├── Doc ├── 01.jpg ├── 02.jpg ├── 03.jpg ├── 04.jpg ├── 05.jpg ├── poisson.png ├── preview.gif ├── quad_mesh.png ├── organic_grid.gif ├── subdivide_tri.png ├── triangulation.png ├── subdivide_quad.png ├── semi_quadrangulation.png └── townscaper_screenshot.jpg ├── ProjectSettings ├── ProjectVersion.txt ├── ClusterInputManager.asset ├── PresetManager.asset ├── EditorBuildSettings.asset ├── XRSettings.asset ├── TimeManager.asset ├── VFXManager.asset ├── AudioManager.asset ├── TagManager.asset ├── UnityConnectSettings.asset ├── EditorSettings.asset ├── DynamicsManager.asset ├── NavMeshAreas.asset ├── Physics2DSettings.asset ├── GraphicsSettings.asset ├── InputManager.asset ├── QualitySettings.asset └── ProjectSettings.asset ├── Assets ├── SampleScene.unity.meta ├── Hexagrid.cs.meta ├── SampleScene.unity └── Hexagrid.cs ├── .gitignore ├── Packages └── manifest.json └── README.md /Doc/01.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/FutaAlice/OrganicQuadGrid/HEAD/Doc/01.jpg -------------------------------------------------------------------------------- /Doc/02.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/FutaAlice/OrganicQuadGrid/HEAD/Doc/02.jpg -------------------------------------------------------------------------------- /Doc/03.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/FutaAlice/OrganicQuadGrid/HEAD/Doc/03.jpg -------------------------------------------------------------------------------- /Doc/04.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/FutaAlice/OrganicQuadGrid/HEAD/Doc/04.jpg -------------------------------------------------------------------------------- /Doc/05.jpg: 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-------------------------------------------------------------------------------- https://raw.githubusercontent.com/FutaAlice/OrganicQuadGrid/HEAD/Doc/subdivide_quad.png -------------------------------------------------------------------------------- /Doc/semi_quadrangulation.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/FutaAlice/OrganicQuadGrid/HEAD/Doc/semi_quadrangulation.png -------------------------------------------------------------------------------- /Doc/townscaper_screenshot.jpg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/FutaAlice/OrganicQuadGrid/HEAD/Doc/townscaper_screenshot.jpg -------------------------------------------------------------------------------- /ProjectSettings/ProjectVersion.txt: -------------------------------------------------------------------------------- 1 | m_EditorVersion: 2019.3.5f1 2 | 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streamingMipmapsMemoryBudget: 512 210 | streamingMipmapsRenderersPerFrame: 512 211 | streamingMipmapsMaxLevelReduction: 2 212 | streamingMipmapsMaxFileIORequests: 1024 213 | particleRaycastBudget: 4096 214 | asyncUploadTimeSlice: 2 215 | asyncUploadBufferSize: 16 216 | asyncUploadPersistentBuffer: 1 217 | resolutionScalingFixedDPIFactor: 1 218 | excludedTargetPlatforms: [] 219 | m_PerPlatformDefaultQuality: 220 | Android: 2 221 | Lumin: 5 222 | Nintendo 3DS: 5 223 | Nintendo Switch: 5 224 | PS4: 5 225 | PSP2: 2 226 | Stadia: 5 227 | Standalone: 5 228 | WebGL: 3 229 | Windows Store Apps: 5 230 | XboxOne: 5 231 | iPhone: 2 232 | tvOS: 2 233 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # 不规则四边形填充平面 2 | 3 | ![preview](Doc/preview.gif) 4 | 5 | ## 前言 6 | 7 | [Townscaper](https://store.steampowered.com/app/1291340/Townscaper/)，一款关于城镇建造的游戏。 8 | 9 | ![townscaper_screenshot](Doc/townscaper_screenshot.jpg) 10 | 11 | 游戏基于一张用不规则凸四边形拼接而成的平面地图，其中每个四边形虽不规则，但又“接近”正方形，适合用于城镇的搭建。 12 | 13 | 本文将用 `Unity` 和 `C#` 实现这个算法，并逐步骤解释。 14 | 15 | ## 算法概述 16 | 17 | 算法分为如下三个步骤： 18 | 19 | ### 1. 把目标平面进行 Delaunay Triangulation 20 | 21 | | 泊松分布的散点 | Delaunay 三角剖分 | 22 | | -------------- | -------------- | 23 | | ![poisson](Doc/poisson.png) | ![triangulation](Doc/triangulation.png) | 24 | 25 | 泊松分布+Delaunay 是为了获取尽量规整的三角形， 26 | 27 | 考虑到拼接无限地图的需求，此处的代码实现我们将用将 “正六边形” 三角形化的方式替代。 28 | 29 | ### 2. 随机剔除三角形的边 30 | 31 | | Delaunay 三角剖分 | 剔除边后的平面 | 32 | | -------------- | -------------- | 33 | | ![triangulation](Doc/triangulation.png) | ![semi_quadrangulation](Doc/semi_quadrangulation.png) | 34 | 35 | 随机剔除三角形的边，使其和邻接三角形形成四边形。（本步骤不能保证所有三角形都被合并为四边形） 36 | 37 | ### 3. 将平面内的 “三角形” 和 “四边形” 细分为更小的四边形 38 | 39 | 我们需要仅由具有四个边的面组成的网格。但是我们当前的网格中仍然存在一些三角形。 40 | 41 | 不过，三角形可以很容易地细分为三个较小的四边形。同样，现有的四边形也可以细分为四个较小的四边形。如下图所示： 42 | 43 | | 三角形 -> 四边形 | 四边形 -> 四边形 | 44 | | -------------- | -------------- | 45 | | ![subdivide_tri](Doc/subdivide_tri.png) | ![subdivide_quad](Doc/subdivide_quad.png) | 46 | 47 | 通过这样做，我们最终得到一个**仅由四边形组成**的网格。 48 | 49 | | 三角形和四边形组成的平面 | 仅由四边形组成的平面 | 50 | | -------------- | -------------- | 51 | | ![semi_quadrangulation](Doc/semi_quadrangulation.png) | ![quad_mesh](Doc/quad_mesh.png) | 52 | 53 | ### 4. 让这些四边形形状更加松弛 54 | 55 | 这一步被称为 `Squaring` 或 `Relaxation`。 56 | 57 | ![organic_grid](Doc/organic_grid.gif) 58 | 59 | 目的是为了让网格看起来更加“美观”，评判标准比较主观，有多种实现方式。 60 | 61 | 我们将采用将不断迭代每个顶点，将其移向相邻顶点中心的方式实现。 62 | 63 | ## 代码实现 64 | 65 | ### 0. 基础代码 66 | 67 | 新建一个 c# 脚本，派生于 MonoBehaviour，此处我们叫他 Hexagird.cs 68 | 69 | ```c# 70 | [ExecuteInEditMode] 71 | public class Hexagrid : MonoBehaviour 72 | { 73 | void Start() ... 74 | void Update() ... 75 | } 76 | ``` 77 | 78 | 点、三角形、四边形 的抽象，便于后续代码实现。 79 | 80 | ```c# 81 | 82 | class Point // 点 83 | { 84 | public Vector2 mPosition; 85 | public bool mSide; // 是否在六边形最外圈 86 | }; 87 | 88 | class Triangle // 三角形 89 | { 90 | public int mA, mB, mC; 91 | public bool mValid; // 用于剔除边的标记，剔除后赋值为 false 92 | }; 93 | 94 | class Quad // 四边形 95 | { 96 | public int mA, mB, mC, mD; 97 | }; 98 | 99 | class Neighbours // “点” 所邻接的其他点 100 | { 101 | public void Add(int i) ... // i 为邻接点索引 102 | public int count 103 | { 104 | get { 105 | return mNeighbour.Count; 106 | } 107 | } 108 | public List mNeighbour; 109 | }; 110 | 111 | ``` 112 | 113 | 最后给 `Hexagrid` 添加一些字段，用于控制生成参数，把脚本挂到场景内的一个空物体上。 114 | 115 | ```c# 116 | [ExecuteInEditMode] 117 | public class Hexagrid : MonoBehaviour 118 | { 119 | [Range(2, 12)] 120 | public int mSideSize = 8; 121 | 122 | [Range(1, 20)] 123 | public int mSearchIterationCount = 12; 124 | 125 | [Range(0, 65535)] 126 | public int mSeed = 15911; 127 | 128 | private int mBaseQuadCount = 0; 129 | 130 | public bool bTriangulation = true; 131 | public bool bRemovingEdges = false; 132 | public bool bSubdivideFaces = false; 133 | public bool bRelax = false; 134 | public bool bReshape = false; 135 | public bool bDrawPositions = false; 136 | 137 | private List mPoints; 138 | private List mTriangles; 139 | private List mQuads; 140 | private Neighbours[] mNeighbours; 141 | 142 | // 分别对应算法的四个步骤，先留空实现，慢慢补全 143 | void Triangulation() {} 144 | void RemovingEdges() {} 145 | void SubdivideFaces() {} 146 | void Relax() {} 147 | void Reshape() {} // 额外的轮廓相形 148 | 149 | // 绘图函数，不重要，从github把代码复制过来就行 150 | private void DrawLine(int a, int b) ... 151 | void OnDrawGizmos() ... 152 | 153 | // 当参数改变时，重新初始化 154 | private void OnValidate() 155 | { 156 | mPoints = new List(); 157 | mTriangles = new List(); 158 | mQuads = new List(); 159 | mNeighbours = new Neighbours[0]; 160 | 161 | if (bTriangulation) { 162 | this.Triangulation(); 163 | } 164 | if (bTriangulation && bRemovingEdges) { 165 | this.RemovingEdges(); 166 | } 167 | if (bTriangulation && bRemovingEdges && bSubdivideFaces) { 168 | this.SubdivideFaces(); 169 | } 170 | } 171 | 172 | // 重写 Update()，逐帧 Relax，方便看效果 173 | void Update() 174 | { 175 | if (bTriangulation && bRemovingEdges && bSubdivideFaces && bRelax) { 176 | if (bRelax) { 177 | this.Relax(); 178 | } 179 | if (bRelax && bReshape) { 180 | this.Reshape(); 181 | } 182 | } 183 | } 184 | } 185 | ``` 186 | 187 | ### 1. 三角形化 188 | 189 | 准备工作完成了，开始干正事： 190 | 191 | ```c# 192 | void Triangulation() 193 | { 194 | mPoints = new List(); 195 | mTriangles = new List(); 196 | mQuads = new List(); 197 | mNeighbours = new Neighbours[0]; 198 | 199 | // 将六边形内散点坐标塞进 mPoints 200 | float sideLength = 0.5f * Mathf.Tan(Mathf.Deg2Rad * 60); // 0.5f* tanf(60deg) 201 | for (int x = 0; x < mSideSize * 2 - 1; ++x) { 202 | int height = (x < mSideSize) ? (mSideSize + x) : (mSideSize * 3 - 2 - x); 203 | float deltaHeight = mSideSize - height * 0.5f; 204 | for (int y = 0; y < height; y++) { 205 | bool isSide = x == 0 || x == (mSideSize * 2 - 2) || y == 0 || y == height - 1; 206 | mPoints.Add(new Point((x - mSideSize + 1) * sideLength, y + deltaHeight, isSide)); 207 | } 208 | } 209 | 210 | // 分别给对称轴左右生成三角形（顶点顺序不同），塞进 mTriangles 211 | int offset = 0; 212 | for (int x = 0; x < (mSideSize * 2 - 2); x++) { 213 | int height = (x < mSideSize) ? (mSideSize + x) : (mSideSize * 3 - 2 - x); 214 | if (x < mSideSize - 1) { 215 | // left side 216 | for (int y = 0; y < height; y++) { 217 | mTriangles.Add(new Triangle(offset + y, offset + y + height, offset + y + height + 1)); 218 | if (y >= height - 1) { 219 | break; 220 | } 221 | mTriangles.Add(new Triangle(offset + y + height + 1, offset + y + 1, offset + y)); 222 | } 223 | } 224 | else { 225 | // right side 226 | for (int y = 0; y < height - 1; y++) { 227 | mTriangles.Add(new Triangle(offset + y, offset + y + height, offset + y + 1)); 228 | if (y >= height - 2) { 229 | break; 230 | } 231 | mTriangles.Add(new Triangle(offset + y + 1, offset + y + height, offset + y + height + 1)); 232 | } 233 | } 234 | offset += height; 235 | } 236 | } 237 | ``` 238 | 239 | 现在我们得到了存储在 `mPoints` 里的正六边形内顶点坐标， 240 | 241 | 以及存储在 `mTriangles` 里的三角形 index buffer. 242 | 243 | ![01](Doc/01.jpg) 244 | 245 | ### 2. 剔除边 246 | 247 | ```c# 248 | private int[] GetAdjacentTriangles(int triIndex); // 获取邻接的三角形索引 249 | 250 | void RemovingEdges() 251 | { 252 | // triangles to quads 253 | System.Random rand = new System.Random(mSeed); 254 | while (true) { 255 | int triIndex; 256 | int searchCount = 0; 257 | do { 258 | triIndex = rand.Next() % mTriangles.Count; 259 | searchCount++; 260 | } while (searchCount < mSearchIterationCount && !mTriangles[triIndex].mValid); 261 | 262 | if (searchCount == mSearchIterationCount) { 263 | break; 264 | } 265 | 266 | int[] adjacents = GetAdjacentTriangles(triIndex); 267 | if (adjacents.Length > 0) { 268 | int i1 = triIndex; 269 | int i2 = adjacents[0]; 270 | int[] indices = new int[6] { 271 | mTriangles[i1].mA, mTriangles[i1].mB, mTriangles[i1].mC, 272 | mTriangles[i2].mA, mTriangles[i2].mB, mTriangles[i2].mC 273 | }; 274 | 275 | Array.Sort(indices); 276 | int[] unique = indices.Distinct().ToArray(); 277 | Debug.Assert(unique.Length == 4); 278 | 279 | mQuads.Add(new Quad(unique[0], unique[2], unique[3], unique[1])); 280 | mTriangles[triIndex].mValid = false; ; 281 | mTriangles[adjacents[0]].mValid = false; 282 | } 283 | } 284 | this.mBaseQuadCount = mQuads.Count(); 285 | } 286 | ``` 287 | 288 | 随机选择三角形，获取一个与其相邻的三角形，剔除一条公用边，更新 mValid 标记。 289 | 290 | 拼接成的四边形塞进 `mQuads` 291 | 292 | ![02](Doc/02.jpg) 293 | 294 | ### 3. 细分成四边形 295 | 296 | ```c# 297 | // 输入三角形/四边形顶点数组，和一个记录中点位置的字典 298 | // 细分得到的顶点和四边形 index buffer 分别塞进 mPoints 和 mQuads 299 | void Subdivide(int[] indices, Dictionary middles); 300 | 301 | void SubdivideFaces() 302 | { 303 | Dictionary middles = new Dictionary(); 304 | 305 | // quads to 4 quads 306 | for (int i = 0; i < mBaseQuadCount; i++) { 307 | var quad = mQuads[i]; 308 | int[] indices = new int[4] { 309 | quad.mA, quad.mB, quad.mC, quad.mD 310 | }; 311 | this.Subdivide(indices, middles); 312 | } 313 | 314 | // triangles to quads 315 | foreach (var triangle in mTriangles) { 316 | if (triangle.mValid) { 317 | int[] indices = new int[3] { 318 | triangle.mA, triangle.mB, triangle.mC 319 | }; 320 | this.Subdivide(indices, middles); 321 | } 322 | } 323 | } 324 | ``` 325 | 326 | ![03](Doc/03.jpg) 327 | 328 | ### 4. 使网格更加松弛 329 | 330 | ```c# 331 | void Relax() 332 | { 333 | mNeighbours = new Neighbours[mPoints.Count]; 334 | for (int i = 0; i < mPoints.Count; ++i) { 335 | mNeighbours[i] = new Neighbours(); 336 | } 337 | for (int i = mBaseQuadCount; i < mQuads.Count(); ++i) { 338 | var quad = mQuads[i]; 339 | int[] indices = new int[4] { 340 | quad.mA, quad.mB, quad.mC, quad.mD 341 | }; 342 | for (int j = 0; j < 4; j++) { 343 | int index1 = indices[j]; 344 | int index2 = indices[(j + 1) & 3]; 345 | { 346 | var neighbour = mNeighbours[index1]; 347 | // check 348 | bool good = true; 349 | for (int k = 0; k < neighbour.count; k++) { 350 | if (neighbour.mNeighbour[k] == index2) { 351 | good = false; 352 | break; 353 | } 354 | } 355 | if (good) { 356 | Debug.Assert(neighbour.count < 6); 357 | neighbour.Add(index2); 358 | } 359 | } 360 | { 361 | var neighbour = mNeighbours[index2]; 362 | // check 363 | bool good = true; 364 | for (int k = 0; k < neighbour.count; k++) { 365 | if (neighbour.mNeighbour[k] == index1) { 366 | good = false; 367 | break; 368 | } 369 | } 370 | if (good) { 371 | Debug.Assert(neighbour.count < 6); 372 | neighbour.Add(index1); 373 | } 374 | } 375 | } 376 | } 377 | 378 | for (int i = 0; i < mPoints.Count; i++) { 379 | if (mPoints[i].mSide) { 380 | continue; 381 | } 382 | var neighbour = mNeighbours[i]; 383 | Vector2 sum = Vector2.zero; 384 | for (int j = 0; j < neighbour.count; j++) { 385 | sum += mPoints[neighbour.mNeighbour[j]].mPosition; 386 | } 387 | sum /= (float)neighbour.count; 388 | mPoints[i].mPosition = sum; 389 | } 390 | } 391 | ``` 392 | 393 | ![04](Doc/04.jpg) 394 | 395 | ### 5. 还可以一定程度扭曲外轮廓 396 | 397 | ```c# 398 | void Reshape() 399 | { 400 | float radius = mSideSize - 1.0f; 401 | Vector2 center = new Vector2(0, (mSideSize * 2 - 1) * 0.5f); 402 | 403 | foreach (var point in mPoints) { 404 | if (!point.mSide) { 405 | continue; 406 | } 407 | Vector2 D = point.mPosition - center; 408 | float distance = radius - Mathf.Sqrt(D.x * D.x + D.y * D.y); 409 | point.mPosition += (D * distance) * 0.1f; 410 | } 411 | } 412 | ``` 413 | 414 | ![05](Doc/05.jpg) -------------------------------------------------------------------------------- /Assets/Hexagrid.cs: -------------------------------------------------------------------------------- 1 | using System; 2 | using System.Collections; 3 | using System.Collections.Generic; 4 | using System.Linq; 5 | using UnityEngine; 6 | using UnityEditor; 7 | 8 | class Point 9 | { 10 | public Point(float x, float y, bool s) 11 | { 12 | mPosition = new Vector2(x, y); 13 | mSide = s; 14 | } 15 | public Point(Vector2 p, bool s) 16 | { 17 | mPosition = p; 18 | mSide = s; 19 | } 20 | public Vector2 mPosition; 21 | public bool mSide; 22 | }; 23 | 24 | class Triangle 25 | { 26 | public Triangle(int a, int b, int c) 27 | { 28 | mA = a; 29 | mB = b; 30 | mC = c; 31 | mValid = true; 32 | } 33 | public int mA, mB, mC; 34 | public bool mValid; 35 | }; 36 | 37 | class Quad 38 | { 39 | public Quad(int a, int b, int c, int d) 40 | { 41 | mA = a; 42 | mB = b; 43 | mC = c; 44 | mD = d; 45 | } 46 | public int mA, mB, mC, mD; 47 | }; 48 | 49 | class Neighbours 50 | { 51 | public Neighbours() 52 | { 53 | mNeighbour = new List(); 54 | } 55 | public void Add(int i) 56 | { 57 | mNeighbour.Add(i); 58 | } 59 | public int count 60 | { 61 | get { 62 | return mNeighbour.Count; 63 | } 64 | } 65 | public List mNeighbour; 66 | }; 67 | 68 | [ExecuteInEditMode] 69 | public class Hexagrid : MonoBehaviour 70 | { 71 | [Range(2, 12)] 72 | public int mSideSize = 8; 73 | 74 | [Range(1, 20)] 75 | public int mSearchIterationCount = 12; 76 | 77 | [Range(0, 65535)] 78 | public int mSeed = 15911; 79 | 80 | private int mBaseQuadCount = 0; 81 | 82 | public bool bTriangulation = true; 83 | public bool bRemovingEdges = false; 84 | public bool bSubdivideFaces = false; 85 | public bool bRelax = false; 86 | public bool bReshape = false; 87 | public bool bDrawPositions = false; 88 | 89 | private List mPoints; 90 | private List mTriangles; 91 | private List mQuads; 92 | private Neighbours[] mNeighbours; 93 | 94 | void Triangulation() 95 | { 96 | mPoints = new List(); 97 | mTriangles = new List(); 98 | mQuads = new List(); 99 | mNeighbours = new Neighbours[0]; 100 | 101 | if (mSideSize < 2) { 102 | return; 103 | } 104 | 105 | float sideLength = 0.5f * Mathf.Tan(Mathf.Deg2Rad * 60); // 0.5f* tanf(60deg) 106 | for (int x = 0; x < mSideSize * 2 - 1; ++x) { 107 | int height = (x < mSideSize) ? (mSideSize + x) : (mSideSize * 3 - 2 - x); 108 | float deltaHeight = mSideSize - height * 0.5f; 109 | for (int y = 0; y < height; y++) { 110 | bool isSide = x == 0 || x == (mSideSize * 2 - 2) || y == 0 || y == height - 1; 111 | mPoints.Add(new Point((x - mSideSize + 1) * sideLength, y + deltaHeight, isSide)); 112 | } 113 | } 114 | 115 | int offset = 0; 116 | for (int x = 0; x < (mSideSize * 2 - 2); x++) { 117 | int height = (x < mSideSize) ? (mSideSize + x) : (mSideSize * 3 - 2 - x); 118 | if (x < mSideSize - 1) { 119 | // left side 120 | for (int y = 0; y < height; y++) { 121 | mTriangles.Add(new Triangle(offset + y, offset + y + height, offset + y + height + 1)); 122 | if (y >= height - 1) { 123 | break; 124 | } 125 | mTriangles.Add(new Triangle(offset + y + height + 1, offset + y + 1, offset + y)); 126 | } 127 | } 128 | else { 129 | // right side 130 | for (int y = 0; y < height - 1; y++) { 131 | mTriangles.Add(new Triangle(offset + y, offset + y + height, offset + y + 1)); 132 | if (y >= height - 2) { 133 | break; 134 | } 135 | mTriangles.Add(new Triangle(offset + y + 1, offset + y + height, offset + y + height + 1)); 136 | } 137 | } 138 | offset += height; 139 | } 140 | } 141 | 142 | private int[] GetAdjacentTriangles(int triIndex) 143 | { 144 | List adjacents = new List(); 145 | 146 | int[] lhs = new int[3] { 147 | mTriangles[triIndex].mA, mTriangles[triIndex].mB, mTriangles[triIndex].mC, 148 | }; 149 | 150 | for (int otherIndex = 0; otherIndex < mTriangles.Count; ++otherIndex) { 151 | if (otherIndex == triIndex || !mTriangles[otherIndex].mValid) { 152 | continue; 153 | } 154 | int[] rhs = new int[3] { 155 | mTriangles[otherIndex].mA, mTriangles[otherIndex].mB, mTriangles[otherIndex].mC, 156 | }; 157 | 158 | int shareCount = 0; 159 | for (int l = 0; l < 3; l++) { 160 | for (int r = 0; r < 3; r++) { 161 | if (lhs[l] == rhs[r]) { 162 | shareCount++; 163 | break; 164 | } 165 | } 166 | } 167 | Debug.Assert(shareCount < 3); 168 | if (shareCount == 2) { 169 | Debug.Assert(adjacents.Count < 3); 170 | adjacents.Add(otherIndex); 171 | } 172 | } 173 | return adjacents.ToArray(); 174 | } 175 | 176 | void RemovingEdges() 177 | { 178 | // triangles to quads 179 | System.Random rand = new System.Random(mSeed); 180 | while (true) { 181 | int triIndex; 182 | int searchCount = 0; 183 | do { 184 | triIndex = rand.Next() % mTriangles.Count; 185 | searchCount++; 186 | } while (searchCount < mSearchIterationCount && !mTriangles[triIndex].mValid); 187 | 188 | if (searchCount == mSearchIterationCount) { 189 | break; 190 | } 191 | 192 | int[] adjacents = GetAdjacentTriangles(triIndex); 193 | if (adjacents.Length > 0) { 194 | int i1 = triIndex; 195 | int i2 = adjacents[0]; 196 | int[] indices = new int[6] { 197 | mTriangles[i1].mA, mTriangles[i1].mB, mTriangles[i1].mC, 198 | mTriangles[i2].mA, mTriangles[i2].mB, mTriangles[i2].mC 199 | }; 200 | 201 | Array.Sort(indices); 202 | int[] unique = indices.Distinct().ToArray(); 203 | Debug.Assert(unique.Length == 4); 204 | 205 | mQuads.Add(new Quad(unique[0], unique[2], unique[3], unique[1])); 206 | mTriangles[triIndex].mValid = false; ; 207 | mTriangles[adjacents[0]].mValid = false; 208 | } 209 | } 210 | this.mBaseQuadCount = mQuads.Count(); 211 | } 212 | 213 | void Subdivide(int[] indices, Dictionary middles) 214 | { 215 | int count = indices.Length; 216 | int[] halfSegmentIndex = new int[count]; 217 | 218 | int indexCenter = mPoints.Count; 219 | { 220 | Vector2 ptCenter = Vector2.zero; 221 | foreach (int i in indices) { 222 | ptCenter += mPoints[i].mPosition; 223 | } 224 | ptCenter /= count; 225 | mPoints.Add(new Point(ptCenter, false)); 226 | } 227 | 228 | for (int x = 0; x < count; ++x) { 229 | int indexA = indices[x]; 230 | int indexB = indices[(x + 1) % count]; 231 | 232 | UInt32 key = Convert.ToUInt32((Mathf.Min(indexA, indexB) << 16) + Mathf.Max(indexA, indexB)); 233 | if (!middles.ContainsKey(key)) { 234 | middles[key] = mPoints.Count; 235 | bool isSide = mPoints[indexA].mSide && mPoints[indexB].mSide; 236 | mPoints.Add(new Point((mPoints[indexA].mPosition + mPoints[indexB].mPosition) * 0.5f, isSide)); 237 | } 238 | halfSegmentIndex[x] = middles[key]; 239 | } 240 | 241 | for (int x = 0; x < count; ++x) { 242 | int indexA = x; 243 | int indexB = (x + 1) % count; 244 | mQuads.Add(new Quad(indexCenter, halfSegmentIndex[indexA], indices[indexB], halfSegmentIndex[indexB])); 245 | } 246 | } 247 | 248 | void SubdivideFaces() 249 | { 250 | Dictionary middles = new Dictionary(); 251 | 252 | // quads to 4 quads 253 | for (int i = 0; i < mBaseQuadCount; i++) { 254 | var quad = mQuads[i]; 255 | int[] indices = new int[4] { 256 | quad.mA, quad.mB, quad.mC, quad.mD 257 | }; 258 | this.Subdivide(indices, middles); 259 | } 260 | 261 | // triangles to quads 262 | foreach (var triangle in mTriangles) { 263 | if (triangle.mValid) { 264 | int[] indices = new int[3] { 265 | triangle.mA, triangle.mB, triangle.mC 266 | }; 267 | this.Subdivide(indices, middles); 268 | } 269 | } 270 | } 271 | 272 | void Relax() 273 | { 274 | mNeighbours = new Neighbours[mPoints.Count]; 275 | for (int i = 0; i < mPoints.Count; ++i) { 276 | mNeighbours[i] = new Neighbours(); 277 | } 278 | for (int i = mBaseQuadCount; i < mQuads.Count(); ++i) { 279 | var quad = mQuads[i]; 280 | int[] indices = new int[4] { 281 | quad.mA, quad.mB, quad.mC, quad.mD 282 | }; 283 | for (int j = 0; j < 4; j++) { 284 | int index1 = indices[j]; 285 | int index2 = indices[(j + 1) & 3]; 286 | { 287 | var neighbour = mNeighbours[index1]; 288 | // check 289 | bool good = true; 290 | for (int k = 0; k < neighbour.count; k++) { 291 | if (neighbour.mNeighbour[k] == index2) { 292 | good = false; 293 | break; 294 | } 295 | } 296 | if (good) { 297 | Debug.Assert(neighbour.count < 6); 298 | neighbour.Add(index2); 299 | } 300 | } 301 | { 302 | var neighbour = mNeighbours[index2]; 303 | // check 304 | bool good = true; 305 | for (int k = 0; k < neighbour.count; k++) { 306 | if (neighbour.mNeighbour[k] == index1) { 307 | good = false; 308 | break; 309 | } 310 | } 311 | if (good) { 312 | Debug.Assert(neighbour.count < 6); 313 | neighbour.Add(index1); 314 | } 315 | } 316 | } 317 | } 318 | 319 | for (int i = 0; i < mPoints.Count; i++) { 320 | if (mPoints[i].mSide) { 321 | continue; 322 | } 323 | var neighbour = mNeighbours[i]; 324 | Vector2 sum = Vector2.zero; 325 | for (int j = 0; j < neighbour.count; j++) { 326 | sum += mPoints[neighbour.mNeighbour[j]].mPosition; 327 | } 328 | sum /= (float)neighbour.count; 329 | mPoints[i].mPosition = sum; 330 | } 331 | } 332 | 333 | void Reshape() 334 | { 335 | float radius = mSideSize - 1.0f; 336 | Vector2 center = new Vector2(0, (mSideSize * 2 - 1) * 0.5f); 337 | 338 | // for (int i = 0; i < mPoints.size(); i++) { 339 | foreach (var point in mPoints) { 340 | if (!point.mSide) { 341 | continue; 342 | } 343 | Vector2 D = point.mPosition - center; 344 | float distance = radius - Mathf.Sqrt(D.x * D.x + D.y * D.y); 345 | point.mPosition += (D * distance) * 0.1f; 346 | } 347 | } 348 | 349 | private void DrawLine(int a, int b) 350 | { 351 | Gizmos.DrawLine(mPoints[a].mPosition, mPoints[b].mPosition); 352 | } 353 | 354 | void OnDrawGizmos() 355 | { 356 | bool hidePoint = !bDrawPositions; 357 | bool hideSector = bTriangulation && bRemovingEdges && bSubdivideFaces && bRelax; 358 | 359 | Gizmos.color = Color.green; 360 | 361 | if (!hidePoint) { 362 | foreach (var point in mPoints) { 363 | Gizmos.DrawSphere(point.mPosition, 0.1f); //参数1绘制坐标，参数2绘制半径 364 | } 365 | } 366 | 367 | if (!hideSector) { 368 | foreach (var tri in mTriangles) { 369 | if (tri.mValid) { 370 | DrawLine(tri.mA, tri.mB); 371 | DrawLine(tri.mB, tri.mC); 372 | DrawLine(tri.mC, tri.mA); 373 | } 374 | } 375 | 376 | foreach (var quad in mQuads) { 377 | DrawLine(quad.mA, quad.mB); 378 | DrawLine(quad.mB, quad.mC); 379 | DrawLine(quad.mC, quad.mD); 380 | DrawLine(quad.mD, quad.mA); 381 | } 382 | } 383 | else { 384 | for (int i = 0; i < mPoints.Count(); i++) { 385 | var neighbour = mNeighbours[i]; 386 | for (int j = 0; j < neighbour.count; j++) { 387 | DrawLine(i, neighbour.mNeighbour[j]); 388 | } 389 | } 390 | } 391 | } 392 | 393 | // Start is called before the first frame update 394 | void Start() 395 | { 396 | } 397 | 398 | // Update is called once per frame 399 | void Update() 400 | { 401 | if (bTriangulation && bRemovingEdges && bSubdivideFaces && bRelax) { 402 | if (bRelax) { 403 | this.Relax(); 404 | } 405 | if (bRelax && bReshape) { 406 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