193 lines
6.1 KiB
C++
193 lines
6.1 KiB
C++
// include/Line.hh
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// This file is part of libpbe; see http://svn.chezphil.org/libpbe/
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// (C) 2007 Philip Endecott
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// This program is free software; you can redistribute it and/or modify
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// it under the terms of the GNU General Public License as published by
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// the Free Software Foundation; either version 2 of the License, or
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// any later version.
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//
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// This program is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU General Public License
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// along with this program; if not, write to the Free Software
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// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
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#ifndef libpbe_Line_hh
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#define libpbe_Line_hh
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#include "Point.hh"
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#include "Vector.hh"
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#include "Box.hh"
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namespace pbe {
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template <typename COORD_T>
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struct Line {
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typedef COORD_T coord_t;
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typedef Point<coord_t> point_t;
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point_t a;
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point_t b;
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Line() {}
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Line(const Line& other):
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a(other.a), b(other.b)
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{}
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Line(point_t a_, point_t b_):
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a(a_), b(b_)
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{}
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bool operator==(const Line& other) const {
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return (a==other.a && b==other.b);
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}
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bool operator!=(const Line& other) const {
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return ! operator==(other);
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}
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};
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template <typename COORD_T>
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bool line_crosses_line(Line<COORD_T> u, Line<COORD_T> v, Point<COORD_T>& cross)
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{
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// Do lines u and v cross? If so, find the point where they cross.
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// Precondition: the lines must not be points.
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//
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// Method:
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// U = u.a + alpha(u.b-u.a)
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// V = v.a + beta(v.b-v.a)
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// Solve for U=V
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// If 0<=alpha<=1 und 0<=beta<=1 then the lines cross.
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//
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// u.x = u.a.x + alpha(u.b.x-u.a.x)
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// u.y = u.a.y + alpha(u.b.y-u.a.y)
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// v.x = v.a.x + beta(v.b.x-v.a.x)
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// v.y = v.a.y + beta(v.b.y-v.a.y)
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//
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// u.a.x + alpha(u.b.x-u.a.x) = v.a.x + beta(v.b.x-v.a.x)
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// u.a.y + alpha(u.b.y-u.a.y) = v.a.y + beta(v.b.y-v.a.y)
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//
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// alpha = ( v.a.x + beta(v.b.x-v.a.x) - u.a.x ) / (u.b.x-u.a.x) provided u.b.x!=u.a.x
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// alpha = ( v.a.y + beta(v.b.y-v.a.y) - u.a.y ) / (u.b.y-u.a.y) provided u.b.y!=u.a.y
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// ( v.a.x + beta(v.b.x-v.a.x) - u.a.x ) / (u.b.x-u.a.x) = ( v.a.y + beta(v.b.y-v.a.y) - u.a.y ) / (u.b.y-u.a.y)
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// ( v.a.x + beta(v.b.x-v.a.x) - u.a.x ) (u.b.y-u.a.y) = ( v.a.y + beta(v.b.y-v.a.y) - u.a.y ) (u.b.x-u.a.x)
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// beta.(v.b.x-v.a.x).(u.b.y-u.a.y) + (v.a.x-u.a.x).(u.b.y-u.a.y) = beta.(v.b.y-v.a.y).(u.b.x-u.a.x) + (v.a.y-u.a.y).(u.b.x-u.a.x)
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// beta.(v.b.x-v.a.x).(u.b.y-u.a.y) - beta.(v.b.y-v.a.y).(u.b.x-u.a.x) = (v.a.y-u.a.y).(u.b.x-u.a.x) - (v.a.x-u.a.x).(u.b.y-u.a.y)
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// beta = ( (v.a.y-u.a.y).(u.b.x-u.a.x) - (v.a.x-u.a.x).(u.b.y-u.a.y) ) / ( (v.b.x-v.a.x).(u.b.y-u.a.y) - (v.b.y-v.a.y).(u.b.x-u.a.x) )
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//
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// beta = ( u.a.x + alpha(u.b.x-u.a.x) - v.a.x ) / (v.b.x-v.a.x)
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// beta = ( u.a.y + alpha(u.b.y-u.a.y) - v.a.y ) / (v.b.y-v.a.y)
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// ( u.a.x + alpha(u.b.x-u.a.x) - v.a.x ) / (v.b.x-v.a.x) = ( u.a.y + alpha(u.b.y-u.a.y) - v.a.y ) / (v.b.y-v.a.y)
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// ( u.a.x + alpha(u.b.x-u.a.x) - v.a.x ) (v.b.y-v.a.y) = ( u.a.y + alpha(u.b.y-u.a.y) - v.a.y ) (v.b.x-v.a.x)
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// alpha.(u.b.x-u.a.x).(v.b.y-v.a.y) + (u.a.x-v.a.x).(v.b.y-v.a.y) = alpha.(u.b.y-u.a.y).(v.b.x-v.a.x) + (u.a.y-v.a.y).(v.b.x-v.a.x)
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// alpha.(u.b.x-u.a.x).(v.b.y-v.a.y) - alpha.(u.b.y-u.a.y).(v.b.x-v.a.x) = (u.a.y-v.a.y).(v.b.x-v.a.x) - (u.a.x-v.a.x).(v.b.y-v.a.y)
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// alpha = ( (u.a.y-v.a.y).(v.b.x-v.a.x) - (u.a.x-v.a.x).(v.b.y-v.a.y) ) / ( (u.b.x-u.a.x).(v.b.y-v.a.y) - (u.b.y-u.a.y).(v.b.x-v.a.x) )
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//
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// Note that the denominators of the expressions for alpha and beta are almost the
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// same, differing only in sign.
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// If this expression is zero it indicates that that lines do not cross because they
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// are parallel, or that they are co-linear.
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double alpha_denom = (u.b.x-u.a.x)*(v.b.y-v.a.y) - (u.b.y-u.a.y)*(v.b.x-v.a.x);
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if (alpha_denom==0) {
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// In the case of co-linear lines, do we consider them to cross if they overlap?
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// It's simplest to say "no", and always return false here.
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return false;
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} else {
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double alpha_num = (u.a.y-v.a.y)*(v.b.x-v.a.x) - (u.a.x-v.a.x)*(v.b.y-v.a.y);
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double alpha = alpha_num / alpha_denom;
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if (alpha<0 || alpha>1) {
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return false;
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}
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double beta_denom = -alpha_denom;
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double beta_num = (v.a.y-u.a.y)*(u.b.x-u.a.x) - (v.a.x-u.a.x)*(u.b.y-u.a.y);
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double beta = beta_num / beta_denom;
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if (beta<0 || beta>1) {
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return false;
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}
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Vector<COORD_T> uvec = u.b-u.a;
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cross = u.a + uvec * alpha;
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return true;
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}
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}
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template <typename COORD_T>
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bool line_crosses_box(Box<COORD_T> b, Line<COORD_T>& l)
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{
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// Does box b contain any part of line l?
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// If line l crosses the boundary of the box, it is modified in place to
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// clip at the boundary.
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if (b.contains(l.a) && b.contains(l.b)) {
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// Both ends inside the box - easy.
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return true;
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}
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if ( (l.a.x < b.x0 && l.b.x < b.x0)
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|| (l.a.x > b.x1 && l.b.x > b.x1)
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|| (l.a.y < b.y0 && l.b.y < b.y0)
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|| (l.a.y > b.y1 && l.b.y > b.y1) ) {
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// Line can't cross the box - easy.
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return false;
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}
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// There's a chance that the line crosses the box, but at least one
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// end is outside it and will need to be clipped.
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Point<COORD_T> cross;
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bool crosses_left = line_crosses_line(l,Line<COORD_T>(b.x0y0(),b.x0y1()),cross);
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if (crosses_left) {
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if (l.a.x<=b.x0) {
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l.a = cross;
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} else {
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l.b = cross;
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}
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}
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bool crosses_top = line_crosses_line(l,Line<COORD_T>(b.x0y1(),b.x1y1()),cross);
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if (crosses_top) {
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if (l.a.y>=b.y1) {
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l.a = cross;
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} else {
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l.b = cross;
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}
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}
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bool crosses_right = line_crosses_line(l,Line<COORD_T>(b.x1y1(),b.x1y0()),cross);
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if (crosses_right) {
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if (l.a.x>=b.x1) {
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l.a = cross;
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} else {
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l.b = cross;
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}
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}
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bool crosses_bottom = line_crosses_line(l,Line<COORD_T>(b.x1y0(),b.x0y0()),cross);
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if (crosses_bottom) {
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if (l.a.y<=b.y0) {
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l.a = cross;
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} else {
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l.b = cross;
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}
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}
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return crosses_left || crosses_top || crosses_right || crosses_bottom;
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}
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};
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#endif
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