mirror of
https://github.com/cosinekitty/astronomy.git
synced 2025-12-30 19:21:23 -05:00
8ef54a58cf
Model Jupiter's moons using the Sphere class, rather than the Spheroid class. Sphere is more efficient to calculate.
88 lines
3.4 KiB
C++
88 lines
3.4 KiB
C++
/*
|
|
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);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|