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cylinder.cc
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cylinder.cc
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// cylinder.cc -- Cylindrical surface
//
// Copyright (C) 2007-2012 Miles Bader <miles@gnu.org>
//
// This source code is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 3, or (at
// your option) any later version. See the file COPYING for more details.
//
// Written by Miles Bader <miles@gnu.org>
//
#include "quadratic-roots.h"
#include "intersect.h"
#include "cylinder.h"
using namespace snogray;
// Return a transformation that will transform a canonical cylinder to a
// cylinder with the given base/axis/radius.
//
Xform
Cylinder::xform (const Pos &base, const Vec &axis, float radius)
{
Vec az = axis.unit ();
Vec ax = az.perpendicular ();
Vec zy = cross (ax, az);
Xform xf;
xf.translate (Vec (0,0,1));
xf.scale (radius,radius,axis.length()/2);
xf.to_basis (ax, zy, az);
xf.translate (Vec (base));
return xf;
}
// intersection
// Return true if a cylinder, with radius 1 and height 2, centered at
// the origin and having an axis on the z-axis, is intersected by an
// infinite ray from RAY_ORIGIN in direction RAY_DIR.
//
// When an intersection occurs, the "parametric distance" of the
// intersection is returned in the out-parameter T: T is the number
// of multiples of RAY_DIR required to reach the intersection point
// from RAY_ORIGIN. Only intersections with a parameter distance of
// MIN_T or greater are considered.
//
static bool
cylinder_intersects (const Pos &ray_origin, const Vec &ray_dir,
dist_t min_t, dist_t &t)
{
// Cylinder parameters.
//
const dist_t radius = 1;
const coord_t min_z = -1, max_z = 1;
// Coefficients of the quadratic equation we'll solve.
//
dist_t a = ray_dir.x * ray_dir.x + ray_dir.y * ray_dir.y;
dist_t b = 2 * (ray_dir.x * ray_origin.x + ray_dir.y * ray_origin.y);
dist_t c = ray_origin.x * ray_origin.x + ray_origin.y * ray_origin.y - radius;
// Compute intersection points.
//
dist_t roots[2];
unsigned nroots = quadratic_roots (a, b, c, roots);
for (unsigned i = 0; i < nroots; i++)
{
t = roots[i];
if (t > min_t)
{
coord_t z = ray_origin.z + t * ray_dir.z;
if (z >= min_z && z <= max_z)
return true;
}
}
return false;
}
// Return true if a cylinder, with radius 1 and height 2, centered at
// the origin and having an axis on the z-axis, is intersected by RAY.
//
// When an intersection occurs, the "parametric distance" of the
// intersection is returned in the out-parameter T: T is the number
// of multiples of RAY's dir field required to reach the intersection
// point from RAY's origin.
//
static bool
cylinder_intersects (Ray &ray, dist_t &t)
{
return cylinder_intersects (ray.origin, ray.dir, ray.t0, t) && t < ray.t1;
}
// If this surface intersects RAY, change RAY's maximum bound (Ray::t1)
// to reflect the point of intersection, and return a Surface::IsecInfo
// object describing the intersection (which should be allocated using
// placement-new with CONTEXT); otherwise return zero.
//
const Surface::IsecInfo *
Cylinder::intersect (Ray &ray, RenderContext &context) const
{
Ray oray = world_to_local (ray);
dist_t t;
if (cylinder_intersects (oray, t))
{
ray.t1 = t;
return new (context) IsecInfo (ray, *this, oray (t));
}
return 0;
}
// Create an Intersect object for this intersection.
//
Intersect
Cylinder::IsecInfo::make_intersect (const Media &media, RenderContext &context)
const
{
Pos point = ray.end ();
Vec onorm (isec_point.x, isec_point.y, 0);
Vec norm = cylinder.normal_to_world (onorm).unit ();
Vec t = cylinder.local_to_world (Vec (0, 0, 1)).unit ();
Vec s = cross (norm, t);
// Calculate partial derivatives of texture coordinates dTds and dTdt,
// where T is the texture coordinates (for bump mapping).
//
UV dTds (INV_PIf * 0.5f, 0), dTdt (0, 0.5f);
return Intersect (ray, media, context, *cylinder.material,
Frame (point, s, t, norm),
cylinder.tex_coords (isec_point), dTds, dTdt);
}
// Return the texture-coordinates of this intersection.
//
TexCoords
Cylinder::IsecInfo::tex_coords () const
{
return TexCoords (ray.end(), cylinder.tex_coords (isec_point));
}
// Return the normal of this intersection (in the world frame).
//
Vec
Cylinder::IsecInfo::normal () const
{
Vec onorm (isec_point.x, isec_point.y, 0);
return cylinder.normal_to_world (onorm).unit ();
}
// Return true if this surface intersects RAY.
//
bool
Cylinder::intersects (const Ray &ray, RenderContext &) const
{
Ray oray = world_to_local (ray);
dist_t t;
return cylinder_intersects (oray, t);
}
// Return true if this surface completely occludes RAY. If it does
// not completely occlude RAY, then return false, and multiply
// TOTAL_TRANSMITTANCE by the transmittance of the surface in medium
// MEDIUM.
//
// Note that this method does not try to handle non-trivial forms of
// transparency/translucency (for instance, a "glass" material is
// probably considered opaque because it changes light direction as
// well as transmitting it).
//
bool
Cylinder::occludes (const Ray &ray, const Medium &medium,
Color &total_transmittance, RenderContext &)
const
{
Ray oray = world_to_local (ray);
dist_t t;
if (cylinder_intersects (oray, t))
{
// avoid calculating texture coords if possible
if (material->fully_occluding ())
return true;
IsecInfo isec_info (Ray (ray, t), *this, oray (t));
return material->occludes (isec_info, medium, total_transmittance);
}
return false;
}
// Return a sampler for this surface, or zero if the surface doesn't
// support sampling. The caller is responsible for destroying
// returned samplers.
//
Surface::Sampler *
Cylinder::make_sampler () const
{
return new Sampler (*this);
}
// Cylinder::Sampler
// A functor for calling Surface::Sampler::sample_with_approx_pdf.
// Returns a sample position in world-space based on an input
// parameter.
//
struct PosSampler
{
PosSampler (const Cylinder &_cylinder) : cylinder (_cylinder) {}
Pos operator() (const UV ¶m) const
{
float theta = param.u * 2 * PIf;
Pos samp (cos (theta), sin (theta), 2 * param.v - 1);
return cylinder.local_to_world (samp);
}
const Cylinder &cylinder;
};
// Return a sample of this surface.
//
Surface::Sampler::AreaSample
Cylinder::Sampler::sample (const UV ¶m) const
{
float theta = param.u * 2 * PIf;
Vec radius (cos (theta), sin (theta), 0);
Vec norm = cylinder.normal_to_world (radius).unit();
return sample_with_approx_area_pdf (PosSampler (cylinder), param, norm);
}
// Return a sample of this surface from VIEWPOINT, based on the
// parameter PARAM.
//
Surface::Sampler::AngularSample
Cylinder::Sampler::sample_from_viewpoint (const Pos &viewpoint, const UV ¶m)
const
{
// Sample the entire cylinder.
//
AreaSample area_sample = sample (param);
// If the normal points away from VIEWPOINT, mirror the sample about
// the cylinder's axis so that it doesn't.
//
if (cos_angle (area_sample.normal, area_sample.pos - viewpoint) > 0)
{
Pos opos = cylinder.world_to_local (area_sample.pos);
opos.x = -opos.x;
opos.y = -opos.y;
area_sample.pos = cylinder.local_to_world (opos);
area_sample.normal = -area_sample.normal;
}
// Because we mirror samples to always point towards VIEWPOINT, double
// the PDF, as the same number of samples is concentrated into half
// the space (the hemisphere facing VIEWPOINT).
//
area_sample.pdf *= 2;
return AngularSample (area_sample, viewpoint);
}
// If a ray from VIEWPOINT in direction DIR intersects this
// surface, return an AngularSample as if the
// Surface::Sampler::sample_from_viewpoint method had returned a
// sample at the intersection position. Otherwise, return an
// AngularSample with a PDF of zero.
//
Surface::Sampler::AngularSample
Cylinder::Sampler::eval_from_viewpoint (const Pos &viewpoint, const Vec &dir)
const
{
// Convert parameters to object-space.
//
Pos oviewpoint = cylinder.world_to_local (viewpoint);
Vec odir = cylinder.world_to_local (dir); // note, not normalized
dist_t t;
if (cylinder_intersects (oviewpoint, odir, 0, t))
{
// Calculate an appropriate sampling parameter and call
// Surface::Sampler::sample_from_viewpoint to turn that into a
// sample.
Pos pos = oviewpoint + t * odir;
float u = float (atan2 (pos.y, pos.x)) * INV_PIf * 0.5f;
if (u < 0)
u += 1;
float v = float (pos.z) * 0.5f + 0.5f;
UV param (clamp01 (u), clamp01 (v));
return sample_from_viewpoint (viewpoint, param);
}
return AngularSample ();
}
// arch-tag: 1a4758de-f640-4ea6-abf2-2626070847e5