Revision 5b4a2d76
Added by Leszek Koltunski over 5 years ago
src/main/AndroidManifest.xml | ||
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52 | 52 |
<activity android:name=".glow.GlowActivity"/> |
53 | 53 |
<activity android:name=".movingglow.MovingGlowActivity"/> |
54 | 54 |
<activity android:name=".earth.EarthActivity"/> |
55 |
<activity android:name=".earth.EarthActivity"/>
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|
55 |
<activity android:name=".rubik.RubikActivity"/>
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|
56 | 56 |
</application> |
57 | 57 |
</manifest> |
src/main/java/org/distorted/examples/TableOfContents.java | ||
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69 | 69 |
import org.distorted.examples.glow.GlowActivity; |
70 | 70 |
import org.distorted.examples.movingglow.MovingGlowActivity; |
71 | 71 |
import org.distorted.examples.earth.EarthActivity; |
72 |
import org.distorted.examples.rubik.RubikActivity; |
|
72 | 73 |
|
73 | 74 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
74 | 75 |
|
... | ... | |
406 | 407 |
activityMapping.put(i++, EarthActivity.class); |
407 | 408 |
} |
408 | 409 |
|
410 |
{ |
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411 |
final Map<String, Object> item = new HashMap<>(); |
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item.put(ITEM_IMAGE, R.drawable.icon_example_wip); |
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413 |
item.put(ITEM_TITLE, (i+1)+". "+getText(R.string.example_rubik)); |
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item.put(ITEM_SUBTITLE, getText(R.string.example_rubik_subtitle)); |
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415 |
data.add(item); |
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416 |
activityMapping.put(i++, RubikActivity.class); |
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417 |
} |
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409 | 419 |
final SimpleAdapter dataAdapter = new SimpleAdapter(this, data, R.layout.toc_item, new String[] {ITEM_IMAGE, ITEM_TITLE, ITEM_SUBTITLE}, new int[] {R.id.Image, R.id.Title, R.id.SubTitle}); |
410 | 420 |
setListAdapter(dataAdapter); |
411 | 421 |
|
src/main/java/org/distorted/examples/flag/FlagRenderer.java | ||
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97 | 97 |
effects.apply( new MatrixEffectQuaternion(mQuat1, mCenter) ); |
98 | 98 |
effects.apply( new MatrixEffectQuaternion(mQuat2, mCenter) ); |
99 | 99 |
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100 |
final int GRIDX = 50; |
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101 |
final int GRIDY = 30; |
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102 |
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final Static4D mapFB = new Static4D(0.0f,0.0f,1.0f ,1.0f ); |
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104 |
final Static4D mapLR = new Static4D(0.0f,0.0f,1.0f/GRIDX,1.0f ); |
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105 |
final Static4D mapTB = new Static4D(0.0f,0.0f,1.0f ,1.0f/GRIDY); |
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106 |
|
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100 | 107 |
mScreen = new DistortedScreen(); |
101 |
mScreen.attach(mTexture, effects, new MeshCubes(50,30,1) );
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mScreen.attach(mTexture, effects, new MeshCubes(GRIDX,GRIDY,1, mapFB, mapFB, mapLR, mapLR, mapTB, mapTB) );
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|
102 | 109 |
} |
103 | 110 |
|
104 | 111 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
src/main/java/org/distorted/examples/objecttree/ObjectTreeRenderer.java | ||
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44 | 44 |
import org.distorted.library.type.Dynamic1D; |
45 | 45 |
import org.distorted.library.type.Static1D; |
46 | 46 |
import org.distorted.library.type.Static3D; |
47 |
import org.distorted.library.type.Static4D; |
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47 | 48 |
|
48 | 49 |
import android.graphics.Bitmap; |
49 | 50 |
import android.graphics.BitmapFactory; |
... | ... | |
181 | 182 |
DistortedEffects gridEffects = new DistortedEffects(); |
182 | 183 |
|
183 | 184 |
final int GRID = 20; |
185 |
final Static4D mapFB = new Static4D(0.0f,0.0f,1.0f ,1.0f ); |
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186 |
final Static4D mapLR = new Static4D(0.0f,0.0f,1.0f/GRID,1.0f ); |
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187 |
final Static4D mapTB = new Static4D(0.0f,0.0f,1.0f ,1.0f/GRID); |
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184 | 188 |
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185 | 189 |
if( mMeshFlat==null ) mMeshFlat = new MeshFlat(1,1); |
186 |
if( mMeshCubes==null) mMeshCubes= new MeshCubes(GRID,GRID,1); |
|
190 |
if( mMeshCubes==null) mMeshCubes= new MeshCubes(GRID,GRID,1, mapFB, mapFB, mapLR, mapLR, mapTB, mapTB); |
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191 |
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|
192 |
int gridDepth = mGridTexture.getDepth(mMeshCubes); |
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187 | 193 |
|
188 | 194 |
mRoot = new DistortedNode(mLisaTexture, mEffects, mMeshFlat); |
189 | 195 |
mRoot.attach(mGridTexture,gridEffects,mMeshCubes); |
... | ... | |
209 | 215 |
Dynamic1D sinkDyn = new Dynamic1D(3000,0.0f); |
210 | 216 |
sinkDyn.add(new Static1D(1.0f)); |
211 | 217 |
sinkDyn.add(new Static1D(0.3f)); |
212 |
VertexEffectSink sink = new VertexEffectSink(sinkDyn, new Static3D(gridWidth/2,gridHeight/2, 0));
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218 |
VertexEffectSink sink = new VertexEffectSink(sinkDyn, new Static3D(gridWidth/2.0f, gridHeight/2.0f, gridDepth/2.0f) );
|
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213 | 219 |
gridEffects.apply(sink); |
214 | 220 |
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215 | 221 |
VertexEffectSink.enable(); |
src/main/java/org/distorted/examples/rubik/RubikActivity.java | ||
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1 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
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2 |
// Copyright 2016 Leszek Koltunski // |
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3 |
// // |
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4 |
// This file is part of Distorted. // |
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5 |
// // |
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// Distorted is free software: you can redistribute it and/or modify // |
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7 |
// it under the terms of the GNU General Public License as published by // |
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8 |
// the Free Software Foundation, either version 2 of the License, or // |
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9 |
// (at your option) any later version. // |
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// // |
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// Distorted is distributed in the hope that it will be useful, // |
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// but WITHOUT ANY WARRANTY; without even the implied warranty of // |
|
13 |
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // |
|
14 |
// GNU General Public License for more details. // |
|
15 |
// // |
|
16 |
// You should have received a copy of the GNU General Public License // |
|
17 |
// along with Distorted. If not, see <http://www.gnu.org/licenses/>. // |
|
18 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
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19 |
|
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20 |
package org.distorted.examples.rubik; |
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21 |
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22 |
import android.app.Activity; |
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23 |
import android.os.Bundle; |
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24 |
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25 |
import org.distorted.library.main.Distorted; |
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26 |
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27 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
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28 |
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29 |
public class RubikActivity extends Activity |
|
30 |
{ |
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31 |
private RubikSurfaceView mView; |
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32 |
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33 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
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34 |
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35 |
@Override |
|
36 |
protected void onCreate(Bundle icicle) |
|
37 |
{ |
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38 |
super.onCreate(icicle); |
|
39 |
mView = new RubikSurfaceView(this); |
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40 |
setContentView(mView); |
|
41 |
} |
|
42 |
|
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43 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
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44 |
|
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45 |
@Override |
|
46 |
protected void onPause() |
|
47 |
{ |
|
48 |
mView.onPause(); |
|
49 |
Distorted.onPause(); |
|
50 |
super.onPause(); |
|
51 |
} |
|
52 |
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53 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
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54 |
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55 |
@Override |
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56 |
protected void onResume() |
|
57 |
{ |
|
58 |
super.onResume(); |
|
59 |
mView.onResume(); |
|
60 |
} |
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61 |
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62 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
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63 |
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64 |
@Override |
|
65 |
protected void onDestroy() |
|
66 |
{ |
|
67 |
Distorted.onDestroy(); |
|
68 |
super.onDestroy(); |
|
69 |
} |
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70 |
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|
71 |
} |
src/main/java/org/distorted/examples/rubik/RubikRenderer.java | ||
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1 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
|
2 |
// Copyright 2016 Leszek Koltunski // |
|
3 |
// // |
|
4 |
// This file is part of Distorted. // |
|
5 |
// // |
|
6 |
// Distorted is free software: you can redistribute it and/or modify // |
|
7 |
// it under the terms of the GNU General Public License as published by // |
|
8 |
// the Free Software Foundation, either version 2 of the License, or // |
|
9 |
// (at your option) any later version. // |
|
10 |
// // |
|
11 |
// Distorted is distributed in the hope that it will be useful, // |
|
12 |
// but WITHOUT ANY WARRANTY; without even the implied warranty of // |
|
13 |
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // |
|
14 |
// GNU General Public License for more details. // |
|
15 |
// // |
|
16 |
// You should have received a copy of the GNU General Public License // |
|
17 |
// along with Distorted. If not, see <http://www.gnu.org/licenses/>. // |
|
18 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
|
19 |
|
|
20 |
package org.distorted.examples.rubik; |
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21 |
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|
22 |
import android.graphics.Bitmap; |
|
23 |
import android.graphics.BitmapFactory; |
|
24 |
import android.opengl.GLSurfaceView; |
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25 |
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26 |
import org.distorted.examples.R; |
|
27 |
import org.distorted.library.effect.MatrixEffectMove; |
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28 |
import org.distorted.library.effect.MatrixEffectQuaternion; |
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29 |
import org.distorted.library.effect.MatrixEffectScale; |
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30 |
import org.distorted.library.effect.VertexEffect; |
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31 |
import org.distorted.library.effect.VertexEffectDistort; |
|
32 |
import org.distorted.library.main.Distorted; |
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33 |
import org.distorted.library.main.DistortedEffects; |
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34 |
import org.distorted.library.main.DistortedScreen; |
|
35 |
import org.distorted.library.main.DistortedTexture; |
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36 |
import org.distorted.library.mesh.MeshCubes; |
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37 |
import org.distorted.library.mesh.MeshFlat; |
|
38 |
import org.distorted.library.type.Dynamic3D; |
|
39 |
import org.distorted.library.type.Static3D; |
|
40 |
import org.distorted.library.type.Static4D; |
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41 |
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|
42 |
import java.io.IOException; |
|
43 |
import java.io.InputStream; |
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44 |
|
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45 |
import javax.microedition.khronos.egl.EGLConfig; |
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46 |
import javax.microedition.khronos.opengles.GL10; |
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47 |
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|
48 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
|
49 |
|
|
50 |
class RubikRenderer implements GLSurfaceView.Renderer |
|
51 |
{ |
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52 |
private static final int CUBE_SIZE = 3; |
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53 |
private static final int VERTICES = 5; |
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54 |
private static final int SIZE = 200; |
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55 |
|
|
56 |
private GLSurfaceView mView; |
|
57 |
private DistortedTexture mTexture; |
|
58 |
private DistortedScreen mScreen; |
|
59 |
private Static3D mMove, mScale, mCenter; |
|
60 |
private MeshCubes[][][] mCubes; |
|
61 |
private DistortedEffects[][][] mEffects; |
|
62 |
|
|
63 |
Static4D mQuat1, mQuat2; |
|
64 |
int mScreenMin; |
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65 |
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66 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
|
67 |
|
|
68 |
RubikRenderer(GLSurfaceView v) |
|
69 |
{ |
|
70 |
mView = v; |
|
71 |
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|
72 |
mScreen = new DistortedScreen(); |
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73 |
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|
74 |
mQuat1 = new Static4D( 0, 0, 0, 1); // unity quaternion |
|
75 |
mQuat2 = new Static4D(-0.25189602f,0.3546389f,0.009657208f,0.90038127f); // something semi-random that looks good |
|
76 |
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|
77 |
mCubes = new MeshCubes[CUBE_SIZE][CUBE_SIZE][CUBE_SIZE]; |
|
78 |
mEffects = new DistortedEffects[CUBE_SIZE][CUBE_SIZE][CUBE_SIZE]; |
|
79 |
Static3D[][][] cubeVectors = new Static3D[CUBE_SIZE][CUBE_SIZE][CUBE_SIZE]; |
|
80 |
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|
81 |
mMove = new Static3D(0,0,0); |
|
82 |
mScale = new Static3D(1,1,1); |
|
83 |
mCenter= new Static3D(0,0,0); |
|
84 |
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|
85 |
MatrixEffectMove move = new MatrixEffectMove(mMove); |
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86 |
MatrixEffectScale scale = new MatrixEffectScale(mScale); |
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87 |
MatrixEffectQuaternion quat1 = new MatrixEffectQuaternion(mQuat1, mCenter); |
|
88 |
MatrixEffectQuaternion quat2 = new MatrixEffectQuaternion(mQuat2, mCenter); |
|
89 |
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|
90 |
for(int x=0; x<CUBE_SIZE; x++) |
|
91 |
for(int y=0; y<CUBE_SIZE; y++) |
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92 |
for(int z=0; z<CUBE_SIZE; z++) |
|
93 |
{ |
|
94 |
mCubes[x][y][z] = new MeshCubes(VERTICES,VERTICES,VERTICES); |
|
95 |
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|
96 |
cubeVectors[x][y][z] = new Static3D( SIZE*(x-0.5f*(CUBE_SIZE-1)), SIZE*(y-0.5f*(CUBE_SIZE-1)), SIZE*(z-0.5f*(CUBE_SIZE-1)) ); |
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97 |
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98 |
mEffects[x][y][z] = new DistortedEffects(); |
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99 |
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100 |
mEffects[x][y][z].apply(move); |
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101 |
mEffects[x][y][z].apply(scale); |
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102 |
mEffects[x][y][z].apply(quat1); |
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103 |
mEffects[x][y][z].apply(quat2); |
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104 |
mEffects[x][y][z].apply( new MatrixEffectMove(cubeVectors[x][y][z]) ); |
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105 |
} |
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106 |
} |
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107 |
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108 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
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109 |
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110 |
public void onDrawFrame(GL10 glUnused) |
|
111 |
{ |
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112 |
mScreen.render( System.currentTimeMillis() ); |
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113 |
} |
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114 |
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|
115 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
|
116 |
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|
117 |
public void onSurfaceChanged(GL10 glUnused, int width, int height) |
|
118 |
{ |
|
119 |
mScreenMin = width<height ? width:height; |
|
120 |
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|
121 |
float w = mTexture.getWidth(); |
|
122 |
float h = mTexture.getHeight(); |
|
123 |
float d = mTexture.getDepth(mCubes[0][0][0]); |
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124 |
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|
125 |
float factor = 0.6f*(width>height ? height/h:width/w)/CUBE_SIZE; |
|
126 |
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|
127 |
mCenter.set(w/2,h/2,d/2); |
|
128 |
mMove.set( (width-factor*w)/2 , (height-factor*h)/2 , -factor*d/2 ); |
|
129 |
mScale.set(factor,factor,factor); |
|
130 |
|
|
131 |
mScreen.resize(width, height); |
|
132 |
} |
|
133 |
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134 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
|
135 |
|
|
136 |
public void onSurfaceCreated(GL10 glUnused, EGLConfig config) |
|
137 |
{ |
|
138 |
InputStream is = mView.getContext().getResources().openRawResource(R.raw.monalisa); |
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139 |
Bitmap bitmap; |
|
140 |
|
|
141 |
try |
|
142 |
{ |
|
143 |
bitmap = BitmapFactory.decodeStream(is); |
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144 |
} |
|
145 |
finally |
|
146 |
{ |
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147 |
try |
|
148 |
{ |
|
149 |
is.close(); |
|
150 |
} |
|
151 |
catch(IOException e) { } |
|
152 |
} |
|
153 |
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|
154 |
if( mTexture==null ) mTexture = new DistortedTexture(SIZE,SIZE); |
|
155 |
mTexture.setTexture(bitmap); |
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156 |
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|
157 |
mScreen.detachAll(); |
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158 |
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159 |
for(int x=0; x<CUBE_SIZE; x++) |
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160 |
for(int y=0; y<CUBE_SIZE; y++) |
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161 |
for(int z=0; z<CUBE_SIZE; z++) |
|
162 |
mScreen.attach(mTexture,mEffects[x][y][z],mCubes[x][y][z]); |
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163 |
|
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164 |
try |
|
165 |
{ |
|
166 |
Distorted.onCreate(mView.getContext()); |
|
167 |
} |
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168 |
catch(Exception ex) |
|
169 |
{ |
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170 |
android.util.Log.e("Rubik", ex.getMessage() ); |
|
171 |
} |
|
172 |
} |
|
173 |
} |
src/main/java/org/distorted/examples/rubik/RubikSurfaceView.java | ||
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1 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
|
2 |
// Copyright 2016 Leszek Koltunski // |
|
3 |
// // |
|
4 |
// This file is part of Distorted. // |
|
5 |
// // |
|
6 |
// Distorted is free software: you can redistribute it and/or modify // |
|
7 |
// it under the terms of the GNU General Public License as published by // |
|
8 |
// the Free Software Foundation, either version 2 of the License, or // |
|
9 |
// (at your option) any later version. // |
|
10 |
// // |
|
11 |
// Distorted is distributed in the hope that it will be useful, // |
|
12 |
// but WITHOUT ANY WARRANTY; without even the implied warranty of // |
|
13 |
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // |
|
14 |
// GNU General Public License for more details. // |
|
15 |
// // |
|
16 |
// You should have received a copy of the GNU General Public License // |
|
17 |
// along with Distorted. If not, see <http://www.gnu.org/licenses/>. // |
|
18 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
|
19 |
|
|
20 |
package org.distorted.examples.rubik; |
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21 |
|
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22 |
import android.app.ActivityManager; |
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23 |
import android.content.Context; |
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24 |
import android.content.pm.ConfigurationInfo; |
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25 |
import android.opengl.GLSurfaceView; |
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26 |
import android.util.AttributeSet; |
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27 |
import android.view.MotionEvent; |
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28 |
|
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29 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
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30 |
|
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31 |
class RubikSurfaceView extends GLSurfaceView |
|
32 |
{ |
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33 |
private int mX, mY; |
|
34 |
private RubikRenderer mRenderer; |
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35 |
|
|
36 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
|
37 |
|
|
38 |
public RubikSurfaceView(Context context) |
|
39 |
{ |
|
40 |
super(context); |
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41 |
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|
42 |
mX = -1; |
|
43 |
mY = -1; |
|
44 |
|
|
45 |
mRenderer = new RubikRenderer(this); |
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46 |
final ActivityManager activityManager = (ActivityManager) context.getSystemService(Context.ACTIVITY_SERVICE); |
|
47 |
final ConfigurationInfo configurationInfo = activityManager.getDeviceConfigurationInfo(); |
|
48 |
setEGLContextClientVersion( (configurationInfo.reqGlEsVersion>>16) >= 3 ? 3:2 ); |
|
49 |
setRenderer(mRenderer); |
|
50 |
} |
|
51 |
|
|
52 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
|
53 |
|
|
54 |
public RubikRenderer getRenderer() |
|
55 |
{ |
|
56 |
return mRenderer; |
|
57 |
} |
|
58 |
|
|
59 |
/////////////////////////////////////////////////////////////////////////////////////////////////// |
|
60 |
|
|
61 |
@Override public boolean onTouchEvent(MotionEvent event) |
|
62 |
{ |
|
63 |
int action = event.getAction(); |
|
64 |
int x = (int)event.getX(); |
|
65 |
int y = (int)event.getY(); |
|
66 |
|
|
67 |
switch(action) |
|
68 |
{ |
|
69 |
case MotionEvent.ACTION_DOWN: mX = x; |
|
70 |
mY = y; |
|
71 |
break; |
|
72 |
|
|
73 |
case MotionEvent.ACTION_MOVE: if( mX>=0 && mY>= 0 ) |
|
74 |
{ |
|
75 |
float px = mY-y; |
|
76 |
float py = mX-x; |
|
77 |
float pz = 0; |
|
78 |
float plen = (float)Math.sqrt(px*px + py*py + pz*pz); |
|
79 |
|
|
80 |
if( plen>0 ) |
|
81 |
{ |
|
82 |
px /= plen; |
|
83 |
py /= plen; |
|
84 |
pz /= plen; |
|
85 |
|
|
86 |
float cosA = (float)Math.cos(plen*3.14f/mRenderer.mScreenMin); |
|
87 |
float sinA = (float)Math.sqrt(1-cosA*cosA); |
|
88 |
|
|
89 |
mRenderer.mQuat1.set(px*sinA, py*sinA, pz*sinA, cosA); |
|
90 |
} |
|
91 |
} |
|
92 |
break; |
|
93 |
|
|
94 |
case MotionEvent.ACTION_UP : mX = -1; |
|
95 |
mY = -1; |
|
96 |
|
|
97 |
float qx = mRenderer.mQuat1.get1(); |
|
98 |
float qy = mRenderer.mQuat1.get2(); |
|
99 |
float qz = mRenderer.mQuat1.get3(); |
|
100 |
float qw = mRenderer.mQuat1.get4(); |
|
101 |
|
|
102 |
float rx = mRenderer.mQuat2.get1(); |
|
103 |
float ry = mRenderer.mQuat2.get2(); |
|
104 |
float rz = mRenderer.mQuat2.get3(); |
|
105 |
float rw = mRenderer.mQuat2.get4(); |
|
106 |
|
|
107 |
// This is quaternion multiplication. (tx.ty.tz.tw) |
|
108 |
// is now equal to (qx,qy,qz,qw)*(rx,ry,rz,rw) |
|
109 |
float tx = rw*qx - rz*qy + ry*qz + rx*qw; |
|
110 |
float ty = rw*qy + rz*qx + ry*qw - rx*qz; |
|
111 |
float tz = rw*qz + rz*qw - ry*qx + rx*qy; |
|
112 |
float tw = rw*qw - rz*qz - ry*qy - rx*qx; |
|
113 |
|
|
114 |
// The point of this is so that there are always |
|
115 |
// exactly 2 quaternions: Quat1 representing the rotation |
|
116 |
// accumulating only since the last screen touch, and Quat2 |
|
117 |
// which remembers the combined effect of all previous |
|
118 |
// swipes. |
|
119 |
// We cannot be accumulating an ever-growing list of quaternions |
|
120 |
// and add a new one every time user swipes the screen - there |
|
121 |
// is a limited number of slots in the EffectQueueMatrix! |
|
122 |
mRenderer.mQuat1.set(0f, 0f, 0f, 1f); |
|
123 |
mRenderer.mQuat2.set(tx, ty, tz, tw); |
|
124 |
|
|
125 |
break; |
|
126 |
} |
|
127 |
|
|
128 |
return true; |
|
129 |
} |
|
130 |
|
|
131 |
} |
|
132 |
|
src/main/res/values/strings.xml | ||
---|---|---|
182 | 182 |
<string name="example_moving_glow_subtitle">See moving objects glowing with light.</string> |
183 | 183 |
<string name="example_earth">Earth</string> |
184 | 184 |
<string name="example_earth_subtitle">Test the sphere Mesh by showing the Earth in cosmos.</string> |
185 |
<string name="example_rubik">Rubik Cube</string> |
|
186 |
<string name="example_rubik_subtitle">Moveable Rubik Cube.</string> |
|
185 | 187 |
|
186 | 188 |
<string name="example_movingeffects_toast">Click on \'RESET\' and define your path by touching the screen. Then click on one of the effects and see it move along your path.</string> |
187 | 189 |
<string name="example_rotate_toast">Rotate the scene by swiping the screen</string> |
Also available in: Unified diff
1) new 'Rubik' app (skeleton)
2) MeshCubes: add support for custom texture mappings on each side (Rubik needs that!)