randRangeUnique(2,8,3)
DIMENSIONS[0]
DIMENSIONS[1]
DIMENSIONS[2]
max(max(LENGTH, WIDTH), HEIGHT)
LENGTH/MAX
WIDTH/MAX
HEIGHT/MAX
"#D7ED3A"
"#38C77F"
"#78D0EF"
"#F0B63A"
HEIGHT * 2
[[LENGTH/MAX,WIDTH/MAX,HEIGHT/MAX],[LENGTH/MAX,WIDTH/MAX,-HEIGHT/MAX],[LENGTH/MAX,-WIDTH/MAX,-HEIGHT/MAX],[LENGTH/MAX,-WIDTH/MAX,HEIGHT/MAX],[-LENGTH/MAX,WIDTH/MAX,HEIGHT/MAX],[-LENGTH/MAX,WIDTH/MAX,-HEIGHT/MAX],[-LENGTH/MAX,-WIDTH/MAX,-HEIGHT/MAX],[-LENGTH/MAX,-WIDTH/MAX,HEIGHT/MAX]]
4.0
[{verts:[3,2,1,0],color:COLOR1,labels:[[[XBORD,0,ZBORD],WIDTH+UNIT_TEXT]]},{verts:[4,5,6,7],color:COLOR1,labels:[[[-XBORD,0,-ZBORD],WIDTH+UNIT_TEXT]]},{verts:[0,1,5,4],color:COLOR3,labels:[[[-XBORD,YBORD,0],HEIGHT+UNIT_TEXT]]},{verts:[2,3,7,6],color:COLOR3,labels:[[[-XBORD,-YBORD,0],HEIGHT+UNIT_TEXT]]},{verts:[1,2,6,5],color:COLOR2,labels:[[[0,-YBORD,-ZBORD],LENGTH+UNIT_TEXT]]},{verts:[3,0,4,7],color:COLOR2,labels:[[[0,YBORD,ZBORD],LENGTH+UNIT_TEXT]]}]
[{verts:[8,9,10,11],color:"#A9A9A9"},{verts:[12,13,14,15],color:"#A9A9A9"}]
{}
{}
$._("base")
$._("altura")
¿Cuál es el volumen de la caja? Arrastra el cursor en la figura para girarla.
init({range:[[-2,2],[-2,2]],scale:[100,100]}),addMouseLayer();for(var i=1;HEIGHT>i;i++)VERTICES.push([LENGTH/MAX,WIDTH/MAX,(-HEIGHT+2*i)/MAX]),VERTICES.push([-LENGTH/MAX,WIDTH/MAX,(-HEIGHT+2*i)/MAX]),VERTICES.push([-LENGTH/MAX,-WIDTH/MAX,(-HEIGHT+2*i)/MAX]),VERTICES.push([LENGTH/MAX,-WIDTH/MAX,(-HEIGHT+2*i)/MAX]);for(var i=1;LENGTH>i;i++)VERTICES.push([(-LENGTH+2*i)/MAX,-WIDTH/MAX,-HEIGHT/MAX]);for(var i=1;LENGTH>i;i++)VERTICES.push([(-LENGTH+2*i)/MAX,WIDTH/MAX,-HEIGHT/MAX]);for(var i=1;WIDTH>i;i++)VERTICES.push([-LENGTH/MAX,(-WIDTH+2*i)/MAX,-HEIGHT/MAX]);for(var i=1;WIDTH>i;i++)VERTICES.push([LENGTH/MAX,(-WIDTH+2*i)/MAX,-HEIGHT/MAX]);for(var i=1;LENGTH>i;i++)VERTICES.push([(-LENGTH+2*i)/MAX,-WIDTH/MAX,(-HEIGHT+2)/MAX]);for(var i=1;LENGTH>i;i++)VERTICES.push([(-LENGTH+2*i)/MAX,WIDTH/MAX,(-HEIGHT+2)/MAX]);for(var i=1;WIDTH>i;i++)VERTICES.push([-LENGTH/MAX,(-WIDTH+2*i)/MAX,(-HEIGHT+2)/MAX]);for(var i=1;WIDTH>i;i++)VERTICES.push([LENGTH/MAX,(-WIDTH+2*i)/MAX,(-HEIGHT+2)/MAX]);graph.obj=make3dObject(VERTICES,{scale:SCALE}),_.each(FACES,function(e){graph.obj.addFace(e)}),graph.obj.setPos([0,0,5]),graph.obj.rotate(1,0,0,PI/3),graph.obj.rotate(0,1,0,0),graph.obj.rotate(0,0,1,PI/8),graph.obj.doDraw(),GRAPH=graph;var spinner;setTimeout(function(){spinner=setInterval(function(){GRAPH.obj.rotate(0,0,1,.01),GRAPH.obj.doDraw()},50)},300);var mouseTarget=mouselayer.rect(0,0,400,400).attr({fill:"#000",opacity:0});$(mouseTarget[0]).bind("vmousedown",function(e){e.preventDefault(),GRAPH.lastX=e.pageX,GRAPH.lastY=e.pageY,clearInterval(spinner),$(document).bind("vmousemove vmouseup",function(e){e.preventDefault();var r=(e.pageX-GRAPH.lastX)/200*PI,a=(e.pageY-GRAPH.lastY)/200*PI;GRAPH.lastX=e.pageX,GRAPH.lastY=e.pageY;var n=normalize(GRAPH.obj.perspective[1]),t=normalize(GRAPH.obj.perspective[0]);GRAPH.obj.rotate(n[0],n[1],n[2],-r/2),GRAPH.obj.rotate(t[0],t[1],t[2],-a/2),GRAPH.obj.doDraw(),"vmouseup"===e.type&&$(document).unbind("vmousemove vmouseup")})})
LENGTH*WIDTH*HEIGHT UNIT_TEXT^3
El volumen de una figura se mide por el número de cubos de un UNIT que conforman la figura.
Para hacer más fácil la cuenta de cubos, rompe la caja en HEIGHT bloques, que cada uno tiene WIDTH UNIT_TEXT de ancho, LENGTH UNIT_TEXT de largo y 1 UNIT_TEXT de alto.
for(var i=0;HEIGHT-1>i;i++)graph.obj.addSketch({verts:[8+4*i,9+4*i,10+4*i,11+4*i,8+4*i]});graph.obj.doDraw()
Cada bloque tiene WIDTH filas que contienen LENGTH cubos, por lo que hay WIDTH \times LENGTH = WIDTH*LENGTH cubos en cada bloque.
for(var start=8+4*(HEIGHT-1)-1,i=1;LENGTH>i;i++)graph.obj.addSketch({verts:[start+i,start+LENGTH+i-1],opacityValue:.5});start+=2*(LENGTH-1);for(var i=1;WIDTH>i;i++)graph.obj.addSketch({verts:[start+i,start+WIDTH+i-1],opacityValue:.5});start+=2*(WIDTH-1);for(var i=1;LENGTH>i;i++)graph.obj.addSketch({verts:[start+i,start+LENGTH+i-1]});start+=2*(LENGTH-1);for(var i=1;WIDTH>i;i++)graph.obj.addSketch({verts:[start+i,start+WIDTH+i-1]});start=8+4*(HEIGHT-1)-1;for(var i=1;2*LENGTH+2*WIDTH-3>i;i++)graph.obj.addSketch({verts:[start+i,start+2*LENGTH-2+2*WIDTH-2+i],opacityValue:.5});graph.obj.addSketch({verts:[1,2,6,5,1],opacityValue:.5}),graph.obj.addSketch({verts:[1,8],opacityValue:.5}),graph.obj.addSketch({verts:[2,11],opacityValue:.5}),graph.obj.addSketch({verts:[5,9],opacityValue:.5}),graph.obj.addSketch({verts:[6,10],opacityValue:.5}),graph.obj.addSketch({verts:[8,9,10,11,8],opacityValue:.5}),graph.obj.doDraw()
Puesto que hay WIDTH*LENGTH cubos en cada bloque, hay un total de HEIGHT \times WIDTH*LENGTH = HEIGHT*WIDTH*LENGTH cubos en la caja entera.
Como cada cubo mide UNIT cúbicos, el volumen de la caja es HEIGHT*WIDTH*LENGTH UNIT_TEXT^3
randRangeUnique(2,8,3)
DIMENSIONS[0]
DIMENSIONS[1]
DIMENSIONS[2]
max(max(LENGTH, WIDTH), HEIGHT)
LENGTH/MAX
WIDTH/MAX
HEIGHT/MAX
"#D7ED3A"
"#38C77F"
"#78D0EF"
"#F0B63A"
HEIGHT * 2
[[LENGTH/MAX,WIDTH/MAX,HEIGHT/MAX],[LENGTH/MAX,WIDTH/MAX,-HEIGHT/MAX],[LENGTH/MAX,-WIDTH/MAX,-HEIGHT/MAX],[LENGTH/MAX,-WIDTH/MAX,HEIGHT/MAX],[-LENGTH/MAX,WIDTH/MAX,HEIGHT/MAX],[-LENGTH/MAX,WIDTH/MAX,-HEIGHT/MAX],[-LENGTH/MAX,-WIDTH/MAX,-HEIGHT/MAX],[-LENGTH/MAX,-WIDTH/MAX,HEIGHT/MAX]]
4.0
[{verts:[3,2,1,0],color:COLOR1,labels:[[[XBORD,0,ZBORD],WIDTH+UNIT_TEXT]]},{verts:[4,5,6,7],color:COLOR1,labels:[[[-XBORD,0,-ZBORD],WIDTH+UNIT_TEXT]]},{verts:[0,1,5,4],color:COLOR3,labels:[[[-XBORD,YBORD,0],"\\Box"+UNIT_TEXT]]},{verts:[2,3,7,6],color:COLOR3,labels:[[[-XBORD,-YBORD,0],"\\Box"+UNIT_TEXT]]},{verts:[1,2,6,5],color:COLOR2,labels:[[[0,-YBORD,-ZBORD],LENGTH+UNIT_TEXT]]},{verts:[3,0,4,7],color:COLOR2,labels:[[[0,YBORD,ZBORD],LENGTH+UNIT_TEXT]]}]
[{verts:[8,9,10,11],color:"#A9A9A9"},{verts:[12,13,14,15],color:"#A9A9A9"}]
{}
{}
$._("base")
$._("altura")
El volumen de esta caja es LENGTH*WIDTH*HEIGHT UNIT_TEXT^3. ¿Cuál es el número marcado \Box abajo?
init({range:[[-2,2],[-2,2]],scale:[100,100]}),addMouseLayer();for(var i=1;HEIGHT>i;i++)VERTICES.push([LENGTH/MAX,WIDTH/MAX,(-HEIGHT+2*i)/MAX]),VERTICES.push([-LENGTH/MAX,WIDTH/MAX,(-HEIGHT+2*i)/MAX]),VERTICES.push([-LENGTH/MAX,-WIDTH/MAX,(-HEIGHT+2*i)/MAX]),VERTICES.push([LENGTH/MAX,-WIDTH/MAX,(-HEIGHT+2*i)/MAX]);for(var i=1;LENGTH>i;i++)VERTICES.push([(-LENGTH+2*i)/MAX,-WIDTH/MAX,-HEIGHT/MAX]);for(var i=1;LENGTH>i;i++)VERTICES.push([(-LENGTH+2*i)/MAX,WIDTH/MAX,-HEIGHT/MAX]);for(var i=1;WIDTH>i;i++)VERTICES.push([-LENGTH/MAX,(-WIDTH+2*i)/MAX,-HEIGHT/MAX]);for(var i=1;WIDTH>i;i++)VERTICES.push([LENGTH/MAX,(-WIDTH+2*i)/MAX,-HEIGHT/MAX]);for(var i=1;LENGTH>i;i++)VERTICES.push([(-LENGTH+2*i)/MAX,-WIDTH/MAX,(-HEIGHT+2)/MAX]);for(var i=1;LENGTH>i;i++)VERTICES.push([(-LENGTH+2*i)/MAX,WIDTH/MAX,(-HEIGHT+2)/MAX]);for(var i=1;WIDTH>i;i++)VERTICES.push([-LENGTH/MAX,(-WIDTH+2*i)/MAX,(-HEIGHT+2)/MAX]);for(var i=1;WIDTH>i;i++)VERTICES.push([LENGTH/MAX,(-WIDTH+2*i)/MAX,(-HEIGHT+2)/MAX]);graph.obj=make3dObject(VERTICES,{scale:SCALE}),_.each(FACES,function(e){graph.obj.addFace(e)}),graph.obj.setPos([0,0,5]),graph.obj.rotate(1,0,0,PI/3),graph.obj.rotate(0,1,0,0),graph.obj.rotate(0,0,1,PI/8),graph.obj.doDraw(),GRAPH=graph;var spinner;setTimeout(function(){spinner=setInterval(function(){GRAPH.obj.rotate(0,0,1,0),GRAPH.obj.doDraw()},50)},300);var mouseTarget=mouselayer.rect(0,0,400,400).attr({fill:"#000",opacity:0});$(mouseTarget[0]).bind("vmousedown",function(e){GRAPH.lastX=e.pageX,GRAPH.lastY=e.pageY,clearInterval(spinner),$(document).bind("vmousemove vmouseup",function(e){e.preventDefault();var r=(e.pageX-GRAPH.lastX)/200*PI,a=(e.pageY-GRAPH.lastY)/200*PI;GRAPH.lastX=e.pageX,GRAPH.lastY=e.pageY;var n=normalize(GRAPH.obj.perspective[1]),t=normalize(GRAPH.obj.perspective[0]);GRAPH.obj.rotate(n[0],n[1],n[2],-r/2),GRAPH.obj.rotate(t[0],t[1],t[2],-a/2),GRAPH.obj.doDraw(),"vmouseup"===e.type&&$(document).unbind("vmousemove vmouseup")})})
HEIGHT
El volumen del LENGTH UNIT_TEXT \times WIDTH UNIT_TEXT \times 1 UNIT_TEXT bloque mostrado arriba es LENGTH*WIDTH UNIT_TEXT^3 puesto que hay LENGTH filas de WIDTH cubos plural_form(UNIT).
for(var start=8+4*(HEIGHT-1)-1,i=1;LENGTH>i;i++)graph.obj.addSketch({verts:[start+i,start+LENGTH+i-1],opacityValue:.5});start+=2*(LENGTH-1);for(var i=1;WIDTH>i;i++)graph.obj.addSketch({verts:[start+i,start+WIDTH+i-1],opacityValue:.5});start+=2*(WIDTH-1);for(var i=1;LENGTH>i;i++)graph.obj.addSketch({verts:[start+i,start+LENGTH+i-1]});start+=2*(LENGTH-1);for(var i=1;WIDTH>i;i++)graph.obj.addSketch({verts:[start+i,start+WIDTH+i-1]});start=8+4*(HEIGHT-1)-1;for(var i=1;2*LENGTH+2*WIDTH-3>i;i++)graph.obj.addSketch({verts:[start+i,start+2*LENGTH-2+2*WIDTH-2+i],opacityValue:.5});graph.obj.addSketch({verts:[1,2,6,5,1],opacityValue:.5}),graph.obj.addSketch({verts:[1,8],opacityValue:.5}),graph.obj.addSketch({verts:[2,11],opacityValue:.5}),graph.obj.addSketch({verts:[5,9],opacityValue:.5}),graph.obj.addSketch({verts:[6,10],opacityValue:.5}),graph.obj.addSketch({verts:[8,9,10,11,8],opacityValue:.5}),graph.obj.doDraw()
Puesto que los bloques tienen una altura de 1 UNIT, \Box es el número de bloques que llenan la caja entera.
Podemos averiguar el número de bloques que se necesitan viendo cuántas veces LENGTH*WIDTH caben en LENGTH*WIDTH*HEIGHT
Así que \Box = LENGTH*WIDTH*HEIGHT \div LENGTH*WIDTH
Por tanto \Box = HEIGHT
for(var i=0;HEIGHT-1>i;i++)graph.obj.addSketch({verts:[8+4*i,9+4*i,10+4*i,11+4*i,8+4*i]});graph.obj.doDraw()