1,57 @@ +// Created in 2018 by Ryan A. Colyer. +// This work is released with CC0 into the public domain. +// https://creativecommons.org/publicdomain/zero/1.0/ + +use + +layer_step = 0.2; + +pedestal_top = 60; +pedestal_ripple = 1; +pedestal_ripple_rad = 4; +pedestal_base_rad = 20; +pedestal_base_thickness = 10; +pedestal_connect_rad = 1.5; + +art_top = 30; +art_radial_ripple = 1; +art_height_ripple = 0.2; +art_ztilt_freq = 3; +art_ztilt_fact = 1; +art_radtilt_freq = 1; +art_radtilt_fact = 1; + +function OneLayer(rad, ztilt, h_off) = + [ + for (a=[0:360]) + [ rad*cos(a), + rad*sin(a), + art_radtilt_fact*rad*sin(art_radtilt_freq*a) + + art_ztilt_fact*ztilt*(cos(art_ztilt_freq*a)+1) + h_off + ] + ]; + +artpointarrays = + [for (h=[0:layer_step:art_top]) + OneLayer( + h*abs(sin(art_radial_ripple*360/art_top)+1.1) + pedestal_connect_rad, + h, + pedestal_top+pedestal_connect_rad + ) + ]; + + +function Pedestal(h) = + let( + r = pedestal_base_rad*exp(-h*h/pedestal_base_thickness) + + pedestal_ripple_rad*pow(sin(h*pedestal_ripple*180/pedestal_top),2) + + pedestal_connect_rad + ) + [ for (a=[0:360]) + [ r*cos(a), r*sin(a), h ] + ]; + +basepointarrays = [for (h=[0:layer_step:pedestal_top]) Pedestal(h)]; + +ClosePoints(concat(basepointarrays, artpointarrays)); + diff --git a/demo_gear_thing.scad b/demo_gear_thing.scad new file mode 100644 index 0000000..5346333 --- /dev/null +++ b/demo_gear_thing.scad @@ -0,0 +1,28 @@ +// Created in 2021 by Ryan A. Colyer. +// This work is released with CC0 into the public domain. +// https://creativecommons.org/publicdomain/zero/1.0/ + + +use + + +function GearRotXY(t) = RotZ(360*t); +function GearRotXZ(t) = RotY(8*360*t); +function Ellipse(t) = Translate([50*cos(360*t), 40*sin(360*t), 0]); + +function PathMatrix(t) = AffMerge([Ellipse(t), GearRotXY(t), GearRotXZ(t)]); + +function ThePolygon(t) = + [for (a=[0:2:359.99]) + ((a < 6 || (a >= 180 && a < 186)) ? 7 : 5)*[cos(a), 0, -sin(a)] + ]; + +pointarrays = + [for (t=[0:0.002:0.99999]) + [for (p=ThePolygon(t)) + Affine(PathMatrix(t), p) + ] + ]; + +CloseLoop(pointarrays); + diff --git a/demo_roller_coaster.scad b/demo_roller_coaster.scad new file mode 100644 index 0000000..433a03d --- /dev/null +++ b/demo_roller_coaster.scad @@ -0,0 +1,30 @@ +// Created in 2021 by Ryan A. Colyer. +// This work is released with CC0 into the public domain. +// https://creativecommons.org/publicdomain/zero/1.0/ + +use + + +function RotZt(t) = RotZ(360*t); + +function hillf(t) = sin(-2*t*360-115)+sin(-3*t*360-57)+2; +function Hills(t) = Translate([0, 0, 20*hillf(t)]); + +function RotXZ(t) = let(a = -45*(4 - hillf(t))/4) RotY(a); + +function ShiftX(t) = Translate([60, 0, 0]); + +function PathMatrix(t) = AffMerge([RotZt(t), Hills(t), ShiftX(t), RotXZ(t)]); + +function ThePolygon(t) = + [[-5,0,0], [-5,0,3], [-3,0,3], [-3,0,1], [3,0,1], [3,0,3], [5,0,3], [5,0,0]]; + +pointarrays = + [for (t=[0:0.002:0.99999]) + [for (p=ThePolygon(t)) + Affine(PathMatrix(t), p) + ] + ]; + +CloseLoop(pointarrays); + diff --git a/demo_roller_coaster2.scad b/demo_roller_coaster2.scad new file mode 100644 index 0000000..4c4f14f --- /dev/null +++ b/demo_roller_coaster2.scad @@ -0,0 +1,91 @@ +// Created in 2021 by Ryan A. Colyer. +// This work is released with CC0 into the public domain. +// https://creativecommons.org/publicdomain/zero/1.0/ + +use + + +function RotZt(t) = RotZ(360*t); + +function hillf(t) = sin(-2*t*360-115)+sin(-3*t*360-57)+2; +function Hills(t) = Translate([0, 0, 20*hillf(t)]); + +function RotXZ(t) = let(a = -45*(4 - hillf(t))/4) RotY(a); + +function ShiftX(t) = Translate([60, 0, 0]); + +function PathMatrix(t) = AffMerge([RotZt(t), Hills(t), ShiftX(t), RotXZ(t)]); + +function ThePolygon(t) = + [[-5,0,0], [-5,0,3], [-3,0,3], [-3,0,1], [3,0,1], [3,0,3], [5,0,3], [5,0,0]]; + +pointarrays = + [for (t=[0:0.002:0.99999]) + [for (p=ThePolygon(t)) + Affine(PathMatrix(t), p) + ] + ]; + +CloseLoop(pointarrays); + +$fa = 4; $fs = 0.4; + +module wheel() { + color("DimGray") + rotate_extrude() + translate([15, 0]) + offset(2) + square([3, 12], center = true); + color("Silver") + for (a = [0:20:179]) + rotate([90, 0, a]) + scale([0.2, 1, 1]) + cylinder(r = 4, h = 30, center = true); +} + +module train() { + color("Black") linear_extrude(10, center = true) offset(5) square([40, 200], center = true); + for (x = [-80, -40, 40, 80]) translate([30, x, 0]) rotate([90, 0, 90]) wheel(); + for (x = [-80, -40, 40, 80]) translate([-30, x, 0]) rotate([90, 0, 90]) wheel(); + translate([0, 0, 22]) { + color("Red") { + hull() { + scale([1, 0.3, 1]) sphere(20); + translate([0, -100, 0]) scale([1, 0.3, 1]) sphere(20); + } + translate([0, -50, 0]) cylinder(r = 6, h = 25); + translate([0, -50, 25]) sphere(6); + translate([0, -80, 0]) cylinder(r = 6, h = 40); + translate([0, -80, 50]) difference() { + sphere(r = 13); + translate([0, 0, 25]) cube(50, center = true); + } + difference() { + translate([0, 40, 30]) cube([42, 70, 100], center = true); + translate([0, 40, 50]) cube([44, 40, 40], center = true); + translate([0, 55, 25]) cube([36, 90, 100], center = true); + } + translate([0, 50, 80]) linear_extrude(8, scale = 1.1) square([42, 90], center = true); + } + color("Black") for(x = [-92, -62, -32, -2]) + translate([0, x, 0]) rotate([90, 0, 0]) cylinder(r = 20.2, h = 5); + } +} + +ztilt = atan2(20*(hillf($t+0.002)-hillf($t-0.002)), 60*0.004*6.28); +multmatrix(AffMerge([RotZt($t), Hills($t), ShiftX($t)])) + translate([0,0,3]) + rotate([ztilt, 0, 0]) + multmatrix(RotXZ($t)) + scale(0.06) mirror([0,1,0]) translate([0,0,18]) train(); + +// Train written in 2019 by Torsten Paul +// +// To the extent possible under law, the author(s) have dedicated all +// copyright and related and neighboring rights to this software to the +// public domain worldwide. This software is distributed without any +// warranty. +// +// You should have received a copy of the CC0 Public Domain +// Dedication along with this software. +// If not, see . diff --git a/demo_wavy_donut.scad b/demo_wavy_donut.scad new file mode 100644 index 0000000..472fbf2 --- /dev/null +++ b/demo_wavy_donut.scad @@ -0,0 +1,31 @@ +// Created in 2021 by Ryan A. Colyer. +// This work is released with CC0 into the public domain. +// https://creativecommons.org/publicdomain/zero/1.0/ + +use + + +// [Scale X] [Shear X along Y] [Shear X along Z] [Translate X] +// [Shear Y along X] [Scale Y] [Shear Y along Z] [Translate Y] +// [Shear Z along X] [Shear Z along Y] [Scale Z] [Translate Z] +// or rotation matrix [[cos,-sin],[sin,cos]] in the 2 axes for a plane. +function PathMatrix(t) = + [[cos(t*360), -sin(t*360), 0, 50*cos(t*360)], + [sin(t*360), cos(t*360), 0, 40*sin(t*360)], + [ 0, 0, 1, 0]]; + +function ThePolygon(t) = + [for (a=[0:2:359.99]) + (5+5*(1+cos(8*t*360))/2)*[cos(a), 0, -sin(a)] + ]; + + +pointarrays = + [for (t=[0:0.002:0.99999]) + [for (p=ThePolygon(t)) + Affine(PathMatrix(t), p) + ] + ]; + +CloseLoop(pointarrays); + diff --git a/images/demo_images.gif b/images/demo_images.gif new file mode 100644 index 0000000..16f5897 Binary files /dev/null and b/images/demo_images.gif differ