JavaFX 3D - Truncated Icosahedron

以下是以JavaFX 8的TriangleMesh類別建構之Truncated Icosahedron (截角二十面體)，屬於Archimedean Solid (阿基米德立體)。

float C0 = length * (float) (1.0 + Math.sqrt(5.0)) / 4.0f;
float C1 = length * (float) (1.0 + Math.sqrt(5.0)) / 2.0f;
float C2 = length * (float) (5.0 + Math.sqrt(5.0)) / 4.0f;
float C3 = length * (float) (2.0 + Math.sqrt(5.0)) / 2.0f;
float C4 = length * (float) (1.0 + Math.sqrt(5.0)) / 4.0f * 3.0f;
float C5 = length * 0.5f;
float C6 = length * 1.0f;

// 建立TriangleMesh
TriangleMesh trianglemesh = new TriangleMesh();

// 設定頂點座標
trianglemesh.getPoints().addAll(
    C5, 0.0f,   C4,
    C5, 0.0f,  -C4,
   -C5, 0.0f,   C4,
   -C5, 0.0f,  -C4,
    C4,   C5, 0.0f,
    C4,  -C5, 0.0f,
   -C4,   C5, 0.0f,
   -C4,  -C5, 0.0f,
  0.0f,   C4,   C5,
  0.0f,   C4,  -C5,
  0.0f,  -C4,   C5,
  0.0f,  -C4,  -C5,
    C6,   C0,   C3,
    C6,   C0,  -C3,
    C6,  -C0,   C3,
    C6,  -C0,  -C3,
   -C6,   C0,   C3,
   -C6,   C0,  -C3,
   -C6,  -C0,   C3,
   -C6,  -C0,  -C3,
    C3,   C6,   C0,
    C3,   C6,  -C0,
    C3,  -C6,   C0,
    C3,  -C6,  -C0,
   -C3,   C6,   C0,
   -C3,   C6,  -C0,
   -C3,  -C6,   C0,
   -C3,  -C6,  -C0,
    C0,   C3,   C6,
    C0,   C3,  -C6,
    C0,  -C3,   C6,
    C0,  -C3,  -C6,
   -C0,   C3,   C6,
   -C0,   C3,  -C6,
   -C0,  -C3,   C6,
   -C0,  -C3,  -C6,
    C5,   C1,   C2,
    C5,   C1,  -C2,
    C5,  -C1,   C2,
    C5,  -C1,  -C2,
   -C5,   C1,   C2,
   -C5,   C1,  -C2,
   -C5,  -C1,   C2,
   -C5,  -C1,  -C2,
    C2,   C5,   C1,
    C2,   C5,  -C1,
    C2,  -C5,   C1,
    C2,  -C5,  -C1,
   -C2,   C5,   C1,
   -C2,   C5,  -C1,
   -C2,  -C5,   C1,
   -C2,  -C5,  -C1,
    C1,   C2,   C5,
    C1,   C2,  -C5,
    C1,  -C2,   C5,
    C1,  -C2,  -C5,
   -C1,   C2,   C5,
   -C1,   C2,  -C5,
   -C1,  -C2,   C5,
   -C1,  -C2,  -C5
);

// 設定貼圖座標
trianglemesh.getTexCoords().addAll(
  0.0f, 0.0f, // 0                         
  0.5f, 0.0f, // 1                          
  1.0f, 0.0f, // 2                               
  0.0f, 0.5f, // 3                               
  0.5f, 0.5f, // 4                               
  1.0f, 0.5f, // 5                              
  0.0f, 1.0f, // 6                               
  0.5f, 1.0f, // 7                               
  1.0f, 1.0f  // 8                          
);

// 設定各三角形的面
trianglemesh.getFaces().addAll(
   0, 0, 14, 4, 46, 1,
   0, 0, 46, 4, 44, 1,
   0, 0, 44, 4, 12, 1,
   1, 0, 13, 4, 45, 1,
   1, 0, 45, 4, 47, 1,
   1, 0, 47, 4, 15, 1,
   2, 0, 16, 4, 48, 1,
   2, 0, 48, 4, 50, 1,
   2, 0, 50, 4, 18, 1,
   3, 0, 19, 4, 51, 1,
   3, 0, 51, 4, 49, 1,
   3, 0, 49, 4, 17, 1,
   4, 0, 21, 4, 53, 1,
   4, 0, 53, 4, 52, 1,
   4, 0, 52, 4, 20, 1,
   5, 0, 22, 4, 54, 1,
   5, 0, 54, 4, 55, 1,
   5, 0, 55, 4, 23, 1,
   6, 0, 24, 4, 56, 1,
   6, 0, 56, 4, 57, 1,
   6, 0, 57, 4, 25, 1,
   7, 0, 27, 4, 59, 1,
   7, 0, 59, 4, 58, 1,
   7, 0, 58, 4, 26, 1,
   8, 0, 32, 4, 40, 1,
   8, 0, 40, 4, 36, 1,
   8, 0, 36, 4, 28, 1,
   9, 0, 29, 4, 37, 1,
   9, 0, 37, 4, 41, 1,
   9, 0, 41, 4, 33, 1,
  10, 0, 30, 4, 38, 1,
  10, 0, 38, 4, 42, 1,
  10, 0, 42, 4, 34, 1,
  11, 0, 35, 4, 43, 1,
  11, 0, 43, 4, 39, 1,
  11, 0, 39, 4, 31, 1,
   0, 1,  2, 5, 18, 2,
   0, 1, 18, 5, 42, 2,
   0, 1, 42, 5, 38, 2,
   0, 1, 38, 5, 14, 2,
   0, 1, 12, 5, 36, 2,
   0, 1, 36, 5, 40, 2,
   0, 1, 40, 5, 16, 2,
   0, 1, 16, 5,  2, 2,
   1, 1,  3, 5, 17, 2,
   1, 1, 17, 5, 41, 2,
   1, 1, 41, 5, 37, 2,
   1, 1, 37, 5, 13, 2,
   1, 1, 15, 5, 39, 2,
   1, 1, 39, 5, 43, 2,
   1, 1, 43, 5, 19, 2,
   1, 1, 19, 5,  3, 2,
  20, 1, 44, 5, 46, 2,
  20, 1, 46, 5, 22, 2,
  20, 1, 22, 5,  5, 2,
  20, 1,  5, 5,  4, 2,
  20, 1, 52, 5, 28, 2,
  20, 1, 28, 5, 36, 2,
  20, 1, 36, 5, 12, 2,
  20, 1, 12, 5, 44, 2,
  23, 1, 47, 5, 45, 2,
  23, 1, 45, 5, 21, 2,
  23, 1, 21, 5,  4, 2,
  23, 1,  4, 5,  5, 2,
  23, 1, 55, 5, 31, 2,
  23, 1, 31, 5, 39, 2,
  23, 1, 39, 5, 15, 2,
  23, 1, 15, 5, 47, 2,
  24, 1, 48, 5, 16, 2,
  24, 1, 16, 5, 40, 2,
  24, 1, 40, 5, 32, 2,
  24, 1, 32, 5, 56, 2,
  24, 1,  6, 5,  7, 2,
  24, 1,  7, 5, 26, 2,
  24, 1, 26, 5, 50, 2,
  24, 1, 50, 5, 48, 2,
  27, 1, 51, 5, 19, 2,
  27, 1, 19, 5, 43, 2,
  27, 1, 43, 5, 35, 2,
  27, 1, 35, 5, 59, 2,
  27, 1,  7, 5,  6, 2,
  27, 1,  6, 5, 25, 2,
  27, 1, 25, 5, 49, 2,
  27, 1, 49, 5, 51, 2,
  29, 1, 53, 5, 21, 2,
  29, 1, 21, 5, 45, 2,
  29, 1, 45, 5, 13, 2,
  29, 1, 13, 5, 37, 2,
  29, 1,  9, 5,  8, 2,
  29, 1,  8, 5, 28, 2,
  29, 1, 28, 5, 52, 2,
  29, 1, 52, 5, 53, 2,
  30, 1, 54, 5, 22, 2,
  30, 1, 22, 5, 46, 2,
  30, 1, 46, 5, 14, 2,
  30, 1, 14, 5, 38, 2,
  30, 1, 10, 5, 11, 2,
  30, 1, 11, 5, 31, 2,
  30, 1, 31, 5, 55, 2,
  30, 1, 55, 5, 54, 2,
  33, 1, 57, 5, 56, 2,
  33, 1, 56, 5, 32, 2,
  33, 1, 32, 5,  8, 2,
  33, 1,  8, 5,  9, 2,
  33, 1, 41, 5, 17, 2,
  33, 1, 17, 5, 49, 2,
  33, 1, 49, 5, 25, 2,
  33, 1, 25, 5, 57, 2,
  34, 1, 58, 5, 59, 2,
  34, 1, 59, 5, 35, 2,
  34, 1, 35, 5, 11, 2,
  34, 1, 11, 5, 10, 2,
  34, 1, 42, 5, 18, 2,
  34, 1, 18, 5, 50, 2,
  34, 1, 50, 5, 26, 2,
  34, 1, 26, 5, 58, 2
);

// 設定各面的平滑參數
trianglemesh.getFaceSmoothingGroups().addAll(
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,      
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,      
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,     
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0,
  0, 0, 0, 0
);

// 建立MeshView
MeshView meshview;

meshview = new MeshView(createMesh(70));
...

【參考資料】

[1] Java Official Web Site：http://www.oracle.com/technetwork/java/index.html
[2] JavaFX：http://www.oracle.com/technetwork/java/javafx
[3] JavaFX 8.0 API Specification.
[4] Java Platform, Standard Edition 8 API Specification.
[5] JDK 8 Certified System Configurations.
[6] H. M. Cundy, A. P. Rollett, Mathematical Models, Tarquin Publications, 1981.
[7] G. Sellers, R. S. Wright, N. Haemel, OpenGL SuperBible: Comprehensive Tutorial and Reference (6th Edition), Addison-Wesley Professional, 2013.
[8] 黃嘉輝, JavaFX 8技術手冊, ISBN: 9789863474050, 碁峰資訊, 2014.

© Chia-Hui Huang