Draw a rotating cube
Draw a rotating cube.
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
It should be oriented with one vertex pointing straight up, and its opposite vertex on the main diagonal (the one farthest away) straight down. It can be solid or wire-frame, and you can use ASCII art if your language doesn't have graphical capabilities. Perspective is optional.
- Related tasks
Ada
<lang Ada>with Ada.Numerics.Elementary_Functions;
with SDL.Video.Windows.Makers; with SDL.Video.Renderers.Makers; with SDL.Events.Events;
procedure Rotating_Cube is
Width : constant := 500; Height : constant := 500; Offset : constant := 500.0 / 2.0;
Window : SDL.Video.Windows.Window; Renderer : SDL.Video.Renderers.Renderer; Event : SDL.Events.Events.Events; Quit : Boolean := False;
type Node_Id is new Natural; type Point_3D is record X, Y, Z : Float; end record; type Edge_Type is record A, B : Node_Id; end record;
Nodes : array (Node_Id range <>) of Point_3D :=
((-100.0, -100.0, -100.0), (-100.0, -100.0, 100.0), (-100.0, 100.0, -100.0),
(-100.0, 100.0, 100.0), (100.0, -100.0, -100.0), (100.0, -100.0, 100.0),
(100.0, 100.0, -100.0), (100.0, 100.0, 100.0));
Edges : constant array (Positive range <>) of Edge_Type :=
((0, 1), (1, 3), (3, 2), (2, 0), (4, 5), (5, 7),
(7, 6), (6, 4), (0, 4), (1, 5), (2, 6), (3, 7));
use Ada.Numerics.Elementary_Functions;
procedure Rotate_Cube (AngleX, AngleY : in Float) is
SinX : constant Float := Sin (AngleX);
CosX : constant Float := Cos (AngleX);
SinY : constant Float := Sin (AngleY);
CosY : constant Float := Cos (AngleY);
X, Y, Z : Float;
begin
for Node of Nodes loop
X := Node.X;
Y := Node.Y;
Z := Node.Z;
Node.X := X * CosX - Z * SinX;
Node.Z := Z * CosX + X * SinX;
Z := Node.Z;
Node.Y := Y * CosY - Z * SinY;
Node.Z := Z * CosY + Y * SinY;
end loop;
end Rotate_Cube;
function Poll_Quit return Boolean is
use type SDL.Events.Event_Types;
begin
while SDL.Events.Events.Poll (Event) loop
if Event.Common.Event_Type = SDL.Events.Quit then
return True;
end if;
end loop;
return False;
end Poll_Quit;
procedure Draw_Cube (Quit : out Boolean) is
use SDL.C;
Pi : constant := Ada.Numerics.Pi;
Xy1, Xy2 : Point_3D;
begin
Rotate_Cube (Pi / 4.0, Arctan (Sqrt (2.0)));
for Frame in 0 .. 359 loop
Renderer.Set_Draw_Colour ((0, 0, 0, 255));
Renderer.Fill (Rectangle => (0, 0, Width, Height));
Renderer.Set_Draw_Colour ((0, 220, 0, 255));
for Edge of Edges loop
Xy1 := Nodes (Edge.A);
Xy2 := Nodes (Edge.B);
Renderer.Draw (Line => ((int (Xy1.X + Offset), int (Xy1.Y + Offset)),
(int (Xy2.X + Offset), int (Xy2.Y + Offset))));
end loop;
Rotate_Cube (Pi / 180.0, 0.0);
Window.Update_Surface;
Quit := Poll_Quit;
exit when Quit;
delay 0.020;
end loop;
end Draw_Cube;
begin
if not SDL.Initialise (Flags => SDL.Enable_Screen) then
return;
end if;
SDL.Video.Windows.Makers.Create (Win => Window,
Title => "Rotating cube",
Position => SDL.Natural_Coordinates'(X => 10, Y => 10),
Size => SDL.Positive_Sizes'(Width, Height),
Flags => 0);
SDL.Video.Renderers.Makers.Create (Renderer, Window.Get_Surface);
while not Quit loop
Draw_Cube (Quit);
end loop;
Window.Finalize; SDL.Finalise;
end Rotating_Cube;</lang>
AutoHotkey
Requires Gdip Library <lang AutoHotkey>; --------------------------------------------------------------- cubeSize := 200 deltaX := A_ScreenWidth/2 deltaY := A_ScreenHeight/2 keyStep := 1 mouseStep := 0.2 zoomStep := 1.1 playSpeed := 1 playTimer := 10 penSize := 5
/* HotKeys: !p:: Play/Stop !x:: change play to x-axis !y:: change play to y-axis !z:: change play to z-axis !NumpadAdd:: Zoom in !WheelUp:: Zoom in !NumpadSub:: Zoom out !WheelDown:: Zoom out !LButton:: Rotate X-axis, follow mouse !Up:: Rotate X-axis, CCW !Down:: Rotate X-axis, CW !LButton:: Rotate Y-axis, follow mouse !Right:: Rotate Y-axis, CCW !Left:: Rotate Y-axis, CW !RButton:: Rotate Z-axis, follow mouse !PGUP:: Rotate Z-axis, CW !PGDN:: Rotate Z-axis, CCW +LButton:: Move, follow mouse ^esc:: Exitapp
- /
visualCube = ( 1+--------+5 |\ \ | 2+--------+6 | | | 3+ | 7+ | \ | | 4+--------+8 )
SetBatchLines, -1 coord := cubeSize/2 nodes :=[[-coord, -coord, -coord] , [-coord, -coord, coord] , [-coord, coord, -coord] , [-coord, coord, coord] , [ coord, -coord, -coord] , [ coord, -coord, coord] , [ coord, coord, -coord] , [ coord, coord, coord]]
edges := [[1, 2], [2, 4], [4, 3], [3, 1] , [5, 6], [6, 8], [8, 7], [7, 5] , [1, 5], [2, 6], [3, 7], [4, 8]]
faces := [[1,2,4,3], [2,4,8,6], [1,2,6,5], [1,3,7,5], [5,7,8,6], [3,4,8,7]]
CP := [(nodes[8,1]+nodes[1,1])/2 , (nodes[8,2]+nodes[1,2])/2]
rotateX3D(-30) rotateY3D(30) Gdip1() draw() return
- --------------------------------------------------------------
draw() { global D := "" for i, n in nodes D .= Sqrt((n.1-CP.1)**2 + (n.2-CP.2)**2) "`t:" i ":`t" n.3 "`n" Sort, D, N p1 := StrSplit(StrSplit(D, "`n", "`r").1, ":").2 p2 := StrSplit(StrSplit(D, "`n", "`r").2, ":").2 hiddenNode := nodes[p1,3] < nodes[p2,3] ? p1 : p2
; Draw Faces loop % faces.count() { n1 := faces[A_Index, 1] n2 := faces[A_Index, 2] n3 := faces[A_Index, 3] n4 := faces[A_Index, 4] if (n1 = hiddenNode) || (n2 = hiddenNode) || (n3 = hiddenNode) || (n4 = hiddenNode) continue points := nodes[n1,1]+deltaX "," nodes[n1,2]+deltaY . "|" nodes[n2,1]+deltaX "," nodes[n2,2]+deltaY . "|" nodes[n3,1]+deltaX "," nodes[n3,2]+deltaY . "|" nodes[n4,1]+deltaX "," nodes[n4,2]+deltaY Gdip_FillPolygon(G, FaceBrush%A_Index%, Points) }
; Draw Node-Numbers ;~ loop % nodes.count() { ;~ Gdip_FillEllipse(G, pBrush, nodes[A_Index, 1]+deltaX, nodes[A_Index, 2]+deltaY, 4, 4) ;~ Options := "x" nodes[A_Index, 1]+deltaX " y" nodes[A_Index, 2]+deltaY "c" TextColor " Bold s" size ;~ Gdip_TextToGraphics(G, A_Index, Options, Font) ;~ }
; Draw Edges loop % edges.count() { n1 := edges[A_Index, 1] n2 := edges[A_Index, 2] if (n1 = hiddenNode) || (n2 = hiddenNode) continue Gdip_DrawLine(G, pPen, nodes[n1,1]+deltaX, nodes[n1,2]+deltaY, nodes[n2,1]+deltaX, nodes[n2,2]+deltaY) } UpdateLayeredWindow(hwnd1, hdc, 0, 0, Width, Height) }
- ---------------------------------------------------------------
rotateZ3D(theta) { ; Rotate shape around the z-axis global theta *= 3.141592653589793/180 sinTheta := sin(theta) cosTheta := cos(theta) loop % nodes.count() { x := nodes[A_Index,1] y := nodes[A_Index,2] nodes[A_Index,1] := x*cosTheta - y*sinTheta nodes[A_Index,2] := y*cosTheta + x*sinTheta } Redraw() }
- ---------------------------------------------------------------
rotateX3D(theta) { ; Rotate shape around the x-axis global theta *= 3.141592653589793/180 sinTheta := sin(theta) cosTheta := cos(theta) loop % nodes.count() { y := nodes[A_Index, 2] z := nodes[A_Index, 3] nodes[A_Index, 2] := y*cosTheta - z*sinTheta nodes[A_Index, 3] := z*cosTheta + y*sinTheta } Redraw() }
- ---------------------------------------------------------------
rotateY3D(theta) { ; Rotate shape around the y-axis global theta *= 3.141592653589793/180 sinTheta := sin(theta) cosTheta := cos(theta) loop % nodes.count() { x := nodes[A_Index, 1] z := nodes[A_Index, 3] nodes[A_Index, 1] := x*cosTheta + z*sinTheta nodes[A_Index, 3] := z*cosTheta - x*sinTheta } Redraw() }
- ---------------------------------------------------------------
Redraw(){ global gdip2() gdip1() draw() }
- ---------------------------------------------------------------
gdip1(){ global If !pToken := Gdip_Startup() { MsgBox, 48, gdiplus error!, Gdiplus failed to start. Please ensure you have gdiplus on your system ExitApp } OnExit, Exit Width := A_ScreenWidth, Height := A_ScreenHeight Gui, 1: -Caption +E0x80000 +LastFound +OwnDialogs +Owner +AlwaysOnTop Gui, 1: Show, NA hwnd1 := WinExist() hbm := CreateDIBSection(Width, Height) hdc := CreateCompatibleDC() obm := SelectObject(hdc, hbm) G := Gdip_GraphicsFromHDC(hdc) Gdip_SetSmoothingMode(G, 4) TextColor:="FFFFFF00", size := 18 Font := "Arial" Gdip_FontFamilyCreate(Font) pBrush := Gdip_BrushCreateSolid(0xFFFF00FF) FaceBrush1 := Gdip_BrushCreateSolid(0xFF0000FF) ; blue FaceBrush2 := Gdip_BrushCreateSolid(0xFFFF0000) ; red FaceBrush3 := Gdip_BrushCreateSolid(0xFFFFFF00) ; yellow FaceBrush4 := Gdip_BrushCreateSolid(0xFFFF7518) ; orange FaceBrush5 := Gdip_BrushCreateSolid(0xFF00FF00) ; lime FaceBrush6 := Gdip_BrushCreateSolid(0xFFFFFFFF) ; white pPen := Gdip_CreatePen(0xFF000000, penSize) }
- ---------------------------------------------------------------
gdip2(){ global Gdip_DeleteBrush(pBrush) Gdip_DeletePen(pPen) SelectObject(hdc, obm) DeleteObject(hbm) DeleteDC(hdc) Gdip_DeleteGraphics(G) }
- Viewing Hotkeys ----------------------------------------------
- HotKey Play/Stop ---------------------------------------------
!p:: SetTimer, rotateTimer, % (toggle:=!toggle)?playTimer:"off" return
rotateTimer: axis := !axis ? "Y" : axis rotate%axis%3D(playSpeed) return
!x:: !y:: !z:: axis := SubStr(A_ThisHotkey, 2, 1) return
- HotKey Zoom in/out -------------------------------------------
!NumpadAdd:: !NumpadSub:: !WheelUp:: !WheelDown:: loop % nodes.count() { nodes[A_Index, 1] := nodes[A_Index, 1] * (InStr(A_ThisHotkey, "Add") || InStr(A_ThisHotkey, "Up") ? zoomStep : 1/zoomStep) nodes[A_Index, 2] := nodes[A_Index, 2] * (InStr(A_ThisHotkey, "Add") || InStr(A_ThisHotkey, "Up") ? zoomStep : 1/zoomStep) nodes[A_Index, 3] := nodes[A_Index, 3] * (InStr(A_ThisHotkey, "Add") || InStr(A_ThisHotkey, "Up") ? zoomStep : 1/zoomStep) } Redraw() return
- HotKey Rotate around Y-Axis ----------------------------------
!Right:: !Left:: rotateY3D(keyStep * (InStr(A_ThisHotkey,"right") ? 1 : -1)) return
- HotKey Rotate around X-Axis ----------------------------------
!Up:: !Down:: rotateX3D(keyStep * (InStr(A_ThisHotkey, "Up") ? 1 : -1)) return
- HotKey Rotate around Z-Axis ----------------------------------
!PGUP:: !PGDN:: rotateZ3D(keyStep * (InStr(A_ThisHotkey, "UP") ? 1 : -1)) return
- HotKey, Rotate around X/Y-Axis -------------------------------
!LButton:: MouseGetPos, pmouseX, pmouseY while GetKeyState("Lbutton", "P") { MouseGetPos, mouseX, mouseY DeltaMX := mouseX - pmouseX DeltaMY := pmouseY - mouseY if (DeltaMX || DeltaMY) { MouseGetPos, pmouseX, pmouseY rotateY3D(DeltaMX) rotateX3D(DeltaMY) } } return
- HotKey Rotate around Z-Axis ----------------------------------
!RButton:: MouseGetPos, pmouseX, pmouseY while GetKeyState("Rbutton", "P") { MouseGetPos, mouseX, mouseY DeltaMX := mouseX - pmouseX DeltaMY := mouseY - pmouseY DeltaMX *= mouseY < deltaY ? mouseStep : -mouseStep DeltaMY *= mouseX > deltaX ? mouseStep : -mouseStep if (DeltaMX || DeltaMY) { MouseGetPos, pmouseX, pmouseY rotateZ3D(DeltaMX) rotateZ3D(DeltaMY) } } return
- HotKey, Move -------------------------------------------------
+LButton:: MouseGetPos, pmouseX, pmouseY while GetKeyState("Lbutton", "P") { MouseGetPos, mouseX, mouseY deltaX += mouseX - pmouseX deltaY += mouseY - pmouseY pmouseX := mouseX pmouseY := mouseY Redraw() } return
- ---------------------------------------------------------------
^esc:: Exit: gdip2() Gdip_Shutdown(pToken) ExitApp Return
- ---------------------------------------------------------------</lang>
C
Rotating wireframe cube in OpenGL, windowing implementation via freeglut <lang C>
- include<gl/freeglut.h>
double rot = 0; float matCol[] = {1,0,0,0};
void display(){ glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT); glPushMatrix(); glRotatef(30,1,1,0); glRotatef(rot,0,1,1); glMaterialfv(GL_FRONT,GL_DIFFUSE,matCol); glutWireCube(1); glPopMatrix(); glFlush(); }
void onIdle(){
rot += 0.1;
glutPostRedisplay();
}
void reshape(int w,int h){ float ar = (float) w / (float) h ;
glViewport(0,0,(GLsizei)w,(GLsizei)h); glTranslatef(0,0,-10); glMatrixMode(GL_PROJECTION); gluPerspective(70,(GLfloat)w/(GLfloat)h,1,12); glLoadIdentity(); glFrustum ( -1.0, 1.0, -1.0, 1.0, 10.0, 100.0 ) ; glMatrixMode(GL_MODELVIEW); glLoadIdentity(); }
void init(){ float pos[] = {1,1,1,0}; float white[] = {1,1,1,0}; float shini[] = {70};
glClearColor(.5,.5,.5,0); glShadeModel(GL_SMOOTH); glLightfv(GL_LIGHT0,GL_AMBIENT,white); glLightfv(GL_LIGHT0,GL_DIFFUSE,white); glMaterialfv(GL_FRONT,GL_SHININESS,shini); glEnable(GL_LIGHTING); glEnable(GL_LIGHT0); glEnable(GL_DEPTH_TEST); }
int main(int argC, char* argV[]) { glutInit(&argC,argV); glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB|GLUT_DEPTH); glutInitWindowSize(600,500); glutCreateWindow("Rossetta's Rotating Cube"); init(); glutDisplayFunc(display); glutReshapeFunc(reshape); glutIdleFunc(onIdle); glutMainLoop(); return 0; } </lang>
C#
<lang csharp>using System; using System.Drawing; using System.Drawing.Drawing2D; using System.Windows.Forms; using System.Windows.Threading;
namespace RotatingCube {
public partial class Form1 : Form
{
double[][] nodes = {
new double[] {-1, -1, -1}, new double[] {-1, -1, 1}, new double[] {-1, 1, -1},
new double[] {-1, 1, 1}, new double[] {1, -1, -1}, new double[] {1, -1, 1},
new double[] {1, 1, -1}, new double[] {1, 1, 1} };
int[][] edges = {
new int[] {0, 1}, new int[] {1, 3}, new int[] {3, 2}, new int[] {2, 0}, new int[] {4, 5},
new int[] {5, 7}, new int[] {7, 6}, new int[] {6, 4}, new int[] {0, 4}, new int[] {1, 5},
new int[] {2, 6}, new int[] {3, 7}};
public Form1()
{
Width = Height = 640;
StartPosition = FormStartPosition.CenterScreen;
SetStyle(
ControlStyles.AllPaintingInWmPaint |
ControlStyles.UserPaint |
ControlStyles.DoubleBuffer,
true);
Scale(100, 100, 100);
RotateCuboid(Math.PI / 4, Math.Atan(Math.Sqrt(2)));
var timer = new DispatcherTimer();
timer.Tick += (s, e) => { RotateCuboid(Math.PI / 180, 0); Refresh(); };
timer.Interval = new TimeSpan(0, 0, 0, 0, 17);
timer.Start();
}
private void RotateCuboid(double angleX, double angleY)
{
double sinX = Math.Sin(angleX);
double cosX = Math.Cos(angleX);
double sinY = Math.Sin(angleY);
double cosY = Math.Cos(angleY);
foreach (var node in nodes)
{
double x = node[0];
double y = node[1];
double z = node[2];
node[0] = x * cosX - z * sinX;
node[2] = z * cosX + x * sinX;
z = node[2];
node[1] = y * cosY - z * sinY;
node[2] = z * cosY + y * sinY;
}
}
private void Scale(int v1, int v2, int v3)
{
foreach (var item in nodes)
{
item[0] *= v1;
item[1] *= v2;
item[2] *= v3;
}
}
protected override void OnPaint(PaintEventArgs args)
{
var g = args.Graphics;
g.SmoothingMode = SmoothingMode.HighQuality;
g.Clear(Color.White);
g.TranslateTransform(Width / 2, Height / 2);
foreach (var edge in edges)
{
double[] xy1 = nodes[edge[0]];
double[] xy2 = nodes[edge[1]];
g.DrawLine(Pens.Black, (int)Math.Round(xy1[0]), (int)Math.Round(xy1[1]),
(int)Math.Round(xy2[0]), (int)Math.Round(xy2[1]));
}
foreach (var node in nodes)
{
g.FillEllipse(Brushes.Black, (int)Math.Round(node[0]) - 4,
(int)Math.Round(node[1]) - 4, 8, 8);
}
}
}
}</lang>
Delphi
<lang Delphi> unit main;
interface
uses
Winapi.Windows, Vcl.Graphics, Vcl.Controls, Vcl.Forms, Vcl.ExtCtrls, System.Math, System.Classes;
type
TForm1 = class(TForm)
tmr1: TTimer;
procedure FormCreate(Sender: TObject);
procedure tmr1Timer(Sender: TObject);
private
{ Private declarations }
public
{ Public declarations }
end;
var
Form1: TForm1; nodes: TArray<TArray<double>> = [[-1, -1, -1], [-1, -1, 1], [-1, 1, -1], [-1, 1, 1], [1, -1, -1], [1, -1, 1], [1, 1, -1], [1, 1, 1]]; edges: TArray<TArray<Integer>> = [[0, 1], [1, 3], [3, 2], [2, 0], [4, 5], [5, 7], [7, 6], [6, 4], [0, 4], [1, 5], [2, 6], [3, 7]];
implementation
{$R *.dfm}
procedure Scale(factor: TArray<double>); begin
if Length(factor) <> 3 then
exit;
for var i := 0 to High(nodes) do
for var f := 0 to High(factor) do
nodes[i][f] := nodes[i][f] * factor[f];
end;
procedure RotateCuboid(angleX, angleY: double); begin
var sinX := sin(angleX); var cosX := cos(angleX); var sinY := sin(angleY); var cosY := cos(angleY);
for var i := 0 to High(nodes) do begin var x := nodes[i][0]; var y := nodes[i][1]; var z := nodes[i][2];
nodes[i][0] := x * cosX - z * sinX; nodes[i][2] := z * cosX + x * sinX;
z := nodes[i][2];
nodes[i][1] := y * cosY - z * sinY; nodes[i][2] := z * cosY + y * sinY; end;
end;
function DrawCuboid(x, y, w, h: Integer): TBitmap; var
offset: TPoint;
begin
Result := TBitmap.Create; Result.SetSize(w, h); rotateCuboid(PI / 180, 0); offset := TPoint.Create(x, y); with Result.canvas do begin Brush.Color := clBlack; Pen.Color := clWhite;
Lock; FillRect(ClipRect);
for var edge in edges do
begin
var p1 := (nodes[edge[0]]);
var p2 := (nodes[edge[1]]);
moveTo(trunc(p1[0]) + offset.x, trunc(p1[1]) + offset.y);
lineTo(trunc(p2[0]) + offset.x, trunc(p2[1]) + offset.y);
end;
Unlock;
end;
end;
procedure TForm1.FormCreate(Sender: TObject); begin
ClientHeight := 360; ClientWidth := 640; DoubleBuffered := true; scale([100, 100, 100]); rotateCuboid(PI / 4, ArcTan(sqrt(2)));
end;
procedure TForm1.tmr1Timer(Sender: TObject); var
buffer: TBitmap;
begin
buffer := DrawCuboid(ClientWidth div 2, ClientHeight div 2, ClientWidth, ClientHeight); Canvas.Draw(0, 0, buffer); buffer.Free;
end;
end.</lang> Resource Form <lang Delphi> object Form1: TForm1
OnCreate = FormCreate object tmr1: TTimer Interval = 17 OnTimer = tmr1Timer end
end </lang>
EasyLang
Draws only the visible edges
<lang>node[][] &= [ -1 -1 -1 ] node[][] &= [ -1 -1 1 ] node[][] &= [ -1 1 -1 ] node[][] &= [ -1 1 1 ] node[][] &= [ 1 -1 -1 ] node[][] &= [ 1 -1 1 ] node[][] &= [ 1 1 -1 ] node[][] &= [ 1 1 1 ]
edge[][] &= [ 0 1 ] edge[][] &= [ 1 3 ] edge[][] &= [ 3 2 ] edge[][] &= [ 2 0 ] edge[][] &= [ 4 5 ] edge[][] &= [ 5 7 ] edge[][] &= [ 7 6 ] edge[][] &= [ 6 4 ] edge[][] &= [ 0 4 ] edge[][] &= [ 1 5 ] edge[][] &= [ 2 6 ] edge[][] &= [ 3 7 ]
func scale f . .
for i range len node[][] swap n[] node[i][] n[0] *= f n[1] *= f n[2] *= f swap n[] node[i][] .
. func rotate angx angy . .
sinx = sin angx cosx = cos angx siny = sin angy cosy = cos angy for i range len node[][] swap n[] node[i][] x = n[0] y = n[1] z = n[2] n[0] = x * cosx - z * sinx n[2] = z * cosx + x * sinx z = n[2] n[1] = y * cosy - z * siny n[2] = z * cosy + y * siny swap n[] node[i][] .
. len nd[] 3 func draw . .
clear_screen
m = 999
mi = -1
for i range len node[][]
if node[i][2] < m
m = node[i][2]
mi = i
.
.
ix = 0
for i range len edge[][]
if edge[i][0] = mi
nd[ix] = edge[i][1]
ix += 1
elif edge[i][1] = mi
nd[ix] = edge[i][0]
ix += 1
.
.
for ni range len nd[]
for i range len edge[][]
if edge[i][0] = nd[ni] or edge[i][1] = nd[ni]
x1 = node[edge[i][0]][0]
y1 = node[edge[i][0]][1]
x2 = node[edge[i][1]][0]
y2 = node[edge[i][1]][1]
move_pen x1 + 50 y1 + 50
draw_line x2 + 50 y2 + 50
.
.
.
. call scale 25 call rotate 45 atan sqrt 2 call draw on animate
call rotate 1 0 call draw
.</lang>
FreeBASIC
<lang freebasic>#define PI 3.14159265358979323
- define SCALE 50
- define SIZE 320
- define zoff 0.5773502691896257645091487805019574556
- define cylr 1.6329931618554520654648560498039275946
screenres SIZE, SIZE, 4
dim as double theta = 0.0, dtheta = 1.5, x(0 to 5), lasttime, dt = 1./30
dim as double cylphi(0 to 5) = {PI/6, 5*PI/6, 3*PI/2, 11*PI/6, PI/2, 7*PI/6}
sub drawcube( x() as double, colour as uinteger )
for i as uinteger = 0 to 2
line (SIZE/2, SIZE/2-SCALE/zoff) - (x(i), SIZE/2-SCALE*zoff), colour
line (SIZE/2, SIZE/2+SCALE/zoff) - (x(5-i), SIZE/2+SCALE*zoff), colour
line ( x(i), SIZE/2-SCALE*zoff ) - ( x(i mod 3 + 3), SIZE/2+SCALE*zoff ), colour
line ( x(i), SIZE/2-SCALE*zoff ) - ( x((i+1) mod 3 + 3), SIZE/2+SCALE*zoff ), colour
next i
end sub
while inkey=""
lasttime = timer
for i as uinteger = 0 to 5
x(i) = SIZE/2 + SCALE*cylr*cos(cylphi(i)+theta)
next i
drawcube x(), 15
while timer < lasttime + dt
wend
theta += dtheta*(timer-lasttime)
drawcube x(),0
wend end</lang>
FutureBasic
Among the capabilities of FutureBasic (or FB as it's called by its developers) is the ability to compile Open GL code as demonstrated here.
<lang futurebasic> include "Tlbx agl.incl" include "Tlbx glut.incl"
output file "Rotating Cube"
local fn AnimateCube '~'1 begin globals dim as double sRotation end globals
// Speed of rotation sRotation += 2.9 glMatrixMode( _GLMODELVIEW )
glLoadIdentity() glTranslated( 0.0, 0.0, 0.0 ) glRotated( sRotation, -0.45, -0.8, -0.6 ) glColor3d( 1.0, 0.0, 0.3 ) glLineWidth( 1.5 ) glutWireCube( 1.0 ) end fn
// Main program dim as GLint attrib(2) dim as CGrafPtr port dim as AGLPixelFormat fmt dim as AGLContext glContext dim as EventRecord ev dim as GLboolean yesOK
window 1, @"Rotating Cube", (0,0) - (500,500)
attrib(0) = _AGLRGBA attrib(1) = _AGLDOUBLEBUFFER attrib(2) = _AGLNONE
fmt = fn aglChoosePixelFormat( 0, 0, attrib(0) ) glContext = fn aglCreateContext( fmt, 0 ) aglDestroyPixelFormat( fmt )
port = window( _wndPort ) yesOK = fn aglSetDrawable( glContext, port ) yesOK = fn aglSetCurrentContext( glContext )
glClearColor( 0.0, 0.0, 0.0, 0.0 )
poke long event - 8, 1 do glClear( _GLCOLORBUFFERBIT ) fn AnimateCube aglSwapBuffers( glContext ) HandleEvents until gFBQuit </lang>
Go
As of Go 1.9, it looks as if the only standard library supporting animated graphics is image/gif - so we create an animated GIF... <lang Go>package main
import ( "image" "image/color" "image/gif" "log" "math" "os" )
const ( width, height = 640, 640 offset = height / 2 fileName = "rotatingCube.gif" )
var nodes = [][]float64{{-100, -100, -100}, {-100, -100, 100}, {-100, 100, -100}, {-100, 100, 100}, {100, -100, -100}, {100, -100, 100}, {100, 100, -100}, {100, 100, 100}} var edges = [][]int{{0, 1}, {1, 3}, {3, 2}, {2, 0}, {4, 5}, {5, 7}, {7, 6}, {6, 4}, {0, 4}, {1, 5}, {2, 6}, {3, 7}}
func main() { var images []*image.Paletted fgCol := color.RGBA{0xff, 0x00, 0xff, 0xff} var palette = []color.Color{color.RGBA{0x00, 0x00, 0x00, 0xff}, fgCol} var delays []int
imgFile, err := os.Create(fileName) if err != nil { log.Fatal(err) } defer imgFile.Close()
rotateCube(math.Pi/4, math.Atan(math.Sqrt(2))) var frame float64 for frame = 0; frame < 360; frame++ { img := image.NewPaletted(image.Rect(0, 0, width, height), palette) images = append(images, img) delays = append(delays, 5) for _, edge := range edges { xy1 := nodes[edge[0]] xy2 := nodes[edge[1]] drawLine(int(xy1[0])+offset, int(xy1[1])+offset, int(xy2[0])+offset, int(xy2[1])+offset, img, fgCol) } rotateCube(math.Pi/180, 0) } if err := gif.EncodeAll(imgFile, &gif.GIF{Image: images, Delay: delays}); err != nil { imgFile.Close() log.Fatal(err) }
}
func rotateCube(angleX, angleY float64) { sinX := math.Sin(angleX) cosX := math.Cos(angleX) sinY := math.Sin(angleY) cosY := math.Cos(angleY) for _, node := range nodes { x := node[0] y := node[1] z := node[2] node[0] = x*cosX - z*sinX node[2] = z*cosX + x*sinX z = node[2] node[1] = y*cosY - z*sinY node[2] = z*cosY + y*sinY } }
func drawLine(x0, y0, x1, y1 int, img *image.Paletted, col color.RGBA) { dx := abs(x1 - x0) dy := abs(y1 - y0) var sx, sy int = -1, -1 if x0 < x1 { sx = 1 } if y0 < y1 { sy = 1 } err := dx - dy for { img.Set(x0, y0, col) if x0 == x1 && y0 == y1 { break } e2 := 2 * err if e2 > -dy { err -= dy x0 += sx } if e2 < dx { err += dx y0 += sy } } }
func abs(x int) int { if x < 0 { return -x } return x }</lang>
Haskell
This implementation compiles to JavaScript that runs in a browser using the ghcjs compiler . The reflex-dom library is used to help with svg rendering and animation.
<lang Haskell>{-# LANGUAGE RecursiveDo #-} import Reflex.Dom import Data.Map as DM (Map, lookup, insert, empty, fromList) import Data.Matrix import Data.Time.Clock import Control.Monad.Trans
size = 500 updateFrequency = 0.2 rotationStep = pi/10
data Color = Red | Green | Blue | Yellow | Orange | Purple | Black deriving (Show,Eq,Ord,Enum)
zRot :: Float -> Matrix Float zRot rotation =
let c = cos rotation
s = sin rotation
in fromLists [[ c, s, 0, 0 ]
,[-s, c, 0, 0 ]
,[ 0, 0, 1, 0 ]
,[ 0, 0, 0, 1 ]
]
xRot :: Float -> Matrix Float xRot rotation =
let c = cos rotation
s = sin rotation
in fromLists [[ 1, 0, 0, 0 ]
,[ 0, c, s, 0 ]
,[ 0, -s, c, 0 ]
,[ 0, 0, 0, 1 ]
]
yRot :: Float -> Matrix Float yRot rotation =
let c = cos rotation
s = sin rotation
in fromLists [[ c, 0, -s, 0 ]
,[ 0, 1, 0, 0 ]
,[ s, 0, c, 0 ]
,[ 0, 0, 0, 1 ]
]
translation :: (Float,Float,Float) -> Matrix Float translation (x,y,z) =
fromLists [[ 1, 0, 0, 0 ]
,[ 0, 1, 0, 0 ]
,[ 0, 0, 1, 0 ]
,[ x, y, z, 1 ]
]
scale :: Float -> Matrix Float scale s =
fromLists [[ s, 0, 0, 0 ]
,[ 0, s, 0, 0 ]
,[ 0, 0, s, 0 ]
,[ 0, 0, 0, 1 ]
]
-- perspective transformation; perspective :: Matrix Float perspective =
fromLists [[ 1, 0, 0, 0 ]
,[ 0, 1, 0, 0 ]
,[ 0, 0, 1, 1 ]
,[ 0, 0, 1, 1 ] ]
transformPoints :: Matrix Float -> Matrix Float -> [(Float,Float)] transformPoints transform points =
let result4d = points `multStd2` transform
result2d = (\[x,y,z,w] -> (x/w,y/w)) <$> toLists result4d
in result2d
showRectangle :: MonadWidget t m => Float -> Float -> Float -> Float -> Color -> Dynamic t (Matrix Float) -> m () showRectangle x0 y0 x1 y1 faceColor dFaceView = do
let points = fromLists [[x0,y0,0,1],[x0,y1,0,1],[x1,y1,0,1],[x1,y0,0,1]]
pointsToString = concatMap (\(x,y) -> show x ++ ", " ++ show y ++ " ")
dAttrs <- mapDyn (\fvk -> DM.fromList [ ("fill", show faceColor)
, ("points", pointsToString (transformPoints fvk points))
] ) dFaceView
elDynAttrSVG "polygon" dAttrs $ return ()
showUnitSquare :: MonadWidget t m => Color -> Float -> Dynamic t (Matrix Float) -> m () showUnitSquare faceColor margin dFaceView =
showRectangle margin margin (1.0 - margin) (1.0 - margin) faceColor dFaceView
-- show colored square on top of black square for outline effect showFace :: MonadWidget t m => Color -> Dynamic t (Matrix Float) -> m () showFace faceColor dFaceView = do
showUnitSquare Black 0 dFaceView showUnitSquare faceColor 0.03 dFaceView
facingCamera :: [Float] -> Matrix Float -> Bool facingCamera viewPoint modelTransform =
let cross [x0,y0,z0] [x1,y1,z1] = [y0*z1-z0*y1, z0*x1-x0*z1, x0*y1-y0*x1 ]
dot v0 v1 = sum $ zipWith (*) v0 v1
vMinus = zipWith (-)
untransformedPoints = fromLists [ [0,0,0,1] -- lower left
, [1,0,0,1] -- lower right
, [0,1,0,1] ] -- upper left
transformedPoints = toLists $ untransformedPoints `multStd2` modelTransform
pt00 = take 3 $ head transformedPoints -- transformed lower left
pt10 = take 3 $ transformedPoints !! 1 -- transformed upper right
pt01 = take 3 $ transformedPoints !! 2 -- transformed upper left
tVec_10_00 = pt10 `vMinus` pt00 -- lower right to lower left
tVec_01_00 = pt01 `vMinus` pt00 -- upper left to lower left
perpendicular = tVec_10_00 `cross` tVec_01_00 -- perpendicular to face
cameraToPlane = pt00 `vMinus` viewPoint -- line of sight to face
-- Perpendicular points away from surface;
-- Camera vector points towards surface
-- Opposed vectors means that face will be visible.
in cameraToPlane `dot` perpendicular < 0
faceView :: Matrix Float -> Matrix Float -> (Bool, Matrix Float) faceView modelOrientation faceOrientation =
let modelTransform = translation (-1/2,-1/2,1/2) -- unit square to origin + z offset
`multStd2` faceOrientation -- orientation specific to each face
`multStd2` scale (1/2) -- shrink cube to fit in view.
`multStd2` modelOrientation -- position the entire cube
isFacingCamera = facingCamera [0,0,-1] modelTransform -- backface elimination
-- combine to get single transform from 2d face to 2d display
viewTransform = modelTransform
`multStd2` perspective
`multStd2` scale size -- scale up to svg box scale
`multStd2` translation (size/2, size/2, 0) -- move to center of svg box
in (isFacingCamera, viewTransform)
updateFaceViews :: Matrix Float -> Map Color (Matrix Float) -> (Color, Matrix Float) -> Map Color (Matrix Float) updateFaceViews modelOrientation prevCollection (faceColor, faceOrientation) =
let (isVisible, newFaceView) = faceView modelOrientation faceOrientation
in if isVisible
then insert faceColor newFaceView prevCollection
else prevCollection
faceViews :: Matrix Float -> Map Color (Matrix Float) faceViews modelOrientation =
foldl (updateFaceViews modelOrientation) empty
[ (Purple , xRot (0.0) )
, (Yellow , xRot (pi/2) )
, (Red , yRot (pi/2) )
, (Green , xRot (-pi/2) )
, (Blue , yRot (-pi/2) )
, (Orange , xRot (pi) )
]
viewModel :: MonadWidget t m => Dynamic t (Matrix Float) -> m () viewModel modelOrientation = do
faceMap <- mapDyn faceViews modelOrientation listWithKey faceMap showFace return ()
view :: MonadWidget t m => Dynamic t (Matrix Float) -> m () view modelOrientation = do
el "h1" $ text "Rotating Cube"
elDynAttrSVG "svg"
(constDyn $ DM.fromList [ ("width", show size), ("height", show size) ])
$ viewModel modelOrientation
main = mainWidget $ do
let initialOrientation = xRot (pi/4) `multStd2` zRot (atan(1/sqrt(2)))
update _ modelOrientation = modelOrientation `multStd2` (yRot (rotationStep) )
tick <- tickLossy updateFrequency =<< liftIO getCurrentTime
rec
view modelOrientation
modelOrientation <- foldDyn update initialOrientation tick
return ()
-- At end because of Rosetta Code handling of unmatched quotes. elDynAttrSVG a2 a3 a4 = do
elDynAttrNS' (Just "http://www.w3.org/2000/svg") a2 a3 a4 return ()</lang>
Link to live demo: https://dc25.github.io/drawRotatingCubeHaskell/
Java
<lang java>import java.awt.*; import java.awt.event.ActionEvent; import static java.lang.Math.*; import javax.swing.*;
public class RotatingCube extends JPanel {
double[][] nodes = {{-1, -1, -1}, {-1, -1, 1}, {-1, 1, -1}, {-1, 1, 1},
{1, -1, -1}, {1, -1, 1}, {1, 1, -1}, {1, 1, 1}};
int[][] edges = {{0, 1}, {1, 3}, {3, 2}, {2, 0}, {4, 5}, {5, 7}, {7, 6},
{6, 4}, {0, 4}, {1, 5}, {2, 6}, {3, 7}};
public RotatingCube() {
setPreferredSize(new Dimension(640, 640));
setBackground(Color.white);
scale(100);
rotateCube(PI / 4, atan(sqrt(2)));
new Timer(17, (ActionEvent e) -> {
rotateCube(PI / 180, 0);
repaint();
}).start();
}
final void scale(double s) {
for (double[] node : nodes) {
node[0] *= s;
node[1] *= s;
node[2] *= s;
}
}
final void rotateCube(double angleX, double angleY) {
double sinX = sin(angleX);
double cosX = cos(angleX);
double sinY = sin(angleY);
double cosY = cos(angleY);
for (double[] node : nodes) {
double x = node[0];
double y = node[1];
double z = node[2];
node[0] = x * cosX - z * sinX;
node[2] = z * cosX + x * sinX;
z = node[2];
node[1] = y * cosY - z * sinY;
node[2] = z * cosY + y * sinY;
}
}
void drawCube(Graphics2D g) {
g.translate(getWidth() / 2, getHeight() / 2);
for (int[] edge : edges) {
double[] xy1 = nodes[edge[0]];
double[] xy2 = nodes[edge[1]];
g.drawLine((int) round(xy1[0]), (int) round(xy1[1]),
(int) round(xy2[0]), (int) round(xy2[1]));
}
for (double[] node : nodes)
g.fillOval((int) round(node[0]) - 4, (int) round(node[1]) - 4, 8, 8);
}
@Override
public void paintComponent(Graphics gg) {
super.paintComponent(gg);
Graphics2D g = (Graphics2D) gg;
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
drawCube(g); }
public static void main(String[] args) {
SwingUtilities.invokeLater(() -> {
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setTitle("Rotating Cube");
f.setResizable(false);
f.add(new RotatingCube(), BorderLayout.CENTER);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
});
}
}</lang>
JavaScript
<lang javascript><!DOCTYPE html> <html lang="en"> <head>
<meta charset="UTF-8">
<style>
canvas {
background-color: black;
}
</style>
</head> <body>
<canvas></canvas>
<script>
var canvas = document.querySelector("canvas");
canvas.width = window.innerWidth;
canvas.height = window.innerHeight;
var g = canvas.getContext("2d");
var nodes = [[-1, -1, -1], [-1, -1, 1], [-1, 1, -1], [-1, 1, 1],
[1, -1, -1], [1, -1, 1], [1, 1, -1], [1, 1, 1]];
var edges = [[0, 1], [1, 3], [3, 2], [2, 0], [4, 5], [5, 7], [7, 6],
[6, 4], [0, 4], [1, 5], [2, 6], [3, 7]];
function scale(factor0, factor1, factor2) {
nodes.forEach(function (node) {
node[0] *= factor0;
node[1] *= factor1;
node[2] *= factor2;
});
}
function rotateCuboid(angleX, angleY) {
var sinX = Math.sin(angleX);
var cosX = Math.cos(angleX);
var sinY = Math.sin(angleY);
var cosY = Math.cos(angleY);
nodes.forEach(function (node) {
var x = node[0];
var y = node[1];
var z = node[2];
node[0] = x * cosX - z * sinX;
node[2] = z * cosX + x * sinX;
z = node[2];
node[1] = y * cosY - z * sinY;
node[2] = z * cosY + y * sinY;
});
}
function drawCuboid() {
g.save();
g.clearRect(0, 0, canvas.width, canvas.height);
g.translate(canvas.width / 2, canvas.height / 2);
g.strokeStyle = "#FFFFFF";
g.beginPath();
edges.forEach(function (edge) {
var p1 = nodes[edge[0]];
var p2 = nodes[edge[1]];
g.moveTo(p1[0], p1[1]);
g.lineTo(p2[0], p2[1]);
});
g.closePath();
g.stroke();
g.restore();
}
scale(200, 200, 200);
rotateCuboid(Math.PI / 4, Math.atan(Math.sqrt(2)));
setInterval(function() {
rotateCuboid(Math.PI / 180, 0);
drawCuboid();
}, 17);
</script>
</body> </html></lang>
Julia
Run at the Julia REPL command line. <lang Julia>using Makie, LinearAlgebra
N = 40 interval = 0.10
scene = mesh(FRect3D(Vec3f0(-0.5), Vec3f0(1)), color = :skyblue2) rect = scene[end]
for rad in 0.5:1/N:8.5
arr = normalize([cospi(rad/2), 0, sinpi(rad/2), -sinpi(rad/2)]) Makie.rotate!(rect, Quaternionf0(arr[1], arr[2], arr[3], arr[4])) sleep(interval)
end</lang>
Kotlin
<lang scala>// version 1.1
import java.awt.* import javax.swing.*
class RotatingCube : JPanel() {
private val nodes = arrayOf(
doubleArrayOf(-1.0, -1.0, -1.0),
doubleArrayOf(-1.0, -1.0, 1.0),
doubleArrayOf(-1.0, 1.0, -1.0),
doubleArrayOf(-1.0, 1.0, 1.0),
doubleArrayOf( 1.0, -1.0, -1.0),
doubleArrayOf( 1.0, -1.0, 1.0),
doubleArrayOf( 1.0, 1.0, -1.0),
doubleArrayOf( 1.0, 1.0, 1.0)
)
private val edges = arrayOf(
intArrayOf(0, 1),
intArrayOf(1, 3),
intArrayOf(3, 2),
intArrayOf(2, 0),
intArrayOf(4, 5),
intArrayOf(5, 7),
intArrayOf(7, 6),
intArrayOf(6, 4),
intArrayOf(0, 4),
intArrayOf(1, 5),
intArrayOf(2, 6),
intArrayOf(3, 7)
)
init {
preferredSize = Dimension(640, 640)
background = Color.white
scale(100.0)
rotateCube(Math.PI / 4.0, Math.atan(Math.sqrt(2.0)))
Timer(17) {
rotateCube(Math.PI / 180.0, 0.0)
repaint()
}.start()
}
private fun scale(s: Double) {
for (node in nodes) {
node[0] *= s
node[1] *= s
node[2] *= s
}
}
private fun rotateCube(angleX: Double, angleY: Double) {
val sinX = Math.sin(angleX)
val cosX = Math.cos(angleX)
val sinY = Math.sin(angleY)
val cosY = Math.cos(angleY)
for (node in nodes) {
val x = node[0]
val y = node[1]
var z = node[2]
node[0] = x * cosX - z * sinX
node[2] = z * cosX + x * sinX
z = node[2]
node[1] = y * cosY - z * sinY
node[2] = z * cosY + y * sinY
}
}
private fun drawCube(g: Graphics2D) {
g.translate(width / 2, height / 2)
for (edge in edges) {
val xy1 = nodes[edge[0]]
val xy2 = nodes[edge[1]]
g.drawLine(Math.round(xy1[0]).toInt(), Math.round(xy1[1]).toInt(),
Math.round(xy2[0]).toInt(), Math.round(xy2[1]).toInt())
}
for (node in nodes) {
g.fillOval(Math.round(node[0]).toInt() - 4, Math.round(node[1]).toInt() - 4, 8, 8)
}
}
override public fun paintComponent(gg: Graphics) {
super.paintComponent(gg)
val g = gg as Graphics2D
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
g.color = Color.blue
drawCube(g)
}
}
fun main(args: Array<String>) {
SwingUtilities.invokeLater {
val f = JFrame()
f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE
f.title = "Rotating cube"
f.isResizable = false
f.add(RotatingCube(), BorderLayout.CENTER)
f.pack()
f.setLocationRelativeTo(null)
f.isVisible = true
}
}</lang>
Lua
<lang lua>local abs,atan,cos,floor,pi,sin,sqrt = math.abs,math.atan,math.cos,math.floor,math.pi,math.sin,math.sqrt local bitmap = {
init = function(self, w, h, value)
self.w, self.h, self.pixels = w, h, {}
for y=1,h do self.pixels[y]={} end
self:clear(value)
end,
clear = function(self, value)
for y=1,self.h do
for x=1,self.w do
self.pixels[y][x] = value or " "
end
end
end,
set = function(self, x, y, value)
x,y = floor(x),floor(y)
if x>0 and y>0 and x<=self.w and y<=self.h then
self.pixels[y][x] = value or "#"
end
end,
line = function(self, x1, y1, x2, y2, c)
x1,y1,x2,y2 = floor(x1),floor(y1),floor(x2),floor(y2)
local dx, sx = abs(x2-x1), x1<x2 and 1 or -1
local dy, sy = abs(y2-y1), y1<y2 and 1 or -1
local err = floor((dx>dy and dx or -dy)/2)
while(true) do
self:set(x1, y1, c)
if (x1==x2 and y1==y2) then break end
if (err > -dx) then
err, x1 = err-dy, x1+sx
if (x1==x2 and y1==y2) then
self:set(x1, y1, c)
break
end
end
if (err < dy) then
err, y1 = err+dx, y1+sy
end
end
end,
render = function(self)
for y=1,self.h do
print(table.concat(self.pixels[y]))
end
end,
} screen = {
clear = function()
os.execute("cls") -- or? os.execute("clear"), or? io.write("\027[2J\027[H"), or etc?
end,
} local camera = { fl = 2.5 } local L = 0.5 local cube = {
verts = { {L,L,L}, {L,-L,L}, {-L,-L,L}, {-L,L,L}, {L,L,-L}, {L,-L,-L}, {-L,-L,-L}, {-L,L,-L} },
edges = { {1,2}, {2,3}, {3,4}, {4,1}, {5,6}, {6,7}, {7,8}, {8,5}, {1,5}, {2,6}, {3,7}, {4,8} },
rotate = function(self, rx, ry)
local cx,sx = cos(rx),sin(rx)
local cy,sy = cos(ry),sin(ry)
for i,v in ipairs(self.verts) do
local x,y,z = v[1],v[2],v[3]
v[1], v[2], v[3] = x*cx-z*sx, y*cy-x*sx*sy-z*cx*sy, x*sx*cy+y*sy+z*cx*cy
end
end,
} local renderer = {
render = function(self, shape, camera, bitmap)
local fl = camera.fl
local ox, oy = bitmap.w/2, bitmap.h/2
local mx, my = bitmap.w/2, bitmap.h/2
local rpverts = {}
for i,v in ipairs(shape.verts) do
local x,y,z = v[1],v[2],v[3]
local px = ox + mx * (fl*x)/(fl-z)
local py = oy + my * (fl*y)/(fl-z)
rpverts[i] = { px,py }
end
for i,e in ipairs(shape.edges) do
local v1, v2 = rpverts[e[1]], rpverts[e[2]]
bitmap:line( v1[1], v1[2], v2[1], v2[2], "██" )
end
end
} -- bitmap:init(40,40) cube:rotate(pi/4, atan(sqrt(2))) for i=1,60 do
cube:rotate(pi/60,0)
bitmap:clear("··")
renderer:render(cube, camera, bitmap)
screen:clear()
bitmap:render()
end</lang>
- Output:
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Maple
<lang maple>plots:-display(
seq(
plots:-display(
plottools[cuboid]( [0,0,0], [1,1,1] ),
axes=none, scaling=constrained, orientation=[0,45,i] ),
i = 0..360, 20 ),
insequence=true );</lang>
Mathematica
<lang Mathematica>Dynamic[
Graphics3D[
GeometricTransformation[
GeometricTransformation[Cuboid[], RotationTransform[Pi/4, {1, 1, 0}]],
RotationTransform[Clock[2 Pi], {0, 0, 1}]
],
Boxed -> False]]</lang>
Nim
<lang Nim>import math import sdl2
const
Width = 500 Height = 500 Offset = 500 / 2
var nodes = [(x: -100.0, y: -100.0, z: -100.0),
(x: -100.0, y: -100.0, z: 100.0),
(x: -100.0, y: 100.0, z: -100.0),
(x: -100.0, y: 100.0, z: 100.0),
(x: 100.0, y: -100.0, z: -100.0),
(x: 100.0, y: -100.0, z: 100.0),
(x: 100.0, y: 100.0, z: -100.0),
(x: 100.0, y: 100.0, z: 100.0)]
const Edges = [(a: 0, b: 1), (a: 1, b: 3), (a: 3, b: 2), (a: 2, b: 0),
(a: 4, b: 5), (a: 5, b: 7), (a: 7, b: 6), (a: 6, b: 4),
(a: 0, b: 4), (a: 1, b: 5), (a: 2, b: 6), (a: 3, b: 7)]
var
window: WindowPtr renderer: RendererPtr event: Event endSimulation = false
- ---------------------------------------------------------------------------------------------------
proc rotateCube(angleX, angleY: float) =
let sinX = sin(angleX) cosX = cos(angleX) sinY = sin(angleY) cosY = cos(angleY)
for node in nodes.mitems: var (x, y, z) = node node.x = x * cosX - z * sinX node.z = z * cosX + x * sinX z = node.z node.y = y * cosY - z * sinY node.z = z * cosY + y * sinY
- ---------------------------------------------------------------------------------------------------
proc pollQuit(): bool =
while pollEvent(event):
if event.kind == QuitEvent:
return true
- ---------------------------------------------------------------------------------------------------
proc drawCube(): bool =
var rect: Rect = (cint(0), cint(0), cint(Width), cint(Height))
rotateCube(PI / 4, arctan(sqrt(2.0)))
for frame in 0..359:
renderer.setDrawColor((0u8, 0u8, 0u8, 255u8))
renderer.fillRect(addr(rect))
renderer.setDrawColor((0u8, 220u8, 0u8, 255u8))
for edge in Edges:
let xy1 = nodes[edge.a]
let xy2 = nodes[edge.b]
renderer.drawLine(cint(xy1.x + Offset), cint(xy1.y + Offset),
cint(xy2.x + Offset), cint(xy2.y + Offset))
rotateCube(PI / 180, 0)
renderer.present()
if pollQuit(): return true
delay 10
- ———————————————————————————————————————————————————————————————————————————————————————————————————
if sdl2.init(INIT_EVERYTHING) == SdlError:
quit(QuitFailure)
window = createWindow("Rotating cube", 10, 10, 500, 500, 0) renderer = createRenderer(window, -1, Renderer_Accelerated)
while not endSimulation:
endSimulation = drawCube()
window.destroy()</lang>
Objeck
<lang objeck> use Collection.Generic; use Game.SDL2; use Game.Framework;
class RotatingCube {
# game framework @framework : GameFramework; @initialized : Bool;
@nodes : Float[,]; @edges : Int[,];
New() {
@initialized := true;
@framework := GameFramework->New(GameConsts->SCREEN_WIDTH, GameConsts->SCREEN_HEIGHT, "Rotating Cube");
@nodes := [[-100.0, -100.0, -100.0], [-100.0, -100.0, 100.0], [-100.0, 100.0, -100.0],
[-100.0, 100.0, 100.0], [100.0, -100.0, -100.0], [100.0, -100.0, 100.0],
[100.0, 100.0, -100.0], [100.0, 100.0, 100.0]];
@edges := [[0, 1], [1, 3], [3, 2], [2, 0], [4, 5], [5, 7],
[7, 6], [6, 4], [0, 4], [1, 5], [2, 6], [3, 7]];
}
function : Main(args : String[]) ~ Nil {
RotatingCube->New()->Play();
}
method : Play() ~ Nil {
if(@initialized) {
# initialization
@framework->SetClearColor(Color->New(0, 0, 0));
RotateCube(Float->Pi(), 2.0->SquareRoot()->ArcTan());
quit := false;
e := @framework->GetEvent();
while(<>quit) {
@framework->FrameStart();
@framework->Clear();
# process input
while(e->Poll() <> 0) {
# joystick
if(e->GetType() = EventType->SDL_QUIT) {
quit := true;
};
};
#draw
DrawCube();
@framework->FrameEnd();
# render
@framework->Show();
Timer->Delay(200);
RotateCube (Float->Pi() / 180.0, 0.0);
};
}
else {
"--- Error Initializing Environment ---"->ErrorLine();
return;
};
leaving {
@framework->FreeShapes();
};
}
method : RotateCube(angleX : Float, angleY : Float) ~ Nil {
sinX := angleX->Sin();
cosX := angleX->Cos();
sinY := angleY->Sin();
cosY := angleY->Cos();
node_sizes := @nodes->Size();
size := node_sizes[0];
for(i := 0; i < size; i += 1;) {
x := @nodes[i, 0];
y := @nodes[i, 1];
z := @nodes[i, 2];
@nodes[i, 0] := x * cosX - z * sinX;
@nodes[i, 2] := z * cosX + x * sinX;
z := @nodes[i, 2];
@nodes[i, 1] := y * cosY - z * sinY;
@nodes[i, 2] := z * cosY + y * sinY;
};
}
method : DrawCube() ~ Nil {
edge_sizes := @edges->Size();
size := edge_sizes[0];
@framework->GetRenderer()->SetDrawColor(0, 220, 0, 0);
for(i := 0; i < size; i += 1;) {
x0y0 := @nodes[@edges[i, 0], 0];
x0y1 := @nodes[@edges[i, 0], 1];
x1y0 := @nodes[@edges[i, 1], 0];
x1y1 := @nodes[@edges[i, 1], 1];
@framework->GetRenderer()->DrawLine(x0y0 + GameConsts->DRAW_OFFSET, x0y1 + GameConsts->DRAW_OFFSET, x1y0 + GameConsts->DRAW_OFFSET, x1y1 + GameConsts->DRAW_OFFSET); }; }
}
consts GameConsts {
SCREEN_WIDTH := 600, SCREEN_HEIGHT := 600, DRAW_OFFSET := 300
}</lang>
Perl
<lang perl>#!/usr/bin/perl
use strict; # http://www.rosettacode.org/wiki/Draw_a_rotating_cube use warnings; use Tk; use Time::HiRes qw( time );
my $size = 600; my $wait = int 1000 / 30; my ($height, $width) = ($size, $size * sqrt 8/9); my $mid = $width / 2; my $rot = atan2(0, -1) / 3; # middle corners every 60 degrees
my $mw = MainWindow->new; my $c = $mw->Canvas(-width => $width, -height => $height)->pack; $c->Tk::bind('<ButtonRelease>' => sub {$mw->destroy}); # click to exit draw(); MainLoop;
sub draw
{
my $angle = time - $^T; # full rotation every 2*PI seconds
my @points = map { $mid + $mid * cos $angle + $_ * $rot,
$height * ($_ % 2 + 1) / 3 } 0 .. 5;
$c->delete('all');
$c->createLine( @points[-12 .. 1], $mid, 0, -width => 5,);
$c->createLine( @points[4, 5], $mid, 0, @points[8, 9], -width => 5,);
$c->createLine( @points[2, 3], $mid, $height, @points[6, 7], -width => 5,);
$c->createLine( $mid, $height, @points[10, 11], -width => 5,);
$mw->after($wait, \&draw);
}</lang>
Phix
<lang Phix>-- demo\rosetta\DrawRotatingCube.exw include pGUI.e
Ihandle canvas cdCanvas cd_canvas
-- -- define 8 corners equidistant from {0,0,0}: -- -- 6-----2 -- 5-----1 3 -- 8-----4 -- -- ie the right face is 1-2-3-4 clockwise, and the left face -- is 5-6-7-8 counter-clockwise (unless using x-ray vision). -- enum X, Y, Z constant l = 100 constant corners = {{+l,+l,+l},
{+l,+l,-l},
{+l,-l,-l},
{+l,-l,+l},
{-l,+l,+l},
{-l,+l,-l},
{-l,-l,-l},
{-l,-l,+l}}
constant faces = {{CD_RED, 1,2,3,4}, -- right
{CD_YELLOW, 1,5,6,2}, -- top
{CD_GREEN, 1,4,8,5}, -- front
{CD_BLUE, 2,3,7,6}, -- back
{CD_WHITE, 3,4,8,7}, -- btm
{CD_ORANGE, 5,6,7,8}} -- left
atom ry = 0 -- rotation angle, 0..359, on a timer
constant naxes = {{Y,Z}, -- (rotate about the X-axis)
{X,Z}, -- (rotate about the Y-axis)
{X,Y}} -- (rotate about the Z-axis)
function rotate(sequence points, atom angle, integer axis) -- -- rotate points by the specified angle about the given axis --
atom radians = angle*CD_DEG2RAD,
sin_t = sin(radians),
cos_t = cos(radians)
integer {nx,ny} = naxes[axis]
for i=1 to length(points) do
atom x = points[i][nx],
y = points[i][ny]
points[i][nx] = x * cos_t - y * sin_t
points[i][ny] = y * cos_t + x * sin_t
end for
return points
end function
function projection(sequence points, atom d) -- -- project points from {0,0,d} onto the perpendicular plane through {0,0,0} --
for i=1 to length(points) do
atom {x,y,z} = points[i]
points[i][X] = x/(1-z/d)
points[i][Y] = y/(1-z/d)
end for
return points
end function
function nearest(sequence points) -- -- return the index of the nearest point (highest z value) --
integer np = 1
atom maxz = points[1][Z]
for i=2 to length(points) do
atom piz = points[i][Z]
if piz>maxz then
maxz = piz
np = i
end if
end for
return np
end function
procedure vertices(integer wx, wh, sequence points, face) -- (common code for line/fill drawing)
for i=2 to length(face) do
integer fi = face[i]
cdCanvasVertex(cd_canvas,wx+points[fi][X],wh-points[fi][Y])
end for
end procedure
procedure draw_cube(integer wx, wh)
sequence points = corners
points = rotate(points,45,X) -- (cube should now look like a H)
atom zr = 90-arctan(sqrt(2))*CD_RAD2DEG -- (about 35 degrees)
points = rotate(points,zr,Z) -- (cube should now look like an italic H)
points = rotate(points,ry,Y) -- (timed, two corners should remain static)
points = projection(points,1000)
integer np = nearest(points)
--
-- find the three faces that contain the nearest point,
-- then order by/draw them furthest diag away first.
-- (one of them, and theoretically two but not at the
-- rotations in use, may be completely obscured, due
-- to the effects of the perspective projection.)
--
sequence faceset = {}
for i=1 to length(faces) do
sequence fi = faces[i]
integer k = find(np,fi)
if k then
integer diag = mod(k,4)+2
diag = fi[diag]
faceset = append(faceset,{points[diag][Z],i})
end if
end for
faceset = sort(faceset)
for i=1 to length(faceset) do
integer fdx = faceset[i][2]
sequence fi = faces[fdx]
cdCanvasSetForeground(cd_canvas,fi[1])
-- draw edges (anti-aliased)
cdCanvasBegin(cd_canvas,CD_CLOSED_LINES)
vertices(wx,wh,points,fi)
cdCanvasEnd(cd_canvas)
-- fill sides (else would get bresenham edges)
cdCanvasBegin(cd_canvas,CD_FILL)
vertices(wx,wh,points,fi)
cdCanvasEnd(cd_canvas)
end for
end procedure
function canvas_action_cb(Ihandle canvas)
cdCanvasActivate(cd_canvas)
cdCanvasClear(cd_canvas)
integer {wx, wh} = sq_floor_div(IupGetIntInt(canvas, "DRAWSIZE"),2)
draw_cube(wx,wh)
cdCanvasFlush(cd_canvas)
return IUP_DEFAULT
end function
function canvas_map_cb(Ihandle canvas)
atom res = IupGetDouble(NULL, "SCREENDPI")/25.4
IupGLMakeCurrent(canvas)
cd_canvas = cdCreateCanvas(CD_GL, "10x10 %g", {res})
cdCanvasSetBackground(cd_canvas, CD_PARCHMENT)
return IUP_DEFAULT
end function
function canvas_unmap_cb(Ihandle canvas)
cdKillCanvas(cd_canvas) return IUP_DEFAULT
end function
function canvas_resize_cb(Ihandle /*canvas*/)
integer {canvas_width, canvas_height} = IupGetIntInt(canvas, "DRAWSIZE")
atom res = IupGetDouble(NULL, "SCREENDPI")/25.4
cdCanvasSetAttribute(cd_canvas, "SIZE", "%dx%d %g", {canvas_width, canvas_height, res})
return IUP_DEFAULT
end function
function timer_cb(Ihandle /*ih*/)
ry = mod(ry+359,360) IupRedraw(canvas) return IUP_IGNORE
end function
procedure main()
IupOpen()
IupImageLibOpen()
canvas = IupGLCanvas()
IupSetAttribute(canvas, "RASTERSIZE", "640x480")
IupSetCallback(canvas, "ACTION", Icallback("canvas_action_cb"))
IupSetCallback(canvas, "MAP_CB", Icallback("canvas_map_cb"))
IupSetCallback(canvas, "UNMAP_CB", Icallback("canvas_unmap_cb"))
IupSetCallback(canvas, "RESIZE_CB", Icallback("canvas_resize_cb"))
Ihandle dlg = IupDialog(IupVbox({canvas}))
IupSetAttribute(dlg,"TITLE","Draw a Rotating Cube");
IupShow(dlg)
IupSetAttribute(canvas, "RASTERSIZE", NULL)
Ihandle hTimer = IupTimer(Icallback("timer_cb"), 40)
IupMainLoop()
IupClose()
end procedure
main()</lang>
PostScript
Don't send this to your printer! <lang postscript>%!PS-Adobe-3.0 %%BoundingBox: 0 0 400 400
/ed { exch def } def /roty { dup sin /s ed cos /c ed [[c 0 s neg] [0 1 0] [s 0 c]] } def /rotz { dup sin /s ed cos /c ed [[c s neg 0] [s c 0] [0 0 1]] } def /dot { /a ed /b ed a 0 get b 0 get mul a 1 get b 1 get mul a 2 get b 2 get mul add add } def
/mmul { /v ed [exch {v dot} forall] } def /transall { /m ed [exch {m exch mmul}forall] } def
/vt [[1 1 1] [-1 1 1] [1 -1 1] [-1 -1 1] [1 1 -1] [-1 1 -1] [1 -1 -1] [-1 -1 -1]] -45 roty transall 2 sqrt 1 atan rotz transall def
/xy { exch get {} forall pop } def /page { /a ed /v vt a roty transall def 0 setlinewidth 100 100 scale 2 2 translate /edge { v xy moveto v xy lineto stroke } def
0 1 2 3 4 5 6 7 0 2 1 3 4 6 5 7 0 4 1 5 2 6 3 7 1 1 12 { pop edge } for showpage } def
0 {3.2 add dup page } loop %%EOF</lang>
Processing
Create a cube in Processing with box(), rotate the scene with rotate(), and drive the rotation with either the built-in millis() or frameCount timers.
<lang Processing>void setup() {
size(500, 500, P3D);
} void draw() {
background(0); // position translate(width/2, height/2, -width/2); // optional fill and lighting colors noStroke(); strokeWeight(4); fill(192, 255, 192); pointLight(255, 255, 255, 0, -500, 500); // rotation driven by built-in timer rotateY(millis()/1000.0); // draw box box(300, 300, 300);
}</lang>
Python
See also: Draw_a_cuboid
Short version
<lang python>from visual import * scene.title = "VPython: Draw a rotating cube"
scene.range = 2 scene.autocenter = True
print "Drag with right mousebutton to rotate view." print "Drag up+down with middle mousebutton to zoom."
deg45 = math.radians(45.0) # 0.785398163397
cube = box() # using defaults, see http://www.vpython.org/contents/docs/defaults.html cube.rotate( angle=deg45, axis=(1,0,0) ) cube.rotate( angle=deg45, axis=(0,0,1) )
while True: # Animation-loop
rate(50) cube.rotate( angle=0.005, axis=(0,1,0) )
</lang>
Racket
<lang racket>#lang racket/gui (require math/matrix math/array)
(define (Rx θ)
(matrix [[1.0 0.0 0.0]
[0.0 (cos θ) (- (sin θ))]
[0.0 (sin θ) (cos θ)]]))
(define (Ry θ)
(matrix [[ (cos θ) 0.0 (sin θ)]
[ 0.0 1.0 0.0 ]
[(- (sin θ)) 0.0 (cos θ)]]))
(define (Rz θ)
(matrix [[(cos θ) (- (sin θ)) 0.0]
[(sin θ) (cos θ) 0.0]
[ 0.0 0.0 1.0]]))
(define base-matrix
(matrix* (identity-matrix 3 100.0)
(Rx (- (/ pi 2) (atan (sqrt 2))))
(Rz (/ pi 4.0))))
(define (current-matrix)
(matrix* (Ry (/ (current-inexact-milliseconds) 1000.))
base-matrix))
(define corners
(for*/list ([x '(-1.0 1.0)]
[y '(-1.0 1.0)]
[z '(-1.0 1.0)])
(matrix [[x] [y] [z]])))
(define lines
'((0 1) (0 2) (0 4) (1 3) (1 5) (2 3) (2 6) (3 7) (4 5) (4 6) (5 7) (6 7)))
(define ox 200.) (define oy 200.)
(define (draw-line dc a b)
(send dc draw-line
(+ ox (array-ref a #(0 0)))
(+ oy (array-ref a #(1 0)))
(+ ox (array-ref b #(0 0)))
(+ oy (array-ref b #(1 0)))))
(define (draw-cube c dc)
(define-values (w h) (send dc get-size))
(set! ox (/ w 2))
(set! oy (/ h 2))
(define cs (for/vector ([c (in-list corners)])
(matrix* (current-matrix) c)))
(for ([l (in-list lines)])
(match-define (list i j) l)
(draw-line dc (vector-ref cs i) (vector-ref cs j))))
(define f (new frame% [label "cube"])) (define c (new canvas% [parent f] [min-width 400] [min-height 400] [paint-callback draw-cube])) (send f show #t)
(send* (send c get-dc)
(set-pen "black" 1 'solid) (set-smoothing 'smoothed))
(define (refresh)
(send c refresh))
(define t (new timer% [notify-callback refresh] [interval 35] [just-once? #f]))</lang>
Raku
(formerly Perl 6)
Raku has no native graphics libraries built in, but makes it fairly easy to bind to third party libraries. Here we'll use bindings to Libcaca, the Color ASCII Art library to generate a rotating cube in an ASCII terminal.
<lang perl6>use Terminal::Caca; given my $canvas = Terminal::Caca.new {
.title('Rosetta Code - Rotating cube - Press any key to exit');
sub scale-and-translate($x, $y, $z) {
$x * 5 / ( 5 + $z ) * 15 + 40,
$y * 5 / ( 5 + $z ) * 7 + 15,
$z;
}
sub rotate3d-x( $x, $y, $z, $angle ) {
my ($cosθ, $sinθ) = cis( $angle * π / 180.0 ).reals;
$x,
$y * $cosθ - $z * $sinθ,
$y * $sinθ + $z * $cosθ;
}
sub rotate3d-y( $x, $y, $z, $angle ) {
my ($cosθ, $sinθ) = cis( $angle * π / 180.0 ).reals;
$x * $cosθ - $z * $sinθ,
$y,
$x * $sinθ + $z * $cosθ;
}
sub rotate3d-z( $x, $y, $z, $angle ) {
my ($cosθ, $sinθ) = cis( $angle * π / 180.0 ).reals;
$x * $cosθ - $y * $sinθ,
$x * $cosθ + $y * $sinθ,
$z;
}
# Unit cube from polygon mesh, aligned to axes
my @mesh =
[ [1, 1, -1], [-1, -1, -1], [-1, 1, -1] ], # far face
[ [1, 1, -1], [-1, -1, -1], [ 1, -1, -1] ],
[ [1, 1, 1], [-1, -1, 1], [-1, 1, 1] ], # near face
[ [1, 1, 1], [-1, -1, 1], [ 1, -1, 1] ];
@mesh.push: [$_».rotate( 1)».Array] for @mesh[^4]; # positive and
@mesh.push: [$_».rotate(-1)».Array] for @mesh[^4]; # negative rotations
# Rotate to correct orientation for task
for ^@mesh X ^@mesh[0] -> ($i, $j) {
@(@mesh[$i;$j]) = rotate3d-x |@mesh[$i;$j], 45;
@(@mesh[$i;$j]) = rotate3d-z |@mesh[$i;$j], 40;
}
my @colors = red, blue, green, cyan, magenta, yellow;
loop {
for ^359 -> $angle {
.color( white, white );
.clear;
# Flatten 3D into 2D and rotate for all faces
my @faces-z;
my $c-index = 0;
for @mesh -> @triangle {
my @points;
my $sum-z = 0;
for @triangle -> @node {
my ($px, $py, $z) = scale-and-translate |rotate3d-y |@node, $angle;
@points.append: $px.Int, $py.Int;
$sum-z += $z;
}
@faces-z.push: %(
color => @colors[$c-index++ div 2],
points => @points,
avg-z => $sum-z / +@points;
);
}
# Draw all faces
# Sort by z to draw farthest first
for @faces-z.sort( -*.<avg-z> ) -> %face {
# Draw filled triangle
.color( %face<color>, %face<color> );
.fill-triangle( |%face<points> );
# And frame
.color( black, black );
.thin-triangle( |%face<points> );
}
.refresh;
exit if .wait-for-event(key-press);
}
}
# Cleanup on scope exit
LEAVE {
.cleanup;
}
}</lang>
Ring
<lang ring>
- ===================================================================#
- Based on Original Sample from RayLib (https://www.raylib.com/)
- Ported to RingRayLib by Ring Team
- ===================================================================#
load "raylib.ring"
screenWidth = 800 screenHeight = 450
InitWindow(screenWidth, screenHeight, "raylib [core] example - 3d picking")
camera = Camera3D( 10, 10, 10, 0, 0, 0 , 0, 1, 0 , 45, CAMERA_PERSPECTIVE )
cubePosition = Vector3( 0, 1, 0 ) cubeSize = Vector3( 2, 2, 2 )
ray = Ray(0,0,0,0,0,0)
collision = false
SetCameraMode(camera, CAMERA_FREE)
SetTargetFPS(60)
while !WindowShouldClose()
UpdateCamera(camera)
if IsMouseButtonPressed(MOUSE_LEFT_BUTTON)
if !collision
ray = GetMouseRay(GetMousePosition(), camera)
collision = CheckCollisionRayBox(ray,
BoundingBox( cubePosition.x - cubeSize.x/2, cubePosition.y - cubeSize.y/2, cubePosition.z - cubeSize.z/2,
cubePosition.x + cubeSize.x/2, cubePosition.y + cubeSize.y/2, cubePosition.z + cubeSize.z/2 ) )
else collision = false
ok
ok
BeginDrawing()
ClearBackground(RAYWHITE)
BeginMode3D(camera)
if collision
DrawCube(cubePosition, cubeSize.x, cubeSize.y, cubeSize.z, RED)
DrawCubeWires(cubePosition, cubeSize.x, cubeSize.y, cubeSize.z, MAROON)
DrawCubeWires(cubePosition, cubeSize.x + 0.2f, cubeSize.y + 0.2f, cubeSize.z + 0.2f, GREEN)
else
DrawCube(cubePosition, cubeSize.x, cubeSize.y, cubeSize.z, GRAY)
DrawCubeWires(cubePosition, cubeSize.x, cubeSize.y, cubeSize.z, DARKGRAY)
ok
DrawRay(ray, MAROON)
DrawGrid(10, 1)
EndMode3D()
DrawText("Try selecting the box with mouse!", 240, 10, 20, DARKGRAY)
if collision DrawText("BOX SELECTED", (screenWidth - MeasureText("BOX SELECTED", 30)) / 2, screenHeight * 0.1f, 30, GREEN) ok
DrawFPS(10, 10)
EndDrawing()
end
CloseWindow() </lang> Rotating a Cube
Scala
Java Swing Interoperability
<lang Scala>import java.awt.event.ActionEvent import java.awt._
import javax.swing.{JFrame, JPanel, Timer}
import scala.math.{Pi, atan, cos, sin, sqrt}
object RotatingCube extends App {
class RotatingCube extends JPanel {
private val vertices: Vector[Array[Double]] =
Vector(Array(-1, -1, -1), Array(-1, -1, 1), Array(-1, 1, -1),
Array(-1, 1, 1), Array(1, -1, -1), Array(1, -1, 1), Array(1, 1, -1), Array(1, 1, 1))
private val edges: Vector[(Int, Int)] =
Vector((0, 1), (1, 3), (3, 2), (2, 0), (4, 5), (5, 7),
(7, 6), (6, 4), (0, 4), (1, 5), (2, 6), (3, 7))
setPreferredSize(new Dimension(640, 640)) setBackground(Color.white) scale(100) rotateCube(Pi / 4, atan(sqrt(2)))
new Timer(17, (_: ActionEvent) => {
rotateCube(Pi / 180, 0)
repaint()
}).start()
override def paintComponent(gg: Graphics): Unit = {
def drawCube(g: Graphics2D): Unit = {
g.translate(getWidth / 2, getHeight / 2)
for {edge <- edges
xy1: Array[Double] = vertices(edge._1)
xy2: Array[Double] = vertices(edge._2)
} {
g.drawLine(xy1(0).toInt, xy1(1).toInt, xy2(0).toInt, xy2(1).toInt)
g.fillOval(xy1(0).toInt -4, xy1(1).toInt - 4, 8, 8)
g.setColor(Color.black)
}
}
super.paintComponent(gg)
val g: Graphics2D = gg.asInstanceOf[Graphics2D]
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
drawCube(g)
}
private def scale(s: Double): Unit = {
for {node <- vertices
i <- node.indices
} node(i) *= s
}
private def rotateCube(angleX: Double, angleY: Double): Unit = {
def sinCos(x: Double) = (sin(x), cos(x))
val ((sinX, cosX), (sinY, cosY)) = (sinCos(angleX), sinCos(angleY))
for {
node <- vertices
x: Double = node(0)
y: Double = node(1)
} {
def f(p: Double, q: Double)(a: Double, b: Double) = a * p + b * q
def fx(a: Double, b: Double) = f(cosX, sinX)(a, b)
def fy(a: Double, b: Double) = f(cosY, sinY)(a, b)
node(0) = fx(x, -node(2))
val z = fx(node(2), x)
node(1) = fy(y, -z)
node(2) = fy(z, y)
}
}
}
new JFrame("Rotating Cube") {
add(new RotatingCube(), BorderLayout.CENTER)
pack()
setDefaultCloseOperation(javax.swing.WindowConstants.EXIT_ON_CLOSE)
setLocationRelativeTo(null)
setResizable(false)
setVisible(true)
}
}</lang>
Tcl
See also Draw a cuboid. This implementation uses tcllib's Linear Algebra module for some matrix ops to handle the screen transform and (animated!) rotation. Rendering is in a Tk canvas.
The *Matrix* procedure is something unique to Tcl: it's essentially a control construct that leverages *expr* to make declaring matrices much more convenient than hand-rolling lists.
There is a bit of wander in the top and bottom points, which might just be due to rounding error in the cube's initial "rotation into position".
See this wiki page (and others linked from it) for many similar examples.
<lang Tcl># matrix operation support: package require math::linearalgebra namespace import ::math::linearalgebra::matmul namespace import ::math::linearalgebra::crossproduct namespace import ::math::linearalgebra::dotproduct namespace import ::math::linearalgebra::sub
- returns a cube as a list of faces,
- where each face is a list of (3space) points
proc make_cube Template:Radius 1 {
set dirs {
A { 1 1 1}
B { 1 1 -1}
C { 1 -1 -1}
D { 1 -1 1}
E {-1 1 1}
F {-1 1 -1}
G {-1 -1 -1}
H {-1 -1 1}
}
set faces {
{A B C D}
{D C G H}
{H G F E}
{E F B A}
{A D H E}
{C B F G}
}
lmap fa $faces {
lmap dir $fa {
lmap x [dict get $dirs $dir] {
expr {1.0 * $x * $radius}
}
}
}
}
- a matrix constructor
proc Matrix {m} {
tailcall lmap row $m {
lmap e $row {
expr 1.0*($e)
}
}
}
proc identity {} {
Matrix {
{1 0 0}
{0 1 0}
{0 0 1}
}
}
- some matrices useful for animation:
proc rotateZ {theta} {
Matrix {
{ cos($theta) -sin($theta) 0 }
{ sin($theta) cos($theta) 0 }
{ 0 0 1 }
}
} proc rotateY {theta} {
Matrix {
{ sin($theta) 0 cos($theta) }
{ 0 1 0 }
{ cos($theta) 0 -sin($theta) }
}
} proc rotateX {theta} {
Matrix {
{ 1 0 0 }
{ 0 cos($theta) -sin($theta) }
{ 0 sin($theta) cos($theta) }
}
}
proc camera {flen} {
Matrix {
{ $flen 0 0 }
{ 0 $flen 0 }
{ 0 0 0 }
}
}
proc render {canvas object} {
set W [winfo width $canvas] set H [winfo height $canvas]
set fl 1.0
set t [expr {[clock microseconds] / 1000000.0}]
set transform [identity]
set transform [matmul $transform [rotateX [expr {atan(1)}]]]
set transform [matmul $transform [rotateZ [expr {atan(1)}]]]
set transform [matmul $transform [rotateY $t]] set transform [matmul $transform [camera $fl]]
foreach face $object {
# do transformations into screen space:
set points [lmap p $face { matmul $p $transform }]
# calculate a normal
set o [lindex $points 0]
set v1 [sub [lindex $points 1] $o]
set v2 [sub [lindex $points 2] $o]
set normal [crossproduct $v1 $v2]
set cosi [dotproduct $normal {0 0 -1.0}]
if {$cosi <= 0} { ;# rear-facing!
continue
}
set points [lmap p $points {
lassign $p x y
list [expr {$x + $W/2}] [expr {$y + $H/2}]
}]
set points [concat {*}$points]
$canvas create poly $points -outline black -fill red
}
}
package require Tk pack [canvas .c] -expand yes -fill both
proc tick {} {
.c delete all render .c $::world after 50 tick
} set ::world [make_cube 100] tick</lang>
TI-83 BASIC
<lang ti83b>:-1→Xmin:1→Xmax
- -1→Ymin:1→Ymax
- AxesOff
- Degrees
- While 1
- For(X,0,359,5
- sin(X-120→I%
- sin(X→PV
- sin(X+120→FV
- Line(0,1,I%,.3
- Line(0,1,PV,.3
- Line(0,1,FV,.3
- Line(0,-1,-I%,-.3
- Line(0,-1,-PV,-.3
- Line(0,-1,-FV,-.3
- Line(.3,I%,-.3,-PV
- Line(.3,I%,-.3,-FV
- Line(.3,PV,-.3,-I%
- Line(.3,PV,-.3,-FV
- Line(.3,FV,-.3,-I%
- Line(.3,FV,-.3,-PV
- End
- End</lang>
I%, PV, and FV are all finance variables that can be found in the finance menu (inside the APPS menu on TI-83+ and up). Finance variables are much faster than normal variables.
XPL0
The main challenge was figuring out the initial coordinates of the cube. Zometool came to the rescue. The program runs much smoother than the animated gif. <lang XPL0>def Size=100., Speed=0.05; \drawing size and rotation speed real X, Y, Z, Farthest; \arrays: 3D coordinates of vertices int I, J, K, ZI, Edge; def R2=sqrt(2.), R3=sqrt(3.), R13=sqrt(1./3.), R23=sqrt(2./3.), R232=R23*2.; \vertex:0 1 2 3 4 5 6 7 [X:= [ 0., R2, 0., -R2, 0., R2, 0., -R2];
Y:= [ -R3, -R13, R13, -R13, -R13, R13, R3, R13]; Z:= [ 0., -R23, -R232, -R23, R232, R23, 0., R23];
Edge:= [0,1, 1,2, 2,3, 3,0, 4,5, 5,6, 6,7, 7,4, 0,4, 1,5, 2,6, 3,7]; SetVid($101); \set 640x480x8 graphics repeat Farthest:= 0.0; \find the farthest vertex
for I:= 0 to 8-1 do
if Z(I) > Farthest then [Farthest:= Z(I); ZI:= I];
Clear; \erase screen
for I:= 0 to 2*12-1 do \for all the vertices...
[J:= Edge(I); I:= I+1; \get vertex numbers for edge
Move(Fix(X(J)*Size)+640/2, Fix(Y(J)*Size)+480/2);
K:= Edge(I);
Line(Fix(X(K)*Size)+640/2, Fix(Y(K)*Size)+480/2,
if J=ZI ! K=ZI then $F001 \dashed blue\ else $0C \red\);
];
DelayUS(55000);
for I:= 0 to 8-1 do
[X(I):= X(I) + Z(I)*Speed; \rotate vertices about Y axis
Z(I):= Z(I) - X(I)*Speed; \ (which rotates in X-Z plane)
];
until KeyHit; \run until a key is struck SetVid(3); \restore normal text mode ]</lang>
- Output:
