Circle passing by three given points in OpenSCAD

thingiverse

This OpenSCAD module calculates the circle passing through three specified points on the XY plane. For quicker access, the code contained in the file is listed below. --- point1 = [0, 0]; point2 = [10, 0]; point3 = [0, -10]; module circle3p(p1, p2, p3) { h = (-((p2.y - p1.y) * pow(p3.y, 2) + (-pow(p2.y, 2) + pow(p1.y, 2) - pow(p2.x, 2) + pow(p1.x, 2)) * p3.y + p1.y * pow(p2.y, 2) + (-pow(p1.y, 2) + pow(p3.x, 2) - pow(p1.x, 2)) * p2.y + (pow(p2.x, 2) - pow(p3.x, 2)) * p1.y)) / ((2 * p2.x - 2 * p1.x) * p3.y + (2 * p1.x - 2 * p3.x) * p2.y + (2 * p3.x - 2 * p2.x) * p1.y); k = ((p2.x - p1.x) * pow(p3.y, 2) + (p1.x - p3.x) * pow(p2.y, 2) + (p3.x - p2.x) * pow(p1.y, 2) + (p2.x - p1.x) * pow(p3.x, 2) + (pow(p1.x, 2) - pow(p2.x, 2)) * p3.x + p1.x * pow(p2.x, 2) - pow(p1.x, 2) * p2.x)) / ((2 * p2.x - 2 * p1.x) * p3.y + (2 * p1.x - 2 * p3.x) * p2.y + (2 * p3.x - 2 * p2.x) * p1.y); r = (sqrt(pow(p2.y, 2) - 2 * p1.y * p2.y + pow(p1.y, 2) + pow(p2.x, 2) - 2 * p1.x * p2.x + pow(p1.x, 2)) * sqrt(pow(p3.y, 2) - 2 * p1.y * p3.y + pow(p1.y, 2) + pow(p3.x, 2) - 2 * p1.x * p3.x + pow(p1.x, 2)) * sqrt(pow(p3.y, 2) - 2 * p2.y * p3.y + pow(p2.y, 2) + pow(p3.x, 2) - 2 * p2.x * p3.x + pow(p2.x, 2))) / abs((2 * p2.x - 2 * p1.x) * p3.y + (2 * p1.x - 2 * p3.x) * p2.y + (2 * p3.x - 2 * p2.x) * p1.y); translate([h, k]) circle(r); } circle3p(point1, point2, point3);