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/*
* plane.cc -- ePiX::plane class and mathematical operators
*
* This file is part of ePiX, a preprocessor for creating high-quality
* line figures in LaTeX
*
* Version 1.0.15
* Last Change: October 09, 2006
*/
/*
* Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006
* Andrew D. Hwang <rot 13 nujnat at zngupf dot ubylpebff dot rqh>
* Department of Mathematics and Computer Science
* College of the Holy Cross
* Worcester, MA, 01610-2395, USA
*/
/*
* ePiX 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 2 of the License, or
* (at your option) any later version.
*
* ePiX is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
* License for more details.
*
* You should have received a copy of the GNU General Public License
* along with ePiX; if not, write to the Free Software Foundation, Inc.,
* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#include "globals.h"
#include "errors.h"
#include "circle.h"
#include "polyhedron.h"
#include "segment.h"
#include "sphere.h"
#include "path.h"
#include "curves.h"
#include "cropping.h"
#include "plane.h"
namespace ePiX {
plane::plane(const P& point, const P& normal)
: m_pt(point), m_perp(normal)
{
double temp(norm(normal));
if (temp < EPIX_EPSILON)
{
epix_warning("Degenerate plane normal, using (0,0,1)");
m_perp=E_3;
}
else
m_perp *= 1.0/temp;
}
plane::plane(const P& p1, const P& p2, const P& p3)
: m_pt(p1)
{
P perp((p3-p1)*(p2-p1));
double norm_perp(norm(perp));
if (norm_perp < EPIX_EPSILON)
throw constructor_error(COLLINEAR_PTS);
else
m_perp = (1/norm_perp)*perp;
}
P plane::normal() const
{
return m_perp;
}
plane& plane::reverse(void)
{
m_perp *= -1;
return *this;
}
plane& plane::operator += (const P& arg)
{
m_pt += arg;
return *this;
}
double plane::height(const P& arg) const
{
return (arg-m_pt)|m_perp;
}
bool plane::contains(const P& arg) const
{
return (fabs(height(arg)) < EPIX_EPSILON);
}
bool plane::separates(const P& arg1, const P& arg2) const
{
return (height(arg1)*height(arg2) <= 0 );
}
bool plane::parallel_to (const plane& arg) const
{
return (norm(m_perp*arg.m_perp)<EPIX_EPSILON);
}
bool plane::operator== (const plane& arg) const
{
// normals parallel and arg.m_pt lies in *this
return ( parallel_to(arg) && ((m_pt - arg.m_pt)|m_perp) < EPIX_EPSILON);
}
P operator* (const plane& knife, const segment& seg)
{
P tail(seg.end1()), head(seg.end2());
double ptail(knife.height(tail)), phead(knife.height(head));
return tail + (ptail/(ptail-phead))*(head-tail);
}
// draw Line of intersection between non-parallel planes
void plane::operator* (const plane& P1) const
{
P N3((P1.m_perp)*m_perp);
double temp(norm(N3));
if (temp < EPIX_EPSILON)
throw join_error(PARALLEL);
else // N3 non-zero, parallel to intersection
{
N3 *= 1/temp; // normalize
P perp((P1.m_perp)*N3); // unit vector in P1, perp to intersection
P point(P1.m_pt + (((m_pt-P1.m_pt)|m_perp)/(perp|m_perp))*perp);
Line(point, point+N3); // draw line through points
}
}
// intersection
circle plane::operator* (const sphere& S) const
{
double rad(S.radius());
// signed dist from S.ctr to *this
double height((m_pt - S.center())|m_perp);
if (rad < fabs(height))
throw join_error(SEPARATED);
else if (rad == fabs(height))
throw join_error(TANGENT);
else
return circle(S.center() + height*m_perp,
sqrt((rad - height)*(rad + height)),
m_perp);
}
void plane::draw() const
{
// clip_box vertices
P vert000(clip1_min(), clip2_min(), clip3_min());
P vert100(clip1_max(), clip2_min(), clip3_min());
P vert010(clip1_min(), clip2_max(), clip3_min());
P vert110(clip1_max(), clip2_max(), clip3_min());
P vert001(clip1_min(), clip2_min(), clip3_max());
P vert101(clip1_max(), clip2_min(), clip3_max());
P vert011(clip1_min(), clip2_max(), clip3_max());
P vert111(clip1_max(), clip2_max(), clip3_max());
segment edge00(vert000, vert001);
segment edge01(vert001, vert011);
segment edge02(vert011, vert010);
segment edge03(vert010, vert000);
segment edge04(vert000, vert100);
segment edge05(vert001, vert101);
segment edge06(vert011, vert111);
segment edge07(vert010, vert110);
segment edge08(vert100, vert101);
segment edge09(vert101, vert111);
segment edge10(vert111, vert110);
segment edge11(vert110, vert100);
// and edges
one_skel walls(12, &edge00, &edge01, &edge02, &edge03, &edge04, &edge05,
&edge06, &edge07, &edge08, &edge09, &edge10, &edge11);
walls.section(*this);
} // end of plane::draw()
} /* end of namespace */
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