vcmi/lib/rmg/PenroseTiling.cpp

/*
 * PenroseTiling.cpp, part of VCMI engine
 *
 * Authors: listed in file AUTHORS in main folder
 *
 * License: GNU General Public License v2.0 or later
 * Full text of license available in license.txt file, in main folder
 *
 */

// Adapted from https://github.com/mpizzzle/penrose by Michael Percival

#include "StdInc.h"
#include "PenroseTiling.h"

VCMI_LIB_NAMESPACE_BEGIN


Point2D Point2D::operator * (float scale) const
{
	return Point2D(x() * scale, y() * scale);
}

Point2D Point2D::operator / (float scale) const
{
	return Point2D(x() / scale, y() / scale);
}

Point2D Point2D::operator + (const Point2D& other) const
{
	return Point2D(x() + other.x(), y() + other.y());
}

Point2D Point2D::operator - (const Point2D& other) const
{
	return Point2D(x() - other.x(), y() - other.y());
}

bool Point2D::operator < (const Point2D& other) const
{
	if (x() != other.x())
		return x() < other.x();

	return y() < other.y();
}

bool Point2D::operator == (const Point2D& other) const
{
	return vstd::isAlmostEqual(x(), other.x()) && vstd::isAlmostEqual(y(), other.y());
}

std::string Point2D::toString() const
{
	//Performance is important here
	std::string result = "(" +
			std::to_string(this->x()) + " " +
			std::to_string(this->y()) + ")";

	return result;
}

Triangle::Triangle(bool t_123, const TIndices & inds):
	tiling(t_123),
	indices(inds)
{}

Triangle::~Triangle()
{
	for (auto * triangle : subTriangles)
	{
		if (triangle)
		{
			delete triangle;
			triangle = nullptr;
		}
	}
}

Point2D Point2D::rotated(float radians) const
{
	float cosAngle = cos(radians);
	float sinAngle = sin(radians);

	// Apply rotation matrix transformation
	float newX = x() * cosAngle - y() * sinAngle;
	float newY = x() * sinAngle + y() * cosAngle;

	return Point2D(newX, newY);
}

void PenroseTiling::split(Triangle& p, std::vector<Point2D>& points,
	std::array<std::vector<uint32_t>, 5>& indices, uint32_t depth) 
{
	uint32_t s = points.size();
	TIndices& i = p.indices;

	const auto p2 = P2;

	if (depth > 0)
	{
		if (p.tiling ^ !p2)
		{
			points.push_back(Point2D((points[i[0]] * (1.0f - PHI) ) + (points[i[2]]) * PHI));
			points.push_back(Point2D((points[i[p2]] * (1.0f - PHI)) + (points[i[!p2]] * PHI)));

			auto * t1 = new Triangle(p2, TIndices({ i[(!p2) + 1], p2 ? i[2] : s, p2 ? s : i[1] }));
			auto * t2 = new Triangle(true, TIndices({ p2 ? i[1] : s, s + 1, p2 ? s : i[1] }));
			auto * t3 = new Triangle(false, TIndices({ s, s + 1, i[0] }));

			p.subTriangles = { t1, t2, t3 };
		}
		else
		{
			points.push_back(Point2D((points[i[p2 * 2]] * (1.0f - PHI)) + (points[i[!p2]]) * PHI));

			auto * t1 = new Triangle(true, TIndices({ i[2], s, i[1] }));
			auto * t2 = new Triangle(false, TIndices({ i[(!p2) + 1], s, i[0] }));

			p.subTriangles = { t1, t2 };
		}

		for (auto& t : p.subTriangles)
		{
			if (depth == 1)
			{
				for (uint32_t k = 0; k < 3; ++k)
				{
					if (k != (t->tiling ^ !p2 ? 2 : 1))
					{
						indices[indices.size() - 1].push_back(t->indices[k]);
						indices[indices.size() - 1].push_back(t->indices[((k + 1) % 3)]);
					}
				}

				indices[t->tiling + (p.tiling ? 0 : 2)].insert(indices[t->tiling + (p.tiling ? 0 : 2)].end(), t->indices.begin(), t->indices.end());
			}

			// Split recursively
			split(*t, points, indices, depth - 1);
		}
	}

	return;
}

std::set<Point2D> PenroseTiling::generatePenroseTiling(size_t numZones, CRandomGenerator * rand)
{
	float scale = 173.2f / (numZones * 1.5f + 20);
	float polyAngle = (2 * PI_CONSTANT) / POLY;

	float randomAngle = rand->nextDouble(0.25 * PI_CONSTANT, 0.75 * PI_CONSTANT);

	std::vector<Point2D> points = { Point2D(0.0f, 0.0f), Point2D(0.0f, 1.0f).rotated(randomAngle) };
	std::array<std::vector<uint32_t>, 5> indices;

	for (uint32_t i = 1; i < POLY; ++i)
	{
		Point2D next = points[i].rotated(polyAngle);
		points.push_back(next);
	}

	for (auto& p : points)
	{
		p.x(p.x() * scale * BASE_SIZE);
	}

	std::set<Point2D> finalPoints;

	for (uint32_t i = 0; i < POLY; i++)
	{
		std::array<uint32_t, 2> p = { (i % (POLY + 1)) + 1, ((i + 1) % POLY) + 1 };

		Triangle t(true, TIndices({ 0, p[i & 1], p[!(i & 1)] }));

		split(t, points, indices, DEPTH);
	}
	// Remove duplicates
	vstd::unique(points);

	// Shift center to (0.5, 0.5)
	for (auto & point : points)
	{
		point = point + Point2D(0.5f, 0.5f);
	};

	// For 8XM8 map, only 650 out of 15971 points are in the range

	vstd::copy_if(points, vstd::set_inserter(finalPoints), [](const Point2D point)
	{
		return vstd::isbetween(point.x(), 0.f, 1.0f) && vstd::isbetween(point.y(), 0.f, 1.0f);
	});

	return finalPoints;
}

VCMI_LIB_NAMESPACE_END