[Learn maths from the beginning] the 191th section space vector and cubic geometry

plot summary:
[Machine Xiao Wei] in the [engineer Ah Wei] accompanied by the [nine turn elixir] of the five-turn of the cultivation.
This time we are going to look at [space vector and cubic geometry].

Drama Start:

Star Calendar April 23, 2016 11:00:22, the Milky Way Galaxy Earles the Chinese Empire Jiangnan Line province.
[Engineer Ah Wei] is working with [machine Xiao Wei] to study [space vector and solid geometry].

<span style= "FONT-SIZE:18PX;" > #例5def dot (A, b):    if (Len (a) >= 3):        return a[0]*b[0] +a[1]*b[1]+a[2]*b[2];    Elif (Len (a) >= 2):        return a[0]*b[0] +a[1]*b[1];    else:        return a*b; #向量的绝对值def RAbs (a):    if (Len (a) >= 3):        return math.sqrt (a[0]**2 +a[1]**2 + a[2]**2);    Elif (Len (a) >= 2):        return math.sqrt (a[0]**2 +a[1]**2);    else:        return a;def angle (A, B):    return Math.acos (dot (b)/(RAbs (a) *rabs (b))) *180/math.pi;    def tmp ():    a = [0,-0.25,1];    b = [0, 0.25, 1];    Print (angle (a, b));</span>

<span style= "FONT-SIZE:18PX;" > #例6 >>> 90.0def tmp ():    a = [ -0.5, -0.5, 0.5];    b = [1, 0, 1];    Print (angle (a, b));</span>

<span style= "FONT-SIZE:18PX;"                  >//plane Vector if (1) {var r = 20;                    Config.setsector (1,1,1,1);                  Config.graphpaper2d (0, 0, R);                                  Config.axis2d (0, 0,190);                Axis set var ScaleX = 2*r, ScaleY = 2*r;                 var SpaceX = 2, SpaceY = 2;                var XS = -10, XE = 10;                var YS = -10, YE = 10;                  Config.axisspacing (XS, XE, SpaceX, ScaleX, ' X ');                                             Config.axisspacing (YS, YE, SpaceY, ScaleY, ' Y ');              var array = [[1, 2], [4, 5], [7,2], [-8,-5], [-5, 3], [-8, 3], [8, 5], [-2, + 5], [2, 1], [7, 3];                          var size = Array.Length;            var transform = new transform ();                        var tmp = [];                          Array = Transform.scale (transform.translate (array, 0, 0), Scalex/spacex, Scaley/spacey);          TMP = [].concat (array); Vectordraw (TMP, ' red ');                  TMP = [].concat (array);                   Shape.pointdraw (tmp, ' Orange ', 1, 1);          Plot.setfillstyle (' Blue ');              Plot.filltext (' Vector graph ',-270,-170, 300); }</span>

<span style= "FONT-SIZE:18PX;"                  >if (1) {var r = 20;                    Config.setsector (1,1,1,1);                  Config.graphpaper2d (0, 0, R);                                  Config.axis2d (0, 0,190);                Axis set var ScaleX = 4*r, ScaleY = 4*r;                 var SpaceX = 2, SpaceY = 2;                var XS = -10, XE = 10;                var YS = -10, YE = 10;                  Config.axisspacing (XS, XE, SpaceX, ScaleX, ' X ');                                             Config.axisspacing (YS, YE, SpaceY, ScaleY, ' Y '); var array = [];for (var x = 2; x <= 2; x+=4) {for (var y =-2, y <= 2; y+=4) {for (var z =-2; z<=2; z+=4) {Arra    Y.push ([x, Y, z]);}}}        Array = shape.xyzsort (array);  var size = Array.Length;                        var array2d = [];for (var i = 0; i < size; i++) {Array2d.push (Shape.point3d (array[i][0], array[i][1], array[i][2]));}            var transform = new transform ();                    var tmp = [];    Array2D = Transform.scale (transform.translate (array2d, 0, 0), Scalex/spacex, Scaley/spacey);          TMP = [].concat (array2d);                    Vectordraw (TMP, ' red ');                  TMP = [].concat (array2d);                   Shape.pointdraw (tmp, ' Orange ', 1, 1);          Plot.setfillstyle (' Blue ');              Plot.filltext (' Vector graph ',-270,-170, 300); }</span>

<span style= "FONT-SIZE:18PX;" >//the distance of any two points in the lattice sequence set function Distancesort (Pointarray) {///incoming lattice column pointarray//format is [[Px1, Py1], [Px2, Py2], ...] document.write (Pointarray.join (', ') + ' <br/> ');//For each point in the Pointarray, the distance from all other points//results are put into distancearray//format for [[  Point 1 ordinal, point 2 ordinal, distance value]]var Distancearray = [number of];//points var size = pointarray.length;//Temp variable var distance = x1 = Y1 = Z1 = x2 = y2 = z2 = 0;var Dimension = pointarray[0].length;//calculated and pressed into the distance for (var i = 0; i < size; i++) {for (var j = i+1; j < size; J + +)  {x1 = pointarray[i][0];y1 = pointarray[i][1];x2 = Pointarray[j][0];y2 = Pointarray[j][1];if (Dimension > 2) {//three-dimensional point processing z1 = POINTARRAY[I][2];Z2 = pointarray[j][2];d istance = math.sqrt (Math.pow (x1-x2, 2) +math.pow (Y1-y2, 2) +Math.pow (Z1-Z2, 2) );} else {distance = Math.sqrt (Math.pow (x1-x2, 2) +math.pow (Y1-y2, 2));} Note that I < j//are guaranteed so that the starting point sequence number must be less than the end sequence number//This is to connect the start and end points of the line does not repeat Distancearray.push ([I, J, distance]);}} Sort//Sort weights for distance array: Starting point ordinal > Distance > End ordinal distancearray.sort (function (A, b) {if (a[0] = b[0]) {if (MAth.abs (A[2]-b[2]) < 0.000001) {return a[1]-b[1];} else {return a[2]-b[2];}} else {return a[0]-b[0];}}); /document.write (Distancearray.join (', ') + ' <br/> '); return distancearray;}                  if (1) {var r = 20;                    Config.setsector (1,1,1,1);                  Config.graphpaper2d (0, 0, R);                                  Config.axis2d (0, 0,190);                Axis set var ScaleX = 4*r, ScaleY = 4*r;                 var SpaceX = 2, SpaceY = 2;                var XS = -10, XE = 10;                var YS = -10, YE = 10;                  Config.axisspacing (XS, XE, SpaceX, ScaleX, ' X ');                                             Config.axisspacing (YS, YE, SpaceY, ScaleY, ' Y '); var array = [];for (var x = 2; x <= 2; x+=4) {for (var y =-2, y <= 2; y+=4) {for (var z =-2; z<=2; z+=4) {Arra    Y.push ([x, Y, z]);}}}        Array = shape.xyzsort (array);  var size = Array.Length; var array2d = [];for (var i = 0; i < size; i++) {Array2d.push (sHape.point3d (Array[i][0], array[i][1], array[i][2]));}          Remove duplicate point var Pointarray = Removeduplicatedpoint (array2d);                    Number of non-repeating points var points = pointarray.length;          Get the distance array//format as [[Point 1 ordinal, point 2 ordinal, distance value], ...]          var Distancearray = Distancesort (Pointarray);                    The number of sides var edges = distancearray.length;          Store the side var linkedarray = [] that need to be connected;                    Number of connected edges var links = 0;                    The set of edges associated with each vertex var edgeofvertex = []; for (var i = 0; i < points; i++) {//Gets a collection of vertex-related edges Edgeofvertex = [              ];                      for (var j = 0; J < edges; J + +) {if (distancearray[j][0] = = I | |                  DISTANCEARRAY[J][1] = = i) {Edgeofvertex.push (distancearray[j]); }}//Based on the starting point, look for the shortest length of two sides edgeofvertex.sort (fuNction (A, b) {return a[2]-b[2];                            });              var choice = 2;              if (Edgeofvertex.length > Choice) {edgeofvertex = Edgeofvertex.slice (0, choice);          } Linkedarray = Linkedarray.concat (Edgeofvertex);          }//document.write (Linkedarray.join (', ') + ' <br/> ');          Linkedarray = Removeduplicatedpoint (Linkedarray);                    Links = linkedarray.length;                        document.write (Linkedarray.join (', ') + ' <br/> ');          var startPoint, EndPoint, x1, y1, x2, y2;                    Scaled var scale = 40;              for (var i = 0; i < links; i++) {startPoint = linkedarray[i][0];              EndPoint = linkedarray[i][1];              x1 = pointarray[startpoint][0];              y1 = pointarray[startpoint][1];              x2 = pointarray[endpoint][0]; y2 = Pointarray[enDPOINT][1];          Shape.vectordraw ([[X1,y1], [X2, Y2]], ' red ', scale);        } shape.pointdraw (Pointarray, ' blue ', scale, 1);        /*//array2d = Shape.angularsort (array2d);            var transform = new transform ();                        var tmp = [];                          Array2D = Transform.scale (transform.translate (array2d, 0, 0), Scalex/spacex, Scaley/spacey);          TMP = [].concat (array2d);                    Vectordraw (TMP, ' red ');                  TMP = [].concat (array2d);       Shape.pointdraw (tmp, ' Orange ', 1, 1);          */Plot.setfillstyle (' Blue ');              Plot.filltext (' Vector graph ',-270,-170, 300); }</span>

<span style= "FONT-SIZE:18PX;" >array = [[0,0,0],  [0, 0, 5], [5,0,5], [0, 5, 0], [0, 5, 5]];</span>

<span style= "FONT-SIZE:18PX;" >array = [[0,0,0],  [0, 0, 5], [5,0,0], [0, 5, 0]];</span>

<span style= "FONT-SIZE:18PX;" >array = [[0,0,0],  [0, 0, 5], [5,0,0], [0, 5, 0], [2, 2, 2], [2, 0, 2]];</span>

<span style= "FONT-SIZE:18PX;" >array = [[0,0,0],  [0, 0, 5], [5,0,0], [0, 5, 0], [2, 2, 2], [2, 0, 2], [ -7,3, -7]];</span>

The end of this section, to know how to funeral, please see tell.

[Learn maths from the beginning] the 191th section space vector and cubic geometry