kannonier8/blender
1
0
Fork 0
forked from bartvdbraak/blender
Code Pull Requests Activity
e84966ac42
blender/extern/carve/lib/math.cpp
Sergey Sharybin 87dcee0c0c Silence some annoying warnings when doing full build with strict flags 
This mainly touches extern libraries and few debug-only places in intern.

Some summary:

- External libraries are not strict at all about missing declarations,
  so we can rather safely remove such warning together with other strict
  flags.

- Bullet has some static functions which are not used.
  Those were commented out.

- Carve now has some unused debug-only functions commented out as well.
  While we're on the way of getting rid of Carve, it makes sense to make
  things a bit cleaner for the time being.

- In LZMA we have some parts disabled which gives some set but unused
  variables which is rather correct.

- Elbeem had quite some variables set and never used because their usage
  is inside of debug-only code which is commented out.

Note about patching upstream libraries: surely one might say that we
have to make local patchset against this, but own experience says it
only gives extra work trying to merge such tweaks to a new upstream
version and usually it's just faster to re-apply such fixes again after
bundling new upstream library.
2016-04-22 10:59:15 +02:00

356 lines
10 KiB
C++
Raw Blame History

// Begin License:
// Copyright (C) 2006-2014 Tobias Sargeant (tobias.sargeant@gmail.com).
// All rights reserved.
//
// This file is part of the Carve CSG Library (http://carve-csg.com/)
//
// This file may be used under the terms of either the GNU General
// Public License version 2 or 3 (at your option) as published by the
// Free Software Foundation and appearing in the files LICENSE.GPL2
// and LICENSE.GPL3 included in the packaging of this file.
//
// This file is provided "AS IS" with NO WARRANTY OF ANY KIND,
// INCLUDING THE WARRANTIES OF DESIGN, MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE.
// End:
#if defined(HAVE_CONFIG_H)
# include <carve_config.h>
#endif
#include <carve/math.hpp>
#include <carve/matrix.hpp>
#include <iostream>
#include <limits>
#include <stdio.h>
#define M_2PI_3 2.0943951023931953
#define M_SQRT_3_4 0.8660254037844386
#define EPS std::numeric_limits<double>::epsilon()
namespace carve {
namespace math {
struct Root {
double root;
int multiplicity;
Root(double r) : root(r), multiplicity(1) {}
Root(double r, int m) : root(r), multiplicity(m) {}
};
namespace {
#if 0
void cplx_sqrt(double re, double im,
double &re_1, double &im_1,
double &re_2, double &im_2) {
if (re == 0.0 && im == 0.0) {
re_1 = re_2 = re;
im_1 = im_2 = im;
} else {
double d = sqrt(re * re + im * im);
re_1 = sqrt((d + re) / 2.0);
re_2 = re_1;
im_1 = fabs(sqrt((d - re) / 2.0));
im_2 = -im_1;
}
}
#endif
#if 0
void cplx_cbrt(double re, double im,
double &re_1, double &im_1,
double &re_2, double &im_2,
double &re_3, double &im_3) {
if (re == 0.0 && im == 0.0) {
re_1 = re_2 = re_3 = re;
im_1 = im_2 = im_3 = im;
} else {
double r = cbrt(sqrt(re * re + im * im));
double t = atan2(im, re) / 3.0;
re_1 = r * cos(t);
im_1 = r * sin(t);
re_2 = r * cos(t + M_TWOPI / 3.0);
im_2 = r * sin(t + M_TWOPI / 3.0);
re_3 = r * cos(t + M_TWOPI * 2.0 / 3.0);
im_3 = r * sin(t + M_TWOPI * 2.0 / 3.0);
}
}
#endif
void add_root(std::vector<Root> &roots, double root) {
for (size_t i = 0; i < roots.size(); ++i) {
if (roots[i].root == root) {
roots[i].multiplicity++;
return;
}
}
roots.push_back(Root(root));
}
void linear_roots(double c1, double c0, std::vector<Root> &roots) {
roots.push_back(Root(c0 / c1));
}
void quadratic_roots(double c2, double c1, double c0, std::vector<Root> &roots) {
if (fabs(c2) < EPS) {
linear_roots(c1, c0, roots);
return;
}
double p = 0.5 * c1 / c2;
double dis = p * p - c0 / c2;
if (dis > 0.0) {
dis = sqrt(dis);
if (-p - dis != -p + dis) {
roots.push_back(Root(-p - dis));
roots.push_back(Root(-p + dis));
} else {
roots.push_back(Root(-p, 2));
}
}
}
void cubic_roots(double c3, double c2, double c1, double c0, std::vector<Root> &roots) {
int n_sol = 0;
double _r[3];
if (fabs(c3) < EPS) {
quadratic_roots(c2, c1, c0, roots);
return;
}
if (fabs(c0) < EPS) {
quadratic_roots(c3, c2, c1, roots);
add_root(roots, 0.0);
return;
}
double xN = -c2 / (3.0 * c3);
double yN = c0 + xN * (c1 + xN * (c2 + c3 * xN));
double delta_sq = (c2 * c2 - 3.0 * c3 * c1) / (9.0 * c3 * c3);
double h_sq = 4.0 / 9.0 * (c2 * c2 - 3.0 * c3 * c1) * (delta_sq * delta_sq);
double dis = yN * yN - h_sq;
if (dis > EPS) {
// One real root, two complex roots.
double dis_sqrt = sqrt(dis);
double r_p = yN - dis_sqrt;
double r_q = yN + dis_sqrt;
double p = cbrt(fabs(r_p)/(2.0 * c3));
double q = cbrt(fabs(r_q)/(2.0 * c3));
if (r_p > 0.0) p = -p;
if (r_q > 0.0) q = -q;
_r[0] = xN + p + q;
n_sol = 1;
double re = xN - p * .5 - q * .5;
double im = p * M_SQRT_3_4 - q * M_SQRT_3_4;
// root 2: xN + p * exp(M_2PI_3.i) + q * exp(-M_2PI_3.i);
// root 3: complex conjugate of root 2
if (im < EPS) {
_r[1] = _r[2] = re;
n_sol += 2;
}
} else if (dis < -EPS) {
// Three distinct real roots.
double theta = acos(-yN / sqrt(h_sq)) / 3.0;
double delta = sqrt(c2 * c2 - 3.0 * c3 * c1) / (3.0 * c3);
_r[0] = xN + (2.0 * delta) * cos(theta);
_r[1] = xN + (2.0 * delta) * cos(M_2PI_3 - theta);
_r[2] = xN + (2.0 * delta) * cos(M_2PI_3 + theta);
n_sol = 3;
} else {
// Three real roots (two or three equal).
double r = yN / (2.0 * c3);
double delta = cbrt(r);
_r[0] = xN + delta;
_r[1] = xN + delta;
_r[2] = xN - 2.0 * delta;
n_sol = 3;
}
for (int i=0; i < n_sol; i++) {
add_root(roots, _r[i]);
}
}
}
static void U(const Matrix3 &m,
double l,
double u[6],
double &u_max,
int &u_argmax) {
u[0] = (m._22 - l) * (m._33 - l) - m._23 * m._23;
u[1] = m._13 * m._23 - m._12 * (m._33 - l);
u[2] = m._12 * m._23 - m._13 * (m._22 - l);
u[3] = (m._11 - l) * (m._33 - l) - m._13 * m._13;
u[4] = m._12 * m._13 - m._23 * (m._11 - l);
u[5] = (m._11 - l) * (m._22 - l) - m._12 * m._12;
u_max = -1.0;
u_argmax = -1;
for (int i = 0; i < 6; ++i) {
if (u_max < fabs(u[i])) { u_max = fabs(u[i]); u_argmax = i; }
}
}
static void eig1(const Matrix3 &m, double l, carve::geom::vector<3> &e) {
double u[6];
double u_max;
int u_argmax;
U(m, l, u, u_max, u_argmax);
switch(u_argmax) {
case 0:
e.x = u[0]; e.y = u[1]; e.z = u[2]; break;
case 1: case 3:
e.x = u[1]; e.y = u[3]; e.z = u[4]; break;
case 2: case 4: case 5:
e.x = u[2]; e.y = u[4]; e.z = u[5]; break;
}
e.normalize();
}
static void eig2(const Matrix3 &m, double l, carve::geom::vector<3> &e1, carve::geom::vector<3> &e2) {
double u[6];
double u_max;
int u_argmax;
U(m, l, u, u_max, u_argmax);
switch(u_argmax) {
case 0: case 1:
e1.x = -m._12; e1.y = m._11; e1.z = 0.0;
e2.x = -m._13 * m._11; e2.y = -m._13 * m._12; e2.z = m._11 * m._11 + m._12 * m._12;
break;
case 2:
e1.x = m._12; e1.y = 0.0; e1.z = -m._11;
e2.x = -m._12 * m._11; e2.y = m._11 * m._11 + m._13 * m._13; e2.z = -m._12 * m._13;
break;
case 3: case 4:
e1.x = 0.0; e1.y = -m._23; e1.z = -m._22;
e2.x = m._22 * m._22 + m._23 * m._23; e2.y = -m._12 * m._22; e2.z = -m._12 * m._23;
break;
case 5:
e1.x = 0.0; e1.y = -m._33; e1.z = m._23;
e2.x = m._23 * m._23 + m._33 * m._33; e2.y = -m._13 * m._23; e2.z = -m._13 * m._33;
}
e1.normalize();
e2.normalize();
}
#if 0
static void eig3(const Matrix3 &m,
double l,
carve::geom::vector<3> &e1,
carve::geom::vector<3> &e2,
carve::geom::vector<3> &e3) {
e1.x = 1.0; e1.y = 0.0; e1.z = 0.0;
e2.x = 0.0; e2.y = 1.0; e2.z = 0.0;
e3.x = 0.0; e3.y = 0.0; e3.z = 1.0;
}
#endif
void eigSolveSymmetric(const Matrix3 &m,
double &l1, carve::geom::vector<3> &e1,
double &l2, carve::geom::vector<3> &e2,
double &l3, carve::geom::vector<3> &e3) {
double c0 =
m._11 * m._22 * m._33 +
2.0 * m._12 * m._13 * m._23 -
m._11 * m._23 * m._23 -
m._22 * m._13 * m._13 -
m._33 * m._12 * m._12;
double c1 =
m._11 * m._22 -
m._12 * m._12 +
m._11 * m._33 -
m._13 * m._13 +
m._22 * m._33 -
m._23 * m._23;
double c2 =
m._11 +
m._22 +
m._33;
double a = (3.0 * c1 - c2 * c2) / 3.0;
double b = (-2.0 * c2 * c2 * c2 + 9.0 * c1 * c2 - 27.0 * c0) / 27.0;
double Q = b * b / 4.0 + a * a * a / 27.0;
if (fabs(Q) < 1e-16) {
l1 = m._11; e1.x = 1.0; e1.y = 0.0; e1.z = 0.0;
l2 = m._22; e2.x = 0.0; e2.y = 1.0; e2.z = 0.0;
l3 = m._33; e3.x = 0.0; e3.y = 0.0; e3.z = 1.0;
} else if (Q > 0) {
l1 = l2 = c2 / 3.0 + cbrt(b / 2.0);
l3 = c2 / 3.0 - 2.0 * cbrt(b / 2.0);
eig2(m, l1, e1, e2);
eig1(m, l3, e3);
} else if (Q < 0) {
double t = atan2(sqrt(-Q), -b / 2.0);
double cos_t3 = cos(t / 3.0);
double sin_t3 = sin(t / 3.0);
double r = cbrt(sqrt(b * b / 4.0 - Q));
l1 = c2 / 3.0 + 2 * r * cos_t3;
l2 = c2 / 3.0 - r * (cos_t3 + M_SQRT_3 * sin_t3);
l3 = c2 / 3.0 - r * (cos_t3 - M_SQRT_3 * sin_t3);
eig1(m, l1, e1);
eig1(m, l2, e2);
eig1(m, l3, e3);
}
}
void eigSolve(const Matrix3 &m, double &l1, double &l2, double &l3) {
double c3, c2, c1, c0;
std::vector<Root> roots;
c3 = -1.0;
c2 = m._11 + m._22 + m._33;
c1 =
-(m._22 * m._33 + m._11 * m._22 + m._11 * m._33)
+(m._23 * m._32 + m._13 * m._31 + m._12 * m._21);
c0 =
+(m._11 * m._22 - m._12 * m._21) * m._33
-(m._11 * m._23 - m._13 * m._21) * m._32
+(m._12 * m._23 - m._13 * m._22) * m._31;
cubic_roots(c3, c2, c1, c0, roots);
for (size_t i = 0; i < roots.size(); i++) {
Matrix3 M(m);
M._11 -= roots[i].root;
M._22 -= roots[i].root;
M._33 -= roots[i].root;
// solve M.v = 0
}
std::cerr << "n_roots=" << roots.size() << std::endl;
for (size_t i = 0; i < roots.size(); i++) {
fprintf(stderr, " %.24f(%d)", roots[i].root, roots[i].multiplicity);
}
std::cerr << std::endl;
}
}
}
View Git Blame Copy Permalink