Revision ebe0476f
Added by Leszek Koltunski over 5 years ago
| src/main/java/org/distorted/library/mesh/MeshSphere.java | ||
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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 dividing each of the 20 faces of the regular icosahedron into smaller triangles and inflating |
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* those to lay on the surface of the sphere. |
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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 = 20;
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private static final int NUMFACES = 16;
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private static final double sqrt2 = Math.sqrt(2.0); |
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private static final double P = Math.PI; |
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private static final double A = 0.463647609; // arctan(0.5), +-latitude of the 10 'middle' vertices |
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// https://en.wikipedia.org/wiki/Regular_icosahedron |
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// An array of 20 entries, each describing a single face of the regular icosahedron in an (admittedly) |
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// weird fashion. |
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// Each face of a regular icosahedron is a equilateral triangle, with 2 vertices on the same latitude. |
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// An array of 16 entries, each describing a single face of the 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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{ 0.0*P, 0.4*P, A, 0.5*P },
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{ 0.4*P, 0.8*P, A, 0.5*P },
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{ 0.8*P, 1.2*P, A, 0.5*P }, // 5 'top' faces with
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{ 1.2*P, 1.6*P, A, 0.5*P }, // the North Pole
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{ 1.6*P, 2.0*P, A, 0.5*P },
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{ 0.0*P, 0.4*P, A, -A },
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{ 0.4*P, 0.8*P, A, -A },
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{ 0.8*P, 1.2*P, A, -A }, // 5 faces mostly above
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{ 1.2*P, 1.6*P, A, -A }, // the equator
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{ 1.6*P, 2.0*P, A, -A },
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{ 0.2*P, 0.6*P, -A, A },
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{ 0.6*P, 1.0*P, -A, A },
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{ 1.0*P, 1.4*P, -A, A }, // 5 faces mostly below
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{ 1.4*P, 1.8*P, -A, A }, // the equator
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{ 1.8*P, 0.2*P, -A, A },
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{ 0.2*P, 0.6*P, -A,-0.5*P },
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{ 0.6*P, 1.0*P, -A,-0.5*P },
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{ 1.0*P, 1.4*P, -A,-0.5*P }, // 5 'bottom' faces with
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{ 1.4*P, 1.8*P, -A,-0.5*P }, // the South Pole
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{ 1.8*P, 0.2*P, -A,-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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{ 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 20 faces of the icosahedron requires (level*level + 4*level) vertices for the face
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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, 20th face, thus the -2.
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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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// |
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// Now to this we need to add 6*(level-1) vertices for the internal seams in the three triangles |
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// in the back ( 2,7,16 in the list above ): 3 triangles, level-1 rows of more than 1 triangle in |
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// each, 2 extra seam vertices in each row. |
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private void computeNumberOfVertices(int level) |
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{
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numVertices = NUMFACES*level*(level+4) -2 + 6*(level-1);
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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 int convertAng(double radian) |
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{
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return (int)(radian*180.0/P); |
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} |
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/////////////////////////////////////////////////////////////////////////////////////////////////// |
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private void repeatVertex(float[] attribs, int diff) |
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private void repeatVertex(float[] attribs) |
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{
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//android.util.Log.e("sphere", "repeat last!");
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if( currentVert>0 ) |
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{
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attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB ] = attribs[VERT_ATTRIBS*(currentVert-diff) + POS_ATTRIB ];
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attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-diff) + POS_ATTRIB+1];
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attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB+2] = attribs[VERT_ATTRIBS*(currentVert-diff) + POS_ATTRIB+2];
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attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB ] = attribs[VERT_ATTRIBS*(currentVert-1) + POS_ATTRIB ];
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attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-1) + POS_ATTRIB+1];
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attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB+2] = attribs[VERT_ATTRIBS*(currentVert-1) + POS_ATTRIB+2];
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attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB ] = attribs[VERT_ATTRIBS*(currentVert-diff) + NOR_ATTRIB ];
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attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-diff) + NOR_ATTRIB+1];
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attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB+2] = attribs[VERT_ATTRIBS*(currentVert-diff) + NOR_ATTRIB+2];
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attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB ] = attribs[VERT_ATTRIBS*(currentVert-1) + NOR_ATTRIB ];
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attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-1) + NOR_ATTRIB+1];
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attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB+2] = attribs[VERT_ATTRIBS*(currentVert-1) + NOR_ATTRIB+2];
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attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB ] = attribs[VERT_ATTRIBS*(currentVert-diff) + INF_ATTRIB ];
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attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-diff) + INF_ATTRIB+1];
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attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB+2] = attribs[VERT_ATTRIBS*(currentVert-diff) + INF_ATTRIB+2];
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attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB ] = attribs[VERT_ATTRIBS*(currentVert-1) + INF_ATTRIB ];
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attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-1) + INF_ATTRIB+1];
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attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB+2] = attribs[VERT_ATTRIBS*(currentVert-1) + INF_ATTRIB+2];
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attribs[VERT_ATTRIBS*currentVert + TEX_ATTRIB ] = attribs[VERT_ATTRIBS*(currentVert-diff) + TEX_ATTRIB ];
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attribs[VERT_ATTRIBS*currentVert + TEX_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-diff) + TEX_ATTRIB+1];
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attribs[VERT_ATTRIBS*currentVert + TEX_ATTRIB ] = attribs[VERT_ATTRIBS*(currentVert-1) + TEX_ATTRIB ];
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attribs[VERT_ATTRIBS*currentVert + TEX_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-1) + TEX_ATTRIB+1];
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currentVert++; |
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} |
| ... | ... | |
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// (level-1, 0, level) -> (lonV2,latV12) |
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private void addVertex(float[] attribs, int column, int row, int level, |
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double lonV1, double lonV2, double latV12, double latV3, boolean lastInRow)
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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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|
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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+epsilon, which looks like a seam with a narrow copy |
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// of the whole texture there. |
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// Solution: each such 'jump' triangle, if it is the last in a row, should have the texX of its |
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// last (and maybe forelast as well) vertex remapped to 1.0. |
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// If such triangle is not the last in its row, we need to add two extra vertices between it and |
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// the next one, remap the old ones' texX to 1.0, and set one of the two new ones' texX to 0.0. |
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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 ) |
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if( currentVert>=3 && texX==0.0 )
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{
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double tex1 = attribs[VERT_ATTRIBS*(currentVert-2) + TEX_ATTRIB]; |
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double tex2 = attribs[VERT_ATTRIBS*(currentVert-3) + TEX_ATTRIB]; |
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double y1 = attribs[VERT_ATTRIBS*(currentVert-2) + INF_ATTRIB + 1]; |
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double y2 = attribs[VERT_ATTRIBS*(currentVert-3) + INF_ATTRIB + 1]; |
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if( tex1!=tex2 || y1!=y2 ) // if the triangle is not degenerate |
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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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double diff1 = Math.abs(texX-tex1); |
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double diff2 = Math.abs(texX-tex2); |
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|
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if( diff1>0.5 || diff2>0.5 ) // a jump in texture coords which can only happen along the |
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{ // 'date change' line. Have to correct!
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if( lastInRow ) |
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{
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attribs[VERT_ATTRIBS*(currentVert-1) + TEX_ATTRIB] = 1.0f; |
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if( tex1<tex2 ) attribs[VERT_ATTRIBS*(currentVert-2) + TEX_ATTRIB] = 1.0f; |
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} |
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else |
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{
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if( latitude> -A ) // one of the top two triangles being corrected |
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{
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if (2*column+row-1 == level) // last such triangle in a row; have to introduce extra 2 vertices. |
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{
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/* |
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android.util.Log.e("sphere", "LAST max diff exceeded: " + convertAng(longitude) + " " + convertAng(latitude) + " texX=" + texX);
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android.util.Log.d("sphere", " tex1=" + tex1 + " tex2=" + tex2 + " y1=" + y1 + " y2=" + y2);
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android.util.Log.d("sphere", " latV12=" + latV12 + " latV3=" + latV3);
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*/ |
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repeatVertex(attribs, 2); |
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repeatVertex(attribs, 2); |
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attribs[VERT_ATTRIBS*(currentVert-2) + TEX_ATTRIB] = 0.0f; |
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attribs[VERT_ATTRIBS*(currentVert-3) + TEX_ATTRIB] = 1.0f; |
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if (tex1 < tex2) attribs[VERT_ATTRIBS*(currentVert-4) + TEX_ATTRIB] = 1.0f; |
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} |
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if (2*column+row == level) // not the last; just remap current vertex' texX to 1.0. |
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{
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/* |
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android.util.Log.e("sphere", "NOT LAST max diff exceeded: " + convertAng(longitude) + " " + convertAng(latitude) + " texX=" + texX);
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android.util.Log.d("sphere", " tex1=" + tex1 + " tex2=" + tex2 + " y1=" + y1 + " y2=" + y2);
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android.util.Log.d("sphere", " latV12=" + latV12 + " latV3=" + latV3);
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*/ |
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attribs[VERT_ATTRIBS*(currentVert-1) + TEX_ATTRIB] = 1.0f; |
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} |
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} |
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else // bottom triangle |
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{
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/* |
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android.util.Log.e("sphere", "BOTTOM LAST max diff exceeded: " + convertAng(longitude) + " " + convertAng(latitude) + " texX=" + texX);
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android.util.Log.d("sphere", " tex1=" + tex1 + " tex2=" + tex2 + " y1=" + y1 + " y2=" + y2);
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android.util.Log.d("sphere", " latV12=" + latV12 + " latV3=" + latV3);
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*/ |
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repeatVertex(attribs, 2); |
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repeatVertex(attribs, 2); |
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attribs[VERT_ATTRIBS*(currentVert-3) + TEX_ATTRIB] = 1.0f; |
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} |
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} |
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} |
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attribs[VERT_ATTRIBS*(currentVert-1) + TEX_ATTRIB] = 1.0f; |
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} |
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} |
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//////////////////////////////////////////////////////////////////////////////////////////////// |
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// End problem |
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//////////////////////////////////////////////////////////////////////////////////////////////// |
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} |
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/////////////////////////////////////////////////////////////////////////////////////////////////// |
| ... | ... | |
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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(attribs, column, row , level, lonV1, lonV2, latV12, latV3, false);
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if (column==0 && !(face==0 && row==0 ) ) repeatVertex(attribs,1);
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addVertex(attribs, column, row+1, level, lonV1, lonV2, latV12, latV3, false);
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addVertex(attribs, column, row , level, lonV1, lonV2, latV12, latV3); |
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if (column==0 && !(face==0 && row==0 ) ) repeatVertex(attribs); |
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addVertex(attribs, column, row+1, level, lonV1, lonV2, latV12, latV3); |
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} |
| 320 | 242 |
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addVertex(attribs, level-row, row , level, lonV1, lonV2, latV12, latV3, true);
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if( row!=level-1 || face!=NUMFACES-1 ) repeatVertex(attribs,1);
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addVertex(attribs, level-row, row , level, lonV1, lonV2, latV12, latV3); |
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if( row!=level-1 || face!=NUMFACES-1 ) repeatVertex(attribs); |
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} |
| 324 | 246 |
} |
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|
Also available in: Unified diff
Simplify MeshSphere by deriving it not from a regular icosahedron (which has a problem of a wiggly seam line at the 'change of date' in the back of the sphere) but something that at the back has a straight vertical border between triangles: a diamond-like 16-faced solid.