libcruft-util/geom/ellipse.cpp

/*
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
 * Copyright 2015-2017 Danny Robson <danny@nerdcruft.net>
 */

#include "ellipse.hpp"

#include "ops.hpp"
#include "aabb.hpp"
#include "ray.hpp"
#include "sphere.hpp"
#include "point.hpp"

#include "../matrix.hpp"

using util::geom::ellipse;


///////////////////////////////////////////////////////////////////////////////
template <size_t S, typename T>
static bool
intersects (ellipse<S,T> e, util::point<S,T> p)
{
    auto mag = (p - e.origin) * (p - e.origin) / (e.radius * e.radius);
    return std::accumulate (mag.begin (), mag.end (), 0) <= 1;
}


//-----------------------------------------------------------------------------
template <size_t S, typename T, template <size_t,typename> class A, template <size_t,typename> class B>
bool
util::geom::intersects (A<S,T> a, B<S,T> b)
{
    return ::intersects (a, b);
}


//-----------------------------------------------------------------------------
template bool util::geom::intersects (ellipse<2,float>, util::point<2,float>);
template bool util::geom::intersects (ellipse<3,float>, util::point<3,float>);


///////////////////////////////////////////////////////////////////////////////
// query a ray-ellipse distance by transforming spaces such that the ellipse is
// a sphere
template <>
float
util::geom::distance (ray<3,float> r, ellipse<3,float> e)
{
    // find a transform that puts the ellipse at origin and scales it to a
    // unit sphere.
    auto const from_scaled = util::scale (e.radius) *
                             util::look_at (e.origin, {0,0,-1}, e.up);
    auto const to_scaled = inverse (from_scaled);

    // transform the ray into this new space and query against a unit sphere
    auto const scaled_r = to_scaled * r;
    auto const scaled_d = distance (scaled_r, sphere3f {0, 1.f});
    auto const scaled_p = scaled_r.at (scaled_d);

    // transform the result back into the original space
    return distance (r.origin, (from_scaled * scaled_p.homog<4> ()).redim<3> ());
}


///////////////////////////////////////////////////////////////////////////////
template <size_t S, typename T>
static util::geom::aabb<S,T>
bounds (ellipse<S,T> e)
{
    return {
        e.origin - e.radius,
        e.origin + e.radius
    };
}


//-----------------------------------------------------------------------------
template <size_t S, typename T, template <size_t,typename> class K>
util::geom::aabb<S,T>
util::geom::bounds (K<S,T> k)
{
    return ::bounds (k);
}


//-----------------------------------------------------------------------------
template util::geom::aabb<2,float> util::geom::bounds (ellipse<2,float>);
template util::geom::aabb<3,float> util::geom::bounds (ellipse<3,float>);