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ImathFrustum.h
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34 
35 
36 
37 #ifndef INCLUDED_IMATHFRUSTUM_H
38 #define INCLUDED_IMATHFRUSTUM_H
39 
40 
41 #include "ImathVec.h"
42 #include "ImathPlane.h"
43 #include "ImathLine.h"
44 #include "ImathMatrix.h"
45 #include "ImathLimits.h"
46 #include "ImathFun.h"
47 #include "ImathNamespace.h"
48 
49 #include "IexMathExc.h"
50 
52 
53 //
54 // template class Frustum<T>
55 //
56 // The frustum is always located with the eye point at the
57 // origin facing down -Z. This makes the Frustum class
58 // compatable with OpenGL (or anything that assumes a camera
59 // looks down -Z, hence with a right-handed coordinate system)
60 // but not with RenderMan which assumes the camera looks down
61 // +Z. Additional functions are provided for conversion from
62 // and from various camera coordinate spaces.
63 //
64 // nearPlane/farPlane: near/far are keywords used by Microsoft's
65 // compiler, so we use nearPlane/farPlane instead to avoid
66 // issues.
67 
68 
69 template<class T>
70 class Frustum
71 {
72  public:
73  Frustum();
74  Frustum(const Frustum &);
75  Frustum(T nearPlane, T farPlane, T left, T right, T top, T bottom, bool ortho=false);
77  virtual ~Frustum();
78 
79  //--------------------
80  // Assignment operator
81  //--------------------
82 
83  const Frustum & operator = (const Frustum &);
84 
85  //--------------------
86  // Operators: ==, !=
87  //--------------------
88 
89  bool operator == (const Frustum<T> &src) const;
90  bool operator != (const Frustum<T> &src) const;
91 
92  //--------------------------------------------------------
93  // Set functions change the entire state of the Frustum
94  //--------------------------------------------------------
95 
96  void set(T nearPlane, T farPlane,
97  T left, T right,
98  T top, T bottom,
99  bool ortho=false);
100 
101  void set(T nearPlane, T farPlane, T fovx, T fovy, T aspect);
102 
103  //------------------------------------------------------
104  // These functions modify an already valid frustum state
105  //------------------------------------------------------
106 
108  void setOrthographic(bool);
109 
110  //--------------
111  // Access
112  //--------------
113 
114  bool orthographic() const { return _orthographic; }
115  T nearPlane() const { return _nearPlane; }
116  T hither() const { return _nearPlane; }
117  T farPlane() const { return _farPlane; }
118  T yon() const { return _farPlane; }
119  T left() const { return _left; }
120  T right() const { return _right; }
121  T bottom() const { return _bottom; }
122  T top() const { return _top; }
123 
124  //-----------------------------------------------------------------------
125  // Sets the planes in p to be the six bounding planes of the frustum, in
126  // the following order: top, right, bottom, left, near, far.
127  // Note that the planes have normals that point out of the frustum.
128  // The version of this routine that takes a matrix applies that matrix
129  // to transform the frustum before setting the planes.
130  //-----------------------------------------------------------------------
131 
132  void planes(Plane3<T> p[6]) const;
133  void planes(Plane3<T> p[6], const Matrix44<T> &M) const;
134 
135  //----------------------
136  // Derived Quantities
137  //----------------------
138 
139  T fovx() const;
140  T fovy() const;
141  T aspect() const;
143  bool degenerate() const;
144 
145  //-----------------------------------------------------------------------
146  // Takes a rectangle in the screen space (i.e., -1 <= left <= right <= 1
147  // and -1 <= bottom <= top <= 1) of this Frustum, and returns a new
148  // Frustum whose near clipping-plane window is that rectangle in local
149  // space.
150  //-----------------------------------------------------------------------
151 
152  Frustum<T> window(T left, T right, T top, T bottom) const;
153 
154  //----------------------------------------------------------
155  // Projection is in screen space / Conversion from Z-Buffer
156  //----------------------------------------------------------
157 
158  Line3<T> projectScreenToRay( const Vec2<T> & ) const;
159  Vec2<T> projectPointToScreen( const Vec3<T> & ) const;
160 
161  T ZToDepth(long zval, long min, long max) const;
162  T normalizedZToDepth(T zval) const;
163  long DepthToZ(T depth, long zmin, long zmax) const;
164 
165  T worldRadius(const Vec3<T> &p, T radius) const;
166  T screenRadius(const Vec3<T> &p, T radius) const;
167 
168 
169  protected:
170 
171  Vec2<T> screenToLocal( const Vec2<T> & ) const;
172  Vec2<T> localToScreen( const Vec2<T> & ) const;
173 
174  protected:
182 };
183 
184 
185 template<class T>
187 {
188  set(T (0.1),
189  T (1000.0),
190  T (-1.0),
191  T (1.0),
192  T (1.0),
193  T (-1.0),
194  false);
195 }
196 
197 template<class T>
199 {
200  *this = f;
201 }
202 
203 template<class T>
204 inline Frustum<T>::Frustum(T n, T f, T l, T r, T t, T b, bool o)
205 {
206  set(n,f,l,r,t,b,o);
207 }
208 
209 template<class T>
210 inline Frustum<T>::Frustum(T nearPlane, T farPlane, T fovx, T fovy, T aspect)
211 {
212  set(nearPlane,farPlane,fovx,fovy,aspect);
213 }
214 
215 template<class T>
217 {
218 }
219 
220 template<class T>
221 const Frustum<T> &
223 {
224  _nearPlane = f._nearPlane;
225  _farPlane = f._farPlane;
226  _left = f._left;
227  _right = f._right;
228  _top = f._top;
229  _bottom = f._bottom;
230  _orthographic = f._orthographic;
231 
232  return *this;
233 }
234 
235 template <class T>
236 bool
238 {
239  return
240  _nearPlane == src._nearPlane &&
241  _farPlane == src._farPlane &&
242  _left == src._left &&
243  _right == src._right &&
244  _top == src._top &&
245  _bottom == src._bottom &&
246  _orthographic == src._orthographic;
247 }
248 
249 template <class T>
250 inline bool
252 {
253  return !operator== (src);
254 }
255 
256 template<class T>
257 void Frustum<T>::set(T n, T f, T l, T r, T t, T b, bool o)
258 {
259  _nearPlane = n;
260  _farPlane = f;
261  _left = l;
262  _right = r;
263  _bottom = b;
264  _top = t;
265  _orthographic = o;
266 }
267 
268 template<class T>
270 {
271  if ( _orthographic )
272  {
273  _nearPlane = n;
274  }
275  else
276  {
277  Line3<T> lowerLeft( Vec3<T>(0,0,0), Vec3<T>(_left,_bottom,-_nearPlane) );
278  Line3<T> upperRight( Vec3<T>(0,0,0), Vec3<T>(_right,_top,-_nearPlane) );
279  Plane3<T> nearPlane( Vec3<T>(0,0,-1), n );
280 
281  Vec3<T> ll,ur;
282  nearPlane.intersect(lowerLeft,ll);
283  nearPlane.intersect(upperRight,ur);
284 
285  _left = ll.x;
286  _right = ur.x;
287  _top = ur.y;
288  _bottom = ll.y;
289  _nearPlane = n;
290  _farPlane = f;
291  }
292 
293  _farPlane = f;
294 }
295 
296 template<class T>
298 {
299  _orthographic = ortho;
300 }
301 
302 template<class T>
303 void Frustum<T>::set(T nearPlane, T farPlane, T fovx, T fovy, T aspect)
304 {
305  if (fovx != 0 && fovy != 0)
306  throw IEX_NAMESPACE::ArgExc ("fovx and fovy cannot both be non-zero.");
307 
308  const T two = static_cast<T>(2);
309 
310  if (fovx != 0)
311  {
312  _right = nearPlane * Math<T>::tan(fovx / two);
313  _left = -_right;
314  _top = ((_right - _left) / aspect) / two;
315  _bottom = -_top;
316  }
317  else
318  {
319  _top = nearPlane * Math<T>::tan(fovy / two);
320  _bottom = -_top;
321  _right = (_top - _bottom) * aspect / two;
322  _left = -_right;
323  }
324  _nearPlane = nearPlane;
325  _farPlane = farPlane;
326  _orthographic = false;
327 }
328 
329 template<class T>
331 {
332  return Math<T>::atan2(_right,_nearPlane) - Math<T>::atan2(_left,_nearPlane);
333 }
334 
335 template<class T>
337 {
338  return Math<T>::atan2(_top,_nearPlane) - Math<T>::atan2(_bottom,_nearPlane);
339 }
340 
341 template<class T>
343 {
344  T rightMinusLeft = _right-_left;
345  T topMinusBottom = _top-_bottom;
346 
347  if (abs(topMinusBottom) < 1 &&
348  abs(rightMinusLeft) > limits<T>::max() * abs(topMinusBottom))
349  {
350  throw IEX_NAMESPACE::DivzeroExc ("Bad viewing frustum: "
351  "aspect ratio cannot be computed.");
352  }
353 
354  return rightMinusLeft / topMinusBottom;
355 }
356 
357 template<class T>
359 {
360  T rightPlusLeft = _right+_left;
361  T rightMinusLeft = _right-_left;
362 
363  T topPlusBottom = _top+_bottom;
364  T topMinusBottom = _top-_bottom;
365 
366  T farPlusNear = _farPlane+_nearPlane;
367  T farMinusNear = _farPlane-_nearPlane;
368 
369  if ((abs(rightMinusLeft) < 1 &&
370  abs(rightPlusLeft) > limits<T>::max() * abs(rightMinusLeft)) ||
371  (abs(topMinusBottom) < 1 &&
372  abs(topPlusBottom) > limits<T>::max() * abs(topMinusBottom)) ||
373  (abs(farMinusNear) < 1 &&
374  abs(farPlusNear) > limits<T>::max() * abs(farMinusNear)))
375  {
376  throw IEX_NAMESPACE::DivzeroExc ("Bad viewing frustum: "
377  "projection matrix cannot be computed.");
378  }
379 
380  if ( _orthographic )
381  {
382  T tx = -rightPlusLeft / rightMinusLeft;
383  T ty = -topPlusBottom / topMinusBottom;
384  T tz = -farPlusNear / farMinusNear;
385 
386  if ((abs(rightMinusLeft) < 1 &&
387  2 > limits<T>::max() * abs(rightMinusLeft)) ||
388  (abs(topMinusBottom) < 1 &&
389  2 > limits<T>::max() * abs(topMinusBottom)) ||
390  (abs(farMinusNear) < 1 &&
391  2 > limits<T>::max() * abs(farMinusNear)))
392  {
393  throw IEX_NAMESPACE::DivzeroExc ("Bad viewing frustum: "
394  "projection matrix cannot be computed.");
395  }
396 
397  T A = 2 / rightMinusLeft;
398  T B = 2 / topMinusBottom;
399  T C = -2 / farMinusNear;
400 
401  return Matrix44<T>( A, 0, 0, 0,
402  0, B, 0, 0,
403  0, 0, C, 0,
404  tx, ty, tz, 1.f );
405  }
406  else
407  {
408  T A = rightPlusLeft / rightMinusLeft;
409  T B = topPlusBottom / topMinusBottom;
410  T C = -farPlusNear / farMinusNear;
411 
412  T farTimesNear = -2 * _farPlane * _nearPlane;
413  if (abs(farMinusNear) < 1 &&
414  abs(farTimesNear) > limits<T>::max() * abs(farMinusNear))
415  {
416  throw IEX_NAMESPACE::DivzeroExc ("Bad viewing frustum: "
417  "projection matrix cannot be computed.");
418  }
419 
420  T D = farTimesNear / farMinusNear;
421 
422  T twoTimesNear = 2 * _nearPlane;
423 
424  if ((abs(rightMinusLeft) < 1 &&
425  abs(twoTimesNear) > limits<T>::max() * abs(rightMinusLeft)) ||
426  (abs(topMinusBottom) < 1 &&
427  abs(twoTimesNear) > limits<T>::max() * abs(topMinusBottom)))
428  {
429  throw IEX_NAMESPACE::DivzeroExc ("Bad viewing frustum: "
430  "projection matrix cannot be computed.");
431  }
432 
433  T E = twoTimesNear / rightMinusLeft;
434  T F = twoTimesNear / topMinusBottom;
435 
436  return Matrix44<T>( E, 0, 0, 0,
437  0, F, 0, 0,
438  A, B, C, -1,
439  0, 0, D, 0 );
440  }
441 }
442 
443 template<class T>
445 {
446  return (_nearPlane == _farPlane) ||
447  (_left == _right) ||
448  (_top == _bottom);
449 }
450 
451 template<class T>
452 Frustum<T> Frustum<T>::window(T l, T r, T t, T b) const
453 {
454  // move it to 0->1 space
455 
456  Vec2<T> bl = screenToLocal( Vec2<T>(l,b) );
457  Vec2<T> tr = screenToLocal( Vec2<T>(r,t) );
458 
459  return Frustum<T>(_nearPlane, _farPlane, bl.x, tr.x, tr.y, bl.y, _orthographic);
460 }
461 
462 
463 template<class T>
465 {
466  return Vec2<T>( _left + (_right-_left) * (1.f+s.x) / 2.f,
467  _bottom + (_top-_bottom) * (1.f+s.y) / 2.f );
468 }
469 
470 template<class T>
472 {
473  T leftPlusRight = _left - T (2) * p.x + _right;
474  T leftMinusRight = _left-_right;
475  T bottomPlusTop = _bottom - T (2) * p.y + _top;
476  T bottomMinusTop = _bottom-_top;
477 
478  if ((abs(leftMinusRight) < T (1) &&
479  abs(leftPlusRight) > limits<T>::max() * abs(leftMinusRight)) ||
480  (abs(bottomMinusTop) < T (1) &&
481  abs(bottomPlusTop) > limits<T>::max() * abs(bottomMinusTop)))
482  {
483  throw IEX_NAMESPACE::DivzeroExc
484  ("Bad viewing frustum: "
485  "local-to-screen transformation cannot be computed");
486  }
487 
488  return Vec2<T>( leftPlusRight / leftMinusRight,
489  bottomPlusTop / bottomMinusTop );
490 }
491 
492 template<class T>
494 {
495  Vec2<T> point = screenToLocal(p);
496  if (orthographic())
497  return Line3<T>( Vec3<T>(point.x,point.y, 0.0),
498  Vec3<T>(point.x,point.y,-1.0));
499  else
500  return Line3<T>( Vec3<T>(0, 0, 0), Vec3<T>(point.x,point.y,-_nearPlane));
501 }
502 
503 template<class T>
505 {
506  if (orthographic() || point.z == T (0))
507  return localToScreen( Vec2<T>( point.x, point.y ) );
508  else
509  return localToScreen( Vec2<T>( point.x * _nearPlane / -point.z,
510  point.y * _nearPlane / -point.z ) );
511 }
512 
513 template<class T>
514 T Frustum<T>::ZToDepth(long zval,long zmin,long zmax) const
515 {
516  int zdiff = zmax - zmin;
517 
518  if (zdiff == 0)
519  {
520  throw IEX_NAMESPACE::DivzeroExc
521  ("Bad call to Frustum::ZToDepth: zmax == zmin");
522  }
523 
524  if ( zval > zmax+1 ) zval -= zdiff;
525 
526  T fzval = (T(zval) - T(zmin)) / T(zdiff);
527  return normalizedZToDepth(fzval);
528 }
529 
530 template<class T>
532 {
533  T Zp = zval * 2.0 - 1;
534 
535  if ( _orthographic )
536  {
537  return -(Zp*(_farPlane-_nearPlane) + (_farPlane+_nearPlane))/2;
538  }
539  else
540  {
541  T farTimesNear = 2 * _farPlane * _nearPlane;
542  T farMinusNear = Zp * (_farPlane - _nearPlane) - _farPlane - _nearPlane;
543 
544  if (abs(farMinusNear) < 1 &&
545  abs(farTimesNear) > limits<T>::max() * abs(farMinusNear))
546  {
547  throw IEX_NAMESPACE::DivzeroExc
548  ("Frustum::normalizedZToDepth cannot be computed. The "
549  "near and far clipping planes of the viewing frustum "
550  "may be too close to each other");
551  }
552 
553  return farTimesNear / farMinusNear;
554  }
555 }
556 
557 template<class T>
558 long Frustum<T>::DepthToZ(T depth,long zmin,long zmax) const
559 {
560  long zdiff = zmax - zmin;
561  T farMinusNear = _farPlane-_nearPlane;
562 
563  if ( _orthographic )
564  {
565  T farPlusNear = 2*depth + _farPlane + _nearPlane;
566 
567  if (abs(farMinusNear) < 1 &&
568  abs(farPlusNear) > limits<T>::max() * abs(farMinusNear))
569  {
570  throw IEX_NAMESPACE::DivzeroExc
571  ("Bad viewing frustum: near and far clipping planes "
572  "are too close to each other");
573  }
574 
575  T Zp = -farPlusNear/farMinusNear;
576  return long(0.5*(Zp+1)*zdiff) + zmin;
577  }
578  else
579  {
580  // Perspective
581 
582  T farTimesNear = 2*_farPlane*_nearPlane;
583  if (abs(depth) < 1 &&
584  abs(farTimesNear) > limits<T>::max() * abs(depth))
585  {
586  throw IEX_NAMESPACE::DivzeroExc
587  ("Bad call to DepthToZ function: value of `depth' "
588  "is too small");
589  }
590 
591  T farPlusNear = farTimesNear/depth + _farPlane + _nearPlane;
592  if (abs(farMinusNear) < 1 &&
593  abs(farPlusNear) > limits<T>::max() * abs(farMinusNear))
594  {
595  throw IEX_NAMESPACE::DivzeroExc
596  ("Bad viewing frustum: near and far clipping planes "
597  "are too close to each other");
598  }
599 
600  T Zp = farPlusNear/farMinusNear;
601  return long(0.5*(Zp+1)*zdiff) + zmin;
602  }
603 }
604 
605 template<class T>
606 T Frustum<T>::screenRadius(const Vec3<T> &p, T radius) const
607 {
608  // Derivation:
609  // Consider X-Z plane.
610  // X coord of projection of p = xp = p.x * (-_nearPlane / p.z)
611  // Let q be p + (radius, 0, 0).
612  // X coord of projection of q = xq = (p.x - radius) * (-_nearPlane / p.z)
613  // X coord of projection of segment from p to q = r = xp - xq
614  // = radius * (-_nearPlane / p.z)
615  // A similar analysis holds in the Y-Z plane.
616  // So r is the quantity we want to return.
617 
618  if (abs(p.z) > 1 || abs(-_nearPlane) < limits<T>::max() * abs(p.z))
619  {
620  return radius * (-_nearPlane / p.z);
621  }
622  else
623  {
624  throw IEX_NAMESPACE::DivzeroExc
625  ("Bad call to Frustum::screenRadius: the magnitude of `p' "
626  "is too small");
627  }
628 
629  return radius * (-_nearPlane / p.z);
630 }
631 
632 template<class T>
633 T Frustum<T>::worldRadius(const Vec3<T> &p, T radius) const
634 {
635  if (abs(-_nearPlane) > 1 || abs(p.z) < limits<T>::max() * abs(-_nearPlane))
636  {
637  return radius * (p.z / -_nearPlane);
638  }
639  else
640  {
641  throw IEX_NAMESPACE::DivzeroExc
642  ("Bad viewing frustum: the near clipping plane is too "
643  "close to zero");
644  }
645 }
646 
647 template<class T>
649 {
650  //
651  // Plane order: Top, Right, Bottom, Left, Near, Far.
652  // Normals point outwards.
653  //
654 
655  if (! _orthographic)
656  {
657  Vec3<T> a( _left, _bottom, -_nearPlane);
658  Vec3<T> b( _left, _top, -_nearPlane);
659  Vec3<T> c( _right, _top, -_nearPlane);
660  Vec3<T> d( _right, _bottom, -_nearPlane);
661  Vec3<T> o(0,0,0);
662 
663  p[0].set( o, c, b );
664  p[1].set( o, d, c );
665  p[2].set( o, a, d );
666  p[3].set( o, b, a );
667  }
668  else
669  {
670  p[0].set( Vec3<T>( 0, 1, 0), _top );
671  p[1].set( Vec3<T>( 1, 0, 0), _right );
672  p[2].set( Vec3<T>( 0,-1, 0),-_bottom );
673  p[3].set( Vec3<T>(-1, 0, 0),-_left );
674  }
675  p[4].set( Vec3<T>(0, 0, 1), -_nearPlane );
676  p[5].set( Vec3<T>(0, 0,-1), _farPlane );
677 }
678 
679 
680 template<class T>
681 void Frustum<T>::planes(Plane3<T> p[6], const Matrix44<T> &M) const
682 {
683  //
684  // Plane order: Top, Right, Bottom, Left, Near, Far.
685  // Normals point outwards.
686  //
687 
688  Vec3<T> a = Vec3<T>( _left, _bottom, -_nearPlane) * M;
689  Vec3<T> b = Vec3<T>( _left, _top, -_nearPlane) * M;
690  Vec3<T> c = Vec3<T>( _right, _top, -_nearPlane) * M;
691  Vec3<T> d = Vec3<T>( _right, _bottom, -_nearPlane) * M;
692  if (! _orthographic)
693  {
694  double s = _farPlane / double(_nearPlane);
695  T farLeft = (T) (s * _left);
696  T farRight = (T) (s * _right);
697  T farTop = (T) (s * _top);
698  T farBottom = (T) (s * _bottom);
699  Vec3<T> e = Vec3<T>( farLeft, farBottom, -_farPlane) * M;
700  Vec3<T> f = Vec3<T>( farLeft, farTop, -_farPlane) * M;
701  Vec3<T> g = Vec3<T>( farRight, farTop, -_farPlane) * M;
702  Vec3<T> o = Vec3<T>(0,0,0) * M;
703  p[0].set( o, c, b );
704  p[1].set( o, d, c );
705  p[2].set( o, a, d );
706  p[3].set( o, b, a );
707  p[4].set( a, d, c );
708  p[5].set( e, f, g );
709  }
710  else
711  {
712  Vec3<T> e = Vec3<T>( _left, _bottom, -_farPlane) * M;
713  Vec3<T> f = Vec3<T>( _left, _top, -_farPlane) * M;
714  Vec3<T> g = Vec3<T>( _right, _top, -_farPlane) * M;
715  Vec3<T> h = Vec3<T>( _right, _bottom, -_farPlane) * M;
716  p[0].set( c, g, f );
717  p[1].set( d, h, g );
718  p[2].set( a, e, h );
719  p[3].set( b, f, e );
720  p[4].set( a, d, c );
721  p[5].set( e, f, g );
722  }
723 }
724 
727 
728 
730 
731 
732 #if defined _WIN32 || defined _WIN64
733  #ifdef _redef_near
734  #define near
735  #endif
736  #ifdef _redef_far
737  #define far
738  #endif
739 #endif
740 
741 #endif // INCLUDED_IMATHFRUSTUM_H
#define IMATH_INTERNAL_NAMESPACE_HEADER_EXIT
T left() const
Definition: ImathFrustum.h:119
T z
Definition: ImathVec.h:275
#define IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
void modifyNearAndFar(T nearPlane, T farPlane)
Definition: ImathFrustum.h:269
T right() const
Definition: ImathFrustum.h:120
const hboost::disable_if_c< VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:128
GLint left
Definition: glcorearb.h:2004
void setOrthographic(bool)
Definition: ImathFrustum.h:297
GLboolean GLboolean g
Definition: glcorearb.h:1221
T aspect() const
Definition: ImathFrustum.h:342
GLboolean GLboolean GLboolean GLboolean a
Definition: glcorearb.h:1221
long DepthToZ(T depth, long zmin, long zmax) const
Definition: ImathFrustum.h:558
T fovy() const
Definition: ImathFrustum.h:336
T hither() const
Definition: ImathFrustum.h:116
T farPlane() const
Definition: ImathFrustum.h:117
static T max()
Line3< T > projectScreenToRay(const Vec2< T > &) const
Definition: ImathFrustum.h:493
const hboost::disable_if_c< VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:132
Vec2< T > localToScreen(const Vec2< T > &) const
Definition: ImathFrustum.h:471
T nearPlane() const
Definition: ImathFrustum.h:115
const Frustum & operator=(const Frustum &)
Definition: ImathFrustum.h:222
GLdouble n
Definition: glcorearb.h:2007
GLfloat f
Definition: glcorearb.h:1925
virtual ~Frustum()
Definition: ImathFrustum.h:216
T x
Definition: ImathVec.h:77
GLint GLint GLsizei GLsizei GLsizei depth
Definition: glcorearb.h:475
T x
Definition: ImathVec.h:275
IMATH_INTERNAL_NAMESPACE_HEADER_ENTER T abs(T a)
Definition: ImathFun.h:55
T normalizedZToDepth(T zval) const
Definition: ImathFrustum.h:531
T yon() const
Definition: ImathFrustum.h:118
T y
Definition: ImathVec.h:77
Vec2< T > screenToLocal(const Vec2< T > &) const
Definition: ImathFrustum.h:464
bool _orthographic
Definition: ImathFrustum.h:181
bool intersect(const Line3< T > &line, Vec3< T > &intersection) const
Definition: ImathPlane.h:187
bool orthographic() const
Definition: ImathFrustum.h:114
Frustum< double > Frustumd
Definition: ImathFrustum.h:726
T worldRadius(const Vec3< T > &p, T radius) const
Definition: ImathFrustum.h:633
T screenRadius(const Vec3< T > &p, T radius) const
Definition: ImathFrustum.h:606
Frustum< float > Frustumf
Definition: ImathFrustum.h:725
GLboolean GLboolean GLboolean b
Definition: glcorearb.h:1221
static T atan2(T x, T y)
Definition: ImathMath.h:97
T bottom() const
Definition: ImathFrustum.h:121
GLint GLint bottom
Definition: glcorearb.h:2004
GLfloat GLfloat GLfloat GLfloat h
Definition: glcorearb.h:2001
T fovx() const
Definition: ImathFrustum.h:330
bool degenerate() const
Definition: ImathFrustum.h:444
T y
Definition: ImathVec.h:275
T top() const
Definition: ImathFrustum.h:122
Vec2< T > projectPointToScreen(const Vec3< T > &) const
Definition: ImathFrustum.h:504
GLboolean r
Definition: glcorearb.h:1221
T ZToDepth(long zval, long min, long max) const
Definition: ImathFrustum.h:514
bool operator!=(const Frustum< T > &src) const
Definition: ImathFrustum.h:251
Matrix44< T > projectionMatrix() const
Definition: ImathFrustum.h:358
void set(T nearPlane, T farPlane, T left, T right, T top, T bottom, bool ortho=false)
Definition: ImathFrustum.h:257
bool operator==(const Frustum< T > &src) const
Definition: ImathFrustum.h:237
void set(const Vec3< T > &normal, T distance)
Definition: ImathPlane.h:159
void planes(Plane3< T > p[6]) const
Definition: ImathFrustum.h:648
bool operator==(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Equality operator, does exact floating point comparisons.
Definition: Mat3.h:596
Frustum< T > window(T left, T right, T top, T bottom) const
Definition: ImathFrustum.h:452
static T tan(T x)
Definition: ImathMath.h:100
GLenum src
Definition: glcorearb.h:1792