1 // Copyright (C) 2006 Mathias Froehlich - Mathias.Froehlich@web.de
3 // This library is free software; you can redistribute it and/or
4 // modify it under the terms of the GNU Library General Public
5 // License as published by the Free Software Foundation; either
6 // version 2 of the License, or (at your option) any later version.
8 // This library is distributed in the hope that it will be useful,
9 // but WITHOUT ANY WARRANTY; without even the implied warranty of
10 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
11 // Library General Public License for more details.
13 // You should have received a copy of the GNU General Public License
14 // along with this program; if not, write to the Free Software
15 // Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
18 #ifndef SGIntersect_HXX
19 #define SGIntersect_HXX
23 intersects(const SGBox<T>& box, const SGSphere<T>& sphere)
27 // Is more or less trivially included in the next tests
31 if (sphere.getCenter().x() < box.getMin().x() - sphere.getRadius())
33 if (sphere.getCenter().y() < box.getMin().y() - sphere.getRadius())
35 if (sphere.getCenter().z() < box.getMin().z() - sphere.getRadius())
38 if (box.getMax().x() + sphere.getRadius() < sphere.getCenter().x())
40 if (box.getMax().y() + sphere.getRadius() < sphere.getCenter().y())
42 if (box.getMax().z() + sphere.getRadius() < sphere.getCenter().z())
50 intersects(const SGSphere<T>& sphere, const SGBox<T>& box)
51 { return intersects(box, sphere); }
56 intersects(const SGVec3<T>& v, const SGBox<T>& box)
58 if (v[0] < box.getMin()[0])
60 if (box.getMax()[0] < v[0])
62 if (v[1] < box.getMin()[1])
64 if (box.getMax()[1] < v[1])
66 if (v[2] < box.getMin()[2])
68 if (box.getMax()[2] < v[2])
74 intersects(const SGBox<T>& box, const SGVec3<T>& v)
75 { return intersects(v, box); }
80 intersects(const SGRay<T>& ray, const SGPlane<T>& plane)
82 // We compute the intersection point
83 // x = origin + \alpha*direction
84 // from the ray origin and non nomalized direction.
85 // For 0 <= \alpha the ray intersects the infinite plane.
86 // The intersection point x can also be written
88 // where n is the planes normal, dist is the distance of the plane from
89 // the origin in normal direction and y is ana aproriate vector
90 // perpendicular to n.
91 // Equate the x values and take the scalar product with the plane normal n.
92 // dot(n, origin) + \alpha*dot(n, direction) = dist
93 // We can now compute alpha from the above equation.
94 // \alpha = (dist - dot(n, origin))/dot(n, direction)
96 // The negative numerator for the \alpha expression
97 T num = plane.getPositiveDist();
98 num -= dot(plane.getNormal(), ray.getOrigin());
100 // If the numerator is zero, we have the rays origin included in the plane
101 if (fabs(num) <= SGLimits<T>::min())
104 // The denominator for the \alpha expression
105 T den = dot(plane.getNormal(), ray.getDirection());
107 // If we get here, we already know that the rays origin is not included
108 // in the plane. Thus if we have a zero denominator we have
109 // a ray paralell to the plane. That is no intersection.
110 if (fabs(den) <= SGLimits<T>::min())
113 // We would now compute \alpha = num/den and compare with 0 and 1.
114 // But to avoid that expensive division, check equation multiplied by
116 T alphaDen = copysign(1, den)*num;
125 intersects(const SGPlane<T>& plane, const SGRay<T>& ray)
126 { return intersects(ray, plane); }
130 intersects(SGVec3<T>& dst, const SGRay<T>& ray, const SGPlane<T>& plane)
132 // We compute the intersection point
133 // x = origin + \alpha*direction
134 // from the ray origin and non nomalized direction.
135 // For 0 <= \alpha the ray intersects the infinite plane.
136 // The intersection point x can also be written
138 // where n is the planes normal, dist is the distance of the plane from
139 // the origin in normal direction and y is ana aproriate vector
140 // perpendicular to n.
141 // Equate the x values and take the scalar product with the plane normal n.
142 // dot(n, origin) + \alpha*dot(n, direction) = dist
143 // We can now compute alpha from the above equation.
144 // \alpha = (dist - dot(n, origin))/dot(n, direction)
146 // The negative numerator for the \alpha expression
147 T num = plane.getPositiveDist();
148 num -= dot(plane.getNormal(), ray.getOrigin());
150 // If the numerator is zero, we have the rays origin included in the plane
151 if (fabs(num) <= SGLimits<T>::min()) {
152 dst = ray.getOrigin();
156 // The denominator for the \alpha expression
157 T den = dot(plane.getNormal(), ray.getDirection());
159 // If we get here, we already know that the rays origin is not included
160 // in the plane. Thus if we have a zero denominator we have
161 // a ray paralell to the plane. That is no intersection.
162 if (fabs(den) <= SGLimits<T>::min())
165 // We would now compute \alpha = num/den and compare with 0 and 1.
166 // But to avoid that expensive division, check equation multiplied by
172 dst = ray.getOrigin() + alpha*ray.getDirection();
178 intersects(SGVec3<T>& dst, const SGPlane<T>& plane, const SGRay<T>& ray)
179 { return intersects(dst, ray, plane); }
183 intersects(const SGLineSegment<T>& lineSegment, const SGPlane<T>& plane)
185 // We compute the intersection point
186 // x = origin + \alpha*direction
187 // from the line segments origin and non nomalized direction.
188 // For 0 <= \alpha <= 1 the line segment intersects the infinite plane.
189 // The intersection point x can also be written
191 // where n is the planes normal, dist is the distance of the plane from
192 // the origin in normal direction and y is ana aproriate vector
193 // perpendicular to n.
194 // Equate the x values and take the scalar product with the plane normal n.
195 // dot(n, origin) + \alpha*dot(n, direction) = dist
196 // We can now compute alpha from the above equation.
197 // \alpha = (dist - dot(n, origin))/dot(n, direction)
199 // The negative numerator for the \alpha expression
200 T num = plane.getPositiveDist();
201 num -= dot(plane.getNormal(), lineSegment.getOrigin());
203 // If the numerator is zero, we have the lines origin included in the plane
204 if (fabs(num) <= SGLimits<T>::min())
207 // The denominator for the \alpha expression
208 T den = dot(plane.getNormal(), lineSegment.getDirection());
210 // If we get here, we already know that the lines origin is not included
211 // in the plane. Thus if we have a zero denominator we have
212 // a line paralell to the plane. That is no intersection.
213 if (fabs(den) <= SGLimits<T>::min())
216 // We would now compute \alpha = num/den and compare with 0 and 1.
217 // But to avoid that expensive division, compare equations
218 // multiplied by |den|. Note that copysign is usually a compiler intrinsic
219 // that expands in assembler code that not even stalls the cpus pipes.
220 T alphaDen = copysign(1, den)*num;
231 intersects(const SGPlane<T>& plane, const SGLineSegment<T>& lineSegment)
232 { return intersects(lineSegment, plane); }
236 intersects(SGVec3<T>& dst, const SGLineSegment<T>& lineSegment, const SGPlane<T>& plane)
238 // We compute the intersection point
239 // x = origin + \alpha*direction
240 // from the line segments origin and non nomalized direction.
241 // For 0 <= \alpha <= 1 the line segment intersects the infinite plane.
242 // The intersection point x can also be written
244 // where n is the planes normal, dist is the distance of the plane from
245 // the origin in normal direction and y is an aproriate vector
246 // perpendicular to n.
247 // Equate the x values and take the scalar product with the plane normal n.
248 // dot(n, origin) + \alpha*dot(n, direction) = dist
249 // We can now compute alpha from the above equation.
250 // \alpha = (dist - dot(n, origin))/dot(n, direction)
252 // The negative numerator for the \alpha expression
253 T num = plane.getPositiveDist();
254 num -= dot(plane.getNormal(), lineSegment.getOrigin());
256 // If the numerator is zero, we have the lines origin included in the plane
257 if (fabs(num) <= SGLimits<T>::min()) {
258 dst = lineSegment.getOrigin();
262 // The denominator for the \alpha expression
263 T den = dot(plane.getNormal(), lineSegment.getDirection());
265 // If we get here, we already know that the lines origin is not included
266 // in the plane. Thus if we have a zero denominator we have
267 // a line paralell to the plane. That is: no intersection.
268 if (fabs(den) <= SGLimits<T>::min())
271 // We would now compute \alpha = num/den and compare with 0 and 1.
272 // But to avoid that expensive division, check equation multiplied by
273 // the denominator. FIXME: shall we do so? or compute like that?
280 dst = lineSegment.getOrigin() + alpha*lineSegment.getDirection();
286 intersects(SGVec3<T>& dst, const SGPlane<T>& plane, const SGLineSegment<T>& lineSegment)
287 { return intersects(dst, lineSegment, plane); }
292 intersects(const SGRay<T>& ray, const SGSphere<T>& sphere)
294 // See Tomas Akeniene - Moeller/Eric Haines: Real Time Rendering,
295 // second edition, page 571
296 SGVec3<T> l = sphere.getCenter() - ray.getOrigin();
297 T s = dot(l, ray.getDirection());
300 T r2 = sphere.getRadius2();
301 if (s < 0 && l2 > r2)
304 T d2 = dot(ray.getDirection(), ray.getDirection());
305 // The original test would read
306 // T m2 = l2 - s*s/d2;
309 // but to avoid the expensive division, we multiply by d2
319 intersects(const SGSphere<T>& sphere, const SGRay<T>& ray)
320 { return intersects(ray, sphere); }
324 intersects(const SGLineSegment<T>& lineSegment, const SGSphere<T>& sphere)
326 // See Tomas Akeniene - Moeller/Eric Haines: Real Time Rendering,
327 // second edition, page 571
328 SGVec3<T> l = sphere.getCenter() - lineSegment.getStart();
329 T ld = length(lineSegment.getDirection());
330 T s = dot(l, lineSegment.getDirection())/ld;
333 T r2 = sphere.getRadius2();
334 if (s < 0 && l2 > r2)
351 intersects(const SGSphere<T>& sphere, const SGLineSegment<T>& lineSegment)
352 { return intersects(lineSegment, sphere); }
357 // FIXME do not use that default argument later. Just for development now
358 intersects(SGVec3<T>& x, const SGTriangle<T>& tri, const SGRay<T>& ray, T eps = 0)
360 // See Tomas Akeniene - Moeller/Eric Haines: Real Time Rendering
362 // Method based on the observation that we are looking for a
363 // point x that can be expressed in terms of the triangle points
364 // x = v_0 + u*(v_1 - v_0) + v*(v_2 - v_0)
365 // with 0 <= u, v and u + v <= 1.
366 // OTOH it could be expressed in terms of the ray
368 // Now we can compute u, v and t.
369 SGVec3<T> p = cross(ray.getDirection(), tri.getEdge(1));
371 T denom = dot(p, tri.getEdge(0));
372 T signDenom = copysign(1, denom);
374 SGVec3<T> s = ray.getOrigin() - tri.getBaseVertex();
375 SGVec3<T> q = cross(s, tri.getEdge(0));
377 // t = 1/denom*dot(q, tri.getEdge(1));
378 // To avoid an expensive division we multiply by |denom|
379 T tDenom = signDenom*dot(q, tri.getEdge(1));
382 // For line segment we would test against
385 // with the original t. The multiplied test would read
386 // if (absDenom < tDenom)
389 T absDenom = fabs(denom);
390 T absDenomEps = absDenom*eps;
392 // T u = 1/denom*dot(p, s);
393 T u = signDenom*dot(p, s);
394 if (u < -absDenomEps)
396 // T v = 1/denom*dot(q, d);
399 T v = signDenom*dot(q, ray.getDirection());
400 if (v < -absDenomEps)
403 if (u + v > absDenom + absDenomEps)
406 // return if paralell ??? FIXME what if paralell and in plane?
407 // may be we are ok below than anyway??
408 if (absDenom <= SGLimits<T>::min())
412 // if we have survived here it could only happen with denom == 0
413 // that the point is already in plane. Then return the origin ...
414 if (SGLimitsd::min() < absDenom)
415 x += (tDenom/absDenom)*ray.getDirection();
422 intersects(const SGTriangle<T>& tri, const SGRay<T>& ray, T eps = 0)
424 // FIXME: for now just wrap the other method. When that has prooven
425 // well optimized, implement that special case
427 return intersects(dummy, tri, ray, eps);
432 // FIXME do not use that default argument later. Just for development now
433 intersects(SGVec3<T>& x, const SGTriangle<T>& tri, const SGLineSegment<T>& lineSegment, T eps = 0)
435 // See Tomas Akeniene - Moeller/Eric Haines: Real Time Rendering
437 // Method based on the observation that we are looking for a
438 // point x that can be expressed in terms of the triangle points
439 // x = v_0 + u*(v_1 - v_0) + v*(v_2 - v_0)
440 // with 0 <= u, v and u + v <= 1.
441 // OTOH it could be expressed in terms of the lineSegment
443 // Now we can compute u, v and t.
444 SGVec3<T> p = cross(lineSegment.getDirection(), tri.getEdge(1));
446 T denom = dot(p, tri.getEdge(0));
447 T signDenom = copysign(1, denom);
449 SGVec3<T> s = lineSegment.getStart() - tri.getBaseVertex();
450 SGVec3<T> q = cross(s, tri.getEdge(0));
452 // t = 1/denom*dot(q, tri.getEdge(1));
453 // To avoid an expensive division we multiply by |denom|
454 T tDenom = signDenom*dot(q, tri.getEdge(1));
457 // For line segment we would test against
460 // with the original t. The multiplied test reads
461 T absDenom = fabs(denom);
462 if (absDenom < tDenom)
465 // take the CPU accuracy in account
466 T absDenomEps = absDenom*eps;
468 // T u = 1/denom*dot(p, s);
469 T u = signDenom*dot(p, s);
470 if (u < -absDenomEps)
472 // T v = 1/denom*dot(q, d);
475 T v = signDenom*dot(q, lineSegment.getDirection());
476 if (v < -absDenomEps)
479 if (u + v > absDenom + absDenomEps)
482 // return if paralell ??? FIXME what if paralell and in plane?
483 // may be we are ok below than anyway??
484 if (absDenom <= SGLimits<T>::min())
487 x = lineSegment.getStart();
488 // if we have survived here it could only happen with denom == 0
489 // that the point is already in plane. Then return the origin ...
490 if (SGLimitsd::min() < absDenom)
491 x += (tDenom/absDenom)*lineSegment.getDirection();
498 intersects(const SGTriangle<T>& tri, const SGLineSegment<T>& lineSegment, T eps = 0)
500 // FIXME: for now just wrap the othr method. When that has prooven
501 // well optimized, implement that special case
503 return intersects(dummy, tri, lineSegment, eps);
509 intersects(const SGVec3<T>& v, const SGSphere<T>& sphere)
513 return distSqr(v, sphere.getCenter()) <= sphere.getRadius2();
517 intersects(const SGSphere<T>& sphere, const SGVec3<T>& v)
518 { return intersects(v, sphere); }
523 intersects(const SGBox<T>& box, const SGLineSegment<T>& lineSegment)
525 // See Tomas Akeniene - Moeller/Eric Haines: Real Time Rendering
527 SGVec3<T> c = lineSegment.getCenter() - box.getCenter();
528 SGVec3<T> w = 0.5*lineSegment.getDirection();
529 SGVec3<T> v(fabs(w.x()), fabs(w.y()), fabs(w.z()));
530 SGVec3<T> h = 0.5*box.getSize();
532 if (fabs(c[0]) > v[0] + h[0])
534 if (fabs(c[1]) > v[1] + h[1])
536 if (fabs(c[2]) > v[2] + h[2])
539 if (fabs(c[1]*w[2] - c[2]*w[1]) > h[1]*v[2] + h[2]*v[1])
541 if (fabs(c[0]*w[2] - c[2]*w[0]) > h[0]*v[2] + h[2]*v[0])
543 if (fabs(c[0]*w[1] - c[1]*w[0]) > h[0]*v[1] + h[1]*v[0])
550 intersects(const SGLineSegment<T>& lineSegment, const SGBox<T>& box)
551 { return intersects(box, lineSegment); }
555 intersects(const SGBox<T>& box, const SGRay<T>& ray)
557 // See Tomas Akeniene - Moeller/Eric Haines: Real Time Rendering
559 for (unsigned i = 0; i < 3; ++i) {
560 T cMin = box.getMin()[i];
561 T cMax = box.getMax()[i];
563 T cOrigin = ray.getOrigin()[i];
565 T cDir = ray.getDirection()[i];
566 if (fabs(cDir) <= SGLimits<T>::min()) {
573 T nearr = - SGLimits<T>::max();
574 T farr = SGLimits<T>::max();
576 T T1 = (cMin - cOrigin) / cDir;
577 T T2 = (cMax - cOrigin) / cDir;
578 if (T1 > T2) std::swap (T1, T2);/* since T1 intersection with near plane */
579 if (T1 > nearr) nearr = T1; /* want largest Tnear */
580 if (T2 < farr) farr = T2; /* want smallest Tfarr */
581 if (nearr > farr) // farr box is missed
583 if (farr < 0) // box is behind ray
592 intersects(const SGRay<T>& ray, const SGBox<T>& box)
593 { return intersects(box, ray); }