/* === S Y N F I G ========================================================= */
/*! \file curve_helper.cpp
** \brief Curve Helper File
**
** $Id$
**
** \legal
** Copyright (c) 2002-2005 Robert B. Quattlebaum Jr., Adrian Bentley
**
** This package 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.
**
** This package 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.
** \endlegal
*/
/* ========================================================================= */
/* === H E A D E R S ======================================================= */
#ifdef USING_PCH
# include "pch.h"
#else
#ifdef HAVE_CONFIG_H
# include <config.h>
#endif
#include "curve_helper.h"
#include <algorithm>
#include <vector>
#endif
/* === U S I N G =========================================================== */
using namespace std;
using namespace etl;
using namespace synfig;
/* === M A C R O S ========================================================= */
#define ERR 1e-11
const Real ERROR = 1e-11;
/* === G L O B A L S ======================================================= */
/* === P R O C E D U R E S ================================================= */
/* === M E T H O D S ======================================================= */
/* === E N T R Y P O I N T ================================================= */
Real synfig::find_closest(const etl::bezier<Point> &curve, const Point &point,
float step, Real *dout, float *tout)
{
#if 0
float time(curve.find_closest(point,4));
Real dist((curve(time)-point).mag());
if(dout) *dout=dist;
if(tout) *tout=time;
return time;
#else
Real d,closest = 1.0e50;
float t,time,closestt = -1;
Vector p0,p1,end;
if(dout && *dout > 0)
closest = *dout;
p0 = curve[0];
end = curve[3];
for(t = step; t < 1; t+=step, p0=p1)
{
p1 = curve(t);
d = line_point_distsq(p0,p1,point,time);
if(d<closest)
{
closest=d;
closestt = t-step + time*step;//t+(time-1)*step; //time between [t-step,t]
}
}
d = line_point_distsq(p0,end,point,time);
if(d<closest)
{
closest = d;
closestt= t-step + time*(1-t+step); //time between [t-step,1.0]
}
//set the time value if we found a closer point
if(closestt >=0)
{
if(tout) *tout = closestt;
}
return closest;
#endif
}
// Line and BezHull Definitions
void BezHull::Bound(const etl::bezier<Point> &b)
{
#if 1
//with a starting vertex, find the only vertex that has all other vertices on its right
int i,j;
int first,cur,last;
float d,ds;
Vector n,vi;
Vector::value_type deqn;
//get left most vertex
d = b[0][0];
first = 0;
for(i = 1; i < 4; ++i)
{
if(b[i][0] < d)
{
d = b[i][0];
first = i;
}
}
cur = last = first;
size = 0;
//find the farthest point with all points on right
ds = 0;
do //should reassign cur so it won't break on first step
{
for(i = 0; i < 4; ++i)
{
if(i == cur || i == last) continue;
//rotate vector to right to make normal
vi = -(b[i] - b[cur]).perp();
d = vi.mag_squared();
//we want only the farthest (solves the case with many points on a line)
if(d > ds)
{
ds = d;
deqn = n*b[cur];
for(j = 0; j < 4; ++j)
{
d = n*b[i] - deqn;
if(d < 0) break; //we're on left, nope!
}
//everyone is on right... yay! :)
if(d >= 0)
{
//advance point and add last one into hull
p[size++] = p[last];
last = cur;
cur = i;
}
}
}
}while(cur != first);
#else
//will work but does not keep winding order
//convex hull alg.
//build set of line segs which have no points on other side...
//start with initial normal segments
//start with single triangle
p[0] = b[0];
p[1] = b[1];
p[2] = b[2];
p[3] = b[3];
//initial reject (if point is inside triangle don't care)
{
Vector v1,v2,vp;
v1 = p[1]-p[0];
v2 = p[2]-p[0];
vp = p[3]-p[0];
float s = (vp*v1) / (v1*v1),
t = (vp*v2) / (v2*v2);
//if we're inside the triangle we don't this sissy point
if( s >= 0 && s <= 1 && t >= 0 && t <= 1 )
{
size = 3;
return;
}
}
//expand triangle based on info...
bool line;
int index,i,j;
float ds,d;
//distance from point to vertices
line = false;
index = 0;
ds = (p[0]-b[3]).mag_squared();
for(i = 1; i < 3; ++i)
{
d = (p[3]-p[i]).mag_squared();
if(d < ds)
{
index = i;
ds = d;
}
}
//distance to line
float t;
j = 2;
for(i = 0; i < 3; j = i++)
{
d = line_point_distsq(p[j],p[i],b[4],t);
if(d < ds)
{
index = j;
ds = d;
line = true;
}
}
//We don't need no stinkin extra vertex, just replace
if(!line)
{
p[index] = p[3];
size = 3;
}else
{
//must expand volume to work with point...
// after the index then
/* Pattern:
0 - push 1,2 -> 2,3
1 - push 2 -> 3
2 - none
*/
for(i = 3; i > index+1; --i)
{
p[i] = p[i-1];
}
p[index] = b[3]; //recopy b3
size = 4;
}
#endif
}
//Line Intersection
int
synfig::intersect(const Point &p1, const Vector &v1, float &t1,
const Point &p2, const Vector &v2, float &t2)
{
/* Parametric intersection:
l1 = p1 + tv1, l2 = p2 + sv2
0 = p1+tv1-(p2+sv2)
group parameters: sv2 - tv1 = p1-p2
^ = transpose
invert matrix (on condition det != 0):
A[t s]^ = [p1-p2]^
A = [-v1 v2]
det = v1y.v2x - v1x.v2y
if non 0 then A^-1 = invdet * | v2y -v2x |
| v1y -v1x |
[t s]^ = A^-1 [p1-p2]^
*/
Vector::value_type det = v1[1]*v2[0] - v1[0]*v2[1];
//is determinant valid?
if(det > ERR || det < -ERR)
{
Vector p_p = p1-p2;
det = 1/det;
t1 = det*(v2[1]*p_p[0] - v2[0]*p_p[1]);
t2 = det*(v1[1]*p_p[0] - v1[0]*p_p[1]);
return 1;
}
return 0;
}
//Returns the true or false intersection of a rectangle and a line
int intersect(const Rect &r, const Point &p, const Vector &v)
{
float t[4] = {0};
/*get horizontal intersections and then vertical intersections
and intersect them
Vertical planes - n = (1,0)
Horizontal planes - n = (0,1)
so if we are solving for ray with implicit line
*/
//solve horizontal
if(v[0] > ERR || v[0] < -ERR)
{
//solve for t0, t1
t[0] = (r.minx - p[0])/v[0];
t[1] = (r.maxx - p[0])/v[0];
}else
{
return (int)(p[1] >= r.miny && p[1] <= r.maxy);
}
//solve vertical
if(v[1] > ERR || v[1] < -ERR)
{
//solve for t0, t1
t[2] = (r.miny - p[1])/v[1];
t[3] = (r.maxy - p[1])/v[1];
}else
{
return (int)(p[0] >= r.minx && p[0] <= r.maxx);
}
return (int)(t[0] <= t[3] && t[1] >= t[2]);
}
int synfig::intersect(const Rect &r, const Point &p)
{
return (p[1] < r.maxy && p[1] > r.miny) && p[0] > r.minx;
}
//returns 0 or 1 for true or false number of intersections of a ray with a bezier convex hull
int intersect(const BezHull &bh, const Point &p, const Vector &v)
{
float mint = 0, maxt = 1e20;
//polygon clipping
Vector n;
Vector::value_type nv;
Point last = bh.p[3];
for(int i = 0; i < bh.size; ++i)
{
n = (bh.p[i] - last).perp(); //rotate 90 deg.
/*
since rotated left
if n.v < 0 - going in
> 0 - going out
= 0 - parallel
*/
nv = n*v;
//going OUT
if(nv > ERR)
{
maxt = min(maxt,(float)((n*(p-last))/nv));
}else
if( nv < -ERR) //going IN
{
mint = max(mint,(float)((n*(p-last))/nv));
}else
{
if( n*(p-last) > 0 ) //outside entirely
{
return 0;
}
}
last = bh.p[i];
}
return 0;
}
int Clip(const Rect &r, const Point &p1, const Point &p2, Point *op1, Point *op2)
{
float t1=0,t2=1;
Vector v=p2-p1;
/*get horizontal intersections and then vertical intersections
and intersect them
Vertical planes - n = (1,0)
Horizontal planes - n = (0,1)
so if we are solving for ray with implicit line
*/
//solve horizontal
if(v[0] > ERR || v[0] < -ERR)
{
//solve for t0, t1
float tt1 = (r.minx - p1[0])/v[0],
tt2 = (r.maxx - p1[0])/v[0];
//line in positive direction (normal comparisons
if(tt1 < tt2)
{
t1 = max(t1,tt1);
t2 = min(t2,tt2);
}else
{
t1 = max(t1,tt2);
t2 = min(t2,tt1);
}
}else
{
if(p1[1] < r.miny || p1[1] > r.maxy)
return 0;
}
//solve vertical
if(v[1] > ERR || v[1] < -ERR)
{
//solve for t0, t1
float tt1 = (r.miny - p1[1])/v[1],
tt2 = (r.maxy - p1[1])/v[1];
//line in positive direction (normal comparisons
if(tt1 < tt2)
{
t1 = max(t1,tt1);
t2 = min(t2,tt2);
}else
{
t1 = max(t1,tt2);
t2 = min(t2,tt1);
}
}else
{
if(p1[0] < r.minx || p1[0] > r.maxx)
return 0;
}
if(op1) *op1 = p1 + v*t1;
if(op2) *op2 = p1 + v*t2;
return 1;
}
static void clean_bez(const bezier<Point> &b, bezier<Point> &out)
{
bezier<Point> temp;
temp = b;
temp.set_r(0);
temp.set_s(1);
if(b.get_r() != 0)
temp.subdivide(0,&temp,b.get_r());
if(b.get_s() != 1)
temp.subdivide(&temp,0,b.get_s());
out = temp;
}
// CIntersect Definitions
CIntersect::CIntersect()
: max_depth(10) //depth of 10 means timevalue parameters will have an approx. error bound of 2^-10
{
}
struct CIntersect::SCurve
{
bezier<Point> b; //the current subdivided curve
float rt,st;
//float mid, //the midpoint time value on this section of the subdivided curve
// scale; //the current delta in time values this curve would be on original curve
float mag; //approximate sum of magnitudes of each edge of control polygon
Rect aabb; //Axis Aligned Bounding Box for quick (albeit less accurate) collision
SCurve(): b(), rt(), st(), mag() {}
SCurve(const bezier<Point> &c,float rin, float sin)
:b(c),rt(rin),st(sin),mag(1)
{
Bound(aabb,b);
}
void Split(SCurve &l, SCurve &r) const
{
b.subdivide(&l.b,&r.b);
l.rt = rt;
r.st = st;
l.st = r.rt = (rt+st)/2;
Bound(l.aabb,l.b);
Bound(r.aabb,r.b);
}
};
//Curve to the left of point test
static int recurse_intersect(const CIntersect::SCurve &b, const Point &p1, int depthleft = 10)
{
//reject when the line does not intersect the bounding box
if(!intersect(b.aabb,p1)) return 0;
//accept curves (and perform super detailed check for intersections)
//if the values are below tolerance
//NOTE FOR BETTERING OF ALGORITHM: SHOULD ALSO/IN-PLACE-OF CHECK MAGNITUDE OF EDGES (or approximate)
if(depthleft <= 0)
{
//NOTE FOR IMPROVEMENT: Polish roots based on original curve
// (may be too expensive to be effective)
int turn = 0;
for(int i = 0; i < 3; ++i)
{
//intersect line segments
//solve for the y_value
Vector v = b.b[i+1] - b.b[i];
if(v[1] > ERROR || v[1] < -ERROR)
{
Real xi = (p1[1] - b.b[i][1])/v[1];
//and add in the turn (up or down) if it's valid
if(xi < p1[0]) turn += (v[1] > 0) ? 1 : -1;
}
}
return turn;
}
//subdivide the curve and continue
CIntersect::SCurve l1,r1;
b.Split(l1,r1); //subdivide left
//test each subdivision against the point
return recurse_intersect(l1,p1) + recurse_intersect(r1,p1);
}
int intersect(const bezier<Point> &b, const Point &p)
{
CIntersect::SCurve sb;
clean_bez(b,sb.b);
sb.rt = 0; sb.st = 1;
sb.mag = 1; Bound(sb.aabb,sb.b);
return recurse_intersect(sb,p);
}
//Curve curve intersection
void CIntersect::recurse_intersect(const SCurve &left, const SCurve &right, int depth)
{
//reject curves that do not overlap with bounding boxes
if(!intersect(left.aabb,right.aabb)) return;
//accept curves (and perform super detailed check for intersections)
//if the values are below tolerance
//NOTE FOR BETTERING OF ALGORITHM: SHOULD ALSO/IN-PLACE-OF CHECK MAGNITUDE OF EDGES (or approximate)
if(depth >= max_depth)
{
//NOTE FOR IMPROVEMENT: Polish roots based on original curve with the Jacobian
// (may be too expensive to be effective)
//perform root approximation
//collide line segments
float t,s;
for(int i = 0; i < 3; ++i)
{
for(int j = 0; j < 3; ++j)
{
//intersect line segments
if(intersect_line_segments(left.b[i],left.b[i+1],t,right.b[j],right.b[j+1],s))
{
//We got one Jimmy
times.push_back(intersect_set::value_type(t,s));
}
}
}
return;
}
//NOTE FOR IMPROVEMENT: only subdivide one curve and choose the one that has
// the highest approximated length
//fast approximation to curve length may be hard (accurate would
// involve 3 square roots), could sum the squares which would be
// quick but inaccurate
SCurve l1,r1,l2,r2;
left.Split(l1,r1); //subdivide left
right.Split(l2,r2); //subdivide right
//Test each candidate against each other
recurse_intersect(l1,l2);
recurse_intersect(l1,r2);
recurse_intersect(r1,l2);
recurse_intersect(r1,r2);
}
bool CIntersect::operator()(const etl::bezier<Point> &c1, const etl::bezier<Point> &c2)
{
times.clear();
//need to subdivide and check recursive bounding regions against each other
//so track a list of dirty curves and compare compare compare
//temporary curves for subdivision
CIntersect intersector;
CIntersect::SCurve left,right;
//Make sure the parameters are normalized (so we don't compare unwanted parts of the curves,
// and don't miss any for that matter)
//left curve
//Compile information about curve
clean_bez(c1,left.b);
left.rt = 0; left.st = 1;
Bound(left.aabb, left.b);
//right curve
//Compile information about right curve
clean_bez(c2,right.b);
right.rt = 0; right.st = 1;
Bound(right.aabb, right.b);
//Perform Curve intersection
intersector.recurse_intersect(left,right);
//Get information about roots (yay! :P)
return times.size() != 0;
}
//point inside curve - return +/- hit up or down edge
int intersect_scurve(const CIntersect::SCurve &b, const Point &p)
{
//initial reject/approve etc.
/*
*-----------*---------
| |
| |
| |
| 1 | 2
| |
| |
| |
| |
*-----------*--------
1,2 are only regions not rejected
*/
if(p[0] < b.aabb.minx || p[1] < b.aabb.miny || p[1] > b.aabb.maxy)
return 0;
//approve only if to the right of rect around 2 end points
{
Rect r;
r.set_point(b.b[0][0],b.b[0][1]);
r.expand(b.b[3][0],b.b[3][1]);
if(p[0] >= r.maxx && p[1] <= r.maxy && p[1] >= r.miny)
{
float df = b.b[3][1] - b.b[0][1];
return df >= 0 ? 1 : -1;
}
}
//subdivide and check again!
CIntersect::SCurve l,r;
b.Split(l,r);
return intersect_scurve(l,p) + intersect_scurve(r,p);
}
int synfig::intersect(const bezier<Point> &b, const Point &p)
{
CIntersect::SCurve c(b,0,1);
return intersect_scurve(c,p);
}