Trefoil knot -- Example of a 3D curve

// Author: Tiago Charters de Azevedo
// Maintainer: Tiago Charters de Azevedo
// URL: http://diale.org/openscad.html
// Version: 1

// Copyright (c) - 2014 Tiago Charters de Azevedo

// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 3, or (at your option)
// any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 51 Franklin Street, Fifth Floor,
// Boston, MA 02110-1301, USA.

// Commentary:

// Usage:  see below.

// Returns the i-the  N linearly spaced elements between XMIN and XMAX.
// The endpoints are always included in the range.
function linspace(xmin,xmax,n,i)=xmin+i*(xmax-xmin)/n;

// Converts from rads to degs.
function deg(x)=180*x/3.141592653589793;

// Point coordinates.

// Examples: Trefoil knot
function coordinates(t) = 10*[(2+cos(3*deg(t)))*cos(2*deg(t)),
    (2+cos(3*deg(t)))*sin(2*deg(t)),
    -sin(3*deg(t))];
function varradius(t) = 5;


// Main module:
// tmin = inicial parameter value
// tmax = end parameter value
// n = number of segments (sphere used)


module curve(tmin=0,tmax=2*3.14,n=20){
    for (i=[0:n-1]){
        hull(){
            translate(coordinates(linspace(tmin,tmax,n,i))){
                sphere(r=varradius(linspace(tmin,tmax,n,i)));}
            translate(coordinates(linspace(tmin,tmax,n,i+1))){
                sphere(r=varradius(linspace(tmin,tmax,n,i+1)));}}}}



//--------------------------------------------------------------------------------

$fn = 10;
curve(n=100);

Created: NaN

Last updated: 16-02-2026 [16:02]

For attribution, please cite this page as:

Charters, T., "Trefoil knot -- Example of a 3D curve": https://nexp.pt/3knot.html (16-02-2026 [16:02])

(cc-by-sa) Tiago Charters - tiagocharters@nexp.pt