// Enhancement of OpenSCAD Primitives Solid with Trinagles // Copyright (C) 2011 Rene BAUMANN, Switzerland // // This library is free software; you can redistribute it and/or // modify it under the terms of the GNU Lesser General Public // License as published by the Free Software Foundation; either // version 2.1 of the License, or (at your option) any later version. // // This library 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 // Lesser General Public License for more details. // // You should have received a copy of the GNU Lesser General Public // License along with this library; If not, see // or write to the Free Software Foundation, Inc., // 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA // ================================================================ // // File providing functions and modules to draw 3D - triangles // created in the X-Y plane with hight h, using various triangle // specification methods. // Standard traingle geometrical definition is used. Vertices are named A,B,C, // side a is opposite vertex A a.s.o. the angle at vertex A is named alpha, // B(beta), C(gamma). // // This SW is a contribution to the Free Software Community doing a marvelous // job of giving anyone access to knowledge and tools to educate himselfe. // // Author: Rene Baumann // Date: 11.09.2011 // Edition: 0.3 11.09.2011 For review by Marius // Edition: 0.4 11.11.2011 Ref to GPL2.1 added // // -------------------------------------------------------------------------------------- // // =========================================== // // FUNCTION: 3dtri_sides2coord // DESCRIPTION: // Enter triangle sides a,b,c and to get the A,B,C - corner // co-ordinates. The trinagle's c-side lies on the x-axis // and A-corner in the co-ordinates center [0,0,0]. Geometry rules // required that a + b is greater then c. The traingle's vertices are // computed such that it is located in the X-Y plane, side c is on the // positive x-axis. // PARAMETER: // a : real length of side a // b : real length of side b // c : real length of side c // RETURNS: // vertices : [Acord,Bcord,Ccord] Array of vertices coordinates // // COMMENT: // vertices = 3dtri_sides2coord (3,4,5); // vertices[0] : Acord vertex A cordinates the like [x,y,z] // ------------------------------------------------------------------------------------- // function 3dtri_sides2coord (a,b,c) = [ [0,0,0], [c,0,0], [(pow(c,2)+pow(a,2)-pow(b,2))/(2*c),sqrt ( pow(a,2) - pow((pow(c,2)+pow(a,2)-pow(b,2))/(2*c),2)),0]]; // // // =========================================== // // FUNCTION: 3dtri_centerOfGravityCoord // DESCRIPTION: // Enter triangle A,B,C - corner coordinates to get the // triangles Center of Gravity coordinates. It is assumed // the triangle is parallel to the X-Y plane. The function // returns always zero for the z-coordinate // PARAMETER: // Acord : [x,y,z] Coordinates of vertex A // Bcord : [x,y,z] Coordinates of vertex B // Ccord : [x,y,z] Coordinates of vertex C // RETURNS: // CG : [x,y,0] Center of gravity coordinate in X-Y-plane // // COMMENT: // vertices = 3dtri_sides2coord (3,4,5); // cg = 3dtri_centerOfGravityCoord(vertices[0],vertices[1],vertices[2]); // ------------------------------------------------------------------------------------- // function 3dtri_centerOfGravityCoord (Acord,Bcord,Ccord) = [ (Acord[0]+Bcord[0]+Ccord[0])/3,(Acord[1]+Bcord[1]+Ccord[1])/3,0]; // // // =========================================== // // FUNCTION: 3dtri_centerOfcircumcircle // DESCRIPTION: // Enter triangle A,B,C - corner coordinates to get the // circum circle coordinates. It is assumed // the triangle is parallel to the X-Y plane. The function // returns always zero for the z-coordinate // PARAMETER: // Acord : [x,y,z] Coordinates of vertex A // Bcord : [x,y,z] Coordinates of vertex B // Ccord : [x,y,z] Coordinates of vertex C // RETURNS: // cc : [x,y,0] Circumcircle center // // COMMENT: // vertices = 3dtri_sides2coord (3,4,5); // cc = 3dtri_centerOfcircumcircle (vertices[0],vertices[1],vertices[2]); // ------------------------------------------------------------------------------------- // function 3dtri_centerOfcircumcircle (Acord,Bcord,Ccord) = [0.5*Bcord[0], 0.5*((pow(Ccord[1],2)+pow(Ccord[0],2)-Bcord[0]*Ccord[0])/Ccord[1]), 0]; // // // // =========================================== // // FUNCTION: 3dtri_radiusOfcircumcircle // DESCRIPTION: // Provides the triangle's radius from circumcircle to the vertices. // It is assumed the triangle is parallel to the X-Y plane. The function // returns always zero for the z-coordinate // PARAMETER: // Vcord : [x,y,z] Coordinates of a vertex A or B,C // CCcord : [x,y,z] Coordinates of circumcircle // r : Radius at vertices if round corner triangle used, // else enter "0" // RETURNS: // cr : Circumcircle radius // // COMMENT: Calculate circumcircle radius of trinagle with round vertices having // radius R = 2 // vertices = 3dtri_sides2coord (3,4,5); // cc = 3dtri_centerOfcircumcircle (vertices[0],vertices[1],vertices[2]); // cr = 3dtri_radiusOfcircumcircle (vertices[0],cc,2); // ------------------------------------------------------------------------------------- // function 3dtri_radiusOfcircumcircle (Vcord,CCcord,R) = sqrt(pow(CCcord[0]-Vcord[0],2)+pow(CCcord[1]-Vcord[1],2))+ R; // // // // =========================================== // // FUNCTION: 3dtri_radiusOfIn_circle // DESCRIPTION: // Enter triangle A,B,C - corner coordinates to get the // in-circle radius. It is assumed the triangle is parallel to the // X-Y plane. The function always returns zero for the z-coordinate. // Formula used for inner circle radius: r = 2A /(a+b+c) // PARAMETER: // Acord : [x,y,z] Coordinates of vertex A // Bcord : [x,y,z] Coordinates of vertex B // Ccord : [x,y,z] Coordinates of vertex C // // RETURNS: // ir : real radius of in-circle // // COMMENT: // vertices = 3dtri_sides2coord (3,4,5); // ir = 3dtri_radiusOfIn_circle (vertices[0],vertices[1],vertices[2]); // ------------------------------------------------------------------------------------- // function 3dtri_radiusOfIn_circle (Acord,Bcord,Ccord) = Bcord[0]*Ccord[1]/(Bcord[0]+sqrt(pow(Ccord[0]-Bcord[0],2)+pow(Ccord[1],2))+ sqrt(pow(Ccord[0],2)+pow(Ccord[1],2))); // // // // =========================================== // // FUNCTION: 3dtri_centerOfIn_circle // DESCRIPTION: // Enter triangle A,B,C - corner coordinates to get the // in-circle coordinates. It is assumed // the triangle is parallel to the X-Y plane. The function // returns always zero for the z-coordinate // PARAMETER: // Acord : [x,y,z] Coordinates of vertex A // Bcord : [x,y,z] Coordinates of vertex B // Ccord : [x,y,z] Coordinates of vertex C // r : real radius of in-circle // RETURNS: // ic : [x,y,0] In-circle center co-ordinates // // COMMENT: // vertices = 3dtri_sides2coord (3,4,5); // ir = 3dtri_radiusOfIn_circle (vertices[0],vertices[1],vertices[2]); // ic = 3dtri_centerOfIn_circle (vertices[0],vertices[1],vertices[2],ir); // ------------------------------------------------------------------------------------- // function 3dtri_centerOfIn_circle (Acord,Bcord,Ccord,r) = [(Bcord[0]+sqrt(pow(Ccord[0]-Bcord[0],2)+pow(Ccord[1],2))+ sqrt(pow(Ccord[0],2)+pow(Ccord[1],2)))/2-sqrt(pow(Ccord[0]-Bcord[0],2)+pow(Ccord[1],2)),r,0]; // // // ============================================ // // MODULE: 3dtri_draw // DESCRIPTION: // Draw a standard solid triangle with A,B,C - vertices specified by its // co-ordinates and height "h", as given by the input parameters. // PARAMETER: // Acord : [x,y,z] Coordinates of vertex A // Bcord : [x,y,z] Coordinates of vertex B // Ccord : [x,y,z] Coordinates of vertex C // h : real Hight of the triangle // RETURNS: // none // // COMMENT: // You might use the result from function 3dtri_sides2coord // to call module 3dtri_draw ( vertices[0],vertices[1],vertices[2], h) // ------------------------------------------------------------------------------------- // module 3dtri_draw ( Acord, Bcord, Ccord, h) { polyhedron (points=[Acord,Bcord,Ccord, Acord+[0,0,h],Bcord+[0,0,h],Ccord+[0,0,h]], triangles=[ [0,1,2],[0,2,3],[3,2,5], [3,5,4],[1,5,2],[4,5,1], [4,1,0],[0,3,4]]); }; // // // ============================================== // // MODULE: 3dtri_rnd_draw // DESCRIPTION: // Draw a round corner triangle with A,B,C - vertices specified by its // co-ordinates, height h and round vertices having radius "r". // As specified by the input parameters. // Please note, the tringles side lenght gets extended by "2 * r", // and the vertices coordinates define the centers of the // circles with radius "r". // PARAMETER: // Acord : [x,y,z] Coordinates of vertex A // Bcord : [x,y,z] Coordinates of vertex B // Ccord : [x,y,z] Coordinates of vertex C // h : real Hight of the triangle // r : real Radius from vertices coordinates // RETURNS: // none // // COMMENT: // You might use the result from function 3dtri_sides2coord // to call module 3dtri_rnd_draw ( vertices[0],vertices[1],vertices[2], h, r) // ------------------------------------------------------------------------------------- // module 3dtri_rnd_draw ( Acord, Bcord, Ccord, h, r) { Avect=Ccord-Bcord; // vector pointing from vertex B to vertex C p0=Acord + [0,-r,0]; p1=Bcord + [0,-r,0]; p2=Bcord + [r*Avect[1]/sqrt(pow(Avect[0],2)+pow(Avect[1],2)), -r*Avect[0]/sqrt(pow(Avect[0],2)+pow(Avect[1],2)) ,0]; p3=Ccord + [r*Avect[1]/sqrt(pow(Avect[0],2)+pow(Avect[1],2)), -r*Avect[0]/sqrt(pow(Avect[0],2)+pow(Avect[1],2)) ,0]; p4=Ccord +[- r*Ccord[1]/sqrt(pow(Ccord[0],2)+pow(Ccord[1],2)), r*Ccord[0]/sqrt(pow(Ccord[0],2)+pow(Ccord[1],2)) ,0]; p5=Acord + [- r*Ccord[1]/sqrt(pow(Ccord[0],2)+pow(Ccord[1],2)), r*Ccord[0]/sqrt(pow(Ccord[0],2)+pow(Ccord[1],2)) ,0]; bottom_triangles = [[0,1,2],[0,2,3],[0,3,4],[0,4,5]]; c_side_triangles = [[7,1,0],[0,6,7]]; a_side_triangles = [[2,8,3],[8,9,3]]; b_side_triangles = [[4,10,5],[10,11,5]]; A_edge_triangles = [[0,5,11],[0,11,6]]; B_edge_triangles = [[1,7,2],[2,7,8]]; C_edge_triangles = [[3,9,4],[9,10,4]]; top_triangles = [[11,7,6],[11,8,7],[11,10,8],[8,10,9]]; union () { polyhedron (points=[p0,p1,p2,p3,p4,p5, p0+[0,0,h],p1+[0,0,h],p2+[0,0,h],p3+[0,0,h],p4+[0,0,h],p5+[0,0,h]], triangles=[ bottom_triangles[0],bottom_triangles[1],bottom_triangles[2],bottom_triangles[3], A_edge_triangles[0],A_edge_triangles[1], c_side_triangles[0],c_side_triangles[1], B_edge_triangles[0],B_edge_triangles[1], a_side_triangles[0],a_side_triangles[1], C_edge_triangles[0],C_edge_triangles[1], b_side_triangles[0],b_side_triangles[1], top_triangles[0],top_triangles[1],top_triangles[2],top_triangles[3]]); translate(Acord) cylinder(r1=r,r2=r,h=h,center=false); translate(Bcord) cylinder(r1=r,r2=r,h=h,center=false); translate(Ccord) cylinder(r1=r,r2=r,h=h,center=false); }; } // // ============================================== // // Demo Application - copy into new file and uncomment or uncomment here but // without uncommenting the use <...> statement, then press F6 - Key // // use <../libraries/mcad/3d_triangle.scad>; //$fn=50; // h =4; // r=2; // echo ("Draws a right angle triangle with its circumcircle and in-circle"); // echo ("The calculated co-ordinates and radius are show in this console window"); // echo ("Geometry rules for a right angle triangle say, that the circumcircle is the"); // echo ("Thales Circle which center must be in the middle of the triangle's c - side"); // echo ("==========================================="); // vertices = 3dtri_sides2coord (30,40,50); // echo("A = ",vertices[0]," B = ",vertices[1]," C = ",vertices[2]); // cg = 3dtri_centerOfGravityCoord (vertices[0],vertices[1],vertices[2]); // echo (" Center of gravity = ",cg); // cc = 3dtri_centerOfcircumcircle (vertices[0],vertices[1],vertices[2]); // echo (" Center of circumcircle = ",cc); // cr = 3dtri_radiusOfcircumcircle (vertices[0],cc,r); // echo(" Radius of circumcircle ",cr); // ir = 3dtri_radiusOfIn_circle (vertices[0],vertices[1],vertices[2]); // echo (" Radius of in-circle = ",ir); // ic = 3dtri_centerOfIn_circle (vertices[0],vertices[1],vertices[2],ir); // echo (" Center of in-circle = ",ic); // translate(cc+[0,0,5*h/2]) difference () { // cylinder (h=5*h,r1=cr+4,r2=cr+4,center=true); // cylinder (h=6*h,r1=cr,r2=cr,center=true);} // difference () { // union () { // difference () { // 3dtri_rnd_draw (vertices[0], vertices[1], vertices[2],5*h,r); // scale([0.8,0.8,1]) translate([6,2,4*h]) 3dtri_rnd_draw (vertices[0], vertices[1], vertices[2],5*h,r); // } // translate (ic+[0,0,5*h]) cylinder(h=10*h,r1=ir+r,r2=ir+r,center=true); // } // translate (ic+[0,0,5*h]) cylinder(h=12*h,r1=0.5*ir,r2=0.5*ir,center=true); // }