Blob Blame Raw
/*
	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) const {
	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 ================================================= */