godot/core/math/geometry_2d.cpp

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/*  geometry_2d.cpp                                                       */
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#include "geometry_2d.h"

#include "thirdparty/clipper2/include/clipper2/clipper.h"
#include "thirdparty/misc/polypartition.h"
#define STB_RECT_PACK_IMPLEMENTATION
#include "thirdparty/misc/stb_rect_pack.h"

const int clipper_precision = 5; // Based on CMP_EPSILON.
const double clipper_scale = Math::pow(10.0, clipper_precision);

void Geometry2D::merge_many_polygons(const Vector<Vector<Vector2>> &p_polygons, Vector<Vector<Vector2>> &r_out_polygons, Vector<Vector<Vector2>> &r_out_holes) {
	using namespace Clipper2Lib;

	PathsD subjects;
	for (const Vector<Vector2> &polygon : p_polygons) {
		PathD path(polygon.size());
		for (int i = 0; i < polygon.size(); i++) {
			const Vector2 &point = polygon[i];
			path[i] = PointD(point.x, point.y);
		}
		subjects.push_back(path);
	}

	PathsD solution = Union(subjects, FillRule::NonZero);
	solution = SimplifyPaths(solution, 0.01);

	r_out_polygons.clear();
	r_out_holes.clear();
	for (PathsD::size_type i = 0; i < solution.size(); ++i) {
		PathD &path = solution[i];

		Vector<Point2> output_polygon;
		output_polygon.resize(path.size());
		for (PathsD::size_type j = 0; j < path.size(); ++j) {
			output_polygon.set(j, Vector2(static_cast<real_t>(path[j].x), static_cast<real_t>(path[j].y)));
		}
		if (IsPositive(path)) {
			r_out_polygons.push_back(output_polygon);
		} else {
			r_out_holes.push_back(output_polygon);
		}
	}
}

Vector<Vector<Vector2>> Geometry2D::decompose_many_polygons_in_convex(const Vector<Vector<Point2>> &p_polygons, const Vector<Vector<Point2>> &p_holes) {
	Vector<Vector<Vector2>> decomp;
	List<TPPLPoly> in_poly, out_poly;

	for (const Vector<Vector2> &polygon : p_polygons) {
		TPPLPoly inp;
		inp.Init(polygon.size());
		for (int i = 0; i < polygon.size(); i++) {
			inp.GetPoint(i) = polygon[i];
		}
		inp.SetOrientation(TPPL_ORIENTATION_CCW);
		in_poly.push_back(inp);
	}
	for (const Vector<Vector2> &polygon : p_holes) {
		TPPLPoly inp;
		inp.Init(polygon.size());
		for (int i = 0; i < polygon.size(); i++) {
			inp.GetPoint(i) = polygon[i];
		}
		inp.SetOrientation(TPPL_ORIENTATION_CW);
		inp.SetHole(true);
		in_poly.push_back(inp);
	}
	TPPLPartition tpart;
	if (tpart.ConvexPartition_HM(&in_poly, &out_poly) == 0) { // Failed.
		ERR_PRINT("Convex decomposing failed!");
		return decomp;
	}

	decomp.resize(out_poly.size());
	int idx = 0;
	for (TPPLPoly &tp : out_poly) {
		decomp.write[idx].resize(tp.GetNumPoints());

		for (int64_t i = 0; i < tp.GetNumPoints(); i++) {
			decomp.write[idx].write[i] = tp.GetPoint(i);
		}

		idx++;
	}

	return decomp;
}

Vector<Vector<Vector2>> Geometry2D::decompose_polygon_in_convex(const Vector<Point2> &p_polygon) {
	return Geometry2D::decompose_many_polygons_in_convex({ p_polygon }, {});
}

struct _AtlasWorkRect {
	Size2i s;
	Point2i p;
	int idx = 0;
	_FORCE_INLINE_ bool operator<(const _AtlasWorkRect &p_r) const { return s.width > p_r.s.width; }
};

struct _AtlasWorkRectResult {
	Vector<_AtlasWorkRect> result;
	int max_w = 0;
	int max_h = 0;
};

void Geometry2D::make_atlas(const Vector<Size2i> &p_rects, Vector<Point2i> &r_result, Size2i &r_size) {
	// Super simple, almost brute force scanline stacking fitter.
	// It's pretty basic for now, but it tries to make sure that the aspect ratio of the
	// resulting atlas is somehow square. This is necessary because video cards have limits
	// on texture size (usually 2048 or 4096), so the squarer a texture, the more the chances
	// that it will work in every hardware.
	// For example, it will prioritize a 1024x1024 atlas (works everywhere) instead of a
	// 256x8192 atlas (won't work anywhere).

	ERR_FAIL_COND(p_rects.is_empty());
	for (int i = 0; i < p_rects.size(); i++) {
		ERR_FAIL_COND(p_rects[i].width <= 0);
		ERR_FAIL_COND(p_rects[i].height <= 0);
	}

	Vector<_AtlasWorkRect> wrects;
	wrects.resize(p_rects.size());
	for (int i = 0; i < p_rects.size(); i++) {
		wrects.write[i].s = p_rects[i];
		wrects.write[i].idx = i;
	}
	wrects.sort();
	int widest = wrects[0].s.width;

	Vector<_AtlasWorkRectResult> results;

	for (int i = 0; i <= 12; i++) {
		int w = 1 << i;
		int max_h = 0;
		int max_w = 0;
		if (w < widest) {
			continue;
		}

		Vector<int> hmax;
		hmax.resize(w);
		for (int j = 0; j < w; j++) {
			hmax.write[j] = 0;
		}

		// Place them.
		int ofs = 0;
		int limit_h = 0;
		for (int j = 0; j < wrects.size(); j++) {
			if (ofs + wrects[j].s.width > w) {
				ofs = 0;
			}

			int from_y = 0;
			for (int k = 0; k < wrects[j].s.width; k++) {
				if (hmax[ofs + k] > from_y) {
					from_y = hmax[ofs + k];
				}
			}

			wrects.write[j].p.x = ofs;
			wrects.write[j].p.y = from_y;
			int end_h = from_y + wrects[j].s.height;
			int end_w = ofs + wrects[j].s.width;
			if (ofs == 0) {
				limit_h = end_h;
			}

			for (int k = 0; k < wrects[j].s.width; k++) {
				hmax.write[ofs + k] = end_h;
			}

			if (end_h > max_h) {
				max_h = end_h;
			}

			if (end_w > max_w) {
				max_w = end_w;
			}

			if (ofs == 0 || end_h > limit_h) { // While h limit not reached, keep stacking.
				ofs += wrects[j].s.width;
			}
		}

		_AtlasWorkRectResult result;
		result.result = wrects;
		result.max_h = max_h;
		result.max_w = max_w;
		results.push_back(result);
	}

	// Find the result with the best aspect ratio.

	int best = -1;
	real_t best_aspect = 1e20;

	for (int i = 0; i < results.size(); i++) {
		real_t h = next_power_of_2(results[i].max_h);
		real_t w = next_power_of_2(results[i].max_w);
		real_t aspect = h > w ? h / w : w / h;
		if (aspect < best_aspect) {
			best = i;
			best_aspect = aspect;
		}
	}

	r_result.resize(p_rects.size());

	for (int i = 0; i < p_rects.size(); i++) {
		r_result.write[results[best].result[i].idx] = results[best].result[i].p;
	}

	r_size = Size2(results[best].max_w, results[best].max_h);
}

Vector<Vector<Point2>> Geometry2D::_polypaths_do_operation(PolyBooleanOperation p_op, const Vector<Point2> &p_polypath_a, const Vector<Point2> &p_polypath_b, bool is_a_open) {
	using namespace Clipper2Lib;

	ClipType op = ClipType::Union;

	switch (p_op) {
		case OPERATION_UNION:
			op = ClipType::Union;
			break;
		case OPERATION_DIFFERENCE:
			op = ClipType::Difference;
			break;
		case OPERATION_INTERSECTION:
			op = ClipType::Intersection;
			break;
		case OPERATION_XOR:
			op = ClipType::Xor;
			break;
	}

	PathD path_a(p_polypath_a.size());
	for (int i = 0; i != p_polypath_a.size(); ++i) {
		path_a[i] = PointD(p_polypath_a[i].x, p_polypath_a[i].y);
	}
	PathD path_b(p_polypath_b.size());
	for (int i = 0; i != p_polypath_b.size(); ++i) {
		path_b[i] = PointD(p_polypath_b[i].x, p_polypath_b[i].y);
	}

	ClipperD clp(clipper_precision); // Scale points up internally to attain the desired precision.
	clp.PreserveCollinear(false); // Remove redundant vertices.
	if (is_a_open) {
		clp.AddOpenSubject({ path_a });
	} else {
		clp.AddSubject({ path_a });
	}
	clp.AddClip({ path_b });

	PathsD paths;

	if (is_a_open) {
		PolyTreeD tree; // Needed to populate polylines.
		clp.Execute(op, FillRule::EvenOdd, tree, paths);
	} else {
		clp.Execute(op, FillRule::EvenOdd, paths); // Works on closed polygons only.
	}

	Vector<Vector<Point2>> polypaths;
	for (PathsD::size_type i = 0; i < paths.size(); ++i) {
		const PathD &path = paths[i];

		Vector<Vector2> polypath;
		for (PathsD::size_type j = 0; j < path.size(); ++j) {
			polypath.push_back(Point2(static_cast<real_t>(path[j].x), static_cast<real_t>(path[j].y)));
		}
		polypaths.push_back(polypath);
	}
	return polypaths;
}

Vector<Vector<Point2>> Geometry2D::_polypath_offset(const Vector<Point2> &p_polypath, real_t p_delta, PolyJoinType p_join_type, PolyEndType p_end_type) {
	using namespace Clipper2Lib;

	JoinType jt = JoinType::Square;

	switch (p_join_type) {
		case JOIN_SQUARE:
			jt = JoinType::Square;
			break;
		case JOIN_ROUND:
			jt = JoinType::Round;
			break;
		case JOIN_MITER:
			jt = JoinType::Miter;
			break;
	}

	EndType et = EndType::Polygon;

	switch (p_end_type) {
		case END_POLYGON:
			et = EndType::Polygon;
			break;
		case END_JOINED:
			et = EndType::Joined;
			break;
		case END_BUTT:
			et = EndType::Butt;
			break;
		case END_SQUARE:
			et = EndType::Square;
			break;
		case END_ROUND:
			et = EndType::Round;
			break;
	}

	PathD polypath(p_polypath.size());
	for (int i = 0; i != p_polypath.size(); ++i) {
		polypath[i] = PointD(p_polypath[i].x, p_polypath[i].y);
	}

	// Inflate/deflate.
	PathsD paths = InflatePaths({ polypath }, p_delta, jt, et, 2.0, clipper_precision, 0.25 * clipper_scale);
	// Here the points are scaled up internally and
	// the arc_tolerance is scaled accordingly
	// to attain the desired precision.

	Vector<Vector<Point2>> polypaths;
	for (PathsD::size_type i = 0; i < paths.size(); ++i) {
		const PathD &path = paths[i];

		Vector<Vector2> polypath2;
		for (PathsD::size_type j = 0; j < path.size(); ++j) {
			polypath2.push_back(Point2(static_cast<real_t>(path[j].x), static_cast<real_t>(path[j].y)));
		}
		polypaths.push_back(polypath2);
	}
	return polypaths;
}

Vector<Vector3i> Geometry2D::partial_pack_rects(const Vector<Vector2i> &p_sizes, const Size2i &p_atlas_size) {
	Vector<stbrp_node> nodes;
	nodes.resize(p_atlas_size.width);
	memset(nodes.ptrw(), 0, sizeof(stbrp_node) * nodes.size());

	stbrp_context context;
	stbrp_init_target(&context, p_atlas_size.width, p_atlas_size.height, nodes.ptrw(), p_atlas_size.width);

	Vector<stbrp_rect> rects;
	rects.resize(p_sizes.size());

	for (int i = 0; i < p_sizes.size(); i++) {
		rects.write[i].id = i;
		rects.write[i].w = p_sizes[i].width;
		rects.write[i].h = p_sizes[i].height;
		rects.write[i].x = 0;
		rects.write[i].y = 0;
		rects.write[i].was_packed = 0;
	}

	stbrp_pack_rects(&context, rects.ptrw(), rects.size());

	Vector<Vector3i> ret;
	ret.resize(p_sizes.size());

	for (int i = 0; i < p_sizes.size(); i++) {
		ret.write[rects[i].id] = Vector3i(rects[i].x, rects[i].y, rects[i].was_packed != 0 ? 1 : 0);
	}

	return ret;
}