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///////////////////////////////////////////////////////////////////////////////////////////////////
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// Copyright 2018 Leszek Koltunski //
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// //
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// This file is part of Distorted. //
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// //
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// Distorted is free software: you can redistribute it and/or modify //
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// it under the terms of the GNU General Public License as published by //
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// the Free Software Foundation, either version 2 of the License, or //
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// (at your option) any later version. //
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// //
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// Distorted is distributed in the hope that it will be useful, //
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// but WITHOUT ANY WARRANTY; without even the implied warranty of //
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the //
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// GNU General Public License for more details. //
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// //
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// You should have received a copy of the GNU General Public License //
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// along with Distorted. If not, see <http://www.gnu.org/licenses/>. //
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///////////////////////////////////////////////////////////////////////////////////////////////////
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package org.distorted.library.mesh;
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///////////////////////////////////////////////////////////////////////////////////////////////////
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/**
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* Create a Mesh which approximates a sphere.
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* <p>
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* Do so by starting off with a 16-faced solid which is basically a regular dodecahedron with each
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* of its 8 faces vertically split into 2 triangles, and which each step divide each of its triangular
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* faces into smaller and smaller subtriangles and inflate their vertices to lay on the surface or the
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* sphere.
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*/
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public class MeshSphere extends MeshBase
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{
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private static final int NUMFACES = 16;
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private static final double P = Math.PI;
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// An array of 16 entries, each describing a single face of a solid in an (admittedly) weird
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// fashion. Each face is a triangle, with 2 vertices on the same latitude.
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// Single row is (longitude of V1, longitude of V2, (common) latitude of V1 and V2, latitude of V3)
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// longitude of V3 is simply midpoint of V1 and V2 so we don't have to specify it here.
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private static final double[][] FACES = {
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{ 0.00*P, 0.25*P, 0.0, 0.5*P },
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{ 0.25*P, 0.50*P, 0.0, 0.5*P },
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{ 0.50*P, 0.75*P, 0.0, 0.5*P },
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{ 0.75*P, 1.00*P, 0.0, 0.5*P },
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{ 1.00*P, 1.25*P, 0.0, 0.5*P },
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{ 1.25*P, 1.50*P, 0.0, 0.5*P },
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{ 1.50*P, 1.75*P, 0.0, 0.5*P },
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{ 1.75*P, 0.00*P, 0.0, 0.5*P },
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{ 0.00*P, 0.25*P, 0.0,-0.5*P },
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{ 0.25*P, 0.50*P, 0.0,-0.5*P },
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{ 0.50*P, 0.75*P, 0.0,-0.5*P },
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{ 0.75*P, 1.00*P, 0.0,-0.5*P },
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{ 1.00*P, 1.25*P, 0.0,-0.5*P },
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{ 1.25*P, 1.50*P, 0.0,-0.5*P },
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{ 1.50*P, 1.75*P, 0.0,-0.5*P },
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{ 1.75*P, 0.00*P, 0.0,-0.5*P },
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};
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private int currentVert;
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private int numVertices;
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// Each of the 16 faces of the solid requires (level*level + 4*level) vertices for the face
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// itself and a join to the next face (which requires 2 vertices). We don't need the join in case
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// of the last, 16th face, thus the -2.
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// (level*level +4*level) because there are level*level little triangles, each requiring new vertex,
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// plus 2 extra vertices to start off a row and 2 to move to the next row (or the next face in case
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// of the last row) and there are 'level' rows.
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private void computeNumberOfVertices(int level)
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{
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numVertices = NUMFACES*level*(level+4) -2;
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currentVert = 0;
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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private void repeatVertex(float[] attribs1, float[] attribs2)
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{
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if( currentVert>0 )
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{
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attribs1[VERT1_ATTRIBS*currentVert + POS_ATTRIB ] = attribs1[VERT1_ATTRIBS*(currentVert-1) + POS_ATTRIB ];
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attribs1[VERT1_ATTRIBS*currentVert + POS_ATTRIB+1] = attribs1[VERT1_ATTRIBS*(currentVert-1) + POS_ATTRIB+1];
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attribs1[VERT1_ATTRIBS*currentVert + POS_ATTRIB+2] = attribs1[VERT1_ATTRIBS*(currentVert-1) + POS_ATTRIB+2];
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attribs1[VERT1_ATTRIBS*currentVert + NOR_ATTRIB ] = attribs1[VERT1_ATTRIBS*(currentVert-1) + NOR_ATTRIB ];
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attribs1[VERT1_ATTRIBS*currentVert + NOR_ATTRIB+1] = attribs1[VERT1_ATTRIBS*(currentVert-1) + NOR_ATTRIB+1];
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attribs1[VERT1_ATTRIBS*currentVert + NOR_ATTRIB+2] = attribs1[VERT1_ATTRIBS*(currentVert-1) + NOR_ATTRIB+2];
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attribs2[VERT2_ATTRIBS*currentVert + TEX_ATTRIB ] = attribs2[VERT2_ATTRIBS*(currentVert-1) + TEX_ATTRIB ];
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attribs2[VERT2_ATTRIBS*currentVert + TEX_ATTRIB+1] = attribs2[VERT2_ATTRIBS*(currentVert-1) + TEX_ATTRIB+1];
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currentVert++;
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}
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// Supposed to return the latitude of the point between two points on the sphere with latitudes
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// lat1 and lat2, so if for example quot=0.2, then it will return the latitude of something 20%
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// along the way from lat1 to lat2.
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//
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// This is approximation only - in general it is of course not true that the midpoint of two points
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// on a unit sphere with spherical coords (A1,B1) and (A2,B2) is ( (A1+A2)/2, (B1+B2)/2 ) - take
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// (0,0) and (PI, epsilon) as a counterexample.
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//
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// Here however, the latitudes we are interested at are the latitudes of the vertices of a regular
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// icosahedron - i.e. +=A and +=PI/2, whose longitudes are close, and we don't really care if the
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// split into smaller triangles is exact.
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//
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// quot better be between 0.0 and 1.0.
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// this is 'directed' i.e. from lat1 to lat2.
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private double midLatitude(double lat1, double lat2, double quot)
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{
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return lat1*(1.0-quot)+lat2*quot;
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// Same in case of longitude. This is for our needs exact, because we are ever only calling this with
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// two longitudes of two vertices with the same latitude. Additional problem: things can wrap around
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// the circle.
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// this is 'undirected' i.e. we don't assume from lon1 to lon2 - just along the smaller arc joining
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// lon1 to lon2.
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private double midLongitude(double lon1, double lon2, double quot)
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{
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double min, max;
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if( lon1<lon2 ) { min=lon1; max=lon2; }
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else { min=lon2; max=lon1; }
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double diff = max-min;
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if( diff>P ) { diff=2*P-diff; min=max; }
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double ret = min+quot*diff;
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if( ret>=2*P ) ret-=2*P;
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return ret;
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// linear map (column,row, level):
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//
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// ( 0, 0, level) -> (lonV1,latV12)
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// ( 0, level-1, level) -> (lonV3,latV3 )
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// (level-1, 0, level) -> (lonV2,latV12)
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private void addVertex(float[] attribs1, float[] attribs2, int column, int row, int level,
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double lonV1, double lonV2, double latV12, double latV3)
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{
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double quotX = (double)column/level;
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double quotY = (double)row /level;
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double quotZ;
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if( latV12*latV3 < 0.0 ) // equatorial triangle
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{
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quotZ = quotX + 0.5*quotY;
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}
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else // polar triangle
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{
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quotZ = (quotY==1.0 ? 0.5 : quotX / (1.0-quotY));
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}
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double longitude = midLongitude(lonV1, lonV2, quotZ );
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double latitude = midLatitude(latV12, latV3, quotY );
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double sinLON = Math.sin(longitude);
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double cosLON = Math.cos(longitude);
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double sinLAT = Math.sin(latitude);
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double cosLAT = Math.cos(latitude);
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float x = (float)(cosLAT*sinLON / 2.0f);
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float y = (float)(sinLAT / 2.0f);
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float z = (float)(cosLAT*cosLON / 2.0f);
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double texX = 0.5 + longitude/(2*P);
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if( texX>=1.0 ) texX-=1.0;
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double texY = 0.5 + latitude/P;
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attribs1[VERT1_ATTRIBS*currentVert + POS_ATTRIB ] = x; //
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attribs1[VERT1_ATTRIBS*currentVert + POS_ATTRIB+1] = y; //
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attribs1[VERT1_ATTRIBS*currentVert + POS_ATTRIB+2] = z; //
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// In case of this Mesh so it happens that
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attribs1[VERT1_ATTRIBS*currentVert + NOR_ATTRIB ] = 2*x;// the vertex coords, normal vector, and
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attribs1[VERT1_ATTRIBS*currentVert + NOR_ATTRIB+1] = 2*y;// inflate vector have identical (x,y,z).
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attribs1[VERT1_ATTRIBS*currentVert + NOR_ATTRIB+2] = 2*z;//
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attribs2[VERT2_ATTRIBS*currentVert + TEX_ATTRIB ] = (float)texX;
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attribs2[VERT2_ATTRIBS*currentVert + TEX_ATTRIB+1] = (float)texY;
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currentVert++;
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////////////////////////////////////////////////////////////////////////////////////////////////
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// Problem: on the 'change of date' line in the back of the sphere, some triangles see texX
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// coords suddenly jump from 1-epsilon to 0, which looks like a seam with a narrow copy of
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// the whole texture there. Solution: remap texX to 1.0.
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////////////////////////////////////////////////////////////////////////////////////////////////
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if( currentVert>=3 && texX==0.0 )
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{
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double tex1 = attribs2[VERT2_ATTRIBS*(currentVert-2) + TEX_ATTRIB];
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double tex2 = attribs2[VERT2_ATTRIBS*(currentVert-3) + TEX_ATTRIB];
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// if the triangle is not degenerate and last vertex was on the western hemisphere
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if( tex1!=tex2 && tex1>0.5 )
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{
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attribs2[VERT2_ATTRIBS*(currentVert-1) + TEX_ATTRIB] = 1.0f;
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}
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}
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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private void buildFace(float[] attribs1, float[] attribs2, int level, int face, double lonV1, double lonV2, double latV12, double latV3)
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{
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for(int row=0; row<level; row++)
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{
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for (int column=0; column<level-row; column++)
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{
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addVertex(attribs1, attribs2, column, row , level, lonV1, lonV2, latV12, latV3);
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if (column==0 && !(face==0 && row==0 ) ) repeatVertex(attribs1, attribs2);
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addVertex(attribs1, attribs2, column, row+1, level, lonV1, lonV2, latV12, latV3);
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}
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addVertex(attribs1, attribs2, level-row, row , level, lonV1, lonV2, latV12, latV3);
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if( row!=level-1 || face!=NUMFACES-1 ) repeatVertex(attribs1, attribs2);
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}
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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// PUBLIC API
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///////////////////////////////////////////////////////////////////////////////////////////////////
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/**
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* Creates the underlying grid of vertices with the usual attribs which approximates a sphere.
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* <p>
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* When level=1, it outputs the 12 vertices of a regular icosahedron.
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* When level=N, it divides each of the 20 icosaherdon's triangular faces into N^2 smaller triangles
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* (by dividing each side into N equal segments) and 'inflates' the internal vertices so that they
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* touch the sphere.
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*
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* @param level Specifies the approximation level. Valid values: level ≥ 1
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*/
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public MeshSphere(int level)
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{
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super();
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computeNumberOfVertices(level);
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float[] attribs1= new float[VERT1_ATTRIBS*numVertices];
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float[] attribs2= new float[VERT2_ATTRIBS*numVertices];
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for(int face=0; face<NUMFACES; face++ )
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{
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buildFace(attribs1, attribs2, level, face, FACES[face][0], FACES[face][1], FACES[face][2], FACES[face][3]);
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}
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if( currentVert!=numVertices )
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android.util.Log.d("MeshSphere", "currentVert= " +currentVert+" numVertices="+numVertices );
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setAttribs(attribs1, attribs2);
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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/**
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* Copy cconstructor.
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*/
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public MeshSphere(MeshSphere mesh, boolean deep)
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{
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super(mesh,deep);
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}
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///////////////////////////////////////////////////////////////////////////////////////////////////
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/**
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* Copy the Mesh.
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*
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* @param deep If to be a deep or shallow copy of mVertAttribs1, i.e. the array holding vertices,
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* normals and inflates (the rest, in particular the mVertAttribs2 containing texture
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* coordinates and effect associations, is always deep copied)
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*/
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public MeshSphere copy(boolean deep)
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{
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return new MeshSphere(this,deep);
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}
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}
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