/*
    sphere.cpp

    Copyright (C) 2013 by Don Cross  -  http://cosinekitty.com/raytrace

    This software is provided 'as-is', without any express or implied
    warranty. In no event will the author be held liable for any damages
    arising from the use of this software.

    Permission is granted to anyone to use this software for any purpose,
    including commercial applications, and to alter it and redistribute it
    freely, subject to the following restrictions:

    1. The origin of this software must not be misrepresented; you must not
       claim that you wrote the original software. If you use this software
       in a product, an acknowledgment in the product documentation would be
       appreciated but is not required.

    2. Altered source versions must be plainly marked as such, and must not be
       misrepresented as being the original software.

    3. This notice may not be removed or altered from any source
       distribution.

    -------------------------------------------------------------------------
    Implements class Sphere, a solid sphere with constant radius 
    whose center may be moved to any point in space.
*/

#include "imager.h"

namespace Imager
{
    void Sphere::AppendAllIntersections(
        const Vector& vantage, 
        const Vector& direction, 
        IntersectionList& intersectionList) const
    {
        // Calculate the coefficients of the quadratic equation 
        //     au^2 + bu + c = 0.
        // Solving this equation gives us the value of u 
        // for any intersection points.
        const Vector displacement = vantage - Center();
        const double a = direction.MagnitudeSquared();
        const double b = 2.0 * DotProduct(direction, displacement);
        const double c = displacement.MagnitudeSquared() - radius*radius;

        // Calculate the radicand of the quadratic equation solution formula.
        // The radicand must be non-negative for there to be real solutions.
        const double radicand = b*b - 4.0*a*c;
        if (radicand >= 0.0)
        {
            // There are two intersection solutions, one involving 
            // +sqrt(radicand), the other -sqrt(radicand).
            // Check both because there are weird special cases, 
            // like the camera being inside the sphere,
            // or the sphere being behind the camera (invisible).
            const double root = sqrt(radicand);
            const double denom = 2.0 * a;
            const double u[2] = {
                (-b + root) / denom,
                (-b - root) / denom
            };

            for (int i=0; i < 2; ++i)
            {
                if (u[i] > EPSILON)
                {
                    Intersection intersection;
                    const Vector vantageToSurface = u[i] * direction;
                    intersection.point = vantage + vantageToSurface;

                    // The normal vector to the surface of 
                    // a sphere is outward from the center.
                    intersection.surfaceNormal = 
                        (intersection.point - Center()).UnitVector();

                    intersection.distanceSquared = 
                        vantageToSurface.MagnitudeSquared();

                    intersection.solid = this;
                    intersectionList.push_back(intersection);
                }
            }
        }
    }
}