/// <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");
}
