[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;">#15
Scubic = 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;
>>> S
2942.48
>>> V = Vcubic(20)+Vcylinder(20, 20)/2;
>>> V
11141.6</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)*50
474.3416490252569

>>> 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
>>> _*50
291.54759474226506
>>> 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。