using System; using System.Collections; using System.Collections.Generic; using UnityEngine; namespace EzySlice { /** * Contains static functionality for performing Triangulation on arbitrary vertices. * Read the individual function descriptions for specific details. */ public sealed class Triangulator { /** * Represents a 3D Vertex which has been mapped onto a 2D surface * and is mainly used in MonotoneChain to triangulate a set of vertices * against a flat plane. */ internal struct Mapped2D { private readonly Vector3 original; private readonly Vector2 mapped; public Mapped2D(Vector3 newOriginal, Vector3 u, Vector3 v) { this.original = newOriginal; this.mapped = new Vector2(Vector3.Dot(newOriginal, u), Vector3.Dot(newOriginal, v)); } public Vector2 mappedValue { get { return this.mapped; } } public Vector3 originalValue { get { return this.original; } } } /** * Overloaded variant of MonotoneChain which will calculate UV coordinates of the Triangles * between 0.0 and 1.0 (default). * * See MonotoneChain(vertices, normal, tri, TextureRegion) for full explanation */ public static bool MonotoneChain(List vertices, Vector3 normal, out List tri) { // default texture region is in coordinates 0,0 to 1,1 return MonotoneChain(vertices, normal, out tri, new TextureRegion(0.0f, 0.0f, 1.0f, 1.0f)); } /** * O(n log n) Convex Hull Algorithm. * Accepts a list of vertices as Vector3 and triangulates them according to a projection * plane defined as planeNormal. Algorithm will output vertices, indices and UV coordinates * as arrays */ public static bool MonotoneChain(List vertices, Vector3 normal, out List tri, TextureRegion texRegion) { int count = vertices.Count; // we cannot triangulate less than 3 points. Use minimum of 3 points if (count < 3) { tri = null; return false; } // first, we map from 3D points into a 2D plane represented by the provided normal Vector3 u = Vector3.Normalize(Vector3.Cross(normal, Vector3.up)); if (Vector3.zero == u) { u = Vector3.Normalize(Vector3.Cross(normal, Vector3.forward)); } Vector3 v = Vector3.Cross(u, normal); // generate an array of mapped values Mapped2D[] mapped = new Mapped2D[count]; // these values will be used to generate new UV coordinates later on float maxDivX = float.MinValue; float maxDivY = float.MinValue; float minDivX = float.MaxValue; float minDivY = float.MaxValue; // map the 3D vertices into the 2D mapped values for (int i = 0; i < count; i++) { Vector3 vertToAdd = vertices[i]; Mapped2D newMappedValue = new Mapped2D(vertToAdd, u, v); Vector2 mapVal = newMappedValue.mappedValue; // grab our maximal values so we can map UV's in a proper range maxDivX = Mathf.Max(maxDivX, mapVal.x); maxDivY = Mathf.Max(maxDivY, mapVal.y); minDivX = Mathf.Min(minDivX, mapVal.x); minDivY = Mathf.Min(minDivY, mapVal.y); mapped[i] = newMappedValue; } // sort our newly generated array values Array.Sort(mapped, (a, b) => { Vector2 x = a.mappedValue; Vector2 p = b.mappedValue; return (x.x < p.x || (x.x == p.x && x.y < p.y)) ? -1 : 1; }); // our final hull mappings will end up in here Mapped2D[] hulls = new Mapped2D[count + 1]; int k = 0; // build the lower hull of the chain for (int i = 0; i < count; i++) { while (k >= 2) { Vector2 mA = hulls[k - 2].mappedValue; Vector2 mB = hulls[k - 1].mappedValue; Vector2 mC = mapped[i].mappedValue; if (Intersector.TriArea2D(mA.x, mA.y, mB.x, mB.y, mC.x, mC.y) > 0.0f) { break; } k--; } hulls[k++] = mapped[i]; } // build the upper hull of the chain for (int i = count - 2, t = k + 1; i >= 0; i--) { while (k >= t) { Vector2 mA = hulls[k - 2].mappedValue; Vector2 mB = hulls[k - 1].mappedValue; Vector2 mC = mapped[i].mappedValue; if (Intersector.TriArea2D(mA.x, mA.y, mB.x, mB.y, mC.x, mC.y) > 0.0f) { break; } k--; } hulls[k++] = mapped[i]; } // finally we can build our mesh, generate all the variables // and fill them up int vertCount = k - 1; int triCount = (vertCount - 2) * 3; // this should not happen, but here just in case if (vertCount < 3) { tri = null; return false; } // ensure List does not dynamically grow, performing copy ops each time! tri = new List(triCount / 3); float width = maxDivX - minDivX; float height = maxDivY - minDivY; int indexCount = 1; // generate both the vertices and uv's in this loop for (int i = 0; i < triCount; i += 3) { // the Vertices in our triangle Mapped2D posA = hulls[0]; Mapped2D posB = hulls[indexCount]; Mapped2D posC = hulls[indexCount + 1]; // generate UV Maps Vector2 uvA = posA.mappedValue; Vector2 uvB = posB.mappedValue; Vector2 uvC = posC.mappedValue; uvA.x = (uvA.x - minDivX) / width; uvA.y = (uvA.y - minDivY) / height; uvB.x = (uvB.x - minDivX) / width; uvB.y = (uvB.y - minDivY) / height; uvC.x = (uvC.x - minDivX) / width; uvC.y = (uvC.y - minDivY) / height; Triangle newTriangle = new Triangle(posA.originalValue, posB.originalValue, posC.originalValue); // ensure our UV coordinates are mapped into the requested TextureRegion newTriangle.SetUV(texRegion.Map(uvA), texRegion.Map(uvB), texRegion.Map(uvC)); // the normals is the same for all vertices since the final mesh is completly flat newTriangle.SetNormal(normal, normal, normal); newTriangle.ComputeTangents(); tri.Add(newTriangle); indexCount++; } return true; } } }