Algorithms.hh 24.7 KB
Newer Older
Jan Möbius's avatar
Jan Möbius committed
1 2 3
/*===========================================================================*\
 *                                                                           *
 *                              OpenFlipper                                  *
Jan Möbius's avatar
Jan Möbius committed
4 5 6 7
 *           Copyright (c) 2001-2015, RWTH-Aachen University                 *
 *           Department of Computer Graphics and Multimedia                  *
 *                          All rights reserved.                             *
 *                            www.openflipper.org                            *
Jan Möbius's avatar
Jan Möbius committed
8 9
 *                                                                           *
 *---------------------------------------------------------------------------*
Jan Möbius's avatar
Jan Möbius committed
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
 * This file is part of OpenFlipper.                                         *
 *---------------------------------------------------------------------------*
 *                                                                           *
 * Redistribution and use in source and binary forms, with or without        *
 * modification, are permitted provided that the following conditions        *
 * are met:                                                                  *
 *                                                                           *
 * 1. Redistributions of source code must retain the above copyright notice, *
 *    this list of conditions and the following disclaimer.                  *
 *                                                                           *
 * 2. Redistributions in binary form must reproduce the above copyright      *
 *    notice, this list of conditions and the following disclaimer in the    *
 *    documentation and/or other materials provided with the distribution.   *
 *                                                                           *
 * 3. Neither the name of the copyright holder nor the names of its          *
 *    contributors may be used to endorse or promote products derived from   *
 *    this software without specific prior written permission.               *
 *                                                                           *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS       *
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED *
 * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A           *
 * PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER *
 * OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,  *
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,       *
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR        *
 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF    *
 * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING      *
 * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS        *
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.              *
Jan Möbius's avatar
Jan Möbius committed
39 40 41 42 43
 *                                                                           *
\*===========================================================================*/

/*===========================================================================*\
 *                                                                           *
Jan Möbius's avatar
Jan Möbius committed
44
 *   $Revision$                                                       *
Jan Möbius's avatar
Jan Möbius committed
45 46 47 48
 *   $Author$                                                      *
 *   $Date$                   *
 *                                                                           *
\*===========================================================================*/
Jan Möbius's avatar
 
Jan Möbius committed
49 50 51 52 53 54 55 56 57 58




#ifndef GEO_ALGORITHMS_HH
#define GEO_ALGORITHMS_HH


//== INCLUDES =================================================================

59
#include <cfloat>
Jan Möbius's avatar
Jan Möbius committed
60
#include <ACG/Math/VectorT.hh>
61
#include <vector>
62
#include <iostream>
Jan Möbius's avatar
 
Jan Möbius committed
63

64 65
#include "../Math/Matrix3x3T.hh"

Jan Möbius's avatar
 
Jan Möbius committed
66 67 68 69 70 71 72

namespace ACG {
namespace Geometry {


//== 3D STUFF =================================================================

Jan Möbius's avatar
Jan Möbius committed
73
 
Jan Möbius's avatar
 
Jan Möbius committed
74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108

/// return circumcenter of tetrahedron (_v0,_v1,_v2,_v3)
template<typename Scalar>
bool
circumCenter( const VectorT<Scalar,3>&  _v0,
	      const VectorT<Scalar,3>&  _v1,
	      const VectorT<Scalar,3>&  _v2,
	      const VectorT<Scalar,3>&  _v3,
	      VectorT<Scalar,3>&        _result );


/// return squared radius of circumcircle of tetrahedron (_v0,_v1,_v2,_v3)
template<typename Scalar>
Scalar
circumRadiusSquared( const VectorT<Scalar,3>&  _v0,
		     const VectorT<Scalar,3>&  _v1,
		     const VectorT<Scalar,3>&  _v2,
		     const VectorT<Scalar,3>&  _v3 )
{
  VectorT<Scalar,3> cc;
  return circumCenter(_v0, _v1, _v2, _v3, cc) ? (cc-_v0).sqrnorm() : FLT_MAX;
}


/// return radius of circumcircle of tetrahedron (_v0,_v1,_v2,_v3)
template<typename Scalar>
Scalar
circumRadius( const VectorT<Scalar,3>&  _v0,
	      const VectorT<Scalar,3>&  _v1,
	      const VectorT<Scalar,3>&  _v2,
	      const VectorT<Scalar,3>&  _v3 )
{
  return sqrt(circumRadiusSquared(_v0, _v1, _v2, _v3));
}

109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
/** \brief Get intersection point of a ray and a convex polygon
 *
 * Gets two vertices, _v0 and _v1, and a convex polygon defined by its vertices stored in _polygon_points
 * Computes the intersection point of the ray defined by _v0 and _v1
 * and stores it to _result
 * Returns true if the intersection point lies inside the polygon
 *
 * @param _v0 The first vertex of a ray
 * @param _v1 The second vertex if a ray
 * @param _polygon_points vector of the points bounding the polygon
 * @param _result contains the intersection point after the computation
 */
template<typename Scalar>
bool edgeConvexPolygonIntersection(std::vector<VectorT<Scalar,3> > _polygon_points,
                                   VectorT<Scalar,3> _v0,
                                   VectorT<Scalar,3> _v1,
                                   VectorT<Scalar,3> &_result);

Jan Möbius's avatar
 
Jan Möbius committed
127

128 129 130
/** \brief Get rotation axis and signed angle of rotation between two vectors
 *
 * Get two vectors, _v0 and _v1, and compute rotation axis _v0 % _v1
131 132 133 134
 * as well the angle between _v0 and _v1. Note that the angle is always negative.
 * We consider the rotation to be performed from _v0 to _v1.
 * The angle is given in degree if not explicitly demanded in radiant
 * (pass false as fifth parameter).
135 136 137 138
 *
 * @param _v0 The first vector
 * @param _v1 The second vector
 * @param _axis A reference to a vector in which the rotation axis is stored
Jan Möbius's avatar
Jan Möbius committed
139
 * @param _angle A reference to a scalar type in which the signed angle is stored ( in degree)
Mike Kremer's avatar
Mike Kremer committed
140
 * @param _degree Indicates whether the angle should be given in degree or radiant
141
 */
142
template<typename Scalar>
143
bool
144 145 146
rotationOfTwoVectors( const VectorT<Scalar,3>&  _v0,
                      const VectorT<Scalar,3>&  _v1,
                      VectorT<Scalar,3>&  _axis,
147 148
                      Scalar& _angle,
                      bool _degree = true);
149 150


Jan Möbius's avatar
Jan Möbius committed
151 152 153
/** \brief find a vector that's perpendicular to _v
 *
 * This function takes a vector and  generates a new arbitrary
Jan Möbius's avatar
Jan Möbius committed
154
 * vector that is perpendicular to the input vector.
Jan Möbius's avatar
Jan Möbius committed
155 156 157 158
 *
 * @param _v Input vector
 * @return Perpendicular vector
 */
Jan Möbius's avatar
 
Jan Möbius committed
159 160 161 162 163
template <typename Scalar>
VectorT<Scalar,3>
perpendicular( const VectorT<Scalar,3>&  _v );


164 165
/**  \brief Intersect a ray and a triangle.
  *
Jan Möbius's avatar
Jan Möbius committed
166 167 168
  * Computes the intersection point between a ray and a triangle. The orientation of the triangle
  * does not matter. The distance returned in t will be negative if the triangle is not in the
  * direction given but in the opposite direction.
169 170 171 172 173 174
  *
  * @param _o origin of the ray
  * @param _dir direction vector of the ray
  * @param _v0 first point of the triangle
  * @param _v1 second point of the triangle
  * @param _v2 third point of the triangle
Jan Möbius's avatar
Jan Möbius committed
175
  * @param _t returned distance from the origin to the intersection, in units of _dir ( negative if before origin!)
176 177 178 179 180 181 182
  * @param _u returned first barycentric coordinate of the intersection point in the triangle
  * @param _v returned second barycentric coordinate of the intersection point in the triangle
  * @return true if an intersection was found
  */
template<typename Vec>
bool
triangleIntersection( const Vec&  _o,
Jan Möbius's avatar
Jan Möbius committed
183 184 185 186 187 188 189
                      const Vec&  _dir,
                      const Vec&  _v0,
                      const Vec&  _v1,
                      const Vec&  _v2,
                      typename Vec::value_type& _t,
                      typename Vec::value_type& _u,
                      typename Vec::value_type& _v );
190 191 192 193 194 195
      

/**  \brief Intersect a ray and an axis aligned bounding box
  *
  * Computes the intersection point between a ray and an axis aligned bounding box
  *
Jan Möbius's avatar
Jan Möbius committed
196 197
  * @param _o     Origin of the ray
  * @param _dir   direction vector of the ray
198 199 200 201
  * @param _bbmin lower left front corner of the bounding box
  * @param _bbmax upper right back corner of the bounding box
  * @param _t0 if there was an intersection, this value marks the entry point
  * @param _t1 if there was an intersection, this value marks the exit point
Jan Möbius's avatar
Jan Möbius committed
202
  * @return       true if an intersection was found
203 204 205 206
  */
template<typename Vec>
bool
axisAlignedBBIntersection( const Vec&  _o,
Jan Möbius's avatar
Jan Möbius committed
207 208 209 210 211
		                       const Vec&  _dir,
		                       const Vec& _bbmin,
		                       const Vec& _bbmax,
		                       typename Vec::value_type& _t0,
		                       typename Vec::value_type& _t1 );
212 213


214
//== 2D STUFF =================================================================
Jan Möbius's avatar
 
Jan Möbius committed
215

216
/// orientation of point _p w.r.t. line through _v0,_v1 in 2D
Jan Möbius's avatar
 
Jan Möbius committed
217 218 219 220 221 222 223 224 225 226 227
template<typename Scalar>
Scalar
pointLineOrientation( const VectorT<Scalar,2>&  _p,
		      const VectorT<Scalar,2>&  _v0,
		      const VectorT<Scalar,2>&  _v1 )
{
  VectorT<Scalar,2> d1(_p-_v0), d2(_v1-_v0);
  return (d1[0]*d2[1]-d1[1]*d2[0]);
}


228
/// are 3 vertices in counterclockwise order? in 2D
Jan Möbius's avatar
 
Jan Möbius committed
229 230 231 232 233 234 235 236 237 238
template<typename Scalar>
bool
isCCW( const VectorT<Scalar,2>&  _v0,
       const VectorT<Scalar,2>&  _v1,
       const VectorT<Scalar,2>&  _v2 )
{
  return ( pointLineOrientation(_v0, _v1, _v2) < Scalar(0.0) );
}


239
/// are 3 vertices in clockwise order? in 2D
Jan Möbius's avatar
 
Jan Möbius committed
240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260
template<typename Scalar>
bool
isCW( const VectorT<Scalar,2>&  _v0,
      const VectorT<Scalar,2>&  _v1,
      const VectorT<Scalar,2>&  _v2 )
{
  return ( pointLineOrientation(_v0, _v1, _v2) > Scalar(0.0) );
}


/// intersect two line segments (_v0,_v1) and (_v2,_v3)
template<typename Scalar>
bool
lineIntersection( const VectorT<Scalar,2>&  _v0,
		  const VectorT<Scalar,2>&  _v1,
		  const VectorT<Scalar,2>&  _v2,
		  const VectorT<Scalar,2>&  _v3,
		  Scalar& _t1,
		  Scalar& _t2 );


261 262 263 264 265 266
//===========================================================================
/** @name Distance Functions ( N-Dimensional )
* @{ */
//===========================================================================     


Jan Möbius's avatar
Jan Möbius committed
267 268 269 270 271 272 273 274
/** \brief squared distance from point _p to line segment (_v0,_v1)
 *
 * @param _p     Point to test
 * @param _v0    Start of line segment
 * @param _v1    End of line segment
 * @param _min_v Pointer to vector, to get the closest point or 0 if it's not required
 * @return Distance to line segment
 */
275 276 277 278 279 280 281
template<class Vec>
typename Vec::value_type
distPointLineSquared( const Vec& _p,
                      const Vec& _v0,
                      const Vec& _v1,
                      Vec*       _min_v=0);

282

Jan Möbius's avatar
Jan Möbius committed
283

Jan Möbius's avatar
Jan Möbius committed
284 285 286 287 288 289 290 291 292 293 294
/** \brief Compute distance from point to line segment
 *
 * Compute the distance from a point p to a line segment and possibly return
 * closest point on segment
 *
 * @param _p   Point to test
 * @param _v0  Start of line segment
 * @param _v1  End of line segment
 * @param _min_v Pointer to vector, to get the closest point or 0 if it's not required
 * @return Distance to line segment
 */
Jan Möbius's avatar
Jan Möbius committed
295 296 297 298 299 300 301 302 303
template<class Vec>
typename Vec::value_type
distPointLine( const Vec& _p,
               const Vec& _v0,
               const Vec& _v1,
               Vec*       _min_v=0 )
{ return sqrt(distPointLineSquared(_p, _v0, _v1, _min_v)); }


304 305 306 307 308 309 310 311 312
/// squared distance from point _p to triangle (_v0, _v1, _v2)
template <class Vec>
typename Vec::value_type
distPointTriangleSquared( const Vec& _p,
                          const Vec& _v0,
                          const Vec& _v1,
                          const Vec& _v2,
                          Vec& _nearestPoint );

313
/** \brief squared distance from point _p to triangle (_v0, _v1, _v2)
314 315 316 317 318
*
*  In the stable version the distance to the longest edge 
*  is returned if the triangle is degenerate.
*
* @param _p   point to test against triangle
Jan Möbius's avatar
Typo  
Jan Möbius committed
319 320 321
* @param _v0  First point of triangle
* @param _v1  Second point of triangle
* @param _v2  Third point of triangle
322
* @return     Computed distance
323 324 325 326 327 328 329 330 331
*/
template <class Vec>
typename Vec::value_type
distPointTriangleSquaredStable( const Vec& _p,
                                const Vec& _v0,
                                const Vec& _v1,
                                const Vec& _v2,
                                Vec& _nearestPoint );

332 333 334 335 336 337 338 339 340 341
/// distance from point _p to triangle (_v0, _v1, _v2)
template <class Vec>
typename Vec::value_type
distPointTriangle( const Vec& _p,
                   const Vec& _v0,
                   const Vec& _v1,
                   const Vec& _v2,
                   Vec& _nearestPoint )
{ return sqrt(distPointTriangleSquared(_p, _v0, _v1, _v2, _nearestPoint)); }

342
/** \brief distance from point _p to triangle (_v0, _v1, _v2)
343 344 345 346
*
*   In the stable version the distance to the longest edge 
*   is returned if the triangle is degenerate.
* 
Jan Möbius's avatar
Typo  
Jan Möbius committed
347 348 349
* @param _v0  First point of triangle
* @param _v1  Second point of triangle
* @param _v2  Third point of triangle
350
* @return     Computed distance
351 352 353 354 355 356 357 358 359 360
 */
template <class Vec>
typename Vec::value_type
distPointTriangleStable( const Vec& _p,
                         const Vec& _v0,
                         const Vec& _v1,
                         const Vec& _v2,
                         Vec& _nearestPoint )
{ return sqrt(distPointTriangleSquaredStable(_p, _v0, _v1, _v2, _nearestPoint)); }

Jan Möbius's avatar
Jan Möbius committed
361 362 363 364 365 366 367 368 369 370 371 372 373 374
/** \brief Checks the distance from a point to a plane
*
*
* @param _porigin Planes origin
* @param _pnormal Plane normal ( has to be normalized!)
* @param _point   point to test
* @return         distance
*/
template < typename VectorT , typename ValueT >
inline
ValueT 
distPointPlane(const VectorT& _porigin, 
               const VectorT& _pnormal, 
               const VectorT&  _point);                          
375

Jan Möbius's avatar
Jan Möbius committed
376 377 378 379 380 381 382 383
          
/** @} */   
          
//===========================================================================
/** @name Distance Functions ( 3-Dimensional )
* @{ */
//===========================================================================                             
                          
384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409
/// squared distance of lines (_v00, _v01) and (_v10, _v11)
template<typename Scalar>
Scalar
distLineLineSquared( const VectorT<Scalar,3>& _v00,
                     const VectorT<Scalar,3>& _v01,
                     const VectorT<Scalar,3>& _v10,
                     const VectorT<Scalar,3>& _v11,
                     VectorT<Scalar,3>*       _min_v0=0,
                     VectorT<Scalar,3>*       _min_v1=0,
                     bool                          _fastApprox=false );


/// distance of lines (_v00, _v01) and (_v10, _v11)
template<typename Scalar>
Scalar
distLineLine( const VectorT<Scalar,3>& _v00,
              const VectorT<Scalar,3>& _v01,
              const VectorT<Scalar,3>& _v10,
              const VectorT<Scalar,3>& _v11,
              VectorT<Scalar,3>*       _min_v0=0,
              VectorT<Scalar,3>*       _min_v1=0 )
{
  return sqrt(distLineLineSquared(_v00, _v01, _v10, _v11,
                                  _min_v0, _min_v1));
}

Jan Möbius's avatar
Jan Möbius committed
410 411
/** @} */   
   
412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481

//===========================================================================
/** @name Projection Functions ( N-Dimensional )
* @{ */
//===========================================================================      


/**
project one point to an edge. If its projection is not on the edge itself, the start or the endpoint is returned
@param _start beginning of edge
@param _end   end of the edge
@param _point point to be projected
*/
template < typename VectorT >
VectorT projectToEdge(const VectorT& _start , 
                      const VectorT& _end , 
                      const VectorT& _point );
                      
                      
/** \brief projects a point to a plane
* @param _porigin Planes origin
* @param _pnormal Plane normal ( has to be normalized! )
* @param _point   point to project
* @return         projected point
*/
template < typename VectorT >
inline
VectorT
projectToPlane(const VectorT& _porigin, 
               const VectorT& _pnormal, 
               const VectorT&  _point);                      
              
/** @} */           

//===========================================================================
/** @name Triangle Functions (2D Only!!)
* @{ */
//===========================================================================   

/** \brief return circumcenter of triangle (_v0,_v1,_v2)
*
*/

/// barycentric coord of _p w.r.t. (_u,_v,_w) in 2D
template<typename Scalar>
bool
baryCoord( const VectorT<Scalar,2>&  _p,
           const VectorT<Scalar,2>&  _u,
           const VectorT<Scalar,2>&  _v,
           const VectorT<Scalar,2>&  _w,
           VectorT<Scalar,3>&        _result );
           

/// is point _p in triangle (_v0,_v1,_v2) in 2D
template<typename Scalar>
bool
isInTriangle( const VectorT<Scalar,2>&  _p,
              const VectorT<Scalar,2>&  _u,
              const VectorT<Scalar,2>&  _v,
              const VectorT<Scalar,2>&  _w )
{
  VectorT<Scalar,3> bary;
  if (baryCoord(_p, _u, _v, _w, bary)) 
    return ((bary[0]>0.0) && (bary[1]>0.0) && (bary[2]>0.0));
  else {
    std::cerr << "point in triangle error\n";
    return false;
  }
}

Jan Möbius's avatar
 
Jan Möbius committed
482 483 484
template<typename Scalar>
bool
circumCenter( const VectorT<Scalar,2>&  _v0,
485 486 487
              const VectorT<Scalar,2>&  _v1,
              const VectorT<Scalar,2>&  _v2,
              VectorT<Scalar,2>&        _result );
Jan Möbius's avatar
 
Jan Möbius committed
488

489
/** @} */   
Jan Möbius's avatar
 
Jan Möbius committed
490

Jan Möbius's avatar
Jan Möbius committed
491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562
//===========================================================================
/** @name Triangle Functions 3-Dimensional
* @{ */
//===========================================================================  
 
/** barycentric coord of _p w.r.t. (_u,_v,_w) in 3D
    _p has to lie in plane (_u,_v,_w) **/
template<typename Scalar>
bool
baryCoord( const VectorT<Scalar,3>&  _p,
           const VectorT<Scalar,3>&  _u,
           const VectorT<Scalar,3>&  _v,
           const VectorT<Scalar,3>&  _w,
           VectorT<Scalar,3>&        _result );


/// construct min. enclosing sphere
template<typename Scalar>
bool
minSphere(const VectorT<Scalar,3>&  _v0,
          const VectorT<Scalar,3>&  _v1,
          const VectorT<Scalar,3>&  _v2,
          VectorT<Scalar,3>&        _center,
          Scalar&                   _radius);


/// return squared radius of min. enclosing circle of triangle (_v0,_v1,_v2)
template<typename Scalar>
Scalar
minRadiusSquared( const VectorT<Scalar,3>&  _v0,
                  const VectorT<Scalar,3>&  _v1,
                  const VectorT<Scalar,3>&  _v2 );

  
/// return radius of min. enclosing circle of triangle (_v0,_v1,_v2)
template<typename Scalar>
Scalar
minRadius( const VectorT<Scalar,3>&  _v0,
           const VectorT<Scalar,3>&  _v1,
           const VectorT<Scalar,3>&  _v2 )
{
  return sqrt(minRadiusSquared(_v0, _v1, _v2));
}


/// return circumcenter of triangle (_v0,_v1,_v2)
template<typename Scalar>
bool
circumCenter( const VectorT<Scalar,3>&  _v0,
              const VectorT<Scalar,3>&  _v1,
              const VectorT<Scalar,3>&  _v2,
              VectorT<Scalar,3>&        _result );


/// return squared radius of circumcircle of triangle (_v0,_v1,_v2)
template<typename Scalar>
Scalar
circumRadiusSquared( const VectorT<Scalar,3>&  _v0,
                     const VectorT<Scalar,3>&  _v1,
                     const VectorT<Scalar,3>&  _v2 );


/// return radius of circumcircle of triangle (_v0,_v1,_v2)
template<typename Scalar>
Scalar
circumRadius( const VectorT<Scalar,3>&  _v0,
              const VectorT<Scalar,3>&  _v1,
              const VectorT<Scalar,3>&  _v2 )
{
  return sqrt(circumRadiusSquared(_v0, _v1, _v2));
}

563 564 565 566 567 568 569 570 571 572 573 574
/**
* test angles in triangle
* return 0 if all smaller than 90?
* return 1 if angle at _p0 ist greater than 90?
* return 2 if angle at _p1 ist greater than 90?
* return 3 if angle at _p2 ist greater than 90?
*/
template<class VectorT>
int isObtuse(const VectorT& _p0,
             const VectorT& _p1,
             const VectorT& _p2 );

Jan Möbius's avatar
Jan Möbius committed
575
/** @} */   
Jan Möbius's avatar
 
Jan Möbius committed
576

577 578 579 580
//===========================================================================
/** @name Triangle Functions N-Dimensional
* @{ */
//===========================================================================   
Jan Möbius's avatar
 
Jan Möbius committed
581

Jan Möbius's avatar
Jan Möbius committed
582

583 584
/** \brief return squared area of triangle (_v0, _v1, _v2)
*
Jan Möbius's avatar
Jan Möbius committed
585 586 587
* @param _v0  First point of triangle
* @param _v1  Second point of triangle
* @param _v2  Third point of triangl
588 589 590 591 592 593 594 595
*/
template <class Vec>
typename Vec::value_type
triangleAreaSquared( const Vec& _v0,
                     const Vec& _v1,
                     const Vec& _v2 );


Jan Möbius's avatar
Jan Möbius committed
596 597
/** \brief return area of triangle (_v0, _v1, _v2)
*
Jan Möbius's avatar
Jan Möbius committed
598 599 600
* @param _v0  First point of triangle
* @param _v1  Second point of triangle
* @param _v2  Third point of triangl
Jan Möbius's avatar
Jan Möbius committed
601 602 603 604 605 606 607 608 609 610 611
*/
template <class Vec>
typename Vec::value_type
triangleArea( const Vec& _v0,
              const Vec& _v1,
              const Vec& _v2 )
{
  return sqrt(triangleAreaSquared(_v0,_v1,_v2));
}
  

Jan Möbius's avatar
Jan Möbius committed
612
/** \brief return aspect ratio (length/height) of triangle
613
*
Jan Möbius's avatar
Jan Möbius committed
614 615 616
* @param _v0  First point of triangle
* @param _v1  Second point of triangle
* @param _v2  Third point of triangl
617
*/
Jan Möbius's avatar
 
Jan Möbius committed
618 619 620
template <typename Scalar, int N>
Scalar
aspectRatio( const VectorT<Scalar, N>& _v0,
621 622
             const VectorT<Scalar, N>& _v1,
             const VectorT<Scalar, N>& _v2 );
Jan Möbius's avatar
 
Jan Möbius committed
623

624 625
/** \brief return roundness of triangle: 1=equilateral, 0=colinear
*
Jan Möbius's avatar
Jan Möbius committed
626 627 628
* @param _v0  First point of triangle
* @param _v1  Second point of triangle
* @param _v2  Third point of triangl
629
*/
Jan Möbius's avatar
 
Jan Möbius committed
630 631 632
template <typename Scalar, int N>
Scalar
roundness( const VectorT<Scalar, N>& _v0,
633 634
           const VectorT<Scalar, N>& _v1,
           const VectorT<Scalar, N>& _v2 );
Jan Möbius's avatar
 
Jan Möbius committed
635

636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701
/** @} */

template<typename Vector>
Vector closestPointLineSegment(Vector x, Vector p1, Vector p2) {
    const auto delta = ((p2-p1)|(x-p1)) / (p2-p1).sqrnorm();
    //std::cout << "\x1b[32mdelta = " << delta << "\x1b[0m" << std::endl;
    if (delta <= 0) {
        //std::cout << "\x1b[43mdelta <= 0\x1b[0m" << std::endl;
        return p1;
    } else if (delta >= 1) {
        //std::cout << "\x1b[43mdelta >= 1\x1b[0m" << std::endl;
        return p2;
    } else if (delta != delta) { // p1 = p2 or x = p1
        //std::cout << "\x1b[43mdelta != delta\x1b[0m" << std::endl;
        return (x-p1).sqrnorm() < (x-p2).sqrnorm() ? p1 : p2;
    } else {
        //std::cout << "\x1b[43mdelta \\in [0, 1]\x1b[0m" << std::endl;
        return (1 - delta) * p1 + delta * p2;
    }
};

template<typename Vector>
Vector closestPointTri(Vector p, Vector a, Vector b, Vector c) {
    constexpr double thresh = 1e-8;

    const auto n = ((b - a) % (c - a)); // normalization unnecessary

    if ((b-a).sqrnorm() < thresh || (c-a).sqrnorm() < thresh || n.sqrnorm() < thresh) {
        //std::cout << "\x1b[42mDegenerate case.\x1b[0m" << std::endl;
        // Degenerate triangle. Find distance to longest segment.
        std::array<ACG::Vec3d, 2> max_segment = {a, b};
        double max_len = (b-a).sqrnorm();
        if ((c-a).sqrnorm() > max_len)
            max_segment = {a, c};
        if ((c-b).sqrnorm() > max_len)
            max_segment = {b, c};

        // closestPointLineSegment is stable, even if the segment is super short
        return closestPointLineSegment(p, max_segment[0], max_segment[1]);
    }

    const auto abd = Matrix3x3d::fromColumns(a-c, b-c, n).inverse() * (p - c);
    const bool alpha = (abd[0] >= 0.0),
            beta = (abd[1] >= 0.0),
            gamma = (1.0-abd[0]-abd[1] >= 0.0);

    if (alpha && beta && gamma) {
        //std::cout << "\x1b[42mInside case.\x1b[0m" << std::endl;
        // Inside triangle.
        return abd[0] * a + abd[1] * b + (1.0 - abd[0] - abd[1]) * c;
    } else if (!alpha) {
        //std::cout << "\x1b[42m!alpha case.\x1b[0m" << std::endl;
        // Closest to line segment (b, c).
        return closestPointLineSegment(p, b, c);
    } else if (!beta) {
        //std::cout << "\x1b[42m!beta case.\x1b[0m" << std::endl;
        // Closest to line segment (a, c).
        return closestPointLineSegment(p, a, c);
    } else if (!gamma) {
        //std::cout << "\x1b[42m!gamma case.\x1b[0m" << std::endl;
        // Closest to line segment (a, b).
        return closestPointLineSegment(p, a, b);
    } else {
        throw std::logic_error("This cannot happen.");
    }
}
Jan Möbius's avatar
 
Jan Möbius committed
702 703 704 705 706 707 708 709 710 711 712 713 714

//=============================================================================
} // namespace Geometry
} // namespace ACG
//=============================================================================
#if defined(INCLUDE_TEMPLATES) && !defined(GEO_ALGORITHMS_C)
#define GEO_ALGORITHMS_TEMPLATES
#include "Algorithms.cc"
#endif
//=============================================================================
#endif // GEO_ALGORITHMS_HH defined
//=============================================================================