Elmo
commit
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327
3d_triangle.scad
Executable file
327
3d_triangle.scad
Executable file
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// Enhancement of OpenSCAD Primitives Solid with Trinagles
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// Copyright (C) 2011 Rene BAUMANN, Switzerland
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//
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// This library is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 2.1 of the License, or (at your option) any later version.
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//
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// This library 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 GNU
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// Lesser General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License along with this library; If not, see <http://www.gnu.org/licenses/>
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// or write to the Free Software Foundation, Inc.,
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// 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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// ================================================================
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//
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// File providing functions and modules to draw 3D - triangles
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// created in the X-Y plane with hight h, using various triangle
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// specification methods.
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// Standard traingle geometrical definition is used. Vertices are named A,B,C,
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// side a is opposite vertex A a.s.o. the angle at vertex A is named alpha,
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// B(beta), C(gamma).
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//
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// This SW is a contribution to the Free Software Community doing a marvelous
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// job of giving anyone access to knowledge and tools to educate himselfe.
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//
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// Author: Rene Baumann
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// Date: 11.09.2011
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// Edition: 0.3 11.09.2011 For review by Marius
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// Edition: 0.4 11.11.2011 Ref to GPL2.1 added
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//
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// --------------------------------------------------------------------------------------
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//
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// ===========================================
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//
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// FUNCTION: 3dtri_sides2coord
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// DESCRIPTION:
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// Enter triangle sides a,b,c and to get the A,B,C - corner
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// co-ordinates. The trinagle's c-side lies on the x-axis
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// and A-corner in the co-ordinates center [0,0,0]. Geometry rules
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// required that a + b is greater then c. The traingle's vertices are
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// computed such that it is located in the X-Y plane, side c is on the
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// positive x-axis.
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// PARAMETER:
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// a : real length of side a
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// b : real length of side b
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// c : real length of side c
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// RETURNS:
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// vertices : [Acord,Bcord,Ccord] Array of vertices coordinates
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//
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// COMMENT:
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// vertices = 3dtri_sides2coord (3,4,5);
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// vertices[0] : Acord vertex A cordinates the like [x,y,z]
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// -------------------------------------------------------------------------------------
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//
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function 3dtri_sides2coord (a,b,c) = [
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[0,0,0],
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[c,0,0],
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[(pow(c,2)+pow(a,2)-pow(b,2))/(2*c),sqrt ( pow(a,2) -
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pow((pow(c,2)+pow(a,2)-pow(b,2))/(2*c),2)),0]];
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//
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//
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// ===========================================
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//
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// FUNCTION: 3dtri_centerOfGravityCoord
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// DESCRIPTION:
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// Enter triangle A,B,C - corner coordinates to get the
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// triangles Center of Gravity coordinates. It is assumed
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// the triangle is parallel to the X-Y plane. The function
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// returns always zero for the z-coordinate
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// PARAMETER:
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// Acord : [x,y,z] Coordinates of vertex A
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// Bcord : [x,y,z] Coordinates of vertex B
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// Ccord : [x,y,z] Coordinates of vertex C
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// RETURNS:
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// CG : [x,y,0] Center of gravity coordinate in X-Y-plane
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//
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// COMMENT:
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// vertices = 3dtri_sides2coord (3,4,5);
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// cg = 3dtri_centerOfGravityCoord(vertices[0],vertices[1],vertices[2]);
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// -------------------------------------------------------------------------------------
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//
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function 3dtri_centerOfGravityCoord (Acord,Bcord,Ccord) = [
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(Acord[0]+Bcord[0]+Ccord[0])/3,(Acord[1]+Bcord[1]+Ccord[1])/3,0];
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//
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//
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// ===========================================
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//
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// FUNCTION: 3dtri_centerOfcircumcircle
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// DESCRIPTION:
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// Enter triangle A,B,C - corner coordinates to get the
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// circum circle coordinates. It is assumed
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// the triangle is parallel to the X-Y plane. The function
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// returns always zero for the z-coordinate
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// PARAMETER:
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// Acord : [x,y,z] Coordinates of vertex A
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// Bcord : [x,y,z] Coordinates of vertex B
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// Ccord : [x,y,z] Coordinates of vertex C
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// RETURNS:
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// cc : [x,y,0] Circumcircle center
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//
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// COMMENT:
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// vertices = 3dtri_sides2coord (3,4,5);
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// cc = 3dtri_centerOfcircumcircle (vertices[0],vertices[1],vertices[2]);
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// -------------------------------------------------------------------------------------
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//
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function 3dtri_centerOfcircumcircle (Acord,Bcord,Ccord) =
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[0.5*Bcord[0],
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0.5*((pow(Ccord[1],2)+pow(Ccord[0],2)-Bcord[0]*Ccord[0])/Ccord[1]),
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0];
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//
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//
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//
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// ===========================================
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//
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// FUNCTION: 3dtri_radiusOfcircumcircle
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// DESCRIPTION:
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// Provides the triangle's radius from circumcircle to the vertices.
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// It is assumed the triangle is parallel to the X-Y plane. The function
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// returns always zero for the z-coordinate
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// PARAMETER:
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// Vcord : [x,y,z] Coordinates of a vertex A or B,C
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// CCcord : [x,y,z] Coordinates of circumcircle
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// r : Radius at vertices if round corner triangle used,
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// else enter "0"
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// RETURNS:
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// cr : Circumcircle radius
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//
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// COMMENT: Calculate circumcircle radius of trinagle with round vertices having
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// radius R = 2
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// vertices = 3dtri_sides2coord (3,4,5);
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// cc = 3dtri_centerOfcircumcircle (vertices[0],vertices[1],vertices[2]);
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// cr = 3dtri_radiusOfcircumcircle (vertices[0],cc,2);
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// -------------------------------------------------------------------------------------
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//
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function 3dtri_radiusOfcircumcircle (Vcord,CCcord,R) =
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sqrt(pow(CCcord[0]-Vcord[0],2)+pow(CCcord[1]-Vcord[1],2))+ R;
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//
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//
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//
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// ===========================================
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//
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// FUNCTION: 3dtri_radiusOfIn_circle
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// DESCRIPTION:
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// Enter triangle A,B,C - corner coordinates to get the
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// in-circle radius. It is assumed the triangle is parallel to the
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// X-Y plane. The function always returns zero for the z-coordinate.
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// Formula used for inner circle radius: r = 2A /(a+b+c)
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// PARAMETER:
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// Acord : [x,y,z] Coordinates of vertex A
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// Bcord : [x,y,z] Coordinates of vertex B
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// Ccord : [x,y,z] Coordinates of vertex C
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//
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// RETURNS:
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// ir : real radius of in-circle
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//
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// COMMENT:
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// vertices = 3dtri_sides2coord (3,4,5);
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// ir = 3dtri_radiusOfIn_circle (vertices[0],vertices[1],vertices[2]);
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// -------------------------------------------------------------------------------------
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//
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function 3dtri_radiusOfIn_circle (Acord,Bcord,Ccord) =
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Bcord[0]*Ccord[1]/(Bcord[0]+sqrt(pow(Ccord[0]-Bcord[0],2)+pow(Ccord[1],2))+
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sqrt(pow(Ccord[0],2)+pow(Ccord[1],2)));
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//
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//
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//
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// ===========================================
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//
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// FUNCTION: 3dtri_centerOfIn_circle
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// DESCRIPTION:
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// Enter triangle A,B,C - corner coordinates to get the
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// in-circle coordinates. It is assumed
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// the triangle is parallel to the X-Y plane. The function
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// returns always zero for the z-coordinate
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// PARAMETER:
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// Acord : [x,y,z] Coordinates of vertex A
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// Bcord : [x,y,z] Coordinates of vertex B
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// Ccord : [x,y,z] Coordinates of vertex C
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// r : real radius of in-circle
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// RETURNS:
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// ic : [x,y,0] In-circle center co-ordinates
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//
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// COMMENT:
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// vertices = 3dtri_sides2coord (3,4,5);
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// ir = 3dtri_radiusOfIn_circle (vertices[0],vertices[1],vertices[2]);
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// ic = 3dtri_centerOfIn_circle (vertices[0],vertices[1],vertices[2],ir);
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// -------------------------------------------------------------------------------------
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//
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function 3dtri_centerOfIn_circle (Acord,Bcord,Ccord,r) =
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[(Bcord[0]+sqrt(pow(Ccord[0]-Bcord[0],2)+pow(Ccord[1],2))+
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sqrt(pow(Ccord[0],2)+pow(Ccord[1],2)))/2-sqrt(pow(Ccord[0]-Bcord[0],2)+pow(Ccord[1],2)),r,0];
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//
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//
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// ============================================
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//
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// MODULE: 3dtri_draw
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// DESCRIPTION:
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// Draw a standard solid triangle with A,B,C - vertices specified by its
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// co-ordinates and height "h", as given by the input parameters.
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// PARAMETER:
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// Acord : [x,y,z] Coordinates of vertex A
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// Bcord : [x,y,z] Coordinates of vertex B
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// Ccord : [x,y,z] Coordinates of vertex C
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// h : real Hight of the triangle
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// RETURNS:
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// none
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//
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// COMMENT:
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// You might use the result from function 3dtri_sides2coord
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// to call module 3dtri_draw ( vertices[0],vertices[1],vertices[2], h)
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// -------------------------------------------------------------------------------------
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//
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module 3dtri_draw ( Acord, Bcord, Ccord, h) {
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polyhedron (points=[Acord,Bcord,Ccord,
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Acord+[0,0,h],Bcord+[0,0,h],Ccord+[0,0,h]],
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triangles=[ [0,1,2],[0,2,3],[3,2,5],
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[3,5,4],[1,5,2],[4,5,1],
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[4,1,0],[0,3,4]]);
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};
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//
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//
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// ==============================================
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//
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// MODULE: 3dtri_rnd_draw
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// DESCRIPTION:
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// Draw a round corner triangle with A,B,C - vertices specified by its
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// co-ordinates, height h and round vertices having radius "r".
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// As specified by the input parameters.
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// Please note, the tringles side lenght gets extended by "2 * r",
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// and the vertices coordinates define the centers of the
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// circles with radius "r".
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// PARAMETER:
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// Acord : [x,y,z] Coordinates of vertex A
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// Bcord : [x,y,z] Coordinates of vertex B
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// Ccord : [x,y,z] Coordinates of vertex C
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// h : real Hight of the triangle
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// r : real Radius from vertices coordinates
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// RETURNS:
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// none
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//
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// COMMENT:
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// You might use the result from function 3dtri_sides2coord
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// to call module 3dtri_rnd_draw ( vertices[0],vertices[1],vertices[2], h, r)
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// -------------------------------------------------------------------------------------
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//
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module 3dtri_rnd_draw ( Acord, Bcord, Ccord, h, r) {
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Avect=Ccord-Bcord; // vector pointing from vertex B to vertex C
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p0=Acord + [0,-r,0];
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p1=Bcord + [0,-r,0];
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p2=Bcord + [r*Avect[1]/sqrt(pow(Avect[0],2)+pow(Avect[1],2)),
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-r*Avect[0]/sqrt(pow(Avect[0],2)+pow(Avect[1],2)) ,0];
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p3=Ccord + [r*Avect[1]/sqrt(pow(Avect[0],2)+pow(Avect[1],2)),
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-r*Avect[0]/sqrt(pow(Avect[0],2)+pow(Avect[1],2)) ,0];
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p4=Ccord +[- r*Ccord[1]/sqrt(pow(Ccord[0],2)+pow(Ccord[1],2)),
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r*Ccord[0]/sqrt(pow(Ccord[0],2)+pow(Ccord[1],2)) ,0];
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p5=Acord + [- r*Ccord[1]/sqrt(pow(Ccord[0],2)+pow(Ccord[1],2)),
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r*Ccord[0]/sqrt(pow(Ccord[0],2)+pow(Ccord[1],2)) ,0];
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bottom_triangles = [[0,1,2],[0,2,3],[0,3,4],[0,4,5]];
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c_side_triangles = [[7,1,0],[0,6,7]];
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a_side_triangles = [[2,8,3],[8,9,3]];
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b_side_triangles = [[4,10,5],[10,11,5]];
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A_edge_triangles = [[0,5,11],[0,11,6]];
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B_edge_triangles = [[1,7,2],[2,7,8]];
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C_edge_triangles = [[3,9,4],[9,10,4]];
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top_triangles = [[11,7,6],[11,8,7],[11,10,8],[8,10,9]];
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union () {
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polyhedron (points=[p0,p1,p2,p3,p4,p5,
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p0+[0,0,h],p1+[0,0,h],p2+[0,0,h],p3+[0,0,h],p4+[0,0,h],p5+[0,0,h]],
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triangles=[ bottom_triangles[0],bottom_triangles[1],bottom_triangles[2],bottom_triangles[3],
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A_edge_triangles[0],A_edge_triangles[1],
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c_side_triangles[0],c_side_triangles[1],
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B_edge_triangles[0],B_edge_triangles[1],
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a_side_triangles[0],a_side_triangles[1],
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C_edge_triangles[0],C_edge_triangles[1],
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b_side_triangles[0],b_side_triangles[1],
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top_triangles[0],top_triangles[1],top_triangles[2],top_triangles[3]]);
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translate(Acord) cylinder(r1=r,r2=r,h=h,center=false);
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translate(Bcord) cylinder(r1=r,r2=r,h=h,center=false);
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translate(Ccord) cylinder(r1=r,r2=r,h=h,center=false);
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};
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}
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//
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// ==============================================
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//
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// Demo Application - copy into new file and uncomment or uncomment here but
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// without uncommenting the use <...> statement, then press F6 - Key
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//
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// use <../libraries/mcad/3d_triangle.scad>;
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//$fn=50;
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// h =4;
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// r=2;
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// echo ("Draws a right angle triangle with its circumcircle and in-circle");
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// echo ("The calculated co-ordinates and radius are show in this console window");
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// echo ("Geometry rules for a right angle triangle say, that the circumcircle is the");
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// echo ("Thales Circle which center must be in the middle of the triangle's c - side");
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// echo ("===========================================");
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// vertices = 3dtri_sides2coord (30,40,50);
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// echo("A = ",vertices[0]," B = ",vertices[1]," C = ",vertices[2]);
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// cg = 3dtri_centerOfGravityCoord (vertices[0],vertices[1],vertices[2]);
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// echo (" Center of gravity = ",cg);
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// cc = 3dtri_centerOfcircumcircle (vertices[0],vertices[1],vertices[2]);
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// echo (" Center of circumcircle = ",cc);
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// cr = 3dtri_radiusOfcircumcircle (vertices[0],cc,r);
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// echo(" Radius of circumcircle ",cr);
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// ir = 3dtri_radiusOfIn_circle (vertices[0],vertices[1],vertices[2]);
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// echo (" Radius of in-circle = ",ir);
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// ic = 3dtri_centerOfIn_circle (vertices[0],vertices[1],vertices[2],ir);
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// echo (" Center of in-circle = ",ic);
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// translate(cc+[0,0,5*h/2]) difference () {
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// cylinder (h=5*h,r1=cr+4,r2=cr+4,center=true);
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// cylinder (h=6*h,r1=cr,r2=cr,center=true);}
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// 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);
|
||||||
|
// }
|
||||||
|
|
||||||
|
|
@ -51,6 +51,7 @@ Other tools (alpha and beta quality):
|
||||||
* servos.scad: servo outlines
|
* servos.scad: servo outlines
|
||||||
* boxes.scad: box with rounded corners
|
* boxes.scad: box with rounded corners
|
||||||
* triangles.scad: simple triangles
|
* triangles.scad: simple triangles
|
||||||
|
* 3d_triangle.scad: more advanced triangles
|
||||||
|
|
||||||
Very generally useful functions and constants:
|
Very generally useful functions and constants:
|
||||||
|
|
||||||
|
|
|
||||||
Loading…
Reference in a new issue