196 lines
7.6 KiB
OpenSCAD
196 lines
7.6 KiB
OpenSCAD
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// path_extrude.scad -- Extrude a path in 3D space
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// usage: add "use <path_extrude.scad>;" to the top of your OpenSCAD source code
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// Copyright (C) 2014-2019 David Eccles (gringer) <bioinformatics@gringene.org>
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// This program is free software: you can redistribute it and/or modify
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// it under the terms of the GNU General Public License as published by
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// the Free Software Foundation, either version 3 of the License, or
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// (at your option) any later version.
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// This program is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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// You should have received a copy of the GNU General Public License
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// along with this program. If not, see <https://www.gnu.org/licenses/>.
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// Determine the projection of a point on a plane centered at c1 with normal n1
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function project(p, c, n) =
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p - (n * (p - c)) * n / (n * n);
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// determine angle between two points with a given normal orientation
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// see https://stackoverflow.com/questions/14066933/
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// direct-way-of-computing-clockwise-angle-between-2-vectors
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// dot = p1 * p2;
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// det = (p1[0]*p2[1]*n1[2] + p2[0]*n1[1]*p1[2] + n1[0]*p1[1]*p2[2]) -
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// (n1[0]*p2[1]*p1[2] + p1[0]*n1[1]*p2[2] + p2[0]*p1[1]*n1[2]);
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// atan2(det, dot);
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// determine angle between two planar points and a centre
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// with a given normal orientation
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function getPlanarAngle(p1, p2, c1, n1) =
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let(p1 = p1-c1, n1=n1 / norm(n1), p2=p2-c1)
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atan2((p1[0]*p2[1]*n1[2] + p2[0]*n1[1]*p1[2] + n1[0]*p1[1]*p2[2]) -
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(n1[0]*p2[1]*p1[2] + p1[0]*n1[1]*p2[2] + p2[0]*p1[1]*n1[2]), p1 * p2);
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function c3D(tPoints) =
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(len(tPoints[0]) == undef) ? // single point
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c3D([tPoints])[0] :
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(len(tPoints[0]) < 3) ? // collection of 2D points
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tPoints * [[1,0,0],[0,1,0]] :
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tPoints; // 3D points
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// translate a point (or points)
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function myTranslate(ofs, points, acc = []) =
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(len(points[0]) == undef) ?
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myTranslate(ofs, [points])[0] :
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[ for(i = [0:(len(points) - 1)])
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[ for(d = [0:(len(points[0])-1)]) (ofs[d] + points[i][d])]];
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// rotate a point (or points)
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function myRotate(rotVec, points) =
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let(rotX = [[1, 0, 0],
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[0, cos(rotVec[0]), -sin(rotVec[0])],
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[0, sin(rotVec[0]), cos(rotVec[0])]],
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rotY = [[ cos(rotVec[1]), 0,-sin(rotVec[1])],
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[ 0, 1, 0],
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[ sin(rotVec[1]), 0, cos(rotVec[1])]],
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rotZ = [[ cos(rotVec[2]), sin(rotVec[2]), 0],
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[ sin(rotVec[2]), -cos(rotVec[2]), 0],
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[0, 0, 1]])
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(len(points[0]) == undef) ?
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myRotate(rotVec, [points])[0] :
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c3D(points) * rotX * rotY * rotZ;
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// Determine spherical rotation for cartesian coordinates
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function rToS(pt) =
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[-acos((pt[2]) / norm(pt)),
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0,
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-atan2(pt[0],pt[1])];
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function calcPreRot(p1, p2, p3) =
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let(n1=p2-p1, // normal between the two points (i.e. the plane that the polygon sits on)
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n2=p3-p2,
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rt1=rToS(n1),
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rt2=rToS(n2),
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pj1=(p2 + myRotate(rt2, [[1e42,0,0]])[0]),
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pj2=project(p=(p1 + myRotate(rt1, [[1e42,0,0]])[0]), c=p2, n=n2))
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getPlanarAngle(p1=pj1, p2=pj2, c1=p2, n1=n2);
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function cumSum(x, res=[]) =
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(len(x) == len(res)) ? concat([0], res) :
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(len(res) == 0) ? cumSum(x=x, res=[x[0]]) :
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cumSum(x=x, res=concat(res, [x[len(res)] + res[len(res)-1]]));
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// Create extrusion side panels for one polygon segment as triangles.
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// Note: panels are not necessarily be planar due to path twists
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function makeSides(shs, pts, ofs=0) =
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concat(
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[for(i=[0:(shs-1)]) [i+ofs, ((i+1) % shs + ofs + shs) % (shs * pts),
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(i+1) % shs + ofs]],
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[for(i=[0:(shs-1)]) [((i+1) % shs + ofs + shs) % (shs * pts),
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i+ofs, (i + ofs + shs) % (shs * pts)]]);
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// Concatenate the contents of the outermost list
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function flatten(A, acc = [], aDone = 0) =
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(aDone >= len(A)) ? acc :
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flatten(A, acc=concat(acc, A[aDone]), aDone = aDone + 1);
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// Linearly interpolate between two shapes
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function makeTween(shape1, shape2, t) =
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(t == 0) ? shape1 :
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(t == 1) ? shape2 :
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[for (i=[0:(len(shape1)-1)])
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(shape1[i]*(1-t) + shape2[i % len(shape2)]*(t))];
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// Extrude a 2D shape through a 3D path
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// Note: merge has two effects:
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// 1) Removes end caps
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// 2) Adjusts the rotation of each path point
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// so that the end and start match up
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module path_extrude(exPath, exShape, exShape2=[],
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exRots = [0], exScale = [1], merge=false, preRotate=true){
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exShapeTween = (len(exShape2) == 0) ?
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exShape : exShape2;
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shs = len(exShape); // shs: shape size
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pts = len(exPath); // pts: path size
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exPathX = (merge) ? concat(exPath, [exPath[0], exPath[1]]) :
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concat(exPath,
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[exPath[pts-1] + (exPath[pts-1] - exPath[pts-2]),
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exPath[pts-1] + 2*(exPath[pts-1] - exPath[pts-2])]);
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exScaleX = (len(exScale) == len(exPath)) ? exScale :
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[for (i = [0:(pts-1)]) exScale[i % len(exScale)]];
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preRots = [for(i = [0:(pts-1)])
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preRotate ?
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calcPreRot(p1=exPathX[i], // "current" point on the path
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p2=exPathX[(i+1)], // "next" point on the path
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p3=exPathX[(i+2)]) :
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0 ];
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cumPreRots = cumSum(preRots);
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seDiff = cumPreRots[len(cumPreRots)-1]; // rotation difference (start - end)
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// rotation adjustment to get start to look like end
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seAdj = -seDiff / (len(cumPreRots));
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adjPreRots = (!merge) ? cumPreRots :
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[for(i = [0:(pts-1)]) (cumPreRots[i] + seAdj * i)];
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adjExRots = (len(exRots) == 1) ?
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[for(i = [0:(len(adjPreRots)-1)]) (adjPreRots[i] + exRots[0])] :
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[for(i = [0:(len(adjPreRots)-1)]) (adjPreRots[i] + exRots[i % len(exRots)])];
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phPoints = flatten([
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for(i = [0:(pts-1)])
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let(p1=exPathX[i],
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p2=exPathX[(i+1)],
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n1=p2-p1, // normal between the two points
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rt1=rToS(n1))
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myTranslate(p1, myRotate(rt1, myRotate([0,0,-adjExRots[i]],
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c3D(makeTween(exShape, exShapeTween, i / (pts-1)) *
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exScaleX[i]))))
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]);
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if(merge){ // just the surface, no end caps
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polyhedron(points=phPoints,
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faces=flatten([
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for(i = [0:(pts-1)])
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makeSides(shs, pts, ofs=shs*i)
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])
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);
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} else {
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polyhedron(points=phPoints,
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faces=concat(
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flatten([
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for(i = [0:(pts-2)])
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makeSides(shs, pts, ofs=shs*i)
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]),
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concat( // add in start / end covers
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[[for(i= [0:(shs-1)]) i]],
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[[for(i= [(len(phPoints)-1):-1:(len(phPoints)-shs)]) i]]
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)
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));
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}
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}
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myPathTrefoil = [ for(t = [0:(360 / 101):359]) [ // trefoil knot
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5*(.41*cos(t) - .18*sin(t) - .83*cos(2*t) - .83*sin(2*t) -
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.11*cos(3*t) + .27*sin(3*t)),
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5*(.36*cos(t) + .27*sin(t) - 1.13*cos(2*t) + .30*sin(2*t) +
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.11*cos(3*t) - .27*sin(3*t)),
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5*(.45*sin(t) - .30*cos(2*t) +1.13*sin(2*t) -
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.11*cos(3*t) + .27*sin(3*t))] ];
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myPointsOctagon =
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let(ofs1=15)
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[ for(t = [0:(360/8):359])
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((t==90)?1:2) * [cos(t+ofs1),sin(t+ofs1)]];
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myPointsChunkOctagon =
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let(ofs1=15)
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[ for(t = [0:(360/8):359])
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((t==90)?0.4:1.9) *
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[cos((t * 135/360 + 45)+ofs1+45)+0.5,sin((t * 135/360 + 45)+ofs1+45)]];
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//myPoints = [ for(t = [0:(360/8):359]) 2 * [cos(t+45),sin(t+45)]];
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pts=[2,0,0.5];
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/*translate([0,0,0]) {
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path_extrude(exRots = [$t*360], exShape=myPointsOctagon,
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exPath=myPathTrefoil, merge=true);
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}*/
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