// 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 ;
//$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);
// }