/*
polyspan.cpp
Polyspan
Copyright (c) 2002-2005 Robert B. Quattlebaum Jr., Adrian Bentley
Copyright (c) 2007, 2008 Chris Moore
Copyright (c) 2012-2013 Carlos López
......... ... 2015 Ivan Mahonin
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.
*/
#include <cassert>
#include "polyspan.h"
using namespace std;
Polyspan::Polyspan():
open_index(0),
cur_x(0.0),
cur_y(0.0),
close_x(0.0),
close_y(0.0),
flags(NotSorted)
{ }
void Polyspan::clear() {
covers.clear();
cur_x = cur_y = close_x = close_y = 0;
open_index = 0;
current.set(0, 0, 0, 0);
flags = NotSorted;
}
// add the current cell, but only if there is information to add
void Polyspan::addcurrent() {
if (current.cover || current.area) {
if (covers.size() == covers.capacity())
covers.reserve(covers.size() + 1024*1024);
covers.push_back(current);
}
}
// move to the next cell (cover values 0 initially), keeping the current if necessary
void Polyspan::move_pen(int x, int y) {
if (y != current.y || x != current.x) {
addcurrent();
current.set(x, y, 0, 0);
}
}
// close the primitives with a line (or rendering will not work as expected)
void Polyspan::close() {
if (flags & NotClosed) {
if (cur_x != close_x || cur_y != close_y) {
line_to(close_x, close_y);
addcurrent();
current.setcover(0,0);
}
flags &= ~NotClosed;
}
}
// Not recommended - destroys any separation of spans currently held
void Polyspan::merge_all() {
sort(covers.begin(), covers.end());
open_index = 0;
}
// will sort the marks if they are not sorted
void Polyspan::sort_marks() {
if (flags & NotSorted) {
// only sort the open index
addcurrent();
current.setcover(0, 0);
sort(covers.begin() + open_index, covers.end());
flags &= ~NotSorted;
}
}
// encapsulate the current sublist of marks (used for drawing)
void Polyspan::encapsulate_current() {
// sort the current list then reposition the open list section
sort_marks();
open_index = covers.size();
}
// move to start a new primitive list (enclose the last primitive if need be)
void Polyspan::move_to(Real x, Real y) {
close();
if (isnan(x)) x=0;
if (isnan(y)) y=0;
move_pen((int)floor(x), (int)floor(y));
close_y = cur_y = y;
close_x = cur_x = x;
}
// primitive_to functions
void Polyspan::line_to(Real x, Real y) {
Real n[4] = {0, 0, 0, 0};
bool afterx = false;
const Real xin(x), yin(y);
Real dx = x - cur_x;
Real dy = y - cur_y;
// CLIP IT!!!!
// outside y - ignore entirely
if ( (cur_y >= window.maxy && y >= window.maxy)
|| (cur_y < window.miny && y < window.miny) )
{
cur_x = x;
cur_y = y;
} else { // not degenerate - more complicated
if (dy > 0) { //be sure it's not tooooo small
// cur_y ... window.miny ... window.maxy ... y
// initial degenerate - initial clip
if (cur_y < window.miny) {
// new clipped start point (must also move pen)
n[2] = cur_x + (window.miny - cur_y)*dx/dy;
cur_x = n[2];
cur_y = window.miny;
move_pen((int)floor(cur_x), window.miny);
}
// generate data for the ending clipped info
if (y > window.maxy) {
// initial line to intersection (and degenerate)
n[2] = x + (window.maxy - y)*dx/dy;
//intersect coords
x = n[2];
y = window.maxy;
}
} else {
// initial degenerate - initial clip
if (cur_y > window.maxy) {
// new clipped start point (must also move pen)
n[2] = cur_x + (window.maxy - cur_y)*dx/dy;
cur_x = n[2];
cur_y = window.maxy;
move_pen((int)floor(cur_x), window.maxy);
}
// generate data for the ending clipped info
if (y < window.miny) {
// initial line to intersection (and degenerate)
n[2] = x + (window.miny - y)*dx/dy;
// intersect coords
x = n[2];
y = window.miny;
}
}
// all degenerate - but require bounded clipped values
if ( (cur_x >= window.maxx && x >= window.maxx)
|| (cur_x < window.minx && x < window.minx) )
{
//clip both vertices - but only needed in the x direction
cur_x = max(cur_x, (Real)window.minx);
cur_x = min(cur_x, (Real)window.maxx);
//clip the dest values - y is already clipped
x = max(x, (Real)window.minx);
x = min(x, (Real)window.maxx);
//must start at new point...
move_pen((int)floor(cur_x), (int)floor(cur_y));
draw_line(cur_x,cur_y,x,y);
cur_x = xin;
cur_y = yin;
} else {
// clip x
if (dx > 0) {
// initial degenerate - initial clip
if (cur_x < window.minx) {
// need to draw an initial segment from clippedx,cur_y to clippedx,intersecty
n[2] = cur_y + (window.minx - cur_x)*dy/dx;
move_pen(window.minx, (int)floor(cur_y));
draw_line(window.minx, cur_y, window.minx, n[2]);
cur_x = window.minx;
cur_y = n[2];
}
// generate data for the ending clipped info
if (x > window.maxx) {
// initial line to intersection (and degenerate)
n[2] = y + (window.maxx - x)*dy/dx;
n[0] = window.maxx;
n[1] = y;
// intersect coords
x = window.maxx;
y = n[2];
afterx = true;
}
} else {
// initial degenerate - initial clip
if (cur_x > window.maxx) {
// need to draw an initial segment from clippedx,cur_y to clippedx,intersecty
n[2] = cur_y + (window.maxx - cur_x)*dy/dx;
move_pen(window.maxx, (int)floor(cur_y));
draw_line(window.maxx, cur_y, window.maxx, n[2]);
cur_x = window.maxx;
cur_y = n[2];
}
// generate data for the ending clipped info
if (x < window.minx) {
//initial line to intersection (and degenerate)
n[2] = y + (window.minx - x)*dy/dx;
n[0] = window.minx;
n[1] = y;
//intersect coords
x = window.minx;
y = n[2];
afterx = true;
}
}
move_pen((int)floor(cur_x), (int)floor(cur_y));
// draw the relevant line (clipped)
draw_line(cur_x, cur_y, x, y);
if (afterx)
draw_line(x, y, n[0], n[1]);
cur_x = xin;
cur_y = yin;
}
}
flags |= NotClosed | NotSorted;
}
bool Polyspan::clip_conic(const Vector *p, const ContextRect &r) {
const Real minx = min(min(p[0][0], p[1][0]), p[2][0]);
const Real miny = min(min(p[0][1], p[1][1]), p[2][1]);
const Real maxx = max(max(p[0][0], p[1][0]), p[2][0]);
const Real maxy = max(max(p[0][1], p[1][1]), p[2][1]);
return (minx > r.maxx) ||
(maxx < r.minx) ||
(miny > r.maxy) ||
(maxy < r.miny);
}
Real Polyspan::max_edges_conic(const Vector *p) {
const Real x1 = p[1][0] - p[0][0];
const Real y1 = p[1][1] - p[0][1];
const Real x2 = p[2][0] - p[1][0];
const Real y2 = p[2][1] - p[1][1];
const Real d1 = x1*x1 + y1*y1;
const Real d2 = x2*x2 + y2*y2;
return max(d1,d2);
}
void Polyspan::subd_conic_stack(Vector *arc) {
/*
b0
* 0+1 a
b1 b * 1+2*1+2 a
* 1+2 b *
b2 *
*
0.1.2 -> 0.1 2 3.4
*/
Real a, b;
arc[4][0] = arc[2][0];
b = arc[1][0];
a = arc[1][0] = (arc[0][0] + b)/2;
b = arc[3][0] = (arc[4][0] + b)/2;
arc[2][0] = (a + b)/2;
arc[4][1] = arc[2][1];
b = arc[1][1];
a = arc[1][1] = (arc[0][1] + b)/2;
b = arc[3][1] = (arc[4][1] + b)/2;
arc[2][1] = (a + b)/2;
/* //USING SIMD
arc[4] = arc[2];
arc[3] = (arc[2] + arc[1])/2;
arc[1] = (arc[0] + arc[1])/2;
arc[2] = (arc[1] + arc[3])/2;
*/
}
void Polyspan::conic_to(Real x1, Real y1, Real x, Real y) {
Vector *current = arc;
int level = 0;
int num = 0;
bool onsecond = false;
arc[0] = Vector(x, y);
arc[1] = Vector(x1, y1);
arc[2] = Vector(cur_x, cur_y);
// just draw the line if it's outside
if (clip_conic(arc, window))
{
line_to(x,y);
return;
}
// Ok so it's not super degenerate, subdivide and draw (run through minimum subdivision levels first)
while(current >= arc) {
assert(num < MAX_SUBDIVISION_SIZE);
// if the curve is clipping then draw degenerate
if (clip_conic(current, window)) {
line_to(current[0][0],current[0][1]); //backwards so front is destination
current -= 2;
if (onsecond) level--;
onsecond = true;
num--;
continue;
} else
// if we are not at the level minimum
if (level < MIN_SUBDIVISION_DRAW_LEVELS) {
subd_conic_stack(current);
current += 2; // cursor on second curve
level ++;
num ++;
onsecond = false;
continue;
} else
// split it again, if it's too big
if (max_edges_conic(current) > 0.25) { // distance of .5 (cover no more than half the pixel)
subd_conic_stack(current);
current += 2; // cursor on second curve
level ++;
num ++;
onsecond = false;
} else { // NOT TOO BIG? RENDER!!!
// cur_x, cur_y = current[2], so we need to go 1,0
line_to(current[1][0], current[1][1]);
line_to(current[0][0], current[0][1]);
current -= 2;
if (onsecond) level--;
num--;
onsecond = true;
}
}
}
bool Polyspan::clip_cubic(const Vector *p, const ContextRect &r) {
return ((p[0][0] > r.maxx) && (p[1][0] > r.maxx) && (p[2][0] > r.maxx) && (p[3][0] > r.maxx)) ||
((p[0][0] < r.minx) && (p[1][0] < r.minx) && (p[2][0] < r.minx) && (p[3][0] < r.minx)) ||
((p[0][1] > r.maxy) && (p[1][1] > r.maxy) && (p[2][1] > r.maxy) && (p[3][1] > r.maxy)) ||
((p[0][1] < r.miny) && (p[1][1] < r.miny) && (p[2][1] < r.miny) && (p[3][1] < r.miny));
}
Real Polyspan::max_edges_cubic(const Vector *p) {
const Real x1 = p[1][0] - p[0][0];
const Real y1 = p[1][1] - p[0][1];
const Real x2 = p[2][0] - p[1][0];
const Real y2 = p[2][1] - p[1][1];
const Real x3 = p[3][0] - p[2][0];
const Real y3 = p[3][1] - p[2][1];
const Real d1 = x1*x1 + y1*y1;
const Real d2 = x2*x2 + y2*y2;
const Real d3 = x3*x3 + y3*y3;
return max(max(d1, d2), d3);
}
void Polyspan::subd_cubic_stack(Vector *arc) {
Real a, b, c;
/*
b0
* 0+1 a
b1 b * 1+2*1+2 a
* 1+2 b * 0+3*1+3*2+3
b2 c * 1+2*2+2 b *
* 2+3 c *
b3 *
*
0.1 2.3 -> 0.1 2 3 4 5.6
*/
arc[6][0] = arc[3][0];
b = arc[1][0];
c = arc[2][0];
a = arc[1][0] = (arc[0][0] + b)/2;
b = (b + c)/2;
c = arc[5][0] = (arc[6][0] + c)/2;
a = arc[2][0] = (a + b)/2;
b = arc[4][0] = (b + c)/2;
arc[3][0] = (a + b)/2;
arc[6][1] = arc[3][1];
b = arc[1][1];
c = arc[2][1];
a = arc[1][1] = (arc[0][1] + b)/2;
b = (b + c)/2;
c = arc[5][1] = (arc[6][1] + c)/2;
a = arc[2][1] = (a + b)/2;
b = arc[4][1] = (b + c)/2;
arc[3][1] = (a + b)/2;
}
void Polyspan::cubic_to(Real x1, Real y1, Real x2, Real y2, Real x, Real y) {
Vector *current = arc;
int num = 0;
int level = 0;
bool onsecond = false;
arc[0] = Vector(x, y);
arc[1] = Vector(x2, y2);
arc[2] = Vector(x1, y1);
arc[3] = Vector(cur_x, cur_y);
// just draw the line if it's outside
if (clip_cubic(arc, window)) {
line_to(x,y);
return;
}
// Ok so it's not super degenerate, subdivide and draw (run through minimum subdivision levels first)
while(current >= arc) { // once current goes below arc, there are no more curves left
assert(num < MAX_SUBDIVISION_SIZE);
// if we are not at the level minimum
if (level < MIN_SUBDIVISION_DRAW_LEVELS) {
subd_cubic_stack(current);
current += 3; // cursor on second curve
level ++;
num ++;
onsecond = false;
continue;
} else
// if the curve is clipping then draw degenerate
if (clip_cubic(current, window)) {
line_to(current[0][0], current[0][1]); // backwards so front is destination
current -= 3;
if (onsecond) level--;
onsecond = true;
num --;
continue;
} else
// split it again, if it's too big
if (max_edges_cubic(current) > 0.25) { //could use max_edges<3>
subd_cubic_stack(current);
current += 3; // cursor on second curve
level ++;
num ++;
onsecond = false;
} else { // NOT TOO BIG? RENDER!!!
// cur_x, cur_y = current[3], so we need to go 2,1,0
line_to(current[2][0], current[2][1]);
line_to(current[1][0], current[1][1]);
line_to(current[0][0], current[0][1]);
current -= 3;
if (onsecond) level--;
num --;
onsecond = true;
}
}
}
void Polyspan::draw_scanline(int y, Real x1, Real y1, Real x2, Real y2) {
int ix1 = (int)floor(x1);
int ix2 = (int)floor(x2);
Real fx1 = x1 - ix1;
Real fx2 = x2 - ix2;
Real dx,dy,dydx,mult;
dx = x2 - x1;
dy = y2 - y1;
// case horizontal line
if (y1 == y2) {
move_pen(ix2, y); // pen needs to be at the last coord
return;
}
// case all in same pixel
if (ix1 == ix2) { // impossible for degenerate case (covered by the previous cases)
current.addcover(dy, (fx1 + fx2)*dy/2); // horizontal trapezoid area
return;
}
if (dx > 0) {
// ----> fx1...1 0...1 ... 0...1 0...fx2
dydx = dy/dx;
// set initial values
// Iterate through the covered pixels
mult = (1 - fx1)*dydx; // next y intersection diff value (at 1)
// first pixel
current.addcover(mult, (1 + fx1)*mult/2); // fx1, fy1, 1, fy@1 - starting trapezoidal area
// move to the next pixel
y1 += mult;
ix1++;
move_pen(ix1, y);
// set up for whole ones
while(ix1 != ix2) {
// trapezoid(0, y1, 1, y1 + dydx);
current.addcover(dydx,dydx/2); // accumulated area 1/2 the cover
// move to next pixel (+1)
ix1++;
y1 += dydx;
move_pen(ix1, y);
}
// last pixel
// final y-pos - last intersect pos
mult = fx2 * dydx;
current.addcover(mult, (0 + fx2)*mult/2);
} else {
// fx2...1 0...1 ... 0...1 0...fx1 <----
// mult = (0 - fx1) * dy / dx;
// neg sign sucked into dydx
dydx = -dy/dx;
// set initial values
// Iterate through the covered pixels
mult = fx1*dydx; // next y intersection diff value
// first pixel
current.addcover(mult, fx1*mult/2); // fx1, fy1, 0, fy@0 - starting trapezoidal area
// move to next pixel
y1 += mult;
ix1--;
move_pen(ix1, y);
// set up for whole ones
while(ix1 != ix2) {
// trapezoid(0, y1, 1, y1+dydx);
current.addcover(dydx, dydx/2); // accumulated area 1/2 the cover
// move to next pixel (-1)
y1 += dydx;
ix1--;
move_pen(ix1, y);
}
// last pixel
mult = y2 - y1; // final y-pos - last intersect pos
current.addcover(mult, (fx2+1)*mult/2);
}
}
void Polyspan::draw_line(Real x1, Real y1, Real x2, Real y2) {
int iy1 = (int)floor(y1);
int iy2 = (int)floor(y2);
Real fy1 = y1 - iy1;
Real fy2 = y2 - iy2;
assert(!isnan(fy1));
assert(!isnan(fy2));
Real dx,dy,dxdy,mult,x_from,x_to;
const Real SLOPE_EPSILON = 1e-10;
// case all one scanline
if (iy1 == iy2) {
draw_scanline(iy1, x1, y1, x2, y2);
return;
}
// difference values
dy = y2 - y1;
dx = x2 - x1;
// case vertical line
if (dx < SLOPE_EPSILON && dx > -SLOPE_EPSILON) {
// calc area and cover on vertical line
if (dy > 0) {
// ----> fx1...1 0...1 ... 0...1 0...fx2
Real sub;
int ix1 = (int)floor(x1);
Real fx1 = x1 - ix1;
// current pixel
sub = 1 - fy1;
current.addcover(sub, fx1*sub);
// next pixel
iy1++;
// move pen to next pixel
move_pen(ix1, iy1);
while(iy1 != iy2) {
// accumulate cover
current.addcover(1,fx1);
// next pixel
iy1++;
move_pen(ix1, iy1);
}
// last pixel
current.addcover(fy2, fy2*fx1);
} else {
Real sub;
int ix1 = (int)floor(x1);
Real fx1 = x1 - ix1;
// current pixel
sub = 0 - fy1;
current.addcover(sub, fx1*sub);
// next pixel
iy1--;
move_pen(ix1, iy1);
while(iy1 != iy2) {
// accumulate in current pixel
current.addcover(-1,-fx1);
// move to next
iy1--;
move_pen(ix1,iy1);
}
current.addcover(fy2-1,(fy2-1)*fx1);
}
return;
}
// case normal line - guaranteed dx != 0 && dy != 0
// calculate the initial intersection with "next" scanline
if (dy > 0) {
dxdy = dx/dy;
mult = (1 - fy1)*dxdy;
// x intersect scanline
x_from = x1 + mult;
draw_scanline(iy1, x1, fy1, x_from, 1);
// move to next line
iy1++;
move_pen((int)floor(x_from), iy1);
while(iy1 != iy2) {
// keep up on the x axis, and render the current scanline
x_to = x_from + dxdy;
draw_scanline(iy1, x_from, 0, x_to, 1);
x_from = x_to;
// move to next pixel
iy1++;
move_pen((int)floor(x_from), iy1);
}
//draw the last one, fractional
draw_scanline(iy2, x_from, 0, x2, fy2);
} else {
dxdy = -dx/dy;
mult = fy1*dxdy;
// x intersect scanline
x_from = x1 + mult;
draw_scanline(iy1,x1,fy1,x_from,0);
// each line after
iy1--;
move_pen((int)floor(x_from), iy1);
while(iy1 != iy2) {
x_to = x_from + dxdy;
draw_scanline(iy1, x_from, 1, x_to, 0);
x_from = x_to;
iy1--;
move_pen((int)floor(x_from), iy1);
}
// draw the last one, fractional
draw_scanline(iy2, x_from, 1, x2, fy2);
}
}
Real Polyspan::extract_alpha(Real area, bool evenodd) {
if (area < 0)
area = -area;
if (evenodd) {
// even-odd winding style
while (area > 1)
area -= 2;
// want pyramid like thing
if (area < 0)
area = -area;
} else {
// non-zero winding style
if (area > 1)
return 1;
}
return area;
}
/* === E N T R Y P O I N T ================================================= */