Draw a simple cube

Question

We don't have a single challenge about drawing a real 3 dimensional cube, so here it goes:

Challenge

Your task is to draw a rotated, cube with perspective. It can be in a separate window or as an image.

Input

Your input is 3 separate numbers between 0 and 359.99... These represent the rotation around the x, y and z axis in degrees.

0 0 0
30 0 40
95 320 12

Output

You can either display it in a separate window or save an image. You can use any type of display (vector based, rasterized, etc.).

Edit: ASCII is allowed too, to allow golfing languages with only textual output.

The output for rasterized or ASCII graphics must be at least 50*50 (pixels for rasterization, characters for ASCII)

Additional information

The positive z axis points out from the window, the x axis is horizontal, and the y axis is vertical. Basically the OpenGL standard.

Rotations are counter-clockwise if you look at the cube in the negative direction of a specific axis, e.g looking down for the y axis.

The camera should be on the z axis at a reasonable distance from the cube in the negative z direction, the cube should be at (0;0;0). The. cube also needs to be fully visible, and take up at least 50% of the drawing frame. The camera should look in the positive z direction at the cube.

The rotations of the cube get applied in the x->y->z order.

The cube is rotated around it's center, it doesn't move.

To project a cube in 2d space, you need to divide the x and y coordinates of the cube with the distance parallel to the z-axis between the point and the camera.

Rules

Rendering libraries are allowed, but the vertices need to be defined in the code. No 3d cube model class.

Test cases

Answer 1

Shoes (Ruby) 235 231

Everything computed from scratch.

Shoes.app{p,a,b,c=ARGV.map{|j|j.to_f/90}
k=1+i="i".to_c
p=(0..3).map{|j|y,z=(k*i**(j+a)).rect
x,z=(((-1)**j+z*i)*i**b).rect
q=(x+y*i)*i**c
[90*(k+q/(z-4)),90*(k+q/(4+z))]}
4.upto(15){|j|line *(p[j%4][0].rect+p[(j+j/4)%4][1].rect)}}

Call from commandline eg shoes cube3d.rb 0 30 0

The idea is to simultaneously generate / rotate the four vertices of a tetrahedron in 3d. Then, as these are reduced to 2d, we generate the four vertices of the inverse tetrahedron (the total 8 vertices being those of the cube.) This gives 4 pairs of vertices corresponding to the 4 body diagonals. Finally the 2d vertices are connected by lines: each vertex of the original tetrahedron must be connected to each vertex of the inverse tetrahedron forming the 12 edges and 4 body diagonals of the cube. The ordering ensures the body diagonals are not plotted.

Test cases output

Note that, to be consistent with the last two test cases, rotation about the z axis is clockwise from the POV of the viewer. This seems to be in contradiction with the spec however. Rotation direction can be reversed by modifying *i**c -> /i**c

ungolfed

Shoes.app{
  p,a,b,c=ARGV.map{|j|j.to_f/90}   #Throw away first argument (script name) and translate next three to fractions of a right angle.
  k=1+i="i".to_c                   #set up constants i=sqrt(-1) and k=1+i

  p=(0..3).map{|j|                 #build an array p of 4 elements (each element wil be a 2-element array containing the ends of a body diagonal in complex number format)
    y,z=(k*i**(j+a)).rect          #generate 4 sides of square: 1+i,i-1,-1-i,-i+1, rotate about x axis by a, and store in y and z as reals 
    x,z=(((-1)**j+z*i)*i**b).rect  #generate x axis displacements 1,-1,1,-1, rotate x and z about y axis by b, store in x and z as reals
    q=(x+y*i)*i**c                 #rotate x and y about z axis, store result in q as complex number
  [90*(k+q/(z-4)),90*(k+q/(4+z))]} #generate "far" vertex q/(4+z) and "near" vertex q/-(4-z) opposite ends of body diagonal in 2d format.

  4.upto(15){|j|                   #iterate through 12 edges, use rect and + to convert the two complex numbers into a 4 element array for line method
    line *(p[j%4][0].rect+         #cycle through 4 vertices of the "normal" tetrahedron
     p[(j+j/4)%4][1].rect)         #draw to three vertices of the "inverted" tetrahedron. j/4=1,2,3, never 0
  }                                #so the three edges are drawn but the body diagonal is not.
}

Note that for historical reasons a scale factor of 90 is applied in line 9 (chosen to be the same as 90 degrees in line 2 for golfing) but in the end there was no golfing advantage in using this particular value, so it has become an arbitrary choice.

Answer 2

HTML/CSS/JS, 739 bytes, probably non-competing

But I just wanted to show off CSS 3D transforms.

w=_=>o.style.transform=`rotateZ(${z.value}deg) rotateY(${y.value}deg) rotateX(${-x.value}deg)`

input {
  width: 5em;
}

#c{width:90px;height:90px;margin:90px;position:relative;perspective:180px}#o{position:absolute;width:90px;height:90px;transform-style:preserve-3d;transform-origin:45px 45px 0px;}#o *{position:absolute;width:90px;height:90px;border:2px solid black}#f{transform:translateZ(45px)}#b{transform:rotateX(180deg)translateZ(45px)}#r{transform:rotateY(90deg)translateZ(45px)}#l{transform:rotateY(-90deg)translateZ(45px)}#u{transform:rotateX(90deg)translateZ(45px)}#d{transform:rotateX(-90deg)translateZ(45px)}

<div oninput=w()>
  X:<input id="x" type="number" value="0" min="0" max="360">
  Y:<input id="y" type="number" value="0" min="0" max="360">
  Z:<input id="z" type="number" value="0" min="0" max="360">
</div>
<!-- Above code for ease of use of snippet. Golfed version: <div oninput=w()><input id=x><input id=y><input id=z></div> -->

<div id=c><div id=o><div id=f></div><div id=b></div><div id=r></div><div id=l></div><div id=u></div><div id=d>

Answer 3

Maple, 130+14 (in progress)

with(plots):f:=(X,Y,Z)->plot3d(0,x=0..1,y=0..1,style=contour,tickmarks=[0,0,0],labels=["","",""],axes=boxed,orientation=[Z,-X,Y]);

This plots a constant function inside a box, then uses plot options to hide ticks, labels and the function itself. Adding projection=.5 to the options brings the camera closer, enabling perspective view.
I wrote this before the specs were finalized and the rotation order is x, y', z'' instead of x, y, z. Until I fix the angles, here is another solution

POV-Ray, 182

#include"a.txt"
#include"shapes.inc"
camera{location 9*z look_at 0}
light_source{9*z color 1}
object{Wire_Box(<-2,-2,-2>,<2,2,2>,.01,0)texture{pigment{color rgb 1}}rotate<R.x,-R.y,-R.z>}

reads input through the a.txt file which should contain
#declare R=<xx,yy,zz>;
with xx,yy,zz being the rotation angles