/// <summary> /// Clips a polygon against an axis aligned half plane. /// The polygons stored in this object are clipped against the half plane at z = -offset. /// </summary> /// <param name="result">Ouput vertices. Only the Y and Z coordinates are calculated. The X coordinates are undefined.</param> /// <param name="multi">Scale factor for the input vertices. Should be +1 or -1. If -1 the negative half plane is kept.</param> /// <param name="offset">Offset to move the input vertices with before cutting</param> public void ClipPolygonAlongZWithYZ(ref VoxelPolygonClipper result, float multi, float offset) { // Number of resulting vertices int m = 0; bool prev, curr; float dj = multi * z[(n - 1)] + offset; for (int i = 0, j = n - 1; i < n; j = i, i++) { float di = multi * z[i] + offset; prev = dj >= 0; curr = di >= 0; if (prev != curr) { float s = dj / (dj - di); result.y[m] = y[j] + (y[i] - y[j]) * s; result.z[m] = z[j] + (z[i] - z[j]) * s; m++; } if (curr) { result.y[m] = y[i]; result.z[m] = z[i]; m++; } dj = di; } result.n = m; }
public void VoxelizeInput(Pathfinding.Util.GraphTransform graphTransform, Bounds graphSpaceBounds) { AstarProfiler.StartProfile("Build Navigation Mesh"); AstarProfiler.StartProfile("Voxelizing - Step 1"); // Transform from voxel space to graph space. // then scale from voxel space (one unit equals one voxel) // Finally add min Matrix4x4 voxelMatrix = Matrix4x4.TRS(graphSpaceBounds.min, Quaternion.identity, Vector3.one) * Matrix4x4.Scale(new Vector3(cellSize, cellHeight, cellSize)); transformVoxel2Graph = new Pathfinding.Util.GraphTransform(voxelMatrix); // Transform from voxel space to world space // add half a voxel to fix rounding transform = graphTransform * voxelMatrix * Matrix4x4.TRS(new Vector3(0.5f, 0, 0.5f), Quaternion.identity, Vector3.one); int maximumVoxelYCoord = (int)(graphSpaceBounds.size.y / cellHeight); AstarProfiler.EndProfile("Voxelizing - Step 1"); AstarProfiler.StartProfile("Voxelizing - Step 2 - Init"); // Cosine of the slope limit in voxel space (some tweaks are needed because the voxel space might be stretched out along the y axis) float slopeLimit = Mathf.Cos(Mathf.Atan(Mathf.Tan(maxSlope * Mathf.Deg2Rad) * (cellSize / cellHeight))); // Temporary arrays used for rasterization var clipperOrig = new VoxelPolygonClipper(3); var clipperX1 = new VoxelPolygonClipper(7); var clipperX2 = new VoxelPolygonClipper(7); var clipperZ1 = new VoxelPolygonClipper(7); var clipperZ2 = new VoxelPolygonClipper(7); if (inputMeshes == null) { throw new System.NullReferenceException("inputMeshes not set"); } // Find the largest lengths of vertex arrays and check for meshes which can be skipped int maxVerts = 0; for (int m = 0; m < inputMeshes.Count; m++) { maxVerts = System.Math.Max(inputMeshes[m].vertices.Length, maxVerts); } // Create buffer, here vertices will be stored multiplied with the local-to-voxel-space matrix var verts = new Vector3[maxVerts]; AstarProfiler.EndProfile("Voxelizing - Step 2 - Init"); AstarProfiler.StartProfile("Voxelizing - Step 2"); // This loop is the hottest place in the whole rasterization process // it usually accounts for around 50% of the time for (int m = 0; m < inputMeshes.Count; m++) { RasterizationMesh mesh = inputMeshes[m]; var meshMatrix = mesh.matrix; // Flip the orientation of all faces if the mesh is scaled in such a way // that the face orientations would change // This happens for example if a mesh has a negative scale along an odd number of axes // e.g it happens for the scale (-1, 1, 1) but not for (-1, -1, 1) or (1,1,1) var flipOrientation = VectorMath.ReversesFaceOrientations(meshMatrix); Vector3[] vs = mesh.vertices; int[] tris = mesh.triangles; int trisLength = mesh.numTriangles; // Transform vertices first to world space and then to voxel space for (int i = 0; i < vs.Length; i++) { verts[i] = transform.InverseTransform(meshMatrix.MultiplyPoint3x4(vs[i])); } int mesharea = mesh.area; for (int i = 0; i < trisLength; i += 3) { Vector3 p1 = verts[tris[i]]; Vector3 p2 = verts[tris[i + 1]]; Vector3 p3 = verts[tris[i + 2]]; if (flipOrientation) { var tmp = p1; p1 = p3; p3 = tmp; } int minX = (int)(Utility.Min(p1.x, p2.x, p3.x)); int minZ = (int)(Utility.Min(p1.z, p2.z, p3.z)); int maxX = (int)System.Math.Ceiling(Utility.Max(p1.x, p2.x, p3.x)); int maxZ = (int)System.Math.Ceiling(Utility.Max(p1.z, p2.z, p3.z)); minX = Mathf.Clamp(minX, 0, voxelArea.width - 1); maxX = Mathf.Clamp(maxX, 0, voxelArea.width - 1); minZ = Mathf.Clamp(minZ, 0, voxelArea.depth - 1); maxZ = Mathf.Clamp(maxZ, 0, voxelArea.depth - 1); // Check if the mesh is completely out of bounds if (minX >= voxelArea.width || minZ >= voxelArea.depth || maxX <= 0 || maxZ <= 0) { continue; } Vector3 normal; int area; //AstarProfiler.StartProfile ("Rasterize..."); normal = Vector3.Cross(p2 - p1, p3 - p1); float cosSlopeAngle = Vector3.Dot(normal.normalized, Vector3.up); if (cosSlopeAngle < slopeLimit) { area = UnwalkableArea; } else { area = 1 + mesharea; } clipperOrig[0] = p1; clipperOrig[1] = p2; clipperOrig[2] = p3; clipperOrig.n = 3; for (int x = minX; x <= maxX; x++) { clipperOrig.ClipPolygonAlongX(ref clipperX1, 1f, -x + 0.5f); if (clipperX1.n < 3) { continue; } clipperX1.ClipPolygonAlongX(ref clipperX2, -1F, x + 0.5F); if (clipperX2.n < 3) { continue; } float clampZ1 = clipperX2.z[0]; float clampZ2 = clipperX2.z[0]; for (int q = 1; q < clipperX2.n; q++) { float val = clipperX2.z[q]; clampZ1 = System.Math.Min(clampZ1, val); clampZ2 = System.Math.Max(clampZ2, val); } int clampZ1I = Mathf.Clamp((int)System.Math.Round(clampZ1), 0, voxelArea.depth - 1); int clampZ2I = Mathf.Clamp((int)System.Math.Round(clampZ2), 0, voxelArea.depth - 1); for (int z = clampZ1I; z <= clampZ2I; z++) { clipperX2.ClipPolygonAlongZWithYZ(ref clipperZ1, 1F, -z + 0.5F); if (clipperZ1.n < 3) { continue; } clipperZ1.ClipPolygonAlongZWithY(ref clipperZ2, -1F, z + 0.5F); if (clipperZ2.n < 3) { continue; } float sMin = clipperZ2.y[0]; float sMax = clipperZ2.y[0]; for (int q = 1; q < clipperZ2.n; q++) { float val = clipperZ2.y[q]; sMin = System.Math.Min(sMin, val); sMax = System.Math.Max(sMax, val); } int maxi = (int)System.Math.Ceiling(sMax); // Skip span if below or above the bounding box if (maxi >= 0 && sMin <= maximumVoxelYCoord) { // Make sure mini >= 0 int mini = System.Math.Max(0, (int)sMin); // Make sure the span is at least 1 voxel high maxi = System.Math.Max(mini + 1, maxi); voxelArea.AddLinkedSpan(z * voxelArea.width + x, (uint)mini, (uint)maxi, area, voxelWalkableClimb); } } } } //AstarProfiler.EndFastProfile(0); //AstarProfiler.EndProfile ("Rasterize..."); } AstarProfiler.EndProfile("Voxelizing - Step 2"); }