[从头学数学] 第104节 整理与复习--图形与几何

剧情提要：
[机器小伟]在[工程师阿伟]的陪同下继续炼化着筑基丹，
这次要炼化的目标是[整理与复习--图形与几何]。

正剧开始：

星历2016年02月23日 11:53:25, 银河系厄尔斯星球中华帝国江南行省。
[工程师阿伟]正在和[机器小伟]一起复习着[图形与几何]。

<span style="font-size:18px;">function myDraw() {     var config = new PlotConfiguration();        config.init();        config.setPreference();   config.setSector(1,1,1,1);config.axis3D(0, 0, 0, 180);var array = [];for (var z = 0; z < 2; z++) {for (var y = 0; y < 3; y++) {for (var x = 0; x < 2; x++) {if (z == 0 && y == 2) {}else {array.push([x, y, z]);}}}}shape.threeView(array);plot.fillText('共有'+array.length.toFixed(0)+'个', 50, 100, 100);    }/*** @usage   把三维点阵列按照z, y, x优先级由小到大排列* @author  mw* @date    2016年02月23日  星期二  09:38:27 * @param   [[x1, y1, z1], [x2,y2, z2], ...]* @return  排序后的[[x, y, z]...]**/this.xyzSort = function(array) {var arr = new Array();arr = array;arr.sort(function(a, b) {if (a[2] != b[2]) {return a[2] - b[2];}else {if (a[1] != b[1]) {return (a[1] - b[1]);}else {return a[0] - b[0];}}});//document.write(arr);return arr;}/*** @usage   三视图* @author  mw* @date    2016年02月23日  星期二  09:49:23 * @param* @return**/this.threeView = function(array) {var cubic = this.xyzSort(array);plot.save();plot.setTransform(1, 0, 0, 1, 0, 0) .translate(300, 200);    //三维图和三视图          var r = 50;          var style = 'red';      var len = cubic.length;              for (var i = 0; i < len; i++) {               this.drawCubic(cubic[i][0], cubic[i][1], cubic[i][2], r, style);          }                    var height = 400;          r = r/3;                    plot.setTransform(1, 0, 0, 1, 0, 0);          plot.fillText('左视图', 20, 20, 100);          plot.fillText('主视图', 20, 20+1*height/3, 100);          plot.fillText('俯视图', 20, 20+2*height/3, 100);                    plot.setFillStyle(style)              .setStrokeStyle('white');                              //左视图          plot.translate(100, 80);          for (var i = 0; i < len; i++) {              //y, z两坐标，z坐标变为x坐标              this.fillRect(cubic[i][2]*r, -cubic[i][1]*r, r, r);              this.strokeRect(cubic[i][2]*r, -cubic[i][1]*r, r, r);          }                    //主视图          plot.translate(0, 130);          for (var i = 0; i < len; i++) {              //x, y两坐标              this.fillRect(cubic[i][0]*r, -cubic[i][1]*r, r, r);              this.strokeRect(cubic[i][0]*r, -cubic[i][1]*r, r, r);          }                    //俯视图          plot.translate(0, 100);         for (var i = 0; i < len; i++) {              //x, z两坐标，z坐标变为y坐标              this.fillRect(cubic[i][0]*r, cubic[i][2]*r, r, r);              this.strokeRect(cubic[i][0]*r, cubic[i][2]*r, r, r);          }  plot.restore();}</span>

<span style="font-size:18px;">#15Scubic = lambda a : a*a;Vcubic = lambda a : a*a*a;Scylinder = lambda d, h : 3.1416/4*d*d*2+3.1416*d*h;Vcylinder = lambda d, h : 3.1416/4*d*d*h;>>> Scubic = lambda a : a*a*6;>>> Vcubic = lambda a : a*a*a;>>> Scylinder = lambda d, h : 3.1416/4*d*d*2+3.1416*d*h;>>> Vcylinder = lambda d, h : 3.1416/4*d*d*h;>>> S = Scubic(20)*5/6+Scylinder(20, 20)/2;>>> S2942.48>>> V = Vcubic(20)+Vcylinder(20, 20)/2;>>> V11141.6</span>

<span style="font-size:18px;">//16题function myDraw() {     var config = new PlotConfiguration();        config.init();        config.setPreference();   config.setSector(1,1,1,1);config.axis3D(0, 0, 0, 180);var array = [];for (var z = 0; z < 3; z++) {for (var y = 0; y < 1; y++) {for (var x = 0; x < 3; x++) {if (z == 0 && x == 2) {}else {array.push([x, y, z]);}}}}array.push([0, 1, 0]);array.push([0, 1, 1]);shape.threeView(array, 'green');plot.fillText('共有'+array.length.toFixed(0)+'个', 50, 100, 100);    }</span>

<span style="font-size:18px;">[0, 0, 0]有3面涂色。[1, 0, 0]有4面涂色。[0, 0, 1]有2面涂色。[1, 0, 1]有2面涂色。[2, 0, 1]有4面涂色。[0, 0, 2]有4面涂色。[1, 0, 2]有3面涂色。[2, 0, 2]有4面涂色。[0, 1, 0]有4面涂色。[0, 1, 1]有4面涂色。总计两面涂色的有2个， 三面涂色的有2个，四面涂色的有6个。#16 正方体着色统计def tmp():    a = [];    for z in range(3):        for y in range(1):            for x in range(3):                if z == 0 and x == 2:                    pass;                else:                    a.append([x, y, z]);    a.append([0, 1, 0]);    a.append([0, 1, 1]);    #print(a);    size = len(a);    b = [6]*size;    #print(b);        for i in range(size):        for j in range(i, size):            xdiff = abs(a[i][0] - a[j][0]);            ydiff = abs(a[i][1] - a[j][1]);            zdiff = abs(a[i][2] - a[j][2]);            #对于相邻的立方体只有一个坐标相差1，其余都相同。            if (xdiff + ydiff + zdiff == 1):                b[i]-=1;                b[j]-=1;    #统计n面涂色的数量。    b2 = 0;    b3 = 0;    b4 = 0;        for i in range(size):        if (b[i] == 2):            b2+=1;        elif (b[i] == 3):            b3+=1;        elif (b[i] == 4):            b4+=1;        print('{0}有{1}面涂色。'.format(a[i], b[i]));    print('总计两面涂色的有{0}个， 三面涂色的有{1}个，四面涂色的有{2}个。'.format(\        b2, b3, b4));</span>

<span style="font-size:18px;">//19题function myDraw() {     var config = new PlotConfiguration();        config.init();        config.setPreference();   config.setSector(1,1,1,1);config.axis3D(0, 0, 0, 180);var array = [];for (var z = 0; z < 2; z++) {for (var y = 0; y < 3; y++) {for (var x = 0; x < 2; x++) {if (x == 1 && y == 2) {}else if (x == 1 && y == 1 && z == 1) {}else {array.push([x, y, z]);}}}}shape.threeView(array, 'green');plot.fillText('共有'+array.length.toFixed(0)+'个', 50, 100, 100);    }</span>

<span style="font-size:18px;">//题3(1)function myDraw() {     var config = new PlotConfiguration();        config.init();        config.setPreference();   config.setSector(1,1,1,1);config.axis2D(0, 0, 180);var r1 = 100, r2 = r1/2;var a = [[1,1], [1,-1], [-1,-1], [-1,1]];plot.setStrokeStyle('red');for (var i = 0; i < 4; i++) {shape.strokeCircle(a[i][0]*r2*0.707, a[i][1]*r2*0.707, r2);}shape.strokeCircle(0, 0, r1);    }</span>

<span style="font-size:18px;">//题3(2)function myDraw() {     var config = new PlotConfiguration();        config.init();        config.setPreference();   config.setSector(1,1,1,1);config.axis2D(0, 0, 180);var r1 = 100;plot.setStrokeStyle('red');shape.strokeCircle(0, 0, r1);shape.strokeDraw(shape.nEdge(0, 0, r1, 6), 'red');shape.strokeDraw(shape.nEdge(0, 0, r1, 3, -Math.PI/2), 'red');var x1, y1, x2, y2, thita = 0;for (var i = 0; i < 3; i++) {x1 = r1*Math.cos(thita-Math.PI), y1 = r1*Math.sin(thita-Math.PI);x2 = r1*Math.cos(thita), y2 = r1*Math.sin(thita);plot.beginPath().moveTo(x1, y1).lineTo(x2, y2).closePath().stroke();thita += Math.PI*2/3;}    }</span>

<span style="font-size:18px;">//题3(3)function myDraw() {     var config = new PlotConfiguration();        config.init();        config.setPreference();   config.setSector(1,1,1,1);config.axis2D(0, 0, 180);var r1 = 100, r2 = r1/2;plot.setStrokeStyle('red');shape.strokeCircle(0, 0, r1);var sAngle = Math.PI/2, eAngle = sAngle-Math.PI;plot.beginPath().arc(0, r2, r2, sAngle, eAngle, 1).moveTo(0,0).closePath().stroke();sAngle = -Math.PI/2, eAngle = sAngle+Math.PI;plot.beginPath().arc(0, -r2, r2, sAngle, eAngle, 1).moveTo(0,0).closePath().stroke();}</span>

<span style="font-size:18px;">>>> import math;>>> dis = lambda x1, y1, x2, y2 : math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));>>> dis(5,0,8,9)*50474.3416490252569>>> angle = lambda x1, y1, x2, y2 : math.atan((y1-y2)/(x1-x2))*180/3.1416;>>> 90-angle(5,0,8,9)18.435116172750895>>> dis(5,0,10,3);5.830951894845301>>> _*50291.54759474226506>>> angle(5,0,10,3);30.963684125510934>>> 90-_59.03631587448906</span>

本节到此结束，欲知后事如何，请看下回分解。