godot/core/math/geometry.cpp

/*************************************************************************/
/*  geometry.cpp                                                         */
/*************************************************************************/
/*                       This file is part of:                           */
/*                           GODOT ENGINE                                */
/*                    http://www.godotengine.org                         */
/*************************************************************************/
/* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur.                 */
/*                                                                       */
/* Permission is hereby granted, free of charge, to any person obtaining */
/* a copy of this software and associated documentation files (the       */
/* "Software"), to deal in the Software without restriction, including   */
/* without limitation the rights to use, copy, modify, merge, publish,   */
/* distribute, sublicense, and/or sell copies of the Software, and to    */
/* permit persons to whom the Software is furnished to do so, subject to */
/* the following conditions:                                             */
/*                                                                       */
/* The above copyright notice and this permission notice shall be        */
/* included in all copies or substantial portions of the Software.       */
/*                                                                       */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
/*************************************************************************/
#include "geometry.h"
#include "print_string.h"



void Geometry::MeshData::optimize_vertices() {

	Map<int,int> vtx_remap;

	for(int i=0;i<faces.size();i++) {

		for(int j=0;j<faces[i].indices.size();j++) {

			int idx = faces[i].indices[j];
			if (!vtx_remap.has(idx)) {
				int ni = vtx_remap.size();
				vtx_remap[idx]=ni;


			}

			faces[i].indices[j]=vtx_remap[idx];
		}
	}

	for(int i=0;i<edges.size();i++) {

		int a = edges[i].a;
		int b = edges[i].b;

		if (!vtx_remap.has(a)) {
			int ni = vtx_remap.size();
			vtx_remap[a]=ni;
		}
		if (!vtx_remap.has(b)) {
			int ni = vtx_remap.size();
			vtx_remap[b]=ni;
		}

		edges[i].a=vtx_remap[a];
		edges[i].b=vtx_remap[b];
	}

	Vector<Vector3> new_vertices;
	new_vertices.resize(vtx_remap.size());

	for(int i=0;i<vertices.size();i++) {

		if (vtx_remap.has(i))
			new_vertices[vtx_remap[i]]=vertices[i];
	}
	vertices=new_vertices;
}

Vector< Vector<Vector2> > (*Geometry::_decompose_func)(const Vector<Vector2>& p_polygon)=NULL;

struct _FaceClassify {

	struct _Link {

		int face;
		int edge;
		void clear() { face=-1; edge=-1; }
		_Link() { face=-1; edge=-1; }
	};
	bool valid;
	int group;
	_Link links[3];
	Face3 face;
	_FaceClassify() {
		group=-1;
		valid=false;
	};
};

static bool _connect_faces(_FaceClassify *p_faces, int len, int p_group) {
	/* connect faces, error will occur if an edge is shared between more than 2 faces */
	/* clear connections */

	bool error=false;

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

		for (int j=0;j<3;j++) {

			p_faces[i].links[j].clear();
		}
	}

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

		if (p_faces[i].group!=p_group)
			continue;
		for (int j=i+1;j<len;j++) {

			if (p_faces[j].group!=p_group)
				continue;

			for (int k=0;k<3;k++) {

				Vector3 vi1=p_faces[i].face.vertex[k];
				Vector3 vi2=p_faces[i].face.vertex[(k+1)%3];

				for (int l=0;l<3;l++) {

					Vector3 vj2=p_faces[j].face.vertex[l];
					Vector3 vj1=p_faces[j].face.vertex[(l+1)%3];

					if (vi1.distance_to(vj1)<0.00001 &&
					    vi2.distance_to(vj2)<0.00001
					   ) {
						if (p_faces[i].links[k].face!=-1) {

							ERR_PRINT("already linked\n");
							error=true;
							break;
						}
						if (p_faces[j].links[l].face!=-1) {

							ERR_PRINT("already linked\n");
							error=true;
							break;
						}

						p_faces[i].links[k].face=j;
						p_faces[i].links[k].edge=l;
						p_faces[j].links[l].face=i;
						p_faces[j].links[l].edge=k;
					   }
				}
				if (error)
					break;

			}
			if (error)
				break;

		}
		if (error)
			break;
	}

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

		p_faces[i].valid=true;
		for (int j=0;j<3;j++) {

			if (p_faces[i].links[j].face==-1)
				p_faces[i].valid=false;
		}
		/*printf("face %i is valid: %i, group %i. connected to %i:%i,%i:%i,%i:%i\n",i,p_faces[i].valid,p_faces[i].group,
			p_faces[i].links[0].face,
			p_faces[i].links[0].edge,
			p_faces[i].links[1].face,
			p_faces[i].links[1].edge,
			p_faces[i].links[2].face,
			p_faces[i].links[2].edge);*/
	}
	return error;
}

static bool _group_face(_FaceClassify *p_faces, int len, int p_index,int p_group) {

	if (p_faces[p_index].group>=0)
		return false;

	p_faces[p_index].group=p_group;

	for (int i=0;i<3;i++) {

		ERR_FAIL_INDEX_V(p_faces[p_index].links[i].face,len,true);
		_group_face(p_faces,len,p_faces[p_index].links[i].face,p_group);
	}

	return true;
}


PoolVector< PoolVector< Face3 > > Geometry::separate_objects( PoolVector< Face3 > p_array ) {

	PoolVector< PoolVector< Face3 > > objects;

	int len = p_array.size();

	PoolVector<Face3>::Read r=p_array.read();

	const Face3* arrayptr = r.ptr();

	PoolVector< _FaceClassify> fc;

	fc.resize( len );

	PoolVector< _FaceClassify >::Write fcw=fc.write();

	_FaceClassify * _fcptr = fcw.ptr();

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

		_fcptr[i].face=arrayptr[i];
	}

	bool error=_connect_faces(_fcptr,len,-1);

	if (error) {

		ERR_FAIL_COND_V(error, PoolVector< PoolVector< Face3 > >() ); // invalid geometry
	}

	/* group connected faces in separate objects */

	int group=0;
	for (int i=0;i<len;i++) {

		if (!_fcptr[i].valid)
			continue;
		if (_group_face(_fcptr,len,i,group)) {
			group++;
		}
	}

	/* group connected faces in separate objects */


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

		_fcptr[i].face=arrayptr[i];
	}

	if (group>=0) {

		objects.resize(group);
		PoolVector< PoolVector<Face3> >::Write obw=objects.write();
		PoolVector< Face3 > *group_faces = obw.ptr();

		for (int i=0;i<len;i++) {
			if (!_fcptr[i].valid)
				continue;
			if (_fcptr[i].group>=0 && _fcptr[i].group<group) {

				group_faces[_fcptr[i].group].push_back( _fcptr[i].face );
			}
		}
	}


	return objects;

}

/*** GEOMETRY WRAPPER ***/

enum _CellFlags {

	_CELL_SOLID=1,
 	_CELL_EXTERIOR=2,
  	_CELL_STEP_MASK=0x1C,
   	_CELL_STEP_NONE=0<<2,
	_CELL_STEP_Y_POS=1<<2,
 	_CELL_STEP_Y_NEG=2<<2,
  	_CELL_STEP_X_POS=3<<2,
   	_CELL_STEP_X_NEG=4<<2,
    	_CELL_STEP_Z_POS=5<<2,
     	_CELL_STEP_Z_NEG=6<<2,
      	_CELL_STEP_DONE=7<<2,
	_CELL_PREV_MASK=0xE0,
	_CELL_PREV_NONE=0<<5,
	_CELL_PREV_Y_POS=1<<5,
	_CELL_PREV_Y_NEG=2<<5,
	_CELL_PREV_X_POS=3<<5,
	_CELL_PREV_X_NEG=4<<5,
	_CELL_PREV_Z_POS=5<<5,
	_CELL_PREV_Z_NEG=6<<5,
	_CELL_PREV_FIRST=7<<5,

};

static inline void _plot_face(uint8_t*** p_cell_status,int x,int y,int z,int len_x,int len_y,int len_z,const Vector3& voxelsize,const Face3& p_face) {

	AABB aabb( Vector3(x,y,z),Vector3(len_x,len_y,len_z));
	aabb.pos=aabb.pos*voxelsize;
	aabb.size=aabb.size*voxelsize;

	if (!p_face.intersects_aabb(aabb))
		return;

	if (len_x==1 && len_y==1 && len_z==1) {

		p_cell_status[x][y][z]=_CELL_SOLID;
		return;
	}



	int div_x=len_x>1?2:1;
	int div_y=len_y>1?2:1;
	int div_z=len_z>1?2:1;

#define _SPLIT(m_i,m_div,m_v,m_len_v,m_new_v,m_new_len_v)\
	if (m_div==1) {\
		m_new_v=m_v;\
		m_new_len_v=1;	\
	} else if (m_i==0) {\
		m_new_v=m_v;\
		m_new_len_v=m_len_v/2;\
	} else {\
		m_new_v=m_v+m_len_v/2;\
		m_new_len_v=m_len_v-m_len_v/2;		\
	}

	int new_x;
	int new_len_x;
	int new_y;
	int new_len_y;
	int new_z;
	int new_len_z;

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


		_SPLIT(i,div_x,x,len_x,new_x,new_len_x);

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

			_SPLIT(j,div_y,y,len_y,new_y,new_len_y);

			for (int k=0;k<div_z;k++) {

				_SPLIT(k,div_z,z,len_z,new_z,new_len_z);

				_plot_face(p_cell_status,new_x,new_y,new_z,new_len_x,new_len_y,new_len_z,voxelsize,p_face);
			}
		}
	}
}

static inline void _mark_outside(uint8_t*** p_cell_status,int x,int y,int z,int len_x,int len_y,int len_z) {

	if (p_cell_status[x][y][z]&3)
		return; // nothing to do, already used and/or visited

	p_cell_status[x][y][z]=_CELL_PREV_FIRST;

	while(true) {

		uint8_t &c = p_cell_status[x][y][z];

		//printf("at %i,%i,%i\n",x,y,z);

		if ( (c&_CELL_STEP_MASK)==_CELL_STEP_NONE) {
			/* Haven't been in here, mark as outside */
			p_cell_status[x][y][z]|=_CELL_EXTERIOR;
			//printf("not marked as anything, marking exterior\n");
		}

		//printf("cell step is %i\n",(c&_CELL_STEP_MASK));

		if ( (c&_CELL_STEP_MASK)!=_CELL_STEP_DONE) {
			/* if not done, increase step */
			c+=1<<2;
			//printf("incrementing cell step\n");
		}

		if ( (c&_CELL_STEP_MASK)==_CELL_STEP_DONE) {
			/* Go back */
			//printf("done, going back a cell\n");

			switch(c&_CELL_PREV_MASK) {
				case _CELL_PREV_FIRST: {
					//printf("at end, finished marking\n");
					return;
				} break;
				case _CELL_PREV_Y_POS: {
					y++;
					ERR_FAIL_COND(y>=len_y);
				} break;
				case _CELL_PREV_Y_NEG: {
					y--;
					ERR_FAIL_COND(y<0);
				} break;
				case _CELL_PREV_X_POS: {
					x++;
					ERR_FAIL_COND(x>=len_x);
				} break;
				case _CELL_PREV_X_NEG: {
					x--;
					ERR_FAIL_COND(x<0);
				} break;
				case _CELL_PREV_Z_POS: {
					z++;
					ERR_FAIL_COND(z>=len_z);
				} break;
				case _CELL_PREV_Z_NEG: {
					z--;
					ERR_FAIL_COND(z<0);
				} break;
				default: {
					ERR_FAIL();
				}
			}
			continue;
		}

		//printf("attempting new cell!\n");

		int next_x=x,next_y=y,next_z=z;
		uint8_t prev=0;

		switch(c&_CELL_STEP_MASK) {

			case _CELL_STEP_Y_POS: {

				next_y++;
				prev=_CELL_PREV_Y_NEG;
			} break;
			case _CELL_STEP_Y_NEG: {
				next_y--;
				prev=_CELL_PREV_Y_POS;
			} break;
			case _CELL_STEP_X_POS: {
				next_x++;
				prev=_CELL_PREV_X_NEG;
			} break;
			case _CELL_STEP_X_NEG: {
				next_x--;
				prev=_CELL_PREV_X_POS;
			} break;
			case _CELL_STEP_Z_POS: {
				next_z++;
				prev=_CELL_PREV_Z_NEG;
			} break;
			case _CELL_STEP_Z_NEG: {
				next_z--;
				prev=_CELL_PREV_Z_POS;
			} break;
			default: ERR_FAIL();

		}

		//printf("testing if new cell will be ok...!\n");

		if (next_x<0 || next_x>=len_x)
			continue;
		if (next_y<0 || next_y>=len_y)
			continue;
		if (next_z<0 || next_z>=len_z)
			continue;

		//printf("testing if new cell is traversable\n");

		if (p_cell_status[next_x][next_y][next_z]&3)
			continue;

		//printf("move to it\n");

		x=next_x;
		y=next_y;
		z=next_z;
		p_cell_status[x][y][z]|=prev;
	}
}

static inline void _build_faces(uint8_t*** p_cell_status,int x,int y,int z,int len_x,int len_y,int len_z,PoolVector<Face3>& p_faces) {

	ERR_FAIL_INDEX(x,len_x);
	ERR_FAIL_INDEX(y,len_y);
	ERR_FAIL_INDEX(z,len_z);

	if (p_cell_status[x][y][z]&_CELL_EXTERIOR)
		return;

/*	static const Vector3 vertices[8]={
		Vector3(0,0,0),
		Vector3(0,0,1),
		Vector3(0,1,0),
		Vector3(0,1,1),
		Vector3(1,0,0),
		Vector3(1,0,1),
		Vector3(1,1,0),
		Vector3(1,1,1),
	};
*/
#define vert(m_idx) Vector3( (m_idx&4)>>2, (m_idx&2)>>1, m_idx&1 )

	static const uint8_t indices[6][4]={
		{7,6,4,5},
		{7,3,2,6},
		{7,5,1,3},
		{0,2,3,1},
		{0,1,5,4},
		{0,4,6,2},

	};
/*

		{0,1,2,3},
		{0,1,4,5},
		{0,2,4,6},
		{4,5,6,7},
		{2,3,7,6},
		{1,3,5,7},

		{0,2,3,1},
		{0,1,5,4},
		{0,4,6,2},
		{7,6,4,5},
		{7,3,2,6},
		{7,5,1,3},
*/

	for (int i=0;i<6;i++) {

		Vector3 face_points[4];
		int disp_x=x+((i%3)==0?((i<3)?1:-1):0);
		int disp_y=y+(((i-1)%3)==0?((i<3)?1:-1):0);
		int disp_z=z+(((i-2)%3)==0?((i<3)?1:-1):0);

		bool plot=false;

		if (disp_x<0 || disp_x>=len_x)
			plot=true;
		if (disp_y<0 || disp_y>=len_y)
			plot=true;
		if (disp_z<0 || disp_z>=len_z)
			plot=true;

		if (!plot && (p_cell_status[disp_x][disp_y][disp_z]&_CELL_EXTERIOR))
			plot=true;

		if (!plot)
			continue;

		for (int j=0;j<4;j++)
			face_points[j]=vert( indices[i][j] ) + Vector3(x,y,z);

		p_faces.push_back(
			Face3(
				face_points[0],
				face_points[1],
				face_points[2]
			     )
		);

		p_faces.push_back(
			Face3(
				face_points[2],
				face_points[3],
				face_points[0]
			     )
		);

	}

}

PoolVector< Face3 > Geometry::wrap_geometry( PoolVector< Face3 > p_array,float *p_error ) {

#define _MIN_SIZE 1.0
#define _MAX_LENGTH 20

	int face_count=p_array.size();
	PoolVector<Face3>::Read facesr=p_array.read();
	const Face3 *faces = facesr.ptr();

	AABB global_aabb;

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

		if (i==0) {

			global_aabb=faces[i].get_aabb();
		} else {

			global_aabb.merge_with( faces[i].get_aabb() );
		}
	}

	global_aabb.grow_by(0.01); // avoid numerical error

	// determine amount of cells in grid axis
	int div_x,div_y,div_z;

	if (global_aabb.size.x/_MIN_SIZE<_MAX_LENGTH)
		div_x=(int)(global_aabb.size.x/_MIN_SIZE)+1;
	else
		div_x=_MAX_LENGTH;

	if (global_aabb.size.y/_MIN_SIZE<_MAX_LENGTH)
		div_y=(int)(global_aabb.size.y/_MIN_SIZE)+1;
	else
		div_y=_MAX_LENGTH;

	if (global_aabb.size.z/_MIN_SIZE<_MAX_LENGTH)
		div_z=(int)(global_aabb.size.z/_MIN_SIZE)+1;
	else
		div_z=_MAX_LENGTH;

	Vector3 voxelsize=global_aabb.size;
	voxelsize.x/=div_x;
	voxelsize.y/=div_y;
	voxelsize.z/=div_z;


	// create and initialize cells to zero
	//print_line("Wrapper: Initializing Cells");

	uint8_t ***cell_status=memnew_arr(uint8_t**,div_x);
	for(int i=0;i<div_x;i++) {

		cell_status[i]=memnew_arr(uint8_t*,div_y);

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

			cell_status[i][j]=memnew_arr(uint8_t,div_z);

			for(int k=0;k<div_z;k++) {

				cell_status[i][j][k]=0;
			}
		}
	}

	// plot faces into cells
	//print_line("Wrapper (1/6): Plotting Faces");

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

		Face3 f=faces[i];
		for (int j=0;j<3;j++) {

			f.vertex[j]-=global_aabb.pos;
		}
		_plot_face(cell_status,0,0,0,div_x,div_y,div_z,voxelsize,f);
	}


	// determine which cells connect to the outside by traversing the outside and recursively flood-fill marking

	//print_line("Wrapper (2/6): Flood Filling");

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

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

			_mark_outside(cell_status,i,j,0,div_x,div_y,div_z);
			_mark_outside(cell_status,i,j,div_z-1,div_x,div_y,div_z);
		}
	}

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

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

			_mark_outside(cell_status,0,j,i,div_x,div_y,div_z);
			_mark_outside(cell_status,div_x-1,j,i,div_x,div_y,div_z);
		}
	}

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

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

			_mark_outside(cell_status,i,0,j,div_x,div_y,div_z);
			_mark_outside(cell_status,i,div_y-1,j,div_x,div_y,div_z);
		}
	}

	// build faces for the inside-outside cell divisors

	//print_line("Wrapper (3/6): Building Faces");

	PoolVector<Face3> wrapped_faces;

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

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

			for (int k=0;k<div_z;k++) {

				_build_faces(cell_status,i,j,k,div_x,div_y,div_z,wrapped_faces);
			}
		}
	}

	//print_line("Wrapper (4/6): Transforming Back Vertices");

	// transform face vertices to global coords

	int wrapped_faces_count=wrapped_faces.size();
	PoolVector<Face3>::Write wrapped_facesw=wrapped_faces.write();
	Face3* wrapped_faces_ptr=wrapped_facesw.ptr();

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

		for(int j=0;j<3;j++) {

			Vector3& v = wrapped_faces_ptr[i].vertex[j];
			v=v*voxelsize;
			v+=global_aabb.pos;
		}
	}

	// clean up grid
	//print_line("Wrapper (5/6): Grid Cleanup");

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

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

			memdelete_arr( cell_status[i][j] );
		}

		memdelete_arr( cell_status[i] );
	}

	memdelete_arr(cell_status);
	if (p_error)
		*p_error=voxelsize.length();

	//print_line("Wrapper (6/6): Finished.");
	return wrapped_faces;
}

Geometry::MeshData Geometry::build_convex_mesh(const PoolVector<Plane> &p_planes) {

	MeshData mesh;


#define SUBPLANE_SIZE 1024.0

	float subplane_size = 1024.0; // should compute this from the actual plane
	for (int i=0;i<p_planes.size();i++) {

		Plane p =p_planes[i];

		Vector3 ref=Vector3(0.0,1.0,0.0);

		if (ABS(p.normal.dot(ref))>0.95)
			ref=Vector3(0.0,0.0,1.0); // change axis

		Vector3 right = p.normal.cross(ref).normalized();
		Vector3 up = p.normal.cross( right ).normalized();

		Vector< Vector3 > vertices;

		Vector3 center = p.get_any_point();
		// make a quad clockwise
		vertices.push_back( center - up * subplane_size + right * subplane_size );
		vertices.push_back( center - up * subplane_size - right * subplane_size );
		vertices.push_back( center + up * subplane_size - right * subplane_size );
		vertices.push_back( center + up * subplane_size + right * subplane_size );

		for (int j=0;j<p_planes.size();j++) {

			if (j==i)
				continue;


			Vector< Vector3 > new_vertices;
			Plane clip=p_planes[j];

			if (clip.normal.dot(p.normal)>0.95)
				continue;

			if (vertices.size()<3)
				break;

			for(int k=0;k<vertices.size();k++) {

				int k_n=(k+1)%vertices.size();

				Vector3 edge0_A=vertices[k];
				Vector3 edge1_A=vertices[k_n];

				real_t dist0 = clip.distance_to(edge0_A);
				real_t dist1 = clip.distance_to(edge1_A);


				if ( dist0 <= 0 ) { // behind plane

					new_vertices.push_back(vertices[k]);
				}


				// check for different sides and non coplanar
				if ( (dist0*dist1) < 0) {

					// calculate intersection
					Vector3 rel = edge1_A - edge0_A;

					real_t den=clip.normal.dot( rel );
					if (Math::abs(den)<CMP_EPSILON)
						continue; // point too short

					real_t dist=-(clip.normal.dot( edge0_A )-clip.d)/den;
					Vector3 inters = edge0_A+rel*dist;
					new_vertices.push_back(inters);
				}
			}

			vertices=new_vertices;
		}

		if (vertices.size()<3)
			continue;


		//result is a clockwise face

		MeshData::Face face;

		// add face indices
		for (int j=0;j<vertices.size();j++) {


			int idx=-1;
			for (int k=0;k<mesh.vertices.size();k++) {

				if (mesh.vertices[k].distance_to(vertices[j])<0.001) {

					idx=k;
					break;
				}
			}

			if (idx==-1) {

				idx=mesh.vertices.size();
				mesh.vertices.push_back(vertices[j]);
			}

			face.indices.push_back(idx);
		}
		face.plane=p;
		mesh.faces.push_back(face);

		//add edge

		for(int j=0;j<face.indices.size();j++) {

			int a=face.indices[j];
			int b=face.indices[(j+1)%face.indices.size()];

			bool found=false;
			for(int k=0;k<mesh.edges.size();k++) {

				if (mesh.edges[k].a==a && mesh.edges[k].b==b) {
					found=true;
					break;
				}
				if (mesh.edges[k].b==a && mesh.edges[k].a==b) {
					found=true;
					break;
				}
			}

			if (found)
				continue;
			MeshData::Edge edge;
			edge.a=a;
			edge.b=b;
			mesh.edges.push_back(edge);
		}


	}

	return mesh;
}


PoolVector<Plane> Geometry::build_box_planes(const Vector3& p_extents) {

	PoolVector<Plane> planes;

	planes.push_back( Plane( Vector3(1,0,0), p_extents.x ) );
	planes.push_back( Plane( Vector3(-1,0,0), p_extents.x ) );
	planes.push_back( Plane( Vector3(0,1,0), p_extents.y ) );
	planes.push_back( Plane( Vector3(0,-1,0), p_extents.y ) );
	planes.push_back( Plane( Vector3(0,0,1), p_extents.z ) );
	planes.push_back( Plane( Vector3(0,0,-1), p_extents.z ) );

	return planes;
}

PoolVector<Plane> Geometry::build_cylinder_planes(float p_radius, float p_height, int p_sides, Vector3::Axis p_axis) {

	PoolVector<Plane> planes;

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

		Vector3 normal;
		normal[(p_axis+1)%3]=Math::cos(i*(2.0*Math_PI)/p_sides);
		normal[(p_axis+2)%3]=Math::sin(i*(2.0*Math_PI)/p_sides);

		planes.push_back( Plane( normal, p_radius ) );
	}

	Vector3 axis;
	axis[p_axis]=1.0;

	planes.push_back( Plane( axis, p_height*0.5 ) );
	planes.push_back( Plane( -axis, p_height*0.5 ) );

	return planes;

}

PoolVector<Plane> Geometry::build_sphere_planes(float p_radius, int p_lats,int p_lons, Vector3::Axis p_axis) {


	PoolVector<Plane> planes;

	Vector3 axis;
	axis[p_axis]=1.0;

	Vector3 axis_neg;
	axis_neg[(p_axis+1)%3]=1.0;
	axis_neg[(p_axis+2)%3]=1.0;
	axis_neg[p_axis]=-1.0;

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

		Vector3 normal;
		normal[(p_axis+1)%3]=Math::cos(i*(2.0*Math_PI)/p_lons);
		normal[(p_axis+2)%3]=Math::sin(i*(2.0*Math_PI)/p_lons);

		planes.push_back( Plane( normal, p_radius ) );

		for (int j=1;j<=p_lats;j++) {

			//todo this is stupid, fix
			Vector3 angle = normal.linear_interpolate(axis,j/(float)p_lats).normalized();
			Vector3 pos = angle*p_radius;
			planes.push_back( Plane( pos, angle ) );
			planes.push_back( Plane( pos * axis_neg, angle * axis_neg) );

		}
	}

	return planes;

}

PoolVector<Plane> Geometry::build_capsule_planes(float p_radius, float p_height, int p_sides, int p_lats, Vector3::Axis p_axis) {

	PoolVector<Plane> planes;

		Vector3 axis;
	axis[p_axis]=1.0;

	Vector3 axis_neg;
	axis_neg[(p_axis+1)%3]=1.0;
	axis_neg[(p_axis+2)%3]=1.0;
	axis_neg[p_axis]=-1.0;

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

		Vector3 normal;
		normal[(p_axis+1)%3]=Math::cos(i*(2.0*Math_PI)/p_sides);
		normal[(p_axis+2)%3]=Math::sin(i*(2.0*Math_PI)/p_sides);

		planes.push_back( Plane( normal, p_radius ) );

		for (int j=1;j<=p_lats;j++) {

			Vector3 angle = normal.linear_interpolate(axis,j/(float)p_lats).normalized();
			Vector3 pos = axis*p_height*0.5 + angle*p_radius;
			planes.push_back( Plane( pos, angle ) );
			planes.push_back( Plane( pos * axis_neg, angle * axis_neg) );

		}
	}


	return planes;

}


struct _AtlasWorkRect {

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

struct _AtlasWorkRectResult {

	Vector<_AtlasWorkRect> result;
	int max_w;
	int max_h;
};

void Geometry::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 necesary because video cards have limits
	//on texture size (usually 2048 or 4096), so the more square a texture, the more chances
	//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.size()==0);

	Vector<_AtlasWorkRect> wrects;
	wrects.resize(p_rects.size());
	for(int i=0;i<p_rects.size();i++) {
		wrects[i].s=p_rects[i];
		wrects[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[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[j].p.x=ofs;
			wrects[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[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 reched, 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;
	float best_aspect=1e20;

	for(int i=0;i<results.size();i++) {

		float h = nearest_power_of_2(results[i].max_h);
		float w = nearest_power_of_2(results[i].max_w);
		float 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[ results[best].result[i].idx ]=results[best].result[i].p;
	}

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

}