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 //--------------------------------------------------------------- //-- Openscad vector library //-- This is a component of the obiscad opescad tools by Obijuan //-- (C) Juan Gonzalez-Gomez (Obijuan) //-- Sep-2012 //--------------------------------------------------------------- //-- Released under the GPL license //--------------------------------------------------------------- obiscad_drawing_resolution = 6; //---------------------------------------- //-- FUNCTIONS FOR WORKING WITH VECTORS //---------------------------------------- //-- Calculate the module of a vector function mod(v) = (sqrt(v[0]*v[0]+v[1]*v[1]+v[2]*v[2])); //-- Calculate the cros product of two vectors function cross(u,v) = [ u[1]*v[2] - v[1]*u[2], -(u[0]*v[2] - v[0]*u[2]) , u[0]*v[1] - v[0]*u[1]]; //-- Calculate the dot product of two vectors function dot(u,v) = u[0]*v[0]+u[1]*v[1]+u[2]*v[2]; //-- Return the unit vector of a vector function unitv(v) = v/mod(v); //-- Return the angle between two vectores function anglev(u,v) = acos( dot(u,v) / (mod(u)*mod(v)) ); //-- Return an arbitrary unitary vector othogonal to v function orthounit2(v) = (v.x == 0 && v.y == 0 && v.z ==0 ) ? undef : (v.x == 0 && v.y == 0) ? [1,0,0] : let (r=norm([v.x, v.y, 0])) [v.y/r, -v.x/r, 0]; //-- Return an arbitrary vector othogonal to v function ortho2(v) = (v.x == 0 && v.y == 0 && v.z== 0) ? undef : (v.x == 0 && v.y == 0) ? [1,0,0] : (v.y == 0) ? [1,0,0] : [1, -v.x/v.y, 0]; //---------------------------------------------------------- //-- Draw a point in the position given by the vector p //---------------------------------------------------------- module point(p) { translate(p) sphere(r=0.7,\$fn=obiscad_drawing_resolution); } //------------------------------------------------------------------ //-- Draw a vector poiting to the z axis //-- This is an auxiliary module for implementing the vector module //-- //-- Parameters: //-- l: total vector length (line + arrow) //-- l_arrow: Vector arrow length //-- mark: If true, a mark is draw in the vector head, for having //-- a visual reference of the rolling angle //------------------------------------------------------------------ module vectorz(l=10, l_arrow=4, mark=false) { //-- vector body length (not including the arrow) lb = l - l_arrow; //-- The vector is locatead at 0,0,0 translate([0,0,lb/2]) union() { //-- Draw the arrow translate([0,0,lb/2]) cylinder(r1=2/2, r2=0.2, h=l_arrow, \$fn=obiscad_drawing_resolution); //-- Draw the mark if (mark) { translate([0,0,lb/2+l_arrow/2]) translate([1,0,0]) cube([2,0.3,l_arrow*0.8],center=true); } //-- Draw the body cylinder(r=1/2, h=lb, center=true, \$fn=obiscad_drawing_resolution); } //-- Draw a sphere in the vector base sphere(r=1/2, \$fn=obiscad_drawing_resolution); } //----------------------------------------------------------------- //-- ORIENTATE OPERATOR //-- //-- Orientate an object to the direction given by the vector v //-- Parameters: //-- v : Target orientation //-- vref: Vector reference. It is the vector of the local frame //-- of the object that want to be poiting in the direction //-- of v //-- roll: Rotation of the object around the v axis //------------------------------------------------------------------- module orientate(v,vref=[0,0,1], roll=0) { //-- Calculate the rotation axis cref = cross(vref, v); raxis = mod(cref) == 0 ? [1,0,0] : cref; //-- Calculate the angle between the vectors ang = anglev(vref,v); //-- Rotate the child! rotate(a=roll, v=v) rotate(a=ang, v=raxis) child(0); } //--------------------------------------------------------------------------- //-- Draw a vector //-- //-- There are two modes of drawing the vector //-- * Mode 1: Given by a cartesian point(x,y,z). A vector from the origin //-- to the end (x,y,z) is drawn. The l parameter (length) must //-- be 0 (l=0) //-- * Mode 2: Give by direction and length //-- A vector of length l pointing to the direction given by //-- v is drawn //--------------------------------------------------------------------------- //-- Parameters: //-- v: Vector cartesian coordinates //-- l: total vector length (line + arrow) //-- l_arrow: Vector arrow length // mark: If true, a mark is draw in the vector head, for having //-- a visual reference of the rolling angle //--------------------------------------------------------------------------- module vector(v,l=0, l_arrow=4, mark=false) { //-- Get the vector length from the coordinates mod = mod(v); //-- The vector is very easy implemented by means of the orientate //-- operator: //-- orientate(v) vectorz(l=mod, l_arrow=l_arrow) //-- BUT... in OPENSCAD 2012.02.22 the recursion does not //-- not work, so that if the user use the orientate operator //-- on a vector, openscad will ignore it.. //-- The solution at the moment (I hope the openscad developers //-- implement the recursion in the near future...) //-- is to repite the orientate operation in this module //---- SAME CALCULATIONS THAN THE ORIENTATE OPERATOR! //-- Calculate the rotation axis vref = [0,0,1]; cref = cross(vref, v); raxis = mod(cref) == 0 ? [1,0,0] : cref; //-- Calculate the angle between the vectors ang = anglev(vref,v); //-- orientate the vector //-- Draw the vector. The vector length is given either //--- by the mod variable (when l=0) or by l (when l!=0) if (l==0) rotate(a=ang, v=raxis) vectorz(l=mod, l_arrow=l_arrow, mark=mark); else rotate(a=ang, v=raxis) vectorz(l=l, l_arrow=l_arrow, mark=mark); } //---------------------------------------------------- //-- Draw a Frame of reference //-- Parameters: //-- l: length of the Unit vectors //----------------------------------------------------- module frame(l=10, l_arrow=4) { //-- Z unit vector color("Blue") vector([0,0,l], l_arrow=l_arrow); //-- X unit vector color("Red") vector([l,0,0], l_arrow=l_arrow ); //-- Y unit vector color("Green") vector([0,l,0],l_arrow=l_arrow); //-- Origin color("Gray") sphere(r=1, \$fn=obiscad_drawing_resolution); } //-------------------------------------------------- //-- Modules for testings and examples //-- Testing that the vector library is working ok //-------------------------------------------------- //-- 22 vectors in total are drawn, poiting to different directions module Test_vectors1() { a = 20; k = 1; //-- Add a frame of reference (in the origin) frame(l=a); //-- Negative vectors, pointing towards the three axis: -x, -y, -z color("Red") vector([-a, 0, 0]); color("Green") vector([0, -a, 0]); color("Blue") vector([0, 0, -a]); //-- It is *not* has been implemented using a for loop on purpose //-- This way, individual vectors can be commented out or highlighted //-- vectors with positive z vector([a, a, a*k]); vector([0, a, a*k]); vector([-a, a, a*k]); vector([-a, 0, a*k]); vector([-a, -a, a*k]); vector([0, -a, a*k]); vector([a, -a, a*k]); vector([a, 0, a*k]); //-- Vectors with negative z vector([a, a, -a*k]); vector([0, a, -a*k]); vector([-a, a, -a*k]); vector([-a, 0, -a*k]); vector([-a, -a, -a*k]); vector([0, -a, -a*k]); vector([a, -a, -a*k]); vector([a, 0, -a*k]); } //--- Another test... module Test_vectors2() { //-- Add the vector into the vector table //-- This vectors are taken as directions //-- All the vectors will be drawn with the same length (l) vector_table = [ [1, 1, 1], [0, 1, 1], [-1, 1, 1], [-1, 0, 1], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [1, 0, 1], [0, 0, -1], // degenerate case [1, 1, -1], [0, 1, -1], [-1, 1, -1], [-1, 0, -1], [-1, -1, -1], [0, -1, -1], [1, -1, -1], [1, 0, -1], ]; //-- Vector length l=20; frame(l=10); //-- Draw all the vector given in the table //-- The vectors point to the direction given in the table //-- They all are drawn with a length equal to l for (v=vector_table) { //-- Vector given by direction and length vector(v,l=l); } } //-- Test the cross product and the angle //-- between vectors module Test_vector3() { //-- Start with 2 unit vectors v=unitv([1,1,1]); u=unitv([0,1,0]); //-- Draw the vector in different colors //-- Increase the length for drawing color("Red") vector(v*20); color("blue") vector(u*20); //-- Get the cross product w = cross(v,u); vector(w*20); //-- The cross product is NOT conmutative... //-- change the order of v and u w2 = cross(u,v); vector(w2*20); //-- w should be perpendicular to v and u //-- Calculate the angles between them: echo("U , V: ", anglev(u,v)); echo("W , U: ", anglev(w,u)); echo("W , V: ", anglev(w,v)); } //-- Test the orientate operator module Test_vector4() { o = [10,10,10]; v = [-10,10,10]; color("Red") vector(o); color("Blue") vector(v); //-- Orientate the vector o in the direction of v orientate(v,o) vector(o); //-- Inverse operation: orientate the v vector in the direction //-- of o orientate(o,v) vector(v); //-- Example of orientation of a cube orientate(o,vref=[10,-2,5],roll=0) cube([10,2,5],center=true); vector([10,-2,5]); } //-- Test the degenerate case ie. the vectors are (anti)collinear module Test_vector5() { o = [0,0,10]; v = [0,0,-10]; color("Red") vector(o); color("Blue") vector(v); //-- Orientate the vector o in the direction of v orientate(v,o) vector(o); //-- Inverse operation: orientate the v vector in the direction //-- of o orientate(o,v) vector(v); } //-------- Perform tests...... Test_vector4(); /* Test_vectors1(); translate([60,0,0]) Test_vectors2(); */
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