mirror of
https://github.com/DJSundog/NopSCADlib.git
synced 2024-11-27 09:10:02 -05:00
94 lines
4.0 KiB
OpenSCAD
94 lines
4.0 KiB
OpenSCAD
//
|
|
// NopSCADlib Copyright Chris Palmer 2018
|
|
// nop.head@gmail.com
|
|
// hydraraptor.blogspot.com
|
|
//
|
|
// This file is part of NopSCADlib.
|
|
//
|
|
// NopSCADlib 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 of
|
|
// the License, or (at your option) any later version.
|
|
//
|
|
// NopSCADlib 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 NopSCADlib.
|
|
// If not, see <https://www.gnu.org/licenses/>.
|
|
//
|
|
|
|
//
|
|
//! Draw a polygon with rounded corners. Each element of the vector is the XY coordinate and a radius. Radius can be negative for a concave corner.
|
|
//!
|
|
//! Because the tangents need to be calculated to find the length these can be calculated separately and re-used when drawing to save calculating them twice.
|
|
//
|
|
include <../utils/core/core.scad>
|
|
|
|
function circle_tangent(p1, p2) =
|
|
let(
|
|
r1 = p1[2],
|
|
r2 = p2[2],
|
|
dx = p2.x - p1.x,
|
|
dy = p2.y - p1.y,
|
|
d = sqrt(dx * dx + dy * dy),
|
|
theta = atan2(dy, dx) + acos((r1 - r2) / d),
|
|
xa = p1.x +(cos(theta) * r1),
|
|
ya = p1.y +(sin(theta) * r1),
|
|
xb = p2.x +(cos(theta) * r2),
|
|
yb = p2.y +(sin(theta) * r2)
|
|
)[ [xa, ya], [xb, yb] ];
|
|
|
|
function rounded_polygon_tangents(points) = //! Compute the straight sections needed to draw and to compute the lengths
|
|
let(len = len(points))
|
|
[for(i = [0 : len - 1])
|
|
let(ends = circle_tangent(points[i], points[(i + 1) % len]))
|
|
for(end = [0, 1])
|
|
ends[end]];
|
|
|
|
function sumv(v, i = 0, sum = 0) = i == len(v) ? sum : sumv(v, i + 1, sum + v[i]);
|
|
|
|
// the cross product of 2D vectors is the area of the parallelogram between them. We use the sign of this to decide if the angle is bigger than 180.
|
|
function rounded_polygon_length(points, tangents) = //! Calculate the length given the point list and the list of tangents computed by ` rounded_polygon_tangents`
|
|
let(
|
|
len = len(points),
|
|
indices = [0 : len - 1],
|
|
straights = [for(i = indices) norm(tangents[2 * i] - tangents[2 * i + 1])],
|
|
arcs = [for(i = indices) let(p1 = tangents[2 * i + 1],
|
|
p2 = tangents[(2 * i + 2) % (2 * len)],
|
|
corner = points[(i + 1) % len],
|
|
c = [corner.x, corner.y],
|
|
v1 = p1 - c,
|
|
v2 = p2 - c,
|
|
r = abs(corner.z),
|
|
a = acos((v1 * v2) / sqr(r))) r ? PI * (cross(v1, v2) <= 0 ? a : 360 - a) * r / 180 : 0]
|
|
)
|
|
sumv(concat(straights, arcs));
|
|
|
|
module rounded_polygon(points, _tangents = undef) { //! Draw the rounded polygon from the point list, can pass the tangent list to save it being calculated
|
|
len = len(points);
|
|
indices = [0 : len - 1];
|
|
tangents = _tangents ? _tangents : rounded_polygon_tangents(points);
|
|
|
|
difference(convexity = points) {
|
|
union() {
|
|
for(i = indices)
|
|
if(points[i][2] > 0)
|
|
hull() {
|
|
translate([points[i].x, points[i].y])
|
|
circle(points[i][2]);
|
|
polygon([tangents[(2 * i - 1 + 2 * len) % (2 * len)], tangents[2 * i], [points[i].x, points[i].y]]);
|
|
}
|
|
|
|
polygon(tangents, convexity = points);
|
|
}
|
|
for(i = indices)
|
|
if(points[i][2] < 0)
|
|
hull() {
|
|
translate([points[i].x, points[i].y])
|
|
circle(-points[i][2]);
|
|
|
|
polygon([tangents[(2 * i - 1 + 2 * len) % (2 *len)], tangents[2 * i], [points[i].x, points[i].y]]);
|
|
}
|
|
}
|
|
}
|