| /////////////////////////////////////////////////////////////////////////// |
| // |
| // Copyright (c) 2002, Industrial Light & Magic, a division of Lucas |
| // Digital Ltd. LLC |
| // |
| // All rights reserved. |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are |
| // met: |
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| // notice, this list of conditions and the following disclaimer. |
| // * 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. |
| // * Neither the name of Industrial Light & Magic 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 |
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| // |
| /////////////////////////////////////////////////////////////////////////// |
| |
| |
| |
| #ifndef INCLUDED_IMATHSPHERE_H |
| #define INCLUDED_IMATHSPHERE_H |
| |
| //------------------------------------- |
| // |
| // A 3D sphere class template |
| // |
| //------------------------------------- |
| |
| #include "ImathVec.h" |
| #include "ImathBox.h" |
| #include "ImathLine.h" |
| |
| namespace Imath { |
| |
| template <class T> |
| class Sphere3 |
| { |
| public: |
| |
| Vec3<T> center; |
| T radius; |
| |
| //--------------- |
| // Constructors |
| //--------------- |
| |
| Sphere3() : center(0,0,0), radius(0) {} |
| Sphere3(const Vec3<T> &c, T r) : center(c), radius(r) {} |
| |
| //------------------------------------------------------------------- |
| // Utilities: |
| // |
| // s.circumscribe(b) sets center and radius of sphere s |
| // so that the s tightly encloses box b. |
| // |
| // s.intersectT (l, t) If sphere s and line l intersect, then |
| // intersectT() computes the smallest t, |
| // t >= 0, so that l(t) is a point on the |
| // sphere. intersectT() then returns true. |
| // |
| // If s and l do not intersect, intersectT() |
| // returns false. |
| // |
| // s.intersect (l, i) If sphere s and line l intersect, then |
| // intersect() calls s.intersectT(l,t) and |
| // computes i = l(t). |
| // |
| // If s and l do not intersect, intersect() |
| // returns false. |
| // |
| //------------------------------------------------------------------- |
| |
| void circumscribe(const Box<Vec3<T> > &box); |
| bool intersect(const Line3<T> &l, Vec3<T> &intersection) const; |
| bool intersectT(const Line3<T> &l, T &t) const; |
| }; |
| |
| |
| //-------------------- |
| // Convenient typedefs |
| //-------------------- |
| |
| typedef Sphere3<float> Sphere3f; |
| typedef Sphere3<double> Sphere3d; |
| |
| |
| //--------------- |
| // Implementation |
| //--------------- |
| |
| template <class T> |
| void Sphere3<T>::circumscribe(const Box<Vec3<T> > &box) |
| { |
| center = T(0.5) * (box.min + box.max); |
| radius = (box.max - center).length(); |
| } |
| |
| |
| template <class T> |
| bool Sphere3<T>::intersectT(const Line3<T> &line, T &t) const |
| { |
| bool doesIntersect = true; |
| |
| Vec3<T> v = line.pos - center; |
| T B = 2.0 * (line.dir ^ v); |
| T C = (v ^ v) - (radius * radius); |
| |
| // compute discriminant |
| // if negative, there is no intersection |
| |
| T discr = B*B - 4.0*C; |
| |
| if (discr < 0.0) |
| { |
| // line and Sphere3 do not intersect |
| |
| doesIntersect = false; |
| } |
| else |
| { |
| // t0: (-B - sqrt(B^2 - 4AC)) / 2A (A = 1) |
| |
| T sqroot = Math<T>::sqrt(discr); |
| t = (-B - sqroot) * 0.5; |
| |
| if (t < 0.0) |
| { |
| // no intersection, try t1: (-B + sqrt(B^2 - 4AC)) / 2A (A = 1) |
| |
| t = (-B + sqroot) * 0.5; |
| } |
| |
| if (t < 0.0) |
| doesIntersect = false; |
| } |
| |
| return doesIntersect; |
| } |
| |
| |
| template <class T> |
| bool Sphere3<T>::intersect(const Line3<T> &line, Vec3<T> &intersection) const |
| { |
| T t; |
| |
| if (intersectT (line, t)) |
| { |
| intersection = line(t); |
| return true; |
| } |
| else |
| { |
| return false; |
| } |
| } |
| |
| |
| } //namespace Imath |
| |
| #endif |