mirror of
https://github.com/NGSolve/netgen.git
synced 2024-11-14 10:08:32 +05:00
356 lines
7.7 KiB
C++
356 lines
7.7 KiB
C++
#include <mystdlib.h>
|
|
|
|
#include <myadt.hpp>
|
|
|
|
#include <linalg.hpp>
|
|
#include <csg.hpp>
|
|
|
|
|
|
namespace netgen
|
|
{
|
|
splinesegment3d :: splinesegment3d (const Point<3> & ap1, const Point<3> & ap2,
|
|
const Point<3> & ap3)
|
|
{
|
|
p1 = ap1;
|
|
p2 = ap2;
|
|
p3 = ap3;
|
|
}
|
|
|
|
|
|
/*
|
|
todo
|
|
Tip von Joerg Stiller:
|
|
setzt Du in
|
|
void splinesegment3d :: Evaluate
|
|
Zeilen 54 und 56
|
|
b2 = 2 * t * (1-t);
|
|
b2 /= sqrt(2);
|
|
Das heisst, Du wichtest das zweite Bersteinpolynom mit
|
|
w2 = 1 / sqrt(2);
|
|
Das ist aber nur fuer 45-Grad-Segmente korrekt. Fuer den
|
|
allgemeinen Fall funktioniert
|
|
w2 = ( e(p3 - p1), e(p2 - p1) ); // also cos(winkel(p3-p1, p2-p1))
|
|
bzw. schoen symmetrisch
|
|
w2 = ( e(p3 - p1), e(p2 - p1) )/2 + ( e(p1 - p3), e(p2 - p3) )/2;
|
|
Das ist natuerlich kein C++ Code sondern symbolisch, wobei
|
|
e(p3 - p1) ist der von p1 zu p3 zeigende Einheitsvektor und
|
|
(a, b) steht fuer das Skalarprodukt zweier Vektoren etc.
|
|
|
|
Eine vergleichbare Information steht auch irgendwo im Hoscheck & Lasser.
|
|
Ich habe das Buch aber eben nicht zur Hand.
|
|
*/
|
|
|
|
void splinesegment3d :: Evaluate (double t, Point<3> & p) const
|
|
{
|
|
double x, y, z, w;
|
|
double b1, b2, b3;
|
|
|
|
b1 = (1-t)*(1-t);
|
|
b2 = 2 * t * (1-t);
|
|
b3 = t * t;
|
|
|
|
b2 /= sqrt(double(2));
|
|
|
|
x = p1(0) * b1 + p2(0) * b2 + p3(0) * b3;
|
|
y = p1(1) * b1 + p2(1) * b2 + p3(1) * b3;
|
|
z = p1(2) * b1 + p2(2) * b2 + p3(2) * b3;
|
|
w = b1 + b2 + b3;
|
|
|
|
p(0) = x / w;
|
|
p(1) = y / w;
|
|
p(2) = z / w;
|
|
}
|
|
|
|
void splinesegment3d :: EvaluateTangent (double t, Vec<3> & tang) const
|
|
{
|
|
double x, y, z, w, xprime, yprime, zprime, wprime;
|
|
double b1, b2, b3, b1prime, b2prime, b3prime;
|
|
|
|
b1 = (1-t)*(1-t);
|
|
b2 = 2 * t * (1-t);
|
|
b3 = t * t;
|
|
b2 /= sqrt(double(2));
|
|
|
|
b1prime = 2 * t - 2;
|
|
b2prime = - 4 * t + 2;
|
|
b3prime = 2 * t;
|
|
b2prime /= sqrt(double(2));
|
|
|
|
|
|
x = p1(0) * b1 + p2(0) * b2 + p3(0) * b3;
|
|
y = p1(1) * b1 + p2(1) * b2 + p3(1) * b3;
|
|
z = p1(2) * b1 + p2(2) * b2 + p3(2) * b3;
|
|
w = b1 + b2 + b3;
|
|
|
|
xprime = p1(0) * b1prime + p2(0) * b2prime + p3(0) * b3prime;
|
|
yprime = p1(1) * b1prime + p2(1) * b2prime + p3(1) * b3prime;
|
|
zprime = p1(2) * b1prime + p2(2) * b2prime + p3(2) * b3prime;
|
|
wprime = b1prime + b2prime + b3prime;
|
|
|
|
tang(0) = (w * xprime - x * wprime) / (w * w);
|
|
tang(1) = (w * yprime - y * wprime) / (w * w);
|
|
tang(2) = (w * zprime - z * wprime) / (w * w);
|
|
}
|
|
|
|
|
|
void spline3d :: AddSegment (const Point<3> & ap1, const Point<3> & ap2,
|
|
const Point<3> & ap3)
|
|
{
|
|
segments.Append (new splinesegment3d (ap1, ap2, ap3));
|
|
}
|
|
|
|
void spline3d :: Evaluate (double t, Point<3> & p) const
|
|
{
|
|
int nr;
|
|
double loct;
|
|
static int cnt = 0;
|
|
|
|
cnt++;
|
|
if (cnt % 10000 == 0) (*mycout) << "Evaluate calls: " << cnt << endl;
|
|
|
|
while (t < 0) t += GetNumSegments();
|
|
while (t >= GetNumSegments()) t -= GetNumSegments();
|
|
nr = 1 + int (t);
|
|
loct = t - nr + 1;
|
|
segments.Get(nr)->Evaluate (loct, p);
|
|
}
|
|
|
|
void spline3d :: EvaluateTangent (double t, Vec<3> & tang) const
|
|
{
|
|
int nr;
|
|
double loct;
|
|
|
|
while (t < 0) t += GetNumSegments();
|
|
while (t >= GetNumSegments()) t -= GetNumSegments();
|
|
nr = 1 + int (t);
|
|
loct = t - nr + 1;
|
|
segments.Get(nr)->EvaluateTangent (loct, tang);
|
|
}
|
|
|
|
|
|
double spline3d :: ProjectToSpline (Point<3> & p) const
|
|
{
|
|
double t, tl, tu, dt, dist, mindist, optt(0);
|
|
Point<3> hp;
|
|
Vec<3> tanx, px;
|
|
|
|
dt = 0.01;
|
|
mindist = 0;
|
|
for (t = 0; t <= GetNumSegments() + dt/2; t += dt)
|
|
{
|
|
Evaluate (t, hp);
|
|
dist = Dist (hp, p);
|
|
if (t == 0 || dist < mindist)
|
|
{
|
|
optt = t;
|
|
mindist = dist;
|
|
}
|
|
}
|
|
|
|
|
|
tu = optt + dt;
|
|
tl = optt - dt;
|
|
while (tu - tl > 1e-2)
|
|
{
|
|
optt = 0.5 * (tu + tl);
|
|
Evaluate (optt, hp);
|
|
EvaluateTangent (optt, tanx);
|
|
if (tanx * (hp - p) > 0)
|
|
tu = optt;
|
|
else
|
|
tl = optt;
|
|
}
|
|
|
|
optt = 0.5 * (tu + tl);
|
|
|
|
optt = ProjectToSpline (p, optt);
|
|
return optt;
|
|
}
|
|
|
|
|
|
double spline3d :: ProjectToSpline (Point<3> & p, double optt) const
|
|
{
|
|
double tl, tu, dt, val, dval, valu, vall;
|
|
Point<3> hp;
|
|
Vec<3> tanx, px;
|
|
int its = 0;
|
|
int cnt = 1000;
|
|
do
|
|
{
|
|
dt = 1e-8;
|
|
tl = optt - dt;
|
|
tu = optt + dt;
|
|
|
|
EvaluateTangent (optt, tanx);
|
|
Evaluate (optt, hp);
|
|
px = hp - p;
|
|
val = px * tanx;
|
|
|
|
EvaluateTangent (tl, tanx);
|
|
Evaluate (tl, hp);
|
|
px = hp - p;
|
|
vall = px * tanx;
|
|
|
|
EvaluateTangent (tu, tanx);
|
|
Evaluate (tu, hp);
|
|
px = hp - p;
|
|
valu = px * tanx;
|
|
|
|
dval = (valu - vall) / (2 * dt);
|
|
|
|
if (its % 100 == 99)
|
|
(*testout) << "optt = " << optt
|
|
<< " val = " << val
|
|
<< " dval = " << dval << endl;
|
|
optt -= val / dval;
|
|
its++;
|
|
if (fabs(val) < 1e-8 && cnt > 5) cnt = 5;
|
|
cnt--;
|
|
}
|
|
while (cnt > 0);
|
|
|
|
Evaluate (optt, p);
|
|
return optt;
|
|
}
|
|
|
|
|
|
splinetube :: splinetube (const spline3d & amiddlecurve, double ar)
|
|
: Surface(), middlecurve (amiddlecurve), r(ar)
|
|
{
|
|
(*mycout) << "Splinetube Allocated, r = " << r << endl;
|
|
|
|
}
|
|
|
|
void splinetube :: DefineTangentialPlane (const Point<3> & ap1,
|
|
const Point<3> & ap2)
|
|
{
|
|
double t;
|
|
double phi, z;
|
|
|
|
p1 = ap1;
|
|
p2 = ap2;
|
|
cp = p1;
|
|
t = middlecurve.ProjectToSpline (cp);
|
|
ex = p1 - cp;
|
|
middlecurve.EvaluateTangent (t, ez);
|
|
ex.Normalize();
|
|
ez.Normalize();
|
|
ey = Cross (ez, ex);
|
|
|
|
phi = r * atan2 (ey * (p2-cp), ex * (p2-cp));
|
|
z = ez * (p2 - cp);
|
|
e2x(0) = phi;
|
|
e2x(1) = z;
|
|
e2x.Normalize();
|
|
e2y(1) = e2x(0);
|
|
e2y(0) = -e2x(1);
|
|
|
|
// (*testout) << "Defineplane: " << endl
|
|
// << "p1 = " << p1 << " p2 = " << p2 << endl
|
|
// << "pc = " << cp << endl
|
|
// << "ex = " << ex << " ey = " << ey << " ez = " << ez << endl
|
|
// << "phi = " << phi << " z = " << z << endl
|
|
// << "e2x = " << e2x << " e2y = " << e2y << endl;
|
|
}
|
|
|
|
void splinetube :: ToPlane (const Point<3> & p3d, Point<2> & pplain, double h,
|
|
int & zone) const
|
|
{
|
|
Vec<2> v;
|
|
v(0) = r * atan2 (ey * (p3d-cp), ex * (p3d-cp));
|
|
v(1) = ez * (p3d - cp);
|
|
zone = 0;
|
|
if (v(0) > r * 2) zone = 1;
|
|
if (v(0) < r * 2) zone = 2;
|
|
|
|
pplain(0) = (v * e2x) / h;
|
|
pplain(1) = (v * e2y) / h;
|
|
}
|
|
|
|
void splinetube :: FromPlane (const Point<2> & pplain, Point<3> & p3d, double h) const
|
|
{
|
|
Vec<2> v;
|
|
|
|
v(0) = pplain(0) * h * e2x(0) + pplain(1) * h * e2y(0);
|
|
v(1) = pplain(0) * h * e2x(1) + pplain(1) * h * e2y(1);
|
|
|
|
p3d = p1 + v(0) * ey + v(1) * ez;
|
|
|
|
Project (p3d);
|
|
}
|
|
|
|
void splinetube :: Project (Point<3> & p3d) const
|
|
{
|
|
Point<3> hp;
|
|
|
|
hp = p3d;
|
|
middlecurve.ProjectToSpline (hp);
|
|
|
|
p3d = hp + (r / Dist(p3d, hp)) * (p3d - hp);
|
|
}
|
|
|
|
|
|
|
|
double splinetube :: CalcFunctionValue (const Point<3> & point) const
|
|
{
|
|
Point<3> hcp;
|
|
double rad;
|
|
|
|
hcp = point;
|
|
middlecurve.ProjectToSpline (hcp);
|
|
rad = Dist (hcp, point);
|
|
return 0.5 * (rad * rad / r - r);
|
|
}
|
|
|
|
void splinetube :: CalcGradient (const Point<3> & point, Vec<3> & grad) const
|
|
{
|
|
Point<3> hcp;
|
|
|
|
hcp = point;
|
|
middlecurve.ProjectToSpline (hcp);
|
|
|
|
grad = point - hcp;
|
|
grad /= r;
|
|
}
|
|
|
|
|
|
|
|
|
|
Point<3> splinetube :: GetSurfacePoint () const
|
|
{
|
|
Point<3> p;
|
|
Vec<3> t, n;
|
|
|
|
middlecurve.Evaluate (0, p);
|
|
middlecurve.EvaluateTangent (0, t);
|
|
n = t.GetNormal ();
|
|
n *= r;
|
|
(*mycout) << "p = " << p << " t = " << t << " n = " << n << endl;
|
|
return p + n;
|
|
}
|
|
|
|
void splinetube :: Print (ostream & str) const
|
|
{
|
|
int i;
|
|
str << "SplineTube, "
|
|
<< middlecurve.GetNumSegments () << " segments, r = " << r << endl;
|
|
for (i = 1; i <= middlecurve.GetNumSegments(); i++)
|
|
str << middlecurve.P1(i) << " - "
|
|
<< middlecurve.P2(i) << " - "
|
|
<< middlecurve.P3(i) << endl;
|
|
}
|
|
|
|
|
|
int splinetube :: BoxInSolid (const BoxSphere<3> & box) const
|
|
// 0 .. no, 1 .. yes, 2 .. maybe
|
|
{
|
|
Point<3> pc = box.Center();
|
|
middlecurve.ProjectToSpline (pc);
|
|
double d = Dist (pc, box.Center());
|
|
|
|
if (d < r - box.Diam()/2) return 1;
|
|
if (d > r + box.Diam()/2) return 0;
|
|
return 2;
|
|
}
|
|
}
|