/// <summary>
/// Returns the signed distance to the field as a whole.
/// </summary>
public float Map(Vector3 p)
{
float minDist = 10000000f;
for (int i = 0; i < m_sdfData.Count; i++)
{
SDFGPUData data = m_sdfData[i];
if (data.IsOperation)
{
p = ElongateSpace(p, data.Data, data.Transform);
}
else
{
if (data.CombineType == 0)
{
minDist = SmoothUnion(minDist, SDF(p, data), data.Smoothing);
}
else if (data.CombineType == 1)
{
minDist = SmoothSubtract(SDF(p, data), minDist, data.Smoothing);
}
else
{
minDist = SmoothIntersect(SDF(p, data), minDist, data.Smoothing);
}
}
}
return(minDist);
}
/// <summary>
/// Get the signed distance to the object represented by the given data object.
/// </summary>
private float SDF(Vector3 p, SDFGPUData data)
{
if (data.IsMesh)
{
Vector3 vec = GetDirectionToMesh(p, data, out float distSign, out Vector3 transformedP);
return(vec.magnitude * distSign * data.Flip);
}
else
{
p = data.Transform.MultiplyPoint(p);
switch ((SDFPrimitiveType)(data.Type - 1))
{
case SDFPrimitiveType.Sphere:
return(MapSphere(p, data.Data.x) * data.Flip);
case SDFPrimitiveType.Torus:
return(MapTorus(p, data.Data) * data.Flip);
case SDFPrimitiveType.Cuboid:
return(MapRoundedBox(p, data.Data, data.Data.w) * data.Flip);
case SDFPrimitiveType.Cylinder:
return(MapCylinder(p, data.Data.x, data.Data.y) * data.Flip);
default:
return(MapBoxFrame(p, data.Data, data.Data.w) * data.Flip);
}
}
}
private static Vector3 CellCoordinateToVertex(int x, int y, int z, SDFGPUData data)
{
float gridSize = data.Size - 1f;
Vector3 minBounds = data.MinBounds;
Vector3 maxBounds = data.MaxBounds;
float xPos = Mathf.Lerp(minBounds.x, maxBounds.x, x / gridSize);
float yPos = Mathf.Lerp(minBounds.y, maxBounds.y, y / gridSize);
float zPos = Mathf.Lerp(minBounds.z, maxBounds.z, z / gridSize);
return(new Vector3(xPos, yPos, zPos));
}
// clamp the input point to an axis aligned bounding cube of the given bounds
// optionally can provide an offset which pushes the bounds in or out.
// this is used to get the position on the bounding cube nearest the given point as
// part of the sdf to mesh calculation. the additional push param is used to ensure we have enough
// samples around our point that we can get a gradient
private static Vector3 GetClosestPointToVolume(Vector3 p, SDFGPUData data, float boundsOffset = 0f)
{
Vector3 minBounds = data.MinBounds;
Vector3 maxBounds = data.MaxBounds;
return(new Vector3(
Mathf.Clamp(p.x, minBounds.x + boundsOffset, maxBounds.x - boundsOffset),
Mathf.Clamp(p.y, minBounds.y + boundsOffset, maxBounds.y - boundsOffset),
Mathf.Clamp(p.z, minBounds.z + boundsOffset, maxBounds.z - boundsOffset)
));
}
private Vector3 ComputeMeshGradient(Vector3 p, SDFGPUData data, float epsilon, float boundsOffset = 0f)
{
// sample the map 4 times to calculate the gradient at that point, then normalize it
Vector2 e = new Vector2(epsilon, -epsilon);
return((
XYY(e) * SampleAssetInterpolated(p + XYY(e), data, boundsOffset) +
YYX(e) * SampleAssetInterpolated(p + YYX(e), data, boundsOffset) +
YXY(e) * SampleAssetInterpolated(p + YXY(e), data, boundsOffset) +
XXX(e) * SampleAssetInterpolated(p + XXX(e), data, boundsOffset)).normalized);
}
// these functions are all specifically to do with SDFMesh objects only
// given a point, return the coords of the cell it's in, and the fractional component for interpolation
private static void GetNearestCoordinates(Vector3 p, SDFGPUData data, out Vector3 coords, out Vector3 fracs, float boundsOffset = 0f)
{
p = ClampAndNormalizeToVolume(p, data, boundsOffset);
int cellsPerSide = data.Size - 1;
// sometimes i'm not good at coming up with names :U
Vector3 floored = Floor(p * cellsPerSide);
coords = Min(floored, cellsPerSide - 1);
fracs = Frac(p * cellsPerSide);
}
// ensure the given point is inside the volume, and then smush into the the [0, 1] range
private static Vector3 ClampAndNormalizeToVolume(Vector3 p, SDFGPUData data, float boundsOffset = 0f)
{
// clamp so we're inside the volume
p = GetClosestPointToVolume(p, data, boundsOffset);
Vector3 minBounds = data.MinBounds;
Vector3 maxBounds = data.MaxBounds;
return(new Vector3(
Mathf.InverseLerp(minBounds.x + boundsOffset, maxBounds.x - boundsOffset, p.x),
Mathf.InverseLerp(minBounds.y + boundsOffset, maxBounds.y - boundsOffset, p.y),
Mathf.InverseLerp(minBounds.z + boundsOffset, maxBounds.z - boundsOffset, p.z)
));
}
private float SampleAssetInterpolated(Vector3 p, SDFGPUData data, float boundsOffset = 0f)
{
GetNearestCoordinates(p, data, out Vector3 coords, out Vector3 fracs, boundsOffset);
int x = (int)coords.x;
int y = (int)coords.y;
int z = (int)coords.z;
float sampleA = GetMeshSignedDistance(x, y, z, data);
float sampleB = GetMeshSignedDistance(x + 1, y, z, data);
float sampleC = GetMeshSignedDistance(x, y + 1, z, data);
float sampleD = GetMeshSignedDistance(x + 1, y + 1, z, data);
float sampleE = GetMeshSignedDistance(x, y, z + 1, data);
float sampleF = GetMeshSignedDistance(x + 1, y, z + 1, data);
float sampleG = GetMeshSignedDistance(x, y + 1, z + 1, data);
float sampleH = GetMeshSignedDistance(x + 1, y + 1, z + 1, data);
return(Utils.TrilinearInterpolate(fracs, sampleA, sampleB, sampleC, sampleD, sampleE, sampleF, sampleG, sampleH));
}
// returns the vector pointing to the surface of the mesh representation, as well as the sign
// (negative for inside, positive for outside)
// this can be used to recreate a signed distance field
private Vector3 GetDirectionToMesh(Vector3 p, SDFGPUData data, out float distSign, out Vector3 transformedP)
{
transformedP = data.Transform.MultiplyPoint(p);
const float epsilon = 0.75f;
const float pushIntoBounds = 0.04f;
// get the distance either at p, or at the point on the bounds nearest p
float sample = SampleAssetInterpolated(transformedP, data);
Vector3 closestPoint = GetClosestPointToVolume(transformedP, data, pushIntoBounds);
Vector3 vecInBounds = (-(ComputeMeshGradient(closestPoint, data, epsilon, pushIntoBounds)).normalized * sample);
Vector3 vecToBounds = (closestPoint - transformedP);
Vector3 finalVec = vecToBounds + vecInBounds;
distSign = Mathf.Sign(sample);
return(finalVec);
}
private static int CellCoordinateToIndex(int x, int y, int z, SDFGPUData data)
{
int size = data.Size;
return(data.SampleStartIndex + (x + y * size + z * size * size));
}
private float SDF_Colour(Vector3 p, SDFGPUData data, SDFMaterialGPU material, out Vector4 colour)
{
colour = material.Colour;
return(SDF(p, data));
}
private float GetMeshSignedDistance(int x, int y, int z, SDFGPUData data)
{
int index = CellCoordinateToIndex(x, y, z, data);
return(m_sdfMeshSamples[index]);
}