public Interval1d IntersectionWith(ref Interval1d o)
{
if (o.a > b || o.b < a)
{
return(Interval1d.Empty);
}
return(new Interval1d(System.Math.Max(a, o.a), System.Math.Min(b, o.b)));
}
public double Dist(Interval1d o) {
if ( b < o.a )
return o.a - b;
else if ( a > o.b )
return a - o.b;
else
return 0;
}
public double SquaredDist(Interval1d o) {
if ( b < o.a )
return (o.a - b)*(o.a - b);
else if ( a > o.b )
return (a - o.b)*(a - o.b);
else
return 0;
}
public ColorMap(float[] t, Colorf[] c)
{
validRange = Interval1d.Empty;
for (int i = 0; i < t.Length; ++i)
{
AddPoint(t[i], c[i]);
}
}
public double Dist(Interval1d o)
{
if (b < o.a)
{
return(o.a - b);
}
else if (a > o.b)
{
return(a - o.b);
}
else
{
return(0);
}
}
public double SquaredDist(Interval1d o)
{
if (b < o.a)
{
return((o.a - b) * (o.a - b));
}
else if (a > o.b)
{
return((a - o.b) * (a - o.b));
}
else
{
return(0);
}
}
/// <summary>
/// Calculate the two most extreme vertices along an axis, with optional transform
/// </summary>
public static Interval1i ExtremeVertices(DMesh3 mesh, Vector3d axis, Func <Vector3d, Vector3d> TransformF = null)
{
Interval1d extent = Interval1d.Empty;
Interval1i extreme = new Interval1i(DMesh3.InvalidID, DMesh3.InvalidID);
if (TransformF == null)
{
foreach (int vid in mesh.VertexIndices())
{
double t = mesh.GetVertex(vid).Dot(ref axis);
if (t < extent.a)
{
extent.a = t;
extreme.a = vid;
}
else if (t > extent.b)
{
extent.b = t;
extreme.b = vid;
}
}
}
else
{
foreach (int vid in mesh.VertexIndices())
{
double t = TransformF(mesh.GetVertex(vid)).Dot(ref axis);
if (t < extent.a)
{
extent.a = t;
extreme.a = vid;
}
else if (t > extent.b)
{
extent.b = t;
extreme.b = vid;
}
}
}
return(extreme);
}
/// <summary>
/// Test if segments intersect. Returns true for parallel-line overlaps.
/// Returns same result as IntrSegment2Segment2.
/// </summary>
public bool Intersects(ref Segment2d seg2, double dotThresh = double.Epsilon, double intervalThresh = 0)
{
// see IntrLine2Line2 and IntrSegment2Segment2 for details on this code
Vector2d diff = seg2.Center - Center;
double D0DotPerpD1 = Direction.DotPerp(seg2.Direction);
if (Math.Abs(D0DotPerpD1) > dotThresh)
{ // Lines intersect in a single point.
double invD0DotPerpD1 = ((double)1) / D0DotPerpD1;
double diffDotPerpD0 = diff.DotPerp(Direction);
double diffDotPerpD1 = diff.DotPerp(seg2.Direction);
double s = diffDotPerpD1 * invD0DotPerpD1;
double s2 = diffDotPerpD0 * invD0DotPerpD1;
return(Math.Abs(s) <= (Extent + intervalThresh) &&
Math.Abs(s2) <= (seg2.Extent + intervalThresh));
}
// Lines are parallel.
diff.Normalize();
double diffNDotPerpD1 = diff.DotPerp(seg2.Direction);
if (Math.Abs(diffNDotPerpD1) <= dotThresh)
{
// Compute the location of segment1 endpoints relative to segment0.
diff = seg2.Center - Center;
double t1 = Direction.Dot(diff);
double tmin = t1 - seg2.Extent;
double tmax = t1 + seg2.Extent;
var extents = new Interval1d(-Extent, Extent);
if (extents.Overlaps(new Interval1d(tmin, tmax)))
{
return(true);
}
return(false);
}
// lines are parallel but not collinear
return(false);
}
/// <summary>
/// Calculate extents of mesh along an axis, with optional transform
/// </summary>
public static Interval1d ExtentsOnAxis(DMesh3 mesh, Vector3d axis, Func <Vector3d, Vector3d> TransformF = null)
{
Interval1d extent = Interval1d.Empty;
if (TransformF == null)
{
foreach (Vector3d v in mesh.Vertices())
{
extent.Contain(v.Dot(ref axis));
}
}
else
{
foreach (Vector3d v in mesh.Vertices())
{
Vector3d vT = TransformF(v);
extent.Contain(vT.Dot(ref axis));
}
}
return(extent);
}
/// <summary>
/// Calculate extents of mesh along an axis, with optional transform
/// </summary>
public static Interval1d ExtentsOnAxis(IMesh mesh, Vector3d axis, Func <Vector3d, Vector3d> TransformF = null)
{
Interval1d extent = Interval1d.Empty;
if (TransformF == null)
{
foreach (int vid in mesh.VertexIndices())
{
extent.Contain(mesh.GetVertex(vid).Dot(ref axis));
}
}
else
{
foreach (int vid in mesh.VertexIndices())
{
Vector3d vT = TransformF(mesh.GetVertex(vid));
extent.Contain(vT.Dot(ref axis));
}
}
return(extent);
}
public virtual int[] AddTriangleStrip(IList <Frame3f> frames, IList <Interval1d> spans, int group_id = -1)
{
int N = frames.Count;
if (N != spans.Count)
{
throw new Exception("MeshEditor.AddTriangleStrip: spans list is not the same size!");
}
int[] new_tris = new int[2 * (N - 1)];
int prev_a = -1, prev_b = -1;
int i = 0, ti = 0;
for (i = 0; i < N; ++i)
{
Frame3f f = frames[i];
Interval1d span = spans[i];
Vector3d va = f.Origin + (float)span.a * f.Y;
Vector3d vb = f.Origin + (float)span.b * f.Y;
// [TODO] could compute normals here...
int a = Mesh.AppendVertex(va);
int b = Mesh.AppendVertex(vb);
if (prev_a != -1)
{
new_tris[ti++] = Mesh.AppendTriangle(prev_a, b, prev_b);
new_tris[ti++] = Mesh.AppendTriangle(prev_a, a, b);
}
prev_a = a; prev_b = b;
}
return(new_tris);
}
int split_tri_set_midpoint(int[] triangles, Vector3d[] centers, int iStart, int iCount, int depth, int minTriCount,
boxes_set tris, boxes_set nodes, out AxisAlignedBox3f box)
{
box = AxisAlignedBox3f.Empty;
int iBox = -1;
if (iCount < minTriCount)
{
// append new triangles box
iBox = tris.iBoxCur++;
tris.box_to_index.insert(tris.iIndicesCur, iBox);
tris.index_list.insert(iCount, tris.iIndicesCur++);
for (int i = 0; i < iCount; ++i)
{
tris.index_list.insert(triangles[iStart + i], tris.iIndicesCur++);
box.Contain(mesh.GetTriBounds(triangles[iStart + i]));
}
tris.box_centers.insert(box.Center, iBox);
tris.box_extents.insert(box.Extents, iBox);
return(-(iBox + 1));
}
//compute interval along an axis and find midpoint
int axis = depth % 3;
Interval1d interval = Interval1d.Empty;
for (int i = 0; i < iCount; ++i)
{
interval.Contain(centers[iStart + i][axis]);
}
double midpoint = interval.Center;
int n0, n1;
if (Math.Abs(interval.a - interval.b) > MathUtil.ZeroTolerance)
{
// we have to re-sort the centers & triangles lists so that centers < midpoint
// are first, so that we can recurse on the two subsets. We walk in from each side,
// until we find two out-of-order locations, then we swap them.
int l = 0;
int r = iCount - 1;
while (l < r)
{
// [RMS] is <= right here? if v.axis == midpoint, then this loop
// can get stuck unless one of these has an equality test. But
// I did not think enough about if this is the right thing to do...
while (centers[iStart + l][axis] <= midpoint)
{
l++;
}
while (centers[iStart + r][axis] > midpoint)
{
r--;
}
if (l >= r)
{
break; //done!
}
//swap
Vector3d tmpc = centers[iStart + l]; centers[iStart + l] = centers[iStart + r]; centers[iStart + r] = tmpc;
int tmpt = triangles[iStart + l]; triangles[iStart + l] = triangles[iStart + r]; triangles[iStart + r] = tmpt;
}
n0 = l;
n1 = iCount - n0;
Debug.Assert(n0 >= 1 && n1 >= 1);
}
else
{
// interval is near-empty, so no point trying to do sorting, just split half and half
n0 = iCount / 2;
n1 = iCount - n0;
}
// create child boxes
AxisAlignedBox3f box1;
int child0 = split_tri_set_midpoint(triangles, centers, iStart, n0, depth + 1, minTriCount, tris, nodes, out box);
int child1 = split_tri_set_midpoint(triangles, centers, iStart + n0, n1, depth + 1, minTriCount, tris, nodes, out box1);
box.Contain(box1);
// append new box
iBox = nodes.iBoxCur++;
nodes.box_to_index.insert(nodes.iIndicesCur, iBox);
nodes.index_list.insert(child0, nodes.iIndicesCur++);
nodes.index_list.insert(child1, nodes.iIndicesCur++);
nodes.box_centers.insert(box.Center, iBox);
nodes.box_extents.insert(box.Extents, iBox);
return(iBox);
}
public override DeformInfo Apply(Frame3f vNextPos)
{
Interval1d edgeRangeSqr = Interval1d.Empty;
int N = Curve.VertexCount;
if (N > NewV.size)
{
NewV.resize(N);
}
if (N > ModifiedV.Length)
{
ModifiedV = new BitArray(2 * N);
}
// clear modified
ModifiedV.SetAll(false);
bool bSmooth = (SmoothAlpha > 0 && SmoothIterations > 0);
double r2 = Radius * Radius;
// deform pass
if (DeformF != null)
{
for (int i = 0; i < N; ++i)
{
Vector3d v = Curve[i];
double d2 = (v - vPreviousPos.Origin).LengthSquared;
if (d2 < r2)
{
double t = WeightFunc(Math.Sqrt(d2), Radius);
Vector3d vNew = DeformF(i, t);
if (bSmooth == false)
{
if (i > 0)
{
edgeRangeSqr.Contain(vNew.DistanceSquared(Curve[i - 1]));
}
if (i < N - 1)
{
edgeRangeSqr.Contain(vNew.DistanceSquared(Curve[i + 1]));
}
}
NewV[i] = vNew;
ModifiedV[i] = true;
}
}
}
else
{
// anything?
}
// smooth pass
if (bSmooth)
{
for (int j = 0; j < SmoothIterations; ++j)
{
int iStart = (Curve.Closed) ? 0 : 1;
int iEnd = (Curve.Closed) ? N : N - 1;
for (int i = iStart; i < iEnd; ++i)
{
Vector3d v = (ModifiedV[i]) ? NewV[i] : Curve[i];
double d2 = (v - vPreviousPos.Origin).LengthSquared;
if (ModifiedV[i] || d2 < r2) // always smooth any modified verts
{
double a = SmoothAlpha * WeightFunc(Math.Sqrt(d2), Radius);
int iPrev = (i == 0) ? N - 1 : i - 1;
int iNext = (i + 1) % N;
Vector3d vPrev = (ModifiedV[iPrev]) ? NewV[iPrev] : Curve[iPrev];
Vector3d vNext = (ModifiedV[iNext]) ? NewV[iNext] : Curve[iNext];
Vector3d c = (vPrev + vNext) * 0.5f;
NewV[i] = (1 - a) * v + (a) * c;
ModifiedV[i] = true;
if (i > 0)
{
edgeRangeSqr.Contain(NewV[i].DistanceSquared(Curve[i - 1]));
}
if (i < N - 1)
{
edgeRangeSqr.Contain(NewV[i].DistanceSquared(Curve[i + 1]));
}
}
}
}
}
// bake
for (int i = 0; i < N; ++i)
{
if (ModifiedV[i])
{
Curve[i] = NewV[i];
}
}
return(new DeformInfo()
{
minEdgeLenSqr = edgeRangeSqr.a, maxEdgeLenSqr = edgeRangeSqr.b
});
}
public ColorMap()
{
validRange = Interval1d.Empty;
}
public Interval1d(Interval1d copy)
{
a = copy.a; b = copy.b;
}
public void Set(Interval1d o)
{
a = o.a; b = o.b;
}
public Interval1d IntersectionWith(ref Interval1d o)
{
if (o.a > b || o.b < a)
return Interval1d.Empty;
return new Interval1d(Math.Max(a, o.a), Math.Min(b, o.b));
}
public ScalarMap()
{
validRange = Interval1d.Empty;
}
public bool Overlaps(Interval1d o)
{
return(!(o.a > b || o.b < a));
}
public Intersector1(Interval1d u, Interval1d v)
{
U = u;
V = v;
}
public Intersector1(double u0, double u1, double v0, double v1)
{
// [TODO] validate 0 < 1
U = new Interval1d(u0, u1);
V = new Interval1d(v0, v1);
}