/**
 * 2D geometry math stuff
 *
 * License:
 *   This Source Code Form is subject to the terms of
 *   the Mozilla Public License, v. 2.0. If a copy of
 *   the MPL was not distributed with this file, You
 *   can obtain one at http://mozilla.org/MPL/2.0/.
 *
 * Authors:
 *   Vladimir Panteleev <ae@cy.md>
 */

module ae.utils.geometry;

import std.traits;
import std.math;

import ae.utils.math;

enum TAU = 2*PI; /// τ=2π

/// `sqrt` disambiguation for integers.
auto sqrtx(T)(T x)
{
	static if (is(T : long))
		return std.math.sqrt(cast(float)x);
	else
		return std.math.sqrt(x);
}

auto dist (T)(T x, T y) { return sqrtx(x*x+y*y); } /// Cartesian distance from origin.
auto dist2(T)(T x, T y) { return       x*x+y*y ; } /// Square of Cartesian distance from origin.

// *****************************************************************************

// Intersection tests between various shapes.

/// Point on a 2D plane.
struct Point(T)
{
	/// The coordinates.
	T x, y;
	void translate(T dx, T dy) { x += dx; y += dy; } ///
	Point!T getCenter() { return this; } ///
}
auto point(T...)(T args) { return Point!(CommonType!T)(args); } /// ditto

/// Orthogonal rectangle.
struct Rect(T)
{
	/// The coordinates.
	T x0, y0, x1, y1;
	@property T w() { return x1-x0; } /// Width.
	@property void w(T value) { x1 = x0 + value; } /// Resize width by moving the second vertical edge.
	@property T h() { return y1-y0; } /// Height.
	@property void h(T value) { y1 = y0 + value; } /// Resize height by moving the second horizontal edge.
	void sort() { sort2(x0, x1); sort2(y0, y1); } /// Flip coordinates if needed, so that `sorted` is `true`.
	@property bool sorted() { return x0 <= x1 && y0 <= y1; } /// `x0<=x1 && y0<=y1`
	void translate(T dx, T dy) { x0 += dx; y0 += dy; x1 += dx; y1 += dy; } ///
	Point!T getCenter() { return Point!T(cast(T)average(x0, x1), cast(T)average(y0, y1)); } ///
}
auto rect(T...)(T args) { return Rect!(CommonType!T)(args); } /// ditto

unittest
{
	Rect!int rint;
}

/// Circle on a plane.
struct Circle(T)
{
	/// The coordinates and radius.
	T x, y, r;
	@property T diameter() { return 2*r; } /// 2r
	void translate(T dx, T dy) { x += dx; y += dy; } ///
	Point!T getCenter() { return Point!T(x, y); } ///
}
auto circle(T...)(T args) { return Circle!(CommonType!T)(args); } /// ditto

/// Discriminated union between `Point`, `Rect` or `Circle`.
enum ShapeKind { none, /***/ point, /***/ rect, /***/ circle /***/ }
struct Shape(T)
{
	/// Wrapped shape.
	ShapeKind kind;
	union
	{
		Point!T point; ///
		Rect!T rect; ///
		Circle!T circle; ///
	} /// ditto

	this(Point!T point)
	{
		this.kind = ShapeKind.point;
		this.point = point;
	} ///

	this(Rect!T rect)
	{
		this.kind = ShapeKind.rect;
		this.rect = rect;
	} ///

	this(Circle!T circle)
	{
		this.kind = ShapeKind.circle;
		this.circle = circle;
	} ///

	/// Dispatches operations common to all shapes.
	auto opDispatch(string s, T...)(T args)
		if (is(typeof(mixin("point ." ~ s ~ "(args)"))) &&
		    is(typeof(mixin("rect  ." ~ s ~ "(args)"))) &&
		    is(typeof(mixin("circle." ~ s ~ "(args)"))))
	{
		switch (kind)
		{
			case ShapeKind.point:
				return mixin("point ." ~ s ~ "(args)");
			case ShapeKind.circle:
				return mixin("circle." ~ s ~ "(args)");
			case ShapeKind.rect:
				return mixin("rect  ." ~ s ~ "(args)");
			default:
				assert(0);
		}
	}
} /// ditto
auto shape(T)(T shape) { return Shape!(typeof(shape.tupleof[0]))(shape); } /// ditto

/// Intersection test.
bool intersects(T)(Shape!T a, Shape!T b)
{
	switch (a.kind)
	{
		case ShapeKind.point:
			switch (b.kind)
			{
			case ShapeKind.point:
				return a.point.x == b.point.x && a.point.y == b.point.y;
			case ShapeKind.circle:
				return dist2(a.point.x-b.circle.x, a.point.y-b.circle.y) < sqr(b.circle.r);
			case ShapeKind.rect:
				assert(b.rect.sorted);
				return between(a.point.x, b.rect.x0, b.rect.x1) && between(a.point.y, b.rect.y0, b.rect.y1);
			default:
				assert(0);
			}
		case ShapeKind.circle:
			switch (b.kind)
			{
			case ShapeKind.point:
				return dist2(a.circle.x-b.point.x, a.circle.y-b.point.y) < sqr(a.circle.r);
			case ShapeKind.circle:
				return dist2(a.circle.x-b.circle.x, a.circle.y-b.circle.y) < sqr(a.circle.r+b.circle.r);
			case ShapeKind.rect:
				return intersects!T(a.circle, b.rect);
			default:
				assert(0);
			}
		case ShapeKind.rect:
			switch (b.kind)
			{
			case ShapeKind.point:
				assert(a.rect.sorted);
				return between(b.point.x, a.rect.x0, a.rect.x1) && between(b.point.y, a.rect.y0, a.rect.y1);
			case ShapeKind.circle:
				return intersects!T(b.circle, a.rect);
			case ShapeKind.rect:
				assert(0); // TODO
			default:
				assert(0);
			}
		default:
			assert(0);
	}
}

/// ditto
bool intersects(T)(Circle!T circle, Rect!T rect)
{
	// http://stackoverflow.com/questions/401847/circle-rectangle-collision-detection-intersection

	Point!T circleDistance;

	auto hw = rect.w/2, hh = rect.h/2;

	circleDistance.x = abs(circle.x - rect.x0 - hw);
	circleDistance.y = abs(circle.y - rect.y0 - hh);

	if (circleDistance.x > (hw + circle.r)) return false;
	if (circleDistance.y > (hh + circle.r)) return false;

	if (circleDistance.x <= hw) return true;
	if (circleDistance.y <= hh) return true;

	auto cornerDistance_sq =
		sqr(circleDistance.x - hw) +
		sqr(circleDistance.y - hh);

	return (cornerDistance_sq <= sqr(circle.r));
}