JavaFX 3D - Isohedral Toroid with 24 Faces

以下是以JavaFX 8的TriangleMesh類別建構之Isohedral Toroid with 24 Faces，Isohedral Toroid with 24 Faces屬於Non-Regular Toroidal Solid的一種。

A toroid is said to be non-regular if not all of its faces have the same number of vertices, or not all of its vertices join the same number of faces. All of the toroids on this page are non-regular.

float C0 = length * 0.0f;
float C1 = length * 0.5f;
float C2 = length * 1.0f;
float C3 = length * (float) (Math.sqrt(2.0) - 1.0) / 4.0f;
float C4 = length * (float) Math.sqrt(3.0) / 2.0f;
float C5 = length * (float) (3.0 + Math.sqrt(.02)) / 4.0f;
float C6 = length * (float) (1.0 + Math.sqrt(2.0)) / 2.0f;
float C7 = length * (float) (Math.sqrt(3.0) + Math.sqrt(6.0)) / 2.0f;
float C8 = length * (float) (1.0 + Math.sqrt(2.0));

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

// 設定頂點座標
trianglemesh.getPoints().addAll(
   C2,  C0,  C5,
  -C2,  C0, -C5,
  -C1,  C4,  C5,
   C1,  C4, -C5,
  -C1, -C4,  C5,
   C1, -C4, -C5,
   C8,  C0,  C3,
  -C8,  C0, -C3,
  -C6,  C7,  C3,
   C6,  C7, -C3,
  -C6, -C7,  C3,
   C6, -C7, -C3
);

// 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, 1,  2, 5,  3, 2,  // Yellow
  0, 1,  3, 5,  2, 2,  // Yellow
  0, 1,  3, 5,  5, 2,  // Yellow
  0, 1,  5, 5,  3, 2,  // Yellow
  0, 1,  5, 5,  4, 2,  // Yellow
  0, 1,  4, 5,  5, 2,  // Yellow
  0, 1,  4, 5, 11, 2,  // Yellow
  0, 1, 11, 5,  4, 2,  // Yellow
  0, 1, 11, 5,  6, 2,  // Yellow
  0, 1,  6, 5, 11, 2,  // Yellow
  0, 1,  6, 5,  9, 2,  // Yellow
  0, 1,  9, 5,  6, 2,  // Yellow
  0, 1,  9, 5,  2, 2,  // Yellow
  0, 1,  2, 5,  9, 2,  // Yellow
  1, 1,  2, 5,  4, 2,  // Yellow
  1, 1,  4, 5,  2, 2,  // Yellow
  1, 1,  4, 5,  5, 2,  // Yellow
  1, 1,  5, 5,  4, 2,  // Yellow
  1, 1,  5, 5, 10, 2,  // Yellow
  1, 1, 10, 5,  5, 2,  // Yellow
  1, 1, 10, 5,  7, 2,  // Yellow
  1, 1,  7, 5, 10, 2,  // Yellow
  1, 1,  7, 5,  8, 2,  // Yellow
  1, 1,  8, 5,  7, 2,  // Yellow
  1, 1,  8, 5,  3, 2,  // Yellow
  1, 1,  3, 5,  8, 2,  // Yellow
  1, 1,  3, 5,  2, 2,  // Yellow
  1, 1,  2, 5,  3, 2,  // Yellow
  2, 1,  9, 5,  8, 2,  // Yellow
  2, 1,  8, 5,  9, 2,  // Yellow
  2, 1,  8, 5,  7, 2,  // Yellow
  2, 1,  7, 5,  8, 2,  // Yellow
  2, 1,  7, 5,  4, 2,  // Yellow
  2, 1,  4, 5,  7, 2,  // Yellow
  3, 1,  8, 5,  9, 2,  // Yellow
  3, 1,  9, 5,  8, 2,  // Yellow
  3, 1,  9, 5,  6, 2,  // Yellow
  3, 1,  6, 5,  9, 2,  // Yellow
  3, 1,  6, 5,  5, 2,  // Yellow
  3, 1,  5, 5,  6, 2,  // Yellow
  4, 1,  7, 5, 10, 2,  // Yellow
  4, 1, 10, 5,  7, 2,  // Yellow
  4, 1, 10, 5, 11, 2,  // Yellow
  4, 1, 11, 5, 10, 2,  // Yellow
  5, 1,  6, 5, 11, 2,  // Yellow
  5, 1, 11, 5,  6, 2,  // Yellow
  5, 1, 11, 5, 10, 2,  // Yellow
  5, 1, 10, 5, 11, 2   // Yellow
);   

// 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
);

// 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