#include <iostream></iostream>

#include <iomanip></iomanip>

#include "log.h"

#include "perspective.h"

namespace {

	const int border_width   = 2;

	const int max_width      = 16384 - 2*border_width;

	const int max_height     = 16384 - 2*border_width;

	const int max_area_width = 4096 - 2*border_width;

	const int max_area       = max_area_width * max_area_width;

	const Real max_overscale = 2.0;

	Real max_overscale_sqr = max_overscale*max_overscale;

	class OptimalResolutionSolver {

	private:

		Matrix3 matrix;

		bool affine;

		Vector2 affine_resolution;

		Vector2 focus_a;

		Vector2 focus_b;

		Vector2 focus_m;

		Vector2 fp_kw;

		Vector2 dir;

		Real len;

	public:

		explicit OptimalResolutionSolver(const Matrix3 &matrix):

			matrix(matrix), affine(), len()

		{

			// w-horizon line equatation is A.z*x + B.z*y + C.z = w

			const Vector3 &A = matrix.row_x();

			const Vector3 &B = matrix.row_y();

			const Vector3 &C = matrix.row_z();

			const Real wsqr = A.z*A.z + B.z*B.z;

			affine = wsqr <= real_precision_sqr;

			affine_resolution = fabs(C.z) > real_precision

							  ? Perspective::calc_optimal_resolution(

									matrix.row_x().vec2()/C.z,

									matrix.row_y().vec2()/C.z )

							  : Vector2();

			const Real wsqr_div = !affine ? 1/wsqr : Real(0);

			// focus points

			bool invertible = false;

			const Matrix3 back_matrix = matrix.inverted(&invertible);

			const bool focus_a_exists = invertible && fabs(back_matrix.m02) > real_precision;

			const bool focus_b_exists = invertible && fabs(back_matrix.m12) > real_precision;

			const bool focus_m_exists = focus_a_exists && focus_b_exists;

			assert(focus_a_exists || focus_b_exists);

			focus_a = focus_a_exists ? back_matrix.row_x().vec2()/back_matrix.m02 : Vector2();

			focus_b = focus_b_exists ? back_matrix.row_y().vec2()/back_matrix.m12 : Vector2();

			focus_m = focus_m_exists ? (focus_a + focus_b)*0.5

									 : focus_a_exists ? focus_a : focus_b;

			const Vector2 dist = focus_m_exists ? focus_b - focus_a : Vector2();

			len = dist.length()*0.5;

			dir = fabs(len) > real_precision ? dist/(2*len) : Vector2();

			// projection of focus points to w-horizon line

			fp_kw = Vector2(A.z, B.z)*wsqr_div;

		}

	private:

		Real ratio_for_point(const Vector2 &point, Real w) const {

			const Vector3 v = matrix*Vector3(point, 1);

			const Vector2 ox( matrix.m00 - matrix.m02*v.x*w,

							  matrix.m10 - matrix.m12*v.x*w );

			const Vector2 oy( matrix.m01 - matrix.m02*v.y*w,

							  matrix.m11 - matrix.m12*v.y*w );

			const Real ratio = -ox.length()-oy.length();

			std::cout << Log::to_string(point, 8) << ": " << ratio << std::endl;

			return ratio;

		}

		Vector2 resolution_for_point(const Vector2 &point, Real w) const {

			const Vector3 v = matrix*Vector3(point, 1);

			const Vector2 ox( (matrix.m00 - matrix.m02*v.x*w)*w,

							  (matrix.m01 - matrix.m02*v.y*w)*w );

			const Vector2 oy( (matrix.m10 - matrix.m12*v.x*w)*w,

							  (matrix.m11 - matrix.m12*v.y*w)*w );

			return Perspective::calc_optimal_resolution(ox, oy);

		}

		// returns (l, ratio)

		Vector2 find_max(const Vector2 &point, const Vector2 &dir, Real maxl, Real w) {

			if (maxl <= 1 || maxl >= 1e+10)

				return Vector2(0, ratio_for_point(point, w));

			Real l0  = 0;

			Real l1  = maxl;

			Real ll0 = (l0 + l1)*0.5;

			std::cout << "begin" << std::endl;

			Real vv0 = ratio_for_point(point + dir*ll0, w);

			while(l1 - l0 > 1) {

				Real ll1, vv1;

				if (ll0 - l0 < l1 - ll0) {

					ll1 = (ll0 + l1)*0.5;

					vv1 = ratio_for_point(point + dir*ll1, w);

				} else {

					ll1 = ll0;

					vv1 = vv0;

					ll0 = (l0 + ll0)*0.5;

					vv0 = ratio_for_point(point + dir*ll0, w);

				}

				if (vv0 > vv1) {

					l1 = ll1;

				} else {

					l0 = ll0;

					ll0 = ll1;

					vv0 = vv1;

				}

			}

			std::cout << "end" << std::endl;

			return Vector2(ll0, vv0);

		}

	public:

		Vector2 solve(Real w, Vector2 *out_center = nullptr) {

			if (out_center) *out_center = Vector2();

			if (affine)

				return affine_resolution;

			if (w < real_precision)

				return Vector2();

			Vector2 center;

			const Vector2 offset_w = fp_kw/w;

			if (len <= 1) {

				center = focus_m + offset_w;

				std::cout << "focus_m:  " << Log::to_string(focus_m, 8) << std::endl;

			} else {

				const Vector2 solution_a = find_max(focus_a + offset_w,  dir, len, w);

				const Vector2 solution_b = find_max(focus_b + offset_w, -dir, len, w);

				center = solution_a.y > solution_b.y

					   ? focus_a + offset_w + dir*solution_a.x

					   : focus_b + offset_w - dir*solution_b.x;

				std::cout << "solution_a: " << Log::to_string(solution_a, 8) << ", len: " << len << std::endl;

				std::cout << "solution_b: " << Log::to_string(solution_b, 8) << std::endl;

				std::cout << "focus_a:  " << Log::to_string(focus_a, 8) << std::endl;

				std::cout << "focus_b:  " << Log::to_string(focus_b, 8) << std::endl;

			}

			std::cout << "offset_w: " << Log::to_string(offset_w, 8) << std::endl;

			std::cout << "center:   " << Log::to_string(center, 8) << std::endl;

			if (out_center) *out_center = center;

			return resolution_for_point(center, w);

		}

	};

}

Matrix3

Perspective::make_matrix(

	const Vector2 &p0,

	const Vector2 &px,

	const Vector2 &py,

	const Vector2 &p1 )

{

	Vector2 A = px - p1;

	Vector2 B = py - p1;

	Vector2 C = p0 + p1 - px - py;

	Real cw = A.y*B.x - A.x*B.y;

	Real aw = B.x*C.y - B.y*C.x;

	Real bw = A.y*C.x - A.x*C.y;

	// normalize and force cw to be positive

	Real k = aw*aw + bw*bw + cw*cw;

	k = k > real_precision ? 1/sqrt(k) : 1;

	if (cw < 0) k = -k;

	aw *= k;

	bw *= k;

	cw *= k;

	Vector2 c = p0*cw;

	Vector2 a = px*(cw + aw) - c;

	Vector2 b = py*(cw + bw) - c;

	return Matrix3( Vector3(a, aw),

					Vector3(b, bw),

					Vector3(c, cw) );

}

Matrix3

Perspective::normalize_matrix_by_w(

	const Matrix3 &matrix )

{

	Real k = matrix.get_col(2).length();

	if (k <= real_precision)

		return matrix;

	k = 1/k;

	Matrix3 m = matrix;

	for(int i = 0; i < 9; ++i)

		m.a[i] *= k;

	return m;

}

int

Perspective::truncate_line(

	Vector2 *out_points,

	const Pair2 &bounds,

	Real a,

	Real b,

	Real c )

{

	// equatation of line is a*x + b*y + c = 0

	int count = 0;

	if (fabs(a) > real_precision) {

		Real x0 = -(c + bounds.p0.y*b)/a;

		if ( x0 + real_precision >= bounds.p0.x

		  && x0 - real_precision <= bounds.p1.x )

		{

			if (out_points) out_points[count] = Vector2(x0, bounds.p0.y);

			if (++count >= 2) return count;

		}

		Real x1 = -(c + bounds.p1.y*b)/a;

		if ( x1 + real_precision >= bounds.p0.x

		  && x1 - real_precision <= bounds.p1.x )

		{

			if (out_points) out_points[count] = Vector2(x1, bounds.p1.y);

			if (++count >= 2) return count;

		}

	}

	if (fabs(b) > real_precision) {

		Real y0 = -(c + bounds.p0.x*a)/b;

		if ( y0 + real_precision >= bounds.p0.y

		  && y0 - real_precision <= bounds.p1.y )

		{

			if (out_points) out_points[count] = Vector2(bounds.p0.x, y0);

			if (++count >= 2) return count;

		}

		Real y1 = -(c + bounds.p1.x*a)/b;

		if ( y1 + real_precision >= bounds.p0.y

		  && y1 - real_precision <= bounds.p1.y )

		{

			if (out_points) out_points[count] = Vector2(bounds.p1.x, y1);

			if (++count >= 2) return count;

		}

	}

	return count;

}

Vector2

Perspective::calc_optimal_resolution(

	const Vector2 &ox,

	const Vector2 &oy )

{

	const Real a = ox.x * ox.x;

	const Real b = ox.y * ox.y;

	const Real c = oy.x * oy.x;

	const Real d = oy.y * oy.y;

	Real e = fabs(ox.x*oy.y - ox.y*oy.x);

	if (e < real_precision_sqr)

		return Vector2(); // matrix 2x2 ox oy is not invertible

	e = 1.0/e;

	const Real sum = a*d + b*c;

	Vector2 scale;

	if (2*a*b + real_precision_sqr >= sum) {

		scale.x = sqrt(2*b)*e;

		scale.y = sqrt(2*a)*e;

	} else

	if (2*c*d + real_precision_sqr >= sum) {

		scale.x = sqrt(2*d)*e;

		scale.y = sqrt(2*c)*e;

	} else {

		const Real dif = a*d - b*c;

		scale.x = sqrt(dif/(a - c))*e;

		scale.y = sqrt(dif/(d - b))*e;

	}

	return scale.x <= real_precision || scale.y <= real_precision

	     ? Vector2() : scale;

}

Vector3

Perspective::make_alpha_matrix_col(

	Real w0,

	Real w1,

	const Vector3 &w_col )

{

	Real k = w1 - w0;

	if (fabs(k) <= real_precision)

		return w_col;

	k = w1/k;

	return Vector3(

		k*w_col.x,

		k*w_col.y,

		k*(w_col.z - w0) );

}

Matrix3

Perspective::make_alpha_matrix(

	Real aw0, Real aw1,

	Real bw0, Real bw1,

	const Vector3 &w_col )

{

	const Vector3 a_col = make_alpha_matrix_col(aw0, aw1, w_col);

	const Vector3 b_col = make_alpha_matrix_col(bw0, bw1, w_col);

	return Matrix3(

		Vector3( a_col.x, b_col.x, w_col.x ),

		Vector3( a_col.y, b_col.y, w_col.y ),

		Vector3( a_col.z, b_col.z, w_col.z ) );

}

void

Perspective::calc_raster_size(

	Pair2 &out_bounds,

	IntVector2 &out_raster_size,

	Matrix3 &out_raster_matrix,

	const Vector2 &resolution,

	const Pair2 &bounds,

	const Vector2 &dst_size )

{

	const Vector2 offset = bounds.p0;

	const Vector2 raster_size_orig(

		(bounds.p1.x - bounds.p0.x)*resolution.x,

		(bounds.p1.y - bounds.p0.y)*resolution.y );

	Vector2 raster_size_float = raster_size_orig;

	Real sqr = raster_size_float.square();

	Real sqr_max = dst_size.square() * max_overscale_sqr;

	if (sqr_max > real_precision && sqr > sqr_max)

		raster_size_float *= sqrt(sqr_max/sqr);

	if (raster_size_float.x > max_width)

		raster_size_float.x = max_width;

	if (raster_size_float.y > max_height)

		raster_size_float.y = max_height;

	IntVector2 raster_size(

		std::max(1, (int)ceil( raster_size_float.x - real_precision )),

		std::max(1, (int)ceil( raster_size_float.y - real_precision )) );

	if (raster_size.x * raster_size.y > max_area) {

		const Real k = sqrt(Real(max_area)/(raster_size.x * raster_size.y));

		raster_size.x = std::max(1, (int)floor(raster_size.x*k + real_precision));

		raster_size.y = std::max(1, (int)floor(raster_size.y*k + real_precision));

	}

	const Vector2 new_resolution(

		raster_size_orig.x > real_precision ? resolution.x * raster_size.x / raster_size_orig.x : resolution.x,

		raster_size_orig.y > real_precision ? resolution.y * raster_size.y / raster_size_orig.y : resolution.y );

	const Vector2 new_border(

		new_resolution.x > real_precision ? border_width/new_resolution.x : Real(0),

		new_resolution.y > real_precision ? border_width/new_resolution.y : Real(0) );

	out_bounds = bounds.inflated( new_border );

	out_raster_size = raster_size + IntVector2(border_width, border_width)*2;

	out_raster_matrix = Matrix3::translation(Vector2(border_width, border_width))

					  * Matrix3::scaling(new_resolution)

					  * Matrix3::translation(-offset);

}

void

Perspective::create_layers(

	LayerList &out_layers,

	const Matrix3 &matrix,

	const IntPair2 &dst_bounds,

	const Real step )

{

	bool is_invertible = false;

	Matrix3 norm_matrix = normalize_matrix_by_w(matrix);

	Matrix3 back_matrix = norm_matrix.inverted(&is_invertible);

	if (!is_invertible)

		return; // matrix is collapsed

	// corners

	Vector3 dst_corners[4] = {

		Vector3(dst_bounds.p0.x, dst_bounds.p0.y, 1),

		Vector3(dst_bounds.p1.x, dst_bounds.p0.y, 1),

		Vector3(dst_bounds.p1.x, dst_bounds.p1.y, 1),

		Vector3(dst_bounds.p0.x, dst_bounds.p1.y, 1) };

	// calc coefficient for equatation of "horizontal" line: A*x + B*y + C = 1/w (aka A*x + B*y = 1/w - C)

	//                     equatation of line of horizon is: A*x + B*y + C = 0   (aka A*x + B*y = -C)

	const Real A = back_matrix.m02;

	const Real B = back_matrix.m12;

	const Real C = back_matrix.m22;

	Real hd = sqrt(A*A + B*B);

	if (hd <= real_precision) {

		// orthogonal projection - no perspective - no subdiviosions

		if (fabs(C) < real_precision)

			return; // only when matrix was not invertible (additional check)

		// calc src resolution

		const Vector2 resolution = calc_optimal_resolution(

			back_matrix.row_x().vec2(),

			back_matrix.row_y().vec2() );

		if (resolution.x <= real_precision || resolution.y <= real_precision)

			return; // cannot calc resolution, this can happen if matrix is (almost) not invertible

		// calc bounds

		Pair2 layer_src_bounds(Vector2(INFINITY, INFINITY), Vector2(-INFINITY, -INFINITY));

		for(int i = 0; i < 4; ++i)

			layer_src_bounds.expand( (back_matrix*dst_corners[i]).vec2() );

		if (layer_src_bounds.empty())

			return;

		std::cout << "debug: layer_src_bounds: " << Log::to_string(layer_src_bounds) << std::endl;

		std::cout << "debug: back_matrix:"<< std::endl << Log::to_string(back_matrix, 10);

		// make layer

		Layer layer;

		layer.dst_bounds = dst_bounds;

		calc_raster_size(

			layer.src_bounds,

			layer.src_size,

			layer.back_matrix,

			resolution,

			layer_src_bounds,

			Vector2(layer.dst_bounds.size()) );

		layer.back_matrix *= back_matrix;

		layer.back_alpha_matrix = Matrix3(

			Vector3(0, 0, 0),

			Vector3(0, 0, 0),

			Vector3(1, 1, 1) );

		out_layers.push_back(layer);

		return; 

	}

	// find visible w range

	hd = 1/hd;

	const Real horizonw1 = hd;

	const Real horizonw2 = hd/std::min(Real(2), step);

	const Real horizonw3 = hd/step;

	Real maxw = -INFINITY, minw = INFINITY;

	Vector3 src_corners[4];

	for(int i = 0; i < 4; ++i) {

		Vector3 src = back_matrix * dst_corners[i];

		if (fabs(src.z) > real_precision) {

			Real w = 1/src.z;

			if (w > 0 && w < horizonw1)

				src_corners[i] = Vector3(src.x*w, src.y*w, w);

			else

				w = horizonw1;

			if (minw > w) minw = w;

			if (maxw < w) maxw = w;

		}

	}

	if (minw >= maxw - real_precision)

		return; // all bounds too thin

	const Real maxw3 = std::min(maxw, horizonw3);

	// steps

	const Real stepLog = log(step);

	int minlog = (int)floor(log(minw)/stepLog + real_precision);

	int maxlog = (int)ceil(log(maxw3)/stepLog - real_precision);

	if (maxlog < minlog) maxlog = minlog;

	OptimalResolutionSolver resolution_solver(back_matrix);

	Real w = pow(step, Real(minlog));

	for(int i = minlog; i <= maxlog; ++i, w *= step) {

		// w range

		const Real w0  = w/step;

		const Real w1  = std::min(w*step, horizonw1);

		// alpha ranges

		const Real aw0 = w0;

		const Real aw1 = w;

		const Real bw0 = i == maxlog ? horizonw1 : w1;

		const Real bw1 = i == maxlog ? horizonw2 : w;

		// calc bounds

		Pair2 layer_src_bounds(Vector2(INFINITY, INFINITY), Vector2(-INFINITY, -INFINITY));

		Pair2 layer_dst_bounds(Vector2(INFINITY, INFINITY), Vector2(-INFINITY, -INFINITY));

		for(int j = 0; j < 4; ++j) {

			if (src_corners[j].z && src_corners[j].z > w0 && src_corners[j].z < w1) {

				layer_src_bounds.expand(src_corners[j].vec2());

				layer_dst_bounds.expand(dst_corners[j].vec2());

			}

		}

		Vector2 line[2];

		int line_count = truncate_line(line, Pair2(dst_bounds), A, B, C - 1/w0);

		for(int j = 0; j < line_count; ++j) {

			layer_src_bounds.expand( (back_matrix * Vector3(line[j], 1)).vec2() * w0 );

			layer_dst_bounds.expand( line[j] );

		}

		line_count = truncate_line(line, Pair2(dst_bounds), A, B, C - 1/w1);

		for(int j = 0; j < line_count; ++j) {

			layer_src_bounds.expand( (back_matrix * Vector3(line[j], 1)).vec2() * w1 );

			layer_dst_bounds.expand( line[j] );

			Vector3 v = back_matrix*Vector3(line[j], 1);

			Vector3 vv = norm_matrix*(v*w1);

			assert(real_equal(v.z, 1/w1));

			assert(real_equal(vv.z, w1));

		}

		if (layer_src_bounds.empty() || layer_dst_bounds.empty())

			continue;

		// make layer

		Layer layer;

		layer.dst_bounds = IntPair2(

			IntVector2( std::max(dst_bounds.p0.x, (int)floor(layer_dst_bounds.p0.x + real_precision)),

						std::max(dst_bounds.p0.y, (int)floor(layer_dst_bounds.p0.y + real_precision)) ),

			IntVector2( std::min(dst_bounds.p1.x, (int)ceil (layer_dst_bounds.p1.x - real_precision)),

						std::min(dst_bounds.p1.y, (int)ceil (layer_dst_bounds.p1.y - real_precision)) ));

		calc_raster_size(

			layer.src_bounds,

			layer.src_size,

			layer.back_matrix,

			resolution_solver.solve(w, &layer.center),

			layer_src_bounds,

			Vector2(layer.dst_bounds.size()) );

		layer.back_matrix *= back_matrix;

		layer.back_alpha_matrix = make_alpha_matrix(

			1/aw0, 1/aw1, 1/bw0, 1/bw1,

			layer.back_matrix.get_col(2) );

		out_layers.push_back(layer);

	}

}

Real

Perspective::find_optimal_step(

	const Matrix3 &matrix,

	const IntPair2 &dst_bounds )

{

	max_overscale_sqr = 1e10;

	ULongInt min_area = -1ull;

	Real optimal_step = 0;

	LayerList layers;

	for(Real step = 2; step < 16; step *= 1.01) {

		create_layers(layers, matrix, dst_bounds, step);

		ULongInt area = 0;

		for(LayerList::const_iterator i = layers.begin(); i != layers.end(); ++i)

			area += i->src_size.square();

		if (area < min_area) {

			min_area = area;

			optimal_step = step;

		}

		layers.clear();

	}

	max_overscale_sqr = max_overscale*max_overscale;

	return optimal_step;

}

void

Perspective::add_premulted(

	const Layer &layer,

	Surface &src_surface,

	Surface &dst_surface )

{

	if (src_surface.empty()) return;

	if (dst_surface.empty()) return;

	const int x0 = std::max(layer.dst_bounds.p0.x, 0);

	const int y0 = std::max(layer.dst_bounds.p0.y, 0);

	const int x1 = std::min(layer.dst_bounds.p1.x, dst_surface.width());

	const int y1 = std::min(layer.dst_bounds.p1.y, dst_surface.height());

	if (x0 >= x1 || y0 >= y1) return;

	const int w = x1 - x0;

	const int h = y1 - y0;

	if (w <= 0 || h <= 0) return;

	const Vector3 coord_dx = layer.back_matrix.row_x();

	const Vector3 coord_dy = layer.back_matrix.row_y() + coord_dx*(x0 - x1);

	Vector3 coord = layer.back_matrix * Vector3(x0, y0, 1);

	const Vector2 alpha_dx = layer.back_alpha_matrix.row_x().vec2();

	const Vector2 alpha_dy = layer.back_alpha_matrix.row_y().vec2() + alpha_dx*(x0 - x1);

	Vector2 alpha = (layer.back_alpha_matrix * Vector3(x0, y0, 1)).vec2();

	const int dr = dst_surface.pitch() - x1 + x0;

	Color *c = &dst_surface[y0][x0];

	for(int r = y0; r < y1; ++r, c += dr, coord += coord_dy, alpha += alpha_dy) {

		for(Color *end = c + w; c != end; ++c, coord += coord_dx, alpha += alpha_dx) {

			if (coord.z > real_precision) {

				const Real w = 1/coord.z;

				const Real a = clamp(alpha.x*w, 0, 1) * clamp(alpha.y*w, 0, 1);

				if (a > real_precision)

					*c += src_surface.get_pixel_premulted(coord.x*w, coord.y*w) * a;

			}

		}

	}

}

void

Perspective::paint_cross(

	Surface &dst_surface,

	const Vector2 &point )

{

	const Color black(0, 0, 0, 1);

	const Color white(1, 1, 1, 1);

	int cx = (int)floor(point.x);

	int cy = (int)floor(point.y);

	for(int i = 0; i < 10; ++i) {

		dst_surface.put_pixel(cx-i, cy, white);

		dst_surface.put_pixel(cx, cy-i, white);

		dst_surface.put_pixel(cx+1+i, cy+1, white);

		dst_surface.put_pixel(cx+1, cy+1+i, white);

		dst_surface.put_pixel(cx+1+i, cy, black);

		dst_surface.put_pixel(cx+1, cy-i, black);

		dst_surface.put_pixel(cx-i, cy+1, black);

		dst_surface.put_pixel(cx, cy+1+i, black);

	}

}

void

Perspective::print_layer(const Layer &layer, const std::string &prefix) {

	const int w = 10;

	std::cout << prefix << "dst_bounds: " << Log::to_string(layer.dst_bounds, w) << std::endl;

	std::cout << prefix << "src_bounds: " << Log::to_string(layer.dst_bounds, w) << std::endl;

	std::cout << prefix << "src_size:   " << Log::to_string(layer.src_size,   w) << std::endl;

	std::cout << prefix << "back_matrix:" << std::endl

			  << Log::to_string(layer.back_matrix, w, prefix + Log::tab()); 

	std::cout << prefix << "back_alpha_matrix:" << std::endl

			  << Log::to_string(layer.back_alpha_matrix, w, prefix + Log::tab()); 

	std::cout << prefix << "cetner:     " << Log::to_string(layer.center,     w) << std::endl;

}

void

Perspective::print_layers(const LayerList &layers, const std::string &prefix) {

	int index = 0;

	for(LayerList::const_iterator i = layers.begin(); i < layers.end(); ++i, ++index) {

		std::cout << prefix << "layer #" << index << std::endl;

		print_layer(*i, prefix + Log::tab());

	}

}