Carve booleans library integration

==================================

Merging Carve library integration project into the trunk.

This commit switches Boolean modifier to another library which handles
mesh boolean operations in much stable and faster way, resolving old
well-known limitations of intern boolop library.

Carve is integrating as alternative interface for boolop library and
which makes it totally transparent for blender sources to switch between
old-fashioned boolop and new Carve backends.

Detailed changes in this commit:

- Integrated needed subset of Carve library sources into extern/
  Added script for re-bundling it (currently works only if repo
  was cloned by git-svn).
- Added BOP_CarveInterface for boolop library which can be used by
  Boolean modifier.
- Carve backend is enabled by default, can be disabled by WITH_BF_CARVE
  SCons option and WITH_CARVE CMake option.
- If Boost library is found in build environment it'll be used for
  unordered collections. If Boost isn't found, it'll fallback to TR1
  implementation for GCC compilers. Boost is obligatory if MSVC is used.

Tested on Linux 64bit and Windows 7 64bit.

NOTE: behavior of flat objects was changed. E.g. Plane-Sphere now gives
      plane with circle hole, not plane with semisphere. Don't think
      it's really issue because it's not actually defined behavior in
      such situations and both of ways might be useful. Since it's
      only known "regression" think it's OK to deal with it.

Details are there http://wiki.blender.org/index.php/User:Nazg-gul/CarveBooleans

Special thanks to:

- Ken Hughes: author of original carve integration patch.
- Campbell Barton: help in project development, review tests.
- Tobias Sargeant: author of Carve library, help in resolving some
                   merge stoppers, bug fixing.

1 files changed, 347 insertions, 0 deletions

diff --git a/extern/carve/lib/math.cpp b/extern/carve/lib/math.cpp
new file mode 100644
index 00000000000..811312c313e
--- /dev/null
+++ b/extern/carve/lib/math.cpp
@@ -0,0 +1,347 @@
+// Begin License:
+// Copyright (C) 2006-2011 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 the GNU General Public
+// License version 2.0 as published by the Free Software Foundation
+// and appearing in the file LICENSE.GPL2 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) {}
+    };
+
+    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;
+      }
+    }
+
+    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);
+      }
+    }
+
+    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();
+    }
+
+    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;
+    }
+
+    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;
+    }
+
+  }
+}
+