// TODO: Test
// ref : https://cvtech.cc/pointdist/
public d3 Distance(d3 p)
{
var v = length(cross(p - a, dot(p - b, p - c))) / 6d;
var s = length(cross(b - a, c - a)) / 2d;
return(3 * v / s);
}
public (TR t1, TR t2, TR t3, TR t4, DN n1, DN n2, DN n3, DN n4) Split(d3 p)
{
var th = tetrahedra;
(DN n, TR t)abc = (new DN(p, th.a, th.b, th.c), new TR(th.a, th.b, th.c));
(DN n, TR t)bcd = (new DN(p, th.b, th.c, th.d), new TR(th.b, th.c, th.d));
(DN n, TR t)cda = (new DN(p, th.c, th.d, th.a), new TR(th.c, th.d, th.a));
(DN n, TR t)dab = (new DN(p, th.d, th.a, th.b), new TR(th.d, th.a, th.b));
abc.n.neighbor = new List <DN> {
bcd.n, cda.n, dab.n
};
bcd.n.neighbor = new List <DN> {
cda.n, dab.n, abc.n
};
cda.n.neighbor = new List <DN> {
dab.n, abc.n, bcd.n
};
dab.n.neighbor = new List <DN> {
abc.n, bcd.n, cda.n
};
this.SetNeighbor(abc.n, abc.t);
this.SetNeighbor(bcd.n, bcd.t);
this.SetNeighbor(cda.n, cda.t);
this.SetNeighbor(dab.n, dab.t);
return(abc.t, bcd.t, cda.t, dab.t, abc.n, bcd.n, cda.n, dab.n);
}
public Sphere GetCircumscribedSphere()
{
/// <summary>
// http://mathworld.wolfram.com/Circumsphere.html
/// </summary>
var a2 = a * a; var a2ex = a2.x + a2.y + a2.z;
var b2 = b * b; var b2ex = b2.x + b2.y + b2.z;
var c2 = c * c; var c2ex = c2.x + c2.y + c2.z;
var d2 = d * d; var d2ex = d2.x + d2.y + d2.z;
var detA = determinant(new d44(
a.x, a.y, a.z, 1,
b.x, b.y, b.z, 1,
c.x, c.y, c.z, 1,
d.x, d.y, d.z, 1));
var detX = determinant(new d44(
a2ex, a.y, a.z, 1,
b2ex, b.y, b.z, 1,
c2ex, c.y, c.z, 1,
d2ex, d.y, d.z, 1));
var detY = -determinant(new d44(
a2ex, a.x, a.z, 1,
b2ex, b.x, b.z, 1,
c2ex, c.x, c.z, 1,
d2ex, d.x, d.z, 1));
var detZ = determinant(new d44(
a2ex, a.x, a.y, 1,
b2ex, b.x, b.y, 1,
c2ex, c.x, c.y, 1,
d2ex, d.x, d.y, 1));
var ctr = new d3(detX, detY, detZ) / (2 * detA);
return(new Sphere(ctr, distance(ctr, a)));
}
Flip32(DN n1, DN n2, DN n3, d3 p31, d3 p12, d3 p23, d3 apex_x, d3 apex_y)
{
d3 a = p31;
d3 b = p12;
d3 c = p23;
DN nx = new DN(a, b, c, apex_x);
DN ny = new DN(a, b, c, apex_y);
nx.neighbor.Add(ny);
ny.neighbor.Add(nx);
TR xab = new TR(apex_x, a, b);
TR yab = new TR(apex_y, a, b);
TR xbc = new TR(apex_x, b, c);
TR ybc = new TR(apex_y, b, c);
TR xca = new TR(apex_x, c, a);
TR yca = new TR(apex_y, c, a);
n1.SetNeighbor(nx, xab);
n2.SetNeighbor(nx, xbc);
n3.SetNeighbor(nx, xca);
n1.SetNeighbor(ny, yab);
n2.SetNeighbor(ny, ybc);
n3.SetNeighbor(ny, yca);
return(xab, xbc, xca, yab, ybc, yca, nx, ny);
}
public bool Contains(d3 p, bool includeOnFacet)
{
var f1 = tris[0].IsSameSide(d, p, includeOnFacet);
var f2 = tris[1].IsSameSide(a, p, includeOnFacet);
var f3 = tris[2].IsSameSide(b, p, includeOnFacet);
var f4 = tris[3].IsSameSide(c, p, includeOnFacet);
return(f1 && f2 && f3 && f4);
}
public GpuData(int index, int order, T val, d3 block, d3 thread, object ext = null)
{
Index = index;
Order = order;
Value = val;
Block = block;
Thread = thread;
Ext = ext;
}
public Triangle(d3 p1, d3 p2, d3 p3)
{
if (Equals(p1, p2) || Equals(p2, p3) || Equals(p3, p1))
{
throw new Exception();
}
this.a = p1;
this.b = p2;
this.c = p3;
}
public bool Intersects(Line l, out d3 p, out bool isOnEdge)
{
if (!CramersLow(l.pos, l.vec, out d3 d, out p))
{
isOnEdge = default;
return(false);
}
isOnEdge = d.x == 0 || d.x == 1 || d.y == 0 || d.y == 1 || d.x + d.y == 1;
return(d.x >= 0 && d.x <= 1 && d.y >= 0 && d.y <= 1 && d.x + d.y <= 1);
}
public void TestKernelNoTile()
{
var blockCount = new d3(4);
var threadCount = new d3(2);
var arrayOut = new GpuArrayWrite <int>(blockCount.Volume() * threadCount.Volume());
GpuDevice.RunGpuKernel(
blockCount,
threadCount,
TestKernels.IntKernelWrap(arrayOut, blockCount, threadCount));
}
public bool Intersects(SG e, out d3 p, out bool isOnEdge)
{
if (!CramersLow(e.a, normalize(e.b - e.a), out d3 d, out p))
{
isOnEdge = default;
return(false);
}
bool f1 = d.x >= 0 && d.x <= 1 && d.y >= 0 && d.y <= 1 && d.x + d.y <= 1;
bool f2 = d.z >= 0 && d.z <= length(e.b - e.a);
isOnEdge = d.x == 0 || d.x == 1 || d.y == 0 || d.y == 1 || d.x + d.y == 1;
return(f1 && f2);
}
void Split(d3 p)
{
var n = nodes.Find(_t => _t.tetrahedra.Contains(p, true));
var o = n.Split(p);
nodes.Remove(n);
nodes.Add(o.n1);
nodes.Add(o.n2);
nodes.Add(o.n3);
nodes.Add(o.n4);
stack.Push(o.t1);
stack.Push(o.t2);
stack.Push(o.t3);
stack.Push(o.t4);
}
int GetType(d3 p)
{
var v = dot(n, p) - w;
var isNearPlane = abs(v) < EPSILON;
var isFacingSide = v > 0;
if (isNearPlane)
{
return(ONPLANE);
}
else
{
return(isFacingSide ? FACE : BACK);
}
}
public Tetrahedra(d3 a, d3 b, d3 c, d3 d)
{
this.vrts = new d34(a, b, c, d);
this.tris = new TR[] {
new TR(a, b, c),
new TR(b, c, d),
new TR(c, d, a),
new TR(d, a, b)
};
if (Equals(a, b) || Equals(a, c) || Equals(a, d) ||
Equals(b, c) || Equals(b, d) || Equals(c, d))
{
throw new Exception();
}
}
public SG Remaining(d3 p)
{
if (p.Equals(a))
{
return(new SG(b, c));
}
if (p.Equals(b))
{
return(new SG(c, a));
}
if (p.Equals(c))
{
return(new SG(a, b));
}
throw new Exception();
}
public bool HasPoint(d3 p)
{
if (p.Equals(a))
{
return(true);
}
if (p.Equals(b))
{
return(true);
}
if (p.Equals(c))
{
return(true);
}
if (p.Equals(d))
{
return(true);
}
return(false);
}
static void IsIntersecting(SG e1, SG e2, out bool flag, out d3 pos, double threshold)
{
var v1 = e1.b - e1.a;
var v2 = e2.b - e2.a;
var n1 = normalize(v1);
var n2 = normalize(v2);
var alpha = dot(n1, n2);
var r = e1.a - e2.a;
var rho = dot(r, n1 - alpha * n2) / (alpha * alpha - 1d);
var tau = dot(r, alpha * n1 - n2) / (alpha * alpha - 1d);
var pos1 = e1.a + rho * n1;
var pos2 = e2.a + tau * n2;
var f1 = lengthsq(pos1 - pos2) < threshold;
var _rho = rho / length(v1);
var _tau = tau / length(v2);
var f2 = _rho >= 0d && _rho <= 1d && _tau >= 0d && _tau <= 1d;
flag = f1 && f2;
pos = pos2;
}
bool CramersLow(d3 ogn, d3 ray, out d3 det, out d3 pos)
{
// using cramer's rule
var e1 = b - a;
var e2 = c - a;
var denominator = determinant(double3x3(e1, e2, -ray));
if (denominator == 0)
{
Debug.LogWarning("parallele");
det = default;
pos = default;
return(false);
}
var d = ogn - a;
var u = determinant(double3x3(d, e2, -ray)) / denominator;
var v = determinant(double3x3(e1, d, -ray)) / denominator;
var t = determinant(double3x3(e1, e2, d)) / denominator;
pos = ogn + ray * t;
det = new d3(u, v, t);
return(true);
}
Flip23(DN n1, DN n2, d3 p1, d3 p2, TR t)
{
DN nab = new DN(p1, p2, t.a, t.b);
DN nbc = new DN(p1, p2, t.b, t.c);
DN nca = new DN(p1, p2, t.c, t.a);
nab.neighbor = new List <DN> {
nbc, nca
};
nbc.neighbor = new List <DN> {
nca, nab
};
nca.neighbor = new List <DN> {
nab, nbc
};
TR t_ab_p1 = new TR(t.a, t.b, p1); n1.SetNeighbor(nab, t_ab_p1);
TR t_ab_p2 = new TR(t.a, t.b, p2); n2.SetNeighbor(nab, t_ab_p2);
TR t_bc_p1 = new TR(t.b, t.c, p1); n1.SetNeighbor(nbc, t_bc_p1);
TR t_bc_p2 = new TR(t.b, t.c, p2); n2.SetNeighbor(nbc, t_bc_p2);
TR t_ca_p1 = new TR(t.c, t.a, p1); n1.SetNeighbor(nca, t_ca_p1);
TR t_ca_p2 = new TR(t.c, t.a, p2); n2.SetNeighbor(nca, t_ca_p2);
return(t_ab_p1, t_ab_p2, t_bc_p1, t_bc_p2, t_ca_p1, t_ca_p2, nab, nbc, nca);
}
public DelaunayGraphNode3D(d3 a, d3 b, d3 c, d3 d)
{
tetrahedra = new Tetrahedra(a, b, c, d);
neighbor = new List <DN>(4);
}
public bool Contains(d3 p, bool inclusive) => tetrahedra.Contains(p, inclusive);
public bool HasVert(d3 p) => p.Equals(a) || p.Equals(b) || p.Equals(c);
public Triangle(SG s, d3 p) : this(s.a, s.b, p)
{
}
public Plane(d3 a, d3 b, d3 c)
{
n = normalize(cross(b - a, c - a));
w = dot(n, a);
}
public bool IsSameSide(d3 p1, d3 p2, bool includeOnPlane)
{
double d = dot(n, p1 - a) * dot(n, p2 - a);
return(includeOnPlane ? d >= 0 : d > 0);
}