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geom/ellipse: add sample_surface function

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This commit is contained in:
Danny Robson 2018-04-17 17:04:17 +10:00
parent 9affc28807
commit 06350b53cf
2 changed files with 69 additions and 9 deletions
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6
geom/ellipse.cpp
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@ -11,7 +11,7 @@
* See the License for the specific language governing permissions and
* limitations under the License.
*
* Copyright 2015-2017 Danny Robson <danny@nerdcruft.net>
* Copyright 2015-2018 Danny Robson <danny@nerdcruft.net>
*/
#include "ellipse.hpp"
@ -46,9 +46,6 @@ util::geom::intersects (A<S,T> a, B<S,T> b)
}
//-----------------------------------------------------------------------------
///////////////////////////////////////////////////////////////////////////////
template <size_t DimensionV, typename ValueT>
util::point<DimensionV,ValueT>
@ -103,7 +100,6 @@ util::geom::bounds (K<S,T> k)
}
///////////////////////////////////////////////////////////////////////////////
#define INSTANTIATE_S_T(S,T) \
template bool util::geom::intersects (ellipse<S,T>, util::point<S,T>); \

72
geom/ellipse.hpp
View File

@ -11,19 +11,21 @@
* See the License for the specific language governing permissions and
* limitations under the License.
*
* Copyright 2015 Danny Robson <danny@nerdcruft.net>
* Copyright 2015-2018 Danny Robson <danny@nerdcruft.net>
*/
#ifndef __UTIL_GEOM_ELLIPSE_HPP
#define __UTIL_GEOM_ELLIPSE_HPP
#include <cstdlib>
#include "fwd.hpp"
#include "../point.hpp"
#include "../vector.hpp"
#include <cstdlib>
#include <random>
namespace util::geom {
///////////////////////////////////////////////////////////////////////////
template <size_t S, typename ValueT>
@ -38,6 +40,40 @@ namespace util::geom {
util::vector<S,ValueT> up;
};
using ellipse3f = ellipse<3,float>;
/// returns the approximate surface area of the ellipse
///
/// the general form involves _substantially_ more expensive and
/// complicated maths which is prohibitive right now.
///
/// the relative error should be at most 1.061%
inline float
area (ellipse3f self)
{
auto const semiprod = self.radius * self.radius.indices<1,2,0> ();
auto const semipow = pow (semiprod, 1.6f);
return 4 * pi<float> * std::pow (sum (semipow) / 3, 1/1.6f);
}
template <typename T>
T
area (ellipse<2,T> self)
{
return pi<T> * product (self.radius);
}
template <size_t S, typename T>
T
volume (ellipse<S,T> self)
{
return 4 / T{3} * pi<T> * product (self.radius);
}
template <size_t DimensionV, typename ValueT>
point<DimensionV,ValueT>
@ -57,7 +93,35 @@ namespace util::geom {
ellipse<DimensionV,ValueT>
);
using ellipse3f = ellipse<3,float>;
/// returns a point that is uniformly distributed about the ellipse
/// surface.
///
/// NOTE: I don't have a strong proof that the below is in fact properly
/// uniformly distributed, so if you need a strong guarantee for your work
/// then it might not be the best option. But visual inspection appears to
/// confirm there aren't obvious patterns.
///
/// the concept was taken from: https://math.stackexchange.com/a/2514182
template <typename RandomT>
util::point3f
sample_surface (ellipse3f self, RandomT &generator)
{
const auto [a, b, c] = self.radius;
const auto a2 = a * a;
const auto b2 = b * b;
const auto c2 = c * c;
// generate a direction vector from a normally distributed random variable
auto const x = std::normal_distribution<float> (0, a2) (generator);
auto const y = std::normal_distribution<float> (0, b2) (generator);
auto const z = std::normal_distribution<float> (0, c2) (generator);
// find the distance to the surface along the direction vector
auto const d = std::sqrt (x * x / a2 + y * y / b2 + z * z / c2);
return self.origin + util::vector3f {x,y,z} / d;
}
}