The subdivision surface algorithm divides and refines (deforms) a given mesh recursively to certain degree (depth). The mesh3d algorithm consists of two stages: divide and deform. The divide step generates for each triangle or quad four new triangles or quads, the deform step drags the points (refinement step).

subdivision3d( x,  ...)
# S3 method for mesh3d
subdivision3d( x, depth = 1, normalize = FALSE, deform = TRUE, ... )
divide.mesh3d(mesh,  vb = mesh$vb, ib = mesh$ib, it = mesh$it ) normalize.mesh3d(mesh) deform.mesh3d(mesh, vb = mesh$vb, ib = mesh$ib, it = mesh$it )

## Arguments

x

3d geometry mesh

mesh

3d geometry mesh

depth

recursion depth

normalize

normalize mesh3d coordinates after division if deform is TRUE

deform

deform mesh

it

indices for triangular faces

ib

vb

matrix of vertices: 4 x n matrix (rows x, y, z, h) or equivalent vector, where h indicates scaling of each plotted quad

...

other arguments (unused)

## Details

subdivision3d takes a mesh object and replaces each triangle or quad with 4 new ones by adding vertices half-way along the edges (and one in the centre of a quad). The positions of the vertices are deformed so that the resulting surface is smoother than the original. These operations are repeated depth times.

The other functions do the individual steps of the subdivision. divide.mesh3d adds the extra vertices. deform.mesh3d does the smoothing by replacing each vertex with the average of each of its neighbours. normalize.mesh3d normalizes the homogeneous coordinates, by setting the 4th coordinate to 1. (The 4th coordinate is used as a weight in the deform step.)

r3d mesh3d
  open3d()
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/LsmBvSRcEj9daFG/\n6r5fvQwRyj64zWq/6r5fvQwRyj64zWq/6r5fvQwRyj64zWq/6r5fvQwRyj64zWq/EKwYvsrt\nuz6ODWu/EKwYvsrtuz6ODWu/EKwYvsrtuz6ODWu/EKwYvsrtuz6ODWu/3QEXvniDEz/gyk2/\n3QEXvniDEz/gyk2/3QEXvniDEz/gyk2/3QEXvniDEz/gyk2/YhOavRxqjj0tp36/YhOavRxq\njj0tp36/YhOavRxqjj0tp36/YhOavRxqjj0tp36/abtRvguaYj0dLHq/abtRvguaYj0dLHq/\nabtRvguaYj0dLHq/abtRvguaYj0dLHq/HSxBvqFmSj5CQna/HSxBvqFmSj5CQna/HSxBvqFm\nSj5CQna/HSxBvqFmSj5CQna/j3qCvWKfWj6rkHm/j3qCvWKfWj6rkHm/j3qCvWKfWj6rkHm/\nj3qCvWKfWj6rkHm/8SIUvwPkmT3f5U+/8SIUvwPkmT3f5U+/8SIUvwPkmT3f5U+/8SIUvwPk\nmT3f5U+/OI8Rv5NnIz4rl06/OI8Rv5NnIz4rl06/OI8Rv5NnIz4rl06/OI8Rv5NnIz4rl06/\n97PJvmyFOj5/oWa/97PJvmyFOj5/oWa/97PJvmyFOj5/oWa/97PJvmyFOj5/oWa/0wrKvof2\nXz3Zzmq/0wrKvof2Xz3Zzmq/0wrKvof2Xz3Zzmq/0wrKvof2Xz3Zzmq/ojwDP3Wxtj7160e/\nojwDP3Wxtj7160e/ojwDP3Wxtj7160e/ojwDP3Wxtj7160e/lzgOPxgMlT44Y0e/lzgOPxgM\nlT44Y0e/lzgOPxgMlT44Y0e/lzgOPxgMlT44Y0e/qmSbPu92uT43nGG/qmSbPu92uT43nGG/\nqmSbPu92uT43nGG/qmSbPu92uT43nGG/C+tyPpQuBz9JvlC/C+tyPpQuBz9JvlC/C+tyPpQu\nBz9JvlC/C+tyPpQuBz9JvlC/JFwSPy7JgT1daFG/JFwSPy7JgT1daFG/JFwSPy7JgT1daFG/\nJFwSPy7JgT1daFG/DBHKPuq+Xz24zWq/DBHKPuq+Xz24zWq/DBHKPuq+Xz24zWq/DBHKPuq+\nXz24zWq/yu27PhCsGD6ODWu/yu27PhCsGD6ODWu/yu27PhCsGD6ODWu/yu27PhCsGD6ODWu/\neIMTP90BFz7gyk2/eIMTP90BFz7gyk2/eIMTP90BFz7gyk2/eIMTP90BFz7gyk2/HGqOPWIT\nmj0tp36/HGqOPWITmj0tp36/HGqOPWITmj0tp36/HGqOPWITmj0tp36/C5piPWm7UT4dLHq/\nC5piPWm7UT4dLHq/C5piPWm7UT4dLHq/C5piPWm7UT4dLHq/oWZKPh0sQT5CQna/oWZKPh0s\nQT5CQna/oWZKPh0sQT5CQna/oWZKPh0sQT5CQna/Yp9aPo96gj2rkHm/Yp9aPo96gj2rkHm/\nYp9aPo96gj2rkHm/Yp9aPo96gj2rkHm/A+SZPfEiFD/f5U+/A+SZPfEiFD/f5U+/A+SZPfEi\nFD/f5U+/A+SZPfEiFD/f5U+/k2cjPjiPET8rl06/k2cjPjiPET8rl06/k2cjPjiPET8rl06/\nk2cjPjiPET8rl06/bIU6PvezyT5/oWa/bIU6PvezyT5/oWa/bIU6PvezyT5/oWa/bIU6Pvez\nyT5/oWa/h/ZfPdMKyj7Zzmq/h/ZfPdMKyj7Zzmq/h/ZfPdMKyj7Zzmq/h/ZfPdMKyj7Zzmq/\ndbG2PqI8A7/160e/dbG2PqI8A7/160e/dbG2PqI8A7/160e/dbG2PqI8A7/160e/GAyVPpc4\nDr84Y0e/GAyVPpc4Dr84Y0e/GAyVPpc4Dr84Y0e/GAyVPpc4Dr84Y0e/73a5Pqpkm743nGG/\n73a5Pqpkm743nGG/73a5Pqpkm743nGG/73a5Pqpkm743nGG/lC4HPwvrcr5JvlC/lC4HPwvr\ncr5JvlC/lC4HPwvrcr5JvlC/lC4HPwvrcr5JvlC/LsmBPSRcEr9daFG/LsmBPSRcEr9daFG/\nLsmBPSRcEr9daFG/LsmBPSRcEr9daFG/6r5fPQwRyr64zWq/6r5fPQwRyr64zWq/6r5fPQwR\nyr64zWq/6r5fPQwRyr64zWq/EKwYPsrtu76ODWu/EKwYPsrtu76ODWu/EKwYPsrtu76ODWu/\nEKwYPsrtu76ODWu/3QEXPniDE7/gyk2/3QEXPniDE7/gyk2/3QEXPniDE7/gyk2/3QEXPniD\nE7/gyk2/YhOaPRxqjr0tp36/YhOaPRxqjr0tp36/YhOaPRxqjr0tp36/YhOaPRxqjr0tp36/\nabtRPguaYr0dLHq/abtRPguaYr0dLHq/abtRPguaYr0dLHq/abtRPguaYr0dLHq/HSxBPqFm\nSr5CQna/HSxBPqFmSr5CQna/HSxBPqFmSr5CQna/HSxBPqFmSr5CQna/j3qCPWKfWr6rkHm/\nj3qCPWKfWr6rkHm/j3qCPWKfWr6rkHm/j3qCPWKfWr6rkHm/8SIUPwPkmb3f5U+/8SIUPwPk\nmb3f5U+/8SIUPwPkmb3f5U+/8SIUPwPkmb3f5U+/OI8RP5NnI74rl06/OI8RP5NnI74rl06/\nOI8RP5NnI74rl06/OI8RP5NnI74rl06/97PJPmyFOr5/oWa/97PJPmyFOr5/oWa/97PJPmyF\nOr5/oWa/97PJPmyFOr5/oWa/0wrKPof2X73Zzmq/0wrKPof2X73Zzmq/0wrKPof2X73Zzmq/\n0wrKPof2X73Zzmq/ojwDv/XrRz91sba+ojwDv/XrRz91sba+ojwDv/XrRz91sba+ojwDv/Xr\nRz91sba+lzgOvzhjRz8YDJW+lzgOvzhjRz8YDJW+lzgOvzhjRz8YDJW+lzgOvzhjRz8YDJW+\nqmSbvjecYT/vdrm+qmSbvjecYT/vdrm+qmSbvjecYT/vdrm+qmSbvjecYT/vdrm+C+tyvkm+\nUD+ULge/C+tyvkm+UD+ULge/C+tyvkm+UD+ULge/C+tyvkm+UD+ULge/JFwSv11oUT8uyYG9\nJFwSv11oUT8uyYG9JFwSv11oUT8uyYG9JFwSv11oUT8uyYG9DBHKvrjNaj/qvl+9DBHKvrjN\naj/qvl+9DBHKvrjNaj/qvl+9DBHKvrjNaj/qvl+9y+27vo8Naz8RrBi+y+27vo8Naz8RrBi+\ny+27vo8Naz8RrBi+y+27vo8Naz8RrBi+eIMTv+DKTT/dARe+eIMTv+DKTT/dARe+eIMTv+DK\nTT/dARe+eIMTv+DKTT/dARe+HGqOvS2nfj9iE5q9HGqOvS2nfj9iE5q9HGqOvS2nfj9iE5q9\nHGqOvS2nfj9iE5q9C5pivR0sej9pu1G+C5pivR0sej9pu1G+C5pivR0sej9pu1G+C5pivR0s\nej9pu1G+oWZKvkJCdj8dLEG+oWZKvkJCdj8dLEG+oWZKvkJCdj8dLEG+oWZKvkJCdj8dLEG+\nYp9avquQeT+PeoK9Yp9avquQeT+PeoK9Yp9avquQeT+PeoK9Yp9avquQeT+PeoK9A+SZvd/l\nTz/xIhS/A+SZvd/lTz/xIhS/A+SZvd/lTz/xIhS/A+SZvd/lTz/xIhS/k2cjviuXTj84jxG/\nk2cjviuXTj84jxG/k2cjviuXTj84jxG/k2cjviuXTj84jxG/bIU6vn+hZj/3s8m+bIU6vn+h\nZj/3s8m+bIU6vn+hZj/3s8m+bIU6vn+hZj/3s8m+h/ZfvdnOaj/TCsq+h/ZfvdnOaj/TCsq+\nh/ZfvdnOaj/TCsq+h/ZfvdnOaj/TCsq+dbG2vvXrRz+iPAM/dbG2vvXrRz+iPAM/dbG2vvXr\nRz+iPAM/dbG2vvXrRz+iPAM/GAyVvjhjRz+XOA4/GAyVvjhjRz+XOA4/GAyVvjhjRz+XOA4/\nGAyVvjhjRz+XOA4/73a5vjecYT+qZJs+73a5vjecYT+qZJs+73a5vjecYT+qZJs+73a5vjec\nYT+qZJs+lC4Hv0m+UD8L63I+lC4Hv0m+UD8L63I+lC4Hv0m+UD8L63I+lC4Hv0m+UD8L63I+\nLsmBvV1oUT8kXBI/LsmBvV1oUT8kXBI/LsmBvV1oUT8kXBI/LsmBvV1oUT8kXBI/6r5fvbjN\naj8MEco+6r5fvbjNaj8MEco+6r5fvbjNaj8MEco+6r5fvbjNaj8MEco+EKwYvo4Naz/K7bs+\nEKwYvo4Naz/K7bs+EKwYvo4Naz/K7bs+EKwYvo4Naz/K7bs+3QEXvuDKTT94gxM/3QEXvuDK\nTT94gxM/3QEXvuDKTT94gxM/3QEXvuDKTT94gxM/YhOavS2nfj8cao49YhOavS2nfj8cao49\nYhOavS2nfj8cao49YhOavS2nfj8cao49abtRvh0sej8LmmI9abtRvh0sej8LmmI9abtRvh0s\nej8LmmI9abtRvh0sej8LmmI9HSxBvkJCdj+hZko+HSxBvkJCdj+hZko+HSxBvkJCdj+hZko+\nHSxBvkJCdj+hZko+j3qCvauQeT9in1o+j3qCvauQeT9in1o+j3qCvauQeT9in1o+j3qCvauQ\neT9in1o+8SIUv9/lTz8D5Jk98SIUv9/lTz8D5Jk98SIUv9/lTz8D5Jk98SIUv9/lTz8D5Jk9\nOI8RvyuXTj+TZyM+OI8RvyuXTj+TZyM+OI8RvyuXTj+TZyM+OI8RvyuXTj+TZyM+97PJvn+h\nZj9shTo+97PJvn+hZj9shTo+97PJvn+hZj9shTo+97PJvn+hZj9shTo+0wrKvtnOaj+H9l89\n0wrKvtnOaj+H9l890wrKvtnOaj+H9l890wrKvtnOaj+H9l89ojwDP/XrRz91sbY+ojwDP/Xr\nRz91sbY+ojwDP/XrRz91sbY+ojwDP/XrRz91sbY+lzgOPzhjRz8YDJU+lzgOPzhjRz8YDJU+\nlzgOPzhjRz8YDJU+lzgOPzhjRz8YDJU+qmSbPjecYT/vdrk+qmSbPjecYT/vdrk+qmSbPjec\nYT/vdrk+qmSbPjecYT/vdrk+C+tyPkm+UD+ULgc/C+tyPkm+UD+ULgc/C+tyPkm+UD+ULgc/\nC+tyPkm+UD+ULgc/JFwSP11oUT8uyYE9JFwSP11oUT8uyYE9JFwSP11oUT8uyYE9JFwSP11o\nUT8uyYE9DBHKPrjNaj/qvl89DBHKPrjNaj/qvl89DBHKPrjNaj/qvl89DBHKPrjNaj/qvl89\ny+27Po8Naz8RrBg+y+27Po8Naz8RrBg+y+27Po8Naz8RrBg+y+27Po8Naz8RrBg+eIMTP+DK\nTT/dARc+eIMTP+DKTT/dARc+eIMTP+DKTT/dARc+eIMTP+DKTT/dARc+HGqOPS2nfj9iE5o9\nHGqOPS2nfj9iE5o9HGqOPS2nfj9iE5o9HGqOPS2nfj9iE5o9C5piPR0sej9pu1E+C5piPR0s\nej9pu1E+C5piPR0sej9pu1E+C5piPR0sej9pu1E+oWZKPkJCdj8dLEE+oWZKPkJCdj8dLEE+\noWZKPkJCdj8dLEE+oWZKPkJCdj8dLEE+Yp9aPquQeT+PeoI9Yp9aPquQeT+PeoI9Yp9aPquQ\neT+PeoI9Yp9aPquQeT+PeoI9A+SZPd/lTz/xIhQ/A+SZPd/lTz/xIhQ/A+SZPd/lTz/xIhQ/\nA+SZPd/lTz/xIhQ/k2cjPiuXTj84jxE/k2cjPiuXTj84jxE/k2cjPiuXTj84jxE/k2cjPiuX\nTj84jxE/bIU6Pn+hZj/3s8k+bIU6Pn+hZj/3s8k+bIU6Pn+hZj/3s8k+bIU6Pn+hZj/3s8k+\nh/ZfPdnOaj/TCso+h/ZfPdnOaj/TCso+h/ZfPdnOaj/TCso+h/ZfPdnOaj/TCso+dbG2PvXr\nRz+iPAO/dbG2PvXrRz+iPAO/dbG2PvXrRz+iPAO/dbG2PvXrRz+iPAO/GAyVPjhjRz+XOA6/\nGAyVPjhjRz+XOA6/GAyVPjhjRz+XOA6/GAyVPjhjRz+XOA6/73a5PjecYT+qZJu+73a5Pjec\nYT+qZJu+73a5PjecYT+qZJu+73a5PjecYT+qZJu+lC4HP0m+UD8L63K+lC4HP0m+UD8L63K+\nlC4HP0m+UD8L63K+lC4HP0m+UD8L63K+LsmBPV1oUT8kXBK/LsmBPV1oUT8kXBK/LsmBPV1o\nUT8kXBK/LsmBPV1oUT8kXBK/6r5fPbjNaj8MEcq+6r5fPbjNaj8MEcq+6r5fPbjNaj8MEcq+\n6r5fPbjNaj8MEcq+EKwYPo4Naz/K7bu+EKwYPo4Naz/K7bu+EKwYPo4Naz/K7bu+EKwYPo4N\naz/K7bu+3QEXPuDKTT94gxO/3QEXPuDKTT94gxO/3QEXPuDKTT94gxO/3QEXPuDKTT94gxO/\nYhOaPS2nfj8cao69YhOaPS2nfj8cao69YhOaPS2nfj8cao69YhOaPS2nfj8cao69abtRPh0s\nej8LmmK9abtRPh0sej8LmmK9abtRPh0sej8LmmK9abtRPh0sej8LmmK9HSxBPkJCdj+hZkq+\nHSxBPkJCdj+hZkq+HSxBPkJCdj+hZkq+HSxBPkJCdj+hZkq+j3qCPauQeT9in1q+j3qCPauQ\neT9in1q+j3qCPauQeT9in1q+j3qCPauQeT9in1q+8SIUP9/lTz8D5Jm98SIUP9/lTz8D5Jm9\n8SIUP9/lTz8D5Jm98SIUP9/lTz8D5Jm9OI8RPyuXTj+TZyO+OI8RPyuXTj+TZyO+OI8RPyuX\nTj+TZyO+OI8RPyuXTj+TZyO+97PJPn+hZj9shTq+97PJPn+hZj9shTq+97PJPn+hZj9shTq+\n97PJPn+hZj9shTq+0wrKPtnOaj+H9l+90wrKPtnOaj+H9l+90wrKPtnOaj+H9l+90wrKPtnO\naj+H9l+99etHP3Wxtr6iPAO/9etHP3Wxtr6iPAO/9etHP3Wxtr6iPAO/9etHP3Wxtr6iPAO/\nOGNHPxgMlb6XOA6/OGNHPxgMlb6XOA6/OGNHPxgMlb6XOA6/OGNHPxgMlb6XOA6/N5xhP+92\nub6qZJu+N5xhP+92ub6qZJu+N5xhP+92ub6qZJu+N5xhP+92ub6qZJu+Sb5QP5QuB78L63K+\nSb5QP5QuB78L63K+Sb5QP5QuB78L63K+Sb5QP5QuB78L63K+XWhRPy7Jgb0kXBK/XWhRPy7J\ngb0kXBK/XWhRPy7Jgb0kXBK/XWhRPy7Jgb0kXBK/uM1qP+q+X70MEcq+uM1qP+q+X70MEcq+\nuM1qP+q+X70MEcq+uM1qP+q+X70MEcq+jg1rPxCsGL7K7bu+jg1rPxCsGL7K7bu+jg1rPxCs\nGL7K7bu+jg1rPxCsGL7K7bu+4MpNP90BF754gxO/4MpNP90BF754gxO/4MpNP90BF754gxO/\n4MpNP90BF754gxO/Lad+P2ITmr0cao69Lad+P2ITmr0cao69Lad+P2ITmr0cao69Lad+P2IT\nmr0cao69HSx6P2m7Ub4LmmK9HSx6P2m7Ub4LmmK9HSx6P2m7Ub4LmmK9HSx6P2m7Ub4LmmK9\nQkJ2Px0sQb6hZkq+QkJ2Px0sQb6hZkq+QkJ2Px0sQb6hZkq+QkJ2Px0sQb6hZkq+q5B5P496\ngr1in1q+q5B5P496gr1in1q+q5B5P496gr1in1q+q5B5P496gr1in1q+3+VPP/EiFL8D5Jm9\n3+VPP/EiFL8D5Jm93+VPP/EiFL8D5Jm93+VPP/EiFL8D5Jm9K5dOPziPEb+TZyO+K5dOPziP\nEb+TZyO+K5dOPziPEb+TZyO+K5dOPziPEb+TZyO+f6FmP/ezyb5shTq+f6FmP/ezyb5shTq+\nf6FmP/ezyb5shTq+f6FmP/ezyb5shTq+2c5qP9MKyr6H9l+92c5qP9MKyr6H9l+92c5qP9MK\nyr6H9l+92c5qP9MKyr6H9l+99etHP6I8Az91sba+9etHP6I8Az91sba+9etHP6I8Az91sba+\n9etHP6I8Az91sba+OGNHP5c4Dj8YDJW+OGNHP5c4Dj8YDJW+OGNHP5c4Dj8YDJW+OGNHP5c4\nDj8YDJW+N5xhP6pkmz7vdrm+N5xhP6pkmz7vdrm+N5xhP6pkmz7vdrm+N5xhP6pkmz7vdrm+\nSb5QPwvrcj6ULge/Sb5QPwvrcj6ULge/Sb5QPwvrcj6ULge/Sb5QPwvrcj6ULge/XWhRPyRc\nEj8uyYG9XWhRPyRcEj8uyYG9XWhRPyRcEj8uyYG9XWhRPyRcEj8uyYG9uM1qPwwRyj7qvl+9\nuM1qPwwRyj7qvl+9uM1qPwwRyj7qvl+9uM1qPwwRyj7qvl+9jw1rP8vtuz4RrBi+jw1rP8vt\nuz4RrBi+jw1rP8vtuz4RrBi+jw1rP8vtuz4RrBi+4MpNP3iDEz/dARe+4MpNP3iDEz/dARe+\n4MpNP3iDEz/dARe+4MpNP3iDEz/dARe+Lad+Pxxqjj1iE5q9Lad+Pxxqjj1iE5q9Lad+Pxxq\njj1iE5q9Lad+Pxxqjj1iE5q9HSx6PwuaYj1pu1G+HSx6PwuaYj1pu1G+HSx6PwuaYj1pu1G+\nHSx6PwuaYj1pu1G+QkJ2P6FmSj4dLEG+QkJ2P6FmSj4dLEG+QkJ2P6FmSj4dLEG+QkJ2P6Fm\nSj4dLEG+q5B5P2KfWj6PeoK9q5B5P2KfWj6PeoK9q5B5P2KfWj6PeoK9q5B5P2KfWj6PeoK9\n3+VPPwPkmT3xIhS/3+VPPwPkmT3xIhS/3+VPPwPkmT3xIhS/3+VPPwPkmT3xIhS/K5dOP5Nn\nIz44jxG/K5dOP5NnIz44jxG/K5dOP5NnIz44jxG/K5dOP5NnIz44jxG/f6FmP2yFOj73s8m+\nf6FmP2yFOj73s8m+f6FmP2yFOj73s8m+f6FmP2yFOj73s8m+2c5qP4f2Xz3TCsq+2c5qP4f2\nXz3TCsq+2c5qP4f2Xz3TCsq+2c5qP4f2Xz3TCsq+9etHP3Wxtj6iPAM/9etHP3Wxtj6iPAM/\n9etHP3Wxtj6iPAM/9etHP3Wxtj6iPAM/OGNHPxgMlT6XOA4/OGNHPxgMlT6XOA4/OGNHPxgM\nlT6XOA4/OGNHPxgMlT6XOA4/N5xhP+92uT6qZJs+N5xhP+92uT6qZJs+N5xhP+92uT6qZJs+\nN5xhP+92uT6qZJs+Sb5QP5QuBz8L63I+Sb5QP5QuBz8L63I+Sb5QP5QuBz8L63I+Sb5QP5Qu\nBz8L63I+XWhRPy7JgT0kXBI/XWhRPy7JgT0kXBI/XWhRPy7JgT0kXBI/XWhRPy7JgT0kXBI/\nuM1qP+q+Xz0MEco+uM1qP+q+Xz0MEco+uM1qP+q+Xz0MEco+uM1qP+q+Xz0MEco+jg1rPxCs\nGD7K7bs+jg1rPxCsGD7K7bs+jg1rPxCsGD7K7bs+jg1rPxCsGD7K7bs+4MpNP90BFz54gxM/\n4MpNP90BFz54gxM/4MpNP90BFz54gxM/4MpNP90BFz54gxM/Lad+P2ITmj0cao49Lad+P2IT\nmj0cao49Lad+P2ITmj0cao49Lad+P2ITmj0cao49HSx6P2m7UT4LmmI9HSx6P2m7UT4LmmI9\nHSx6P2m7UT4LmmI9HSx6P2m7UT4LmmI9QkJ2Px0sQT6hZko+QkJ2Px0sQT6hZko+QkJ2Px0s\nQT6hZko+QkJ2Px0sQT6hZko+q5B5P496gj1in1o+q5B5P496gj1in1o+q5B5P496gj1in1o+\nq5B5P496gj1in1o+3+VPP/EiFD8D5Jk93+VPP/EiFD8D5Jk93+VPP/EiFD8D5Jk93+VPP/Ei\nFD8D5Jk9K5dOPziPET+TZyM+K5dOPziPET+TZyM+K5dOPziPET+TZyM+K5dOPziPET+TZyM+\nf6FmP/ezyT5shTo+f6FmP/ezyT5shTo+f6FmP/ezyT5shTo+f6FmP/ezyT5shTo+2c5qP9MK\nyj6H9l892c5qP9MKyj6H9l892c5qP9MKyj6H9l892c5qP9MKyj6H9l899etHP6I8A791sbY+\n9etHP6I8A791sbY+9etHP6I8A791sbY+9etHP6I8A791sbY+OGNHP5c4Dr8YDJU+OGNHP5c4\nDr8YDJU+OGNHP5c4Dr8YDJU+OGNHP5c4Dr8YDJU+N5xhP6pkm77vdrk+N5xhP6pkm77vdrk+\nN5xhP6pkm77vdrk+N5xhP6pkm77vdrk+Sb5QPwvrcr6ULgc/Sb5QPwvrcr6ULgc/Sb5QPwvr\ncr6ULgc/Sb5QPwvrcr6ULgc/XWhRPyRcEr8uyYE9XWhRPyRcEr8uyYE9XWhRPyRcEr8uyYE9\nXWhRPyRcEr8uyYE9uM1qPwwRyr7qvl89uM1qPwwRyr7qvl89uM1qPwwRyr7qvl89uM1qPwwR\nyr7qvl89jw1rP8vtu74RrBg+jw1rP8vtu74RrBg+jw1rP8vtu74RrBg+jw1rP8vtu74RrBg+\n4MpNP3iDE7/dARc+4MpNP3iDE7/dARc+4MpNP3iDE7/dARc+4MpNP3iDE7/dARc+Lad+Pxxq\njr1iE5o9Lad+Pxxqjr1iE5o9Lad+Pxxqjr1iE5o9Lad+Pxxqjr1iE5o9HSx6PwuaYr1pu1E+\nHSx6PwuaYr1pu1E+HSx6PwuaYr1pu1E+HSx6PwuaYr1pu1E+QkJ2P6FmSr4dLEE+QkJ2P6Fm\nSr4dLEE+QkJ2P6FmSr4dLEE+QkJ2P6FmSr4dLEE+q5B5P2KfWr6PeoI9q5B5P2KfWr6PeoI9\nq5B5P2KfWr6PeoI9q5B5P2KfWr6PeoI93+VPPwPkmb3xIhQ/3+VPPwPkmb3xIhQ/3+VPPwPk\nmb3xIhQ/3+VPPwPkmb3xIhQ/K5dOP5NnI744jxE/K5dOP5NnI744jxE/K5dOP5NnI744jxE/\nK5dOP5NnI744jxE/f6FmP2yFOr73s8k+f6FmP2yFOr73s8k+f6FmP2yFOr73s8k+f6FmP2yF\nOr73s8k+2c5qP4f2X73TCso+2c5qP4f2X73TCso+2c5qP4f2X73TCso+2c5qP4f2X73TCso+\n9etHv6I8A791sba+9etHv6I8A791sba+9etHv6I8A791sba+9etHv6I8A791sba+OGNHv5c4\nDr8YDJW+OGNHv5c4Dr8YDJW+OGNHv5c4Dr8YDJW+OGNHv5c4Dr8YDJW+N5xhv6pkm77vdrm+\nN5xhv6pkm77vdrm+N5xhv6pkm77vdrm+N5xhv6pkm77vdrm+Sb5Qvwvrcr6ULge/Sb5Qvwvr\ncr6ULge/Sb5Qvwvrcr6ULge/Sb5Qvwvrcr6ULge/XWhRvyRcEr8uyYG9XWhRvyRcEr8uyYG9\nXWhRvyRcEr8uyYG9XWhRvyRcEr8uyYG9uM1qvwwRyr7qvl+9uM1qvwwRyr7qvl+9uM1qvwwR\nyr7qvl+9uM1qvwwRyr7qvl+9jw1rv8vtu74RrBi+jw1rv8vtu74RrBi+jw1rv8vtu74RrBi+\njw1rv8vtu74RrBi+4MpNv3iDE7/dARe+4MpNv3iDE7/dARe+4MpNv3iDE7/dARe+4MpNv3iD\nE7/dARe+Lad+vxxqjr1iE5q9Lad+vxxqjr1iE5q9Lad+vxxqjr1iE5q9Lad+vxxqjr1iE5q9\nHSx6vwuaYr1pu1G+HSx6vwuaYr1pu1G+HSx6vwuaYr1pu1G+HSx6vwuaYr1pu1G+QkJ2v6Fm\nSr4dLEG+QkJ2v6FmSr4dLEG+QkJ2v6FmSr4dLEG+QkJ2v6FmSr4dLEG+q5B5v2KfWr6PeoK9\nq5B5v2KfWr6PeoK9q5B5v2KfWr6PeoK9q5B5v2KfWr6PeoK93+VPvwPkmb3xIhS/3+VPvwPk\nmb3xIhS/3+VPvwPkmb3xIhS/3+VPvwPkmb3xIhS/K5dOv5NnI744jxG/K5dOv5NnI744jxG/\nK5dOv5NnI744jxG/K5dOv5NnI744jxG/f6Fmv2yFOr73s8m+f6Fmv2yFOr73s8m+f6Fmv2yF\nOr73s8m+f6Fmv2yFOr73s8m+2c5qv4f2X73TCsq+2c5qv4f2X73TCsq+2c5qv4f2X73TCsq+\n2c5qv4f2X73TCsq+9etHv3Wxtr6iPAM/9etHv3Wxtr6iPAM/9etHv3Wxtr6iPAM/9etHv3Wx\ntr6iPAM/OGNHvxgMlb6XOA4/OGNHvxgMlb6XOA4/OGNHvxgMlb6XOA4/OGNHvxgMlb6XOA4/\nN5xhv+92ub6qZJs+N5xhv+92ub6qZJs+N5xhv+92ub6qZJs+N5xhv+92ub6qZJs+Sb5Qv5Qu\nB78L63I+Sb5Qv5QuB78L63I+Sb5Qv5QuB78L63I+Sb5Qv5QuB78L63I+XWhRvy7Jgb0kXBI/\nXWhRvy7Jgb0kXBI/XWhRvy7Jgb0kXBI/XWhRvy7Jgb0kXBI/uM1qv+q+X70MEco+uM1qv+q+\nX70MEco+uM1qv+q+X70MEco+uM1qv+q+X70MEco+jg1rvxCsGL7K7bs+jg1rvxCsGL7K7bs+\njg1rvxCsGL7K7bs+jg1rvxCsGL7K7bs+4MpNv90BF754gxM/4MpNv90BF754gxM/4MpNv90B\nF754gxM/4MpNv90BF754gxM/Lad+v2ITmr0cao49Lad+v2ITmr0cao49Lad+v2ITmr0cao49\nLad+v2ITmr0cao49HSx6v2m7Ub4LmmI9HSx6v2m7Ub4LmmI9HSx6v2m7Ub4LmmI9HSx6v2m7\nUb4LmmI9QkJ2vx0sQb6hZko+QkJ2vx0sQb6hZko+QkJ2vx0sQb6hZko+QkJ2vx0sQb6hZko+\nq5B5v496gr1in1o+q5B5v496gr1in1o+q5B5v496gr1in1o+q5B5v496gr1in1o+3+VPv/Ei\nFL8D5Jk93+VPv/EiFL8D5Jk93+VPv/EiFL8D5Jk93+VPv/EiFL8D5Jk9K5dOvziPEb+TZyM+\nK5dOvziPEb+TZyM+K5dOvziPEb+TZyM+K5dOvziPEb+TZyM+f6Fmv/ezyb5shTo+f6Fmv/ez\nyb5shTo+f6Fmv/ezyb5shTo+f6Fmv/ezyb5shTo+2c5qv9MKyr6H9l892c5qv9MKyr6H9l89\n2c5qv9MKyr6H9l892c5qv9MKyr6H9l899etHv6I8Az91sbY+9etHv6I8Az91sbY+9etHv6I8\nAz91sbY+9etHv6I8Az91sbY+OGNHv5c4Dj8YDJU+OGNHv5c4Dj8YDJU+OGNHv5c4Dj8YDJU+\nOGNHv5c4Dj8YDJU+N5xhv6pkmz7vdrk+N5xhv6pkmz7vdrk+N5xhv6pkmz7vdrk+N5xhv6pk\nmz7vdrk+Sb5Qvwvrcj6ULgc/Sb5Qvwvrcj6ULgc/Sb5Qvwvrcj6ULgc/Sb5Qvwvrcj6ULgc/\nXWhRvyRcEj8uyYE9XWhRvyRcEj8uyYE9XWhRvyRcEj8uyYE9XWhRvyRcEj8uyYE9uM1qvwwR\nyj7qvl89uM1qvwwRyj7qvl89uM1qvwwRyj7qvl89uM1qvwwRyj7qvl89jw1rv8vtuz4RrBg+\njw1rv8vtuz4RrBg+jw1rv8vtuz4RrBg+jw1rv8vtuz4RrBg+4MpNv3iDEz/dARc+4MpNv3iD\nEz/dARc+4MpNv3iDEz/dARc+4MpNv3iDEz/dARc+Lad+vxxqjj1iE5o9Lad+vxxqjj1iE5o9\nLad+vxxqjj1iE5o9Lad+vxxqjj1iE5o9HSx6vwuaYj1pu1E+HSx6vwuaYj1pu1E+HSx6vwua\nYj1pu1E+HSx6vwuaYj1pu1E+QkJ2v6FmSj4dLEE+QkJ2v6FmSj4dLEE+QkJ2v6FmSj4dLEE+\nQkJ2v6FmSj4dLEE+q5B5v2KfWj6PeoI9q5B5v2KfWj6PeoI9q5B5v2KfWj6PeoI9q5B5v2Kf\nWj6PeoI93+VPvwPkmT3xIhQ/3+VPvwPkmT3xIhQ/3+VPvwPkmT3xIhQ/3+VPvwPkmT3xIhQ/\nK5dOv5NnIz44jxE/K5dOv5NnIz44jxE/K5dOv5NnIz44jxE/K5dOv5NnIz44jxE/f6Fmv2yF\nOj73s8k+f6Fmv2yFOj73s8k+f6Fmv2yFOj73s8k+f6Fmv2yFOj73s8k+2c5qv4f2Xz3TCso+\n2c5qv4f2Xz3TCso+2c5qv4f2Xz3TCso+2c5qv4f2Xz3TCso+9etHv3Wxtj6iPAO/9etHv3Wx\ntj6iPAO/9etHv3Wxtj6iPAO/9etHv3Wxtj6iPAO/OGNHvxgMlT6XOA6/OGNHvxgMlT6XOA6/\nOGNHvxgMlT6XOA6/OGNHvxgMlT6XOA6/N5xhv+92uT6qZJu+N5xhv+92uT6qZJu+N5xhv+92\nuT6qZJu+N5xhv+92uT6qZJu+Sb5Qv5QuBz8L63K+Sb5Qv5QuBz8L63K+Sb5Qv5QuBz8L63K+\nSb5Qv5QuBz8L63K+XWhRvy7JgT0kXBK/XWhRvy7JgT0kXBK/XWhRvy7JgT0kXBK/XWhRvy7J\ngT0kXBK/uM1qv+q+Xz0MEcq+uM1qv+q+Xz0MEcq+uM1qv+q+Xz0MEcq+uM1qv+q+Xz0MEcq+\njg1rvxCsGD7K7bu+jg1rvxCsGD7K7bu+jg1rvxCsGD7K7bu+jg1rvxCsGD7K7bu+4MpNv90B\nFz54gxO/4MpNv90BFz54gxO/4MpNv90BFz54gxO/4MpNv90BFz54gxO/Lad+v2ITmj0cao69\nLad+v2ITmj0cao69Lad+v2ITmj0cao69Lad+v2ITmj0cao69HSx6v2m7UT4LmmK9HSx6v2m7\nUT4LmmK9HSx6v2m7UT4LmmK9HSx6v2m7UT4LmmK9QkJ2vx0sQT6hZkq+QkJ2vx0sQT6hZkq+\nQkJ2vx0sQT6hZkq+QkJ2vx0sQT6hZkq+q5B5v496gj1in1q+q5B5v496gj1in1q+q5B5v496\ngj1in1q+q5B5v496gj1in1q+3+VPv/EiFD8D5Jm93+VPv/EiFD8D5Jm93+VPv/EiFD8D5Jm9\n3+VPv/EiFD8D5Jm9K5dOvziPET+TZyO+K5dOvziPET+TZyO+K5dOvziPET+TZyO+K5dOvziP\nET+TZyO+f6Fmv/ezyT5shTq+f6Fmv/ezyT5shTq+f6Fmv/ezyT5shTq+f6Fmv/ezyT5shTq+\n2c5qv9MKyj6H9l+92c5qv9MKyj6H9l+92c5qv9MKyj6H9l+92c5qv9MKyj6H9l+9dbG2vvXr\nR7+iPAO/dbG2vvXrR7+iPAO/dbG2vvXrR7+iPAO/dbG2vvXrR7+iPAO/GAyVvjhjR7+XOA6/\nGAyVvjhjR7+XOA6/GAyVvjhjR7+XOA6/GAyVvjhjR7+XOA6/73a5vjecYb+qZJu+73a5vjec\nYb+qZJu+73a5vjecYb+qZJu+73a5vjecYb+qZJu+lC4Hv0m+UL8L63K+lC4Hv0m+UL8L63K+\nlC4Hv0m+UL8L63K+lC4Hv0m+UL8L63K+LsmBvV1oUb8kXBK/LsmBvV1oUb8kXBK/LsmBvV1o\nUb8kXBK/LsmBvV1oUb8kXBK/6r5fvbjNar8MEcq+6r5fvbjNar8MEcq+6r5fvbjNar8MEcq+\n6r5fvbjNar8MEcq+EKwYvo4Na7/K7bu+EKwYvo4Na7/K7bu+EKwYvo4Na7/K7bu+EKwYvo4N\na7/K7bu+3QEXvuDKTb94gxO/3QEXvuDKTb94gxO/3QEXvuDKTb94gxO/3QEXvuDKTb94gxO/\nYhOavS2nfr8cao69YhOavS2nfr8cao69YhOavS2nfr8cao69YhOavS2nfr8cao69abtRvh0s\ner8LmmK9abtRvh0ser8LmmK9abtRvh0ser8LmmK9abtRvh0ser8LmmK9HSxBvkJCdr+hZkq+\nHSxBvkJCdr+hZkq+HSxBvkJCdr+hZkq+HSxBvkJCdr+hZkq+j3qCvauQeb9in1q+j3qCvauQ\neb9in1q+j3qCvauQeb9in1q+j3qCvauQeb9in1q+8SIUv9/lT78D5Jm98SIUv9/lT78D5Jm9\n8SIUv9/lT78D5Jm98SIUv9/lT78D5Jm9OI8RvyuXTr+TZyO+OI8RvyuXTr+TZyO+OI8RvyuX\nTr+TZyO+OI8RvyuXTr+TZyO+97PJvn+hZr9shTq+97PJvn+hZr9shTq+97PJvn+hZr9shTq+\n97PJvn+hZr9shTq+0wrKvtnOar+H9l+90wrKvtnOar+H9l+90wrKvtnOar+H9l+90wrKvtnO\nar+H9l+9ojwDP/XrR791sba+ojwDP/XrR791sba+ojwDP/XrR791sba+ojwDP/XrR791sba+\nlzgOPzhjR78YDJW+lzgOPzhjR78YDJW+lzgOPzhjR78YDJW+lzgOPzhjR78YDJW+qmSbPjec\nYb/vdrm+qmSbPjecYb/vdrm+qmSbPjecYb/vdrm+qmSbPjecYb/vdrm+C+tyPkm+UL+ULge/\nC+tyPkm+UL+ULge/C+tyPkm+UL+ULge/C+tyPkm+UL+ULge/JFwSP11oUb8uyYG9JFwSP11o\nUb8uyYG9JFwSP11oUb8uyYG9JFwSP11oUb8uyYG9DBHKPrjNar/qvl+9DBHKPrjNar/qvl+9\nDBHKPrjNar/qvl+9DBHKPrjNar/qvl+9y+27Po8Na78RrBi+y+27Po8Na78RrBi+y+27Po8N\na78RrBi+y+27Po8Na78RrBi+eIMTP+DKTb/dARe+eIMTP+DKTb/dARe+eIMTP+DKTb/dARe+\neIMTP+DKTb/dARe+HGqOPS2nfr9iE5q9HGqOPS2nfr9iE5q9HGqOPS2nfr9iE5q9HGqOPS2n\nfr9iE5q9C5piPR0ser9pu1G+C5piPR0ser9pu1G+C5piPR0ser9pu1G+C5piPR0ser9pu1G+\noWZKPkJCdr8dLEG+oWZKPkJCdr8dLEG+oWZKPkJCdr8dLEG+oWZKPkJCdr8dLEG+Yp9aPquQ\neb+PeoK9Yp9aPquQeb+PeoK9Yp9aPquQeb+PeoK9Yp9aPquQeb+PeoK9A+SZPd/lT7/xIhS/\nA+SZPd/lT7/xIhS/A+SZPd/lT7/xIhS/A+SZPd/lT7/xIhS/k2cjPiuXTr84jxG/k2cjPiuX\nTr84jxG/k2cjPiuXTr84jxG/k2cjPiuXTr84jxG/bIU6Pn+hZr/3s8m+bIU6Pn+hZr/3s8m+\nbIU6Pn+hZr/3s8m+bIU6Pn+hZr/3s8m+h/ZfPdnOar/TCsq+h/ZfPdnOar/TCsq+h/ZfPdnO\nar/TCsq+h/ZfPdnOar/TCsq+dbG2PvXrR7+iPAM/dbG2PvXrR7+iPAM/dbG2PvXrR7+iPAM/\ndbG2PvXrR7+iPAM/GAyVPjhjR7+XOA4/GAyVPjhjR7+XOA4/GAyVPjhjR7+XOA4/GAyVPjhj\nR7+XOA4/73a5PjecYb+qZJs+73a5PjecYb+qZJs+73a5PjecYb+qZJs+73a5PjecYb+qZJs+\nlC4HP0m+UL8L63I+lC4HP0m+UL8L63I+lC4HP0m+UL8L63I+lC4HP0m+UL8L63I+LsmBPV1o\nUb8kXBI/LsmBPV1oUb8kXBI/LsmBPV1oUb8kXBI/LsmBPV1oUb8kXBI/6r5fPbjNar8MEco+\n6r5fPbjNar8MEco+6r5fPbjNar8MEco+6r5fPbjNar8MEco+EKwYPo4Na7/K7bs+EKwYPo4N\na7/K7bs+EKwYPo4Na7/K7bs+EKwYPo4Na7/K7bs+3QEXPuDKTb94gxM/3QEXPuDKTb94gxM/\n3QEXPuDKTb94gxM/3QEXPuDKTb94gxM/YhOaPS2nfr8cao49YhOaPS2nfr8cao49YhOaPS2n\nfr8cao49YhOaPS2nfr8cao49abtRPh0ser8LmmI9abtRPh0ser8LmmI9abtRPh0ser8LmmI9\nabtRPh0ser8LmmI9HSxBPkJCdr+hZko+HSxBPkJCdr+hZko+HSxBPkJCdr+hZko+HSxBPkJC\ndr+hZko+j3qCPauQeb9in1o+j3qCPauQeb9in1o+j3qCPauQeb9in1o+j3qCPauQeb9in1o+\n8SIUP9/lT78D5Jk98SIUP9/lT78D5Jk98SIUP9/lT78D5Jk98SIUP9/lT78D5Jk9OI8RPyuX\nTr+TZyM+OI8RPyuXTr+TZyM+OI8RPyuXTr+TZyM+OI8RPyuXTr+TZyM+97PJPn+hZr9shTo+\n97PJPn+hZr9shTo+97PJPn+hZr9shTo+97PJPn+hZr9shTo+0wrKPtnOar+H9l890wrKPtnO\nar+H9l890wrKPtnOar+H9l890wrKPtnOar+H9l89ojwDv/XrR791sbY+ojwDv/XrR791sbY+\nojwDv/XrR791sbY+ojwDv/XrR791sbY+lzgOvzhjR78YDJU+lzgOvzhjR78YDJU+lzgOvzhj\nR78YDJU+lzgOvzhjR78YDJU+qmSbvjecYb/vdrk+qmSbvjecYb/vdrk+qmSbvjecYb/vdrk+\nqmSbvjecYb/vdrk+C+tyvkm+UL+ULgc/C+tyvkm+UL+ULgc/C+tyvkm+UL+ULgc/C+tyvkm+\nUL+ULgc/JFwSv11oUb8uyYE9JFwSv11oUb8uyYE9JFwSv11oUb8uyYE9JFwSv11oUb8uyYE9\nDBHKvrjNar/qvl89DBHKvrjNar/qvl89DBHKvrjNar/qvl89DBHKvrjNar/qvl89y+27vo8N\na78RrBg+y+27vo8Na78RrBg+y+27vo8Na78RrBg+y+27vo8Na78RrBg+eIMTv+DKTb/dARc+\neIMTv+DKTb/dARc+eIMTv+DKTb/dARc+eIMTv+DKTb/dARc+HGqOvS2nfr9iE5o9HGqOvS2n\nfr9iE5o9HGqOvS2nfr9iE5o9HGqOvS2nfr9iE5o9C5pivR0ser9pu1E+C5pivR0ser9pu1E+\nC5pivR0ser9pu1E+C5pivR0ser9pu1E+oWZKvkJCdr8dLEE+oWZKvkJCdr8dLEE+oWZKvkJC\ndr8dLEE+oWZKvkJCdr8dLEE+Yp9avquQeb+PeoI9Yp9avquQeb+PeoI9Yp9avquQeb+PeoI9\nYp9avquQeb+PeoI9A+SZvd/lT7/xIhQ/A+SZvd/lT7/xIhQ/A+SZvd/lT7/xIhQ/A+SZvd/l\nT7/xIhQ/k2cjviuXTr84jxE/k2cjviuXTr84jxE/k2cjviuXTr84jxE/k2cjviuXTr84jxE/\nbIU6vn+hZr/3s8k+bIU6vn+hZr/3s8k+bIU6vn+hZr/3s8k+bIU6vn+hZr/3s8k+h/ZfvdnO\nar/TCso+h/ZfvdnOar/TCso+h/ZfvdnOar/TCso+h/ZfvdnOar/TCso+dbG2vqI8A7/160c/\ndbG2vqI8A7/160c/dbG2vqI8A7/160c/dbG2vqI8A7/160c/GAyVvpc4Dr84Y0c/GAyVvpc4\nDr84Y0c/GAyVvpc4Dr84Y0c/GAyVvpc4Dr84Y0c/73a5vqpkm743nGE/73a5vqpkm743nGE/\n73a5vqpkm743nGE/73a5vqpkm743nGE/lC4Hvwvrcr5JvlA/lC4Hvwvrcr5JvlA/lC4Hvwvr\ncr5JvlA/lC4Hvwvrcr5JvlA/LsmBvSRcEr9daFE/LsmBvSRcEr9daFE/LsmBvSRcEr9daFE/\nLsmBvSRcEr9daFE/6r5fvQwRyr64zWo/6r5fvQwRyr64zWo/6r5fvQwRyr64zWo/6r5fvQwR\nyr64zWo/EKwYvsrtu76ODWs/EKwYvsrtu76ODWs/EKwYvsrtu76ODWs/EKwYvsrtu76ODWs/\n3QEXvniDE7/gyk0/3QEXvniDE7/gyk0/3QEXvniDE7/gyk0/3QEXvniDE7/gyk0/YhOavRxq\njr0tp34/YhOavRxqjr0tp34/YhOavRxqjr0tp34/YhOavRxqjr0tp34/abtRvguaYr0dLHo/\nabtRvguaYr0dLHo/abtRvguaYr0dLHo/abtRvguaYr0dLHo/HSxBvqFmSr5CQnY/HSxBvqFm\nSr5CQnY/HSxBvqFmSr5CQnY/HSxBvqFmSr5CQnY/j3qCvWKfWr6rkHk/j3qCvWKfWr6rkHk/\nj3qCvWKfWr6rkHk/j3qCvWKfWr6rkHk/8SIUvwPkmb3f5U8/8SIUvwPkmb3f5U8/8SIUvwPk\nmb3f5U8/8SIUvwPkmb3f5U8/OI8Rv5NnI74rl04/OI8Rv5NnI74rl04/OI8Rv5NnI74rl04/\nOI8Rv5NnI74rl04/97PJvmyFOr5/oWY/97PJvmyFOr5/oWY/97PJvmyFOr5/oWY/97PJvmyF\nOr5/oWY/0wrKvof2X73Zzmo/0wrKvof2X73Zzmo/0wrKvof2X73Zzmo/0wrKvof2X73Zzmo/\nojwDP3Wxtr7160c/ojwDP3Wxtr7160c/ojwDP3Wxtr7160c/ojwDP3Wxtr7160c/lzgOPxgM\nlb44Y0c/lzgOPxgMlb44Y0c/lzgOPxgMlb44Y0c/lzgOPxgMlb44Y0c/qmSbPu92ub43nGE/\nqmSbPu92ub43nGE/qmSbPu92ub43nGE/qmSbPu92ub43nGE/C+tyPpQuB79JvlA/C+tyPpQu\nB79JvlA/C+tyPpQuB79JvlA/C+tyPpQuB79JvlA/JFwSPy7Jgb1daFE/JFwSPy7Jgb1daFE/\nJFwSPy7Jgb1daFE/JFwSPy7Jgb1daFE/DBHKPuq+X724zWo/DBHKPuq+X724zWo/DBHKPuq+\nX724zWo/DBHKPuq+X724zWo/yu27PhCsGL6ODWs/yu27PhCsGL6ODWs/yu27PhCsGL6ODWs/\nyu27PhCsGL6ODWs/eIMTP90BF77gyk0/eIMTP90BF77gyk0/eIMTP90BF77gyk0/eIMTP90B\nF77gyk0/HGqOPWITmr0tp34/HGqOPWITmr0tp34/HGqOPWITmr0tp34/HGqOPWITmr0tp34/\nC5piPWm7Ub4dLHo/C5piPWm7Ub4dLHo/C5piPWm7Ub4dLHo/C5piPWm7Ub4dLHo/oWZKPh0s\nQb5CQnY/oWZKPh0sQb5CQnY/oWZKPh0sQb5CQnY/oWZKPh0sQb5CQnY/Yp9aPo96gr2rkHk/\nYp9aPo96gr2rkHk/Yp9aPo96gr2rkHk/Yp9aPo96gr2rkHk/A+SZPfEiFL/f5U8/A+SZPfEi\nFL/f5U8/A+SZPfEiFL/f5U8/A+SZPfEiFL/f5U8/k2cjPjiPEb8rl04/k2cjPjiPEb8rl04/\nk2cjPjiPEb8rl04/k2cjPjiPEb8rl04/bIU6Pvezyb5/oWY/bIU6Pvezyb5/oWY/bIU6Pvez\nyb5/oWY/bIU6Pvezyb5/oWY/h/ZfPdMKyr7Zzmo/h/ZfPdMKyr7Zzmo/h/ZfPdMKyr7Zzmo/\nh/ZfPdMKyr7Zzmo/dbG2PqI8Az/160c/dbG2PqI8Az/160c/dbG2PqI8Az/160c/dbG2PqI8\nAz/160c/GAyVPpc4Dj84Y0c/GAyVPpc4Dj84Y0c/GAyVPpc4Dj84Y0c/GAyVPpc4Dj84Y0c/\n73a5Pqpkmz43nGE/73a5Pqpkmz43nGE/73a5Pqpkmz43nGE/73a5Pqpkmz43nGE/lC4HPwvr\ncj5JvlA/lC4HPwvrcj5JvlA/lC4HPwvrcj5JvlA/lC4HPwvrcj5JvlA/LsmBPSRcEj9daFE/\nLsmBPSRcEj9daFE/LsmBPSRcEj9daFE/LsmBPSRcEj9daFE/6r5fPQwRyj64zWo/6r5fPQwR\nyj64zWo/6r5fPQwRyj64zWo/6r5fPQwRyj64zWo/EKwYPsrtuz6ODWs/EKwYPsrtuz6ODWs/\nEKwYPsrtuz6ODWs/EKwYPsrtuz6ODWs/3QEXPniDEz/gyk0/3QEXPniDEz/gyk0/3QEXPniD\nEz/gyk0/3QEXPniDEz/gyk0/YhOaPRxqjj0tp34/YhOaPRxqjj0tp34/YhOaPRxqjj0tp34/\nYhOaPRxqjj0tp34/abtRPguaYj0dLHo/abtRPguaYj0dLHo/abtRPguaYj0dLHo/abtRPgua\nYj0dLHo/HSxBPqFmSj5CQnY/HSxBPqFmSj5CQnY/HSxBPqFmSj5CQnY/HSxBPqFmSj5CQnY/\nj3qCPWKfWj6rkHk/j3qCPWKfWj6rkHk/j3qCPWKfWj6rkHk/j3qCPWKfWj6rkHk/8SIUPwPk\nmT3f5U8/8SIUPwPkmT3f5U8/8SIUPwPkmT3f5U8/8SIUPwPkmT3f5U8/OI8RP5NnIz4rl04/\nOI8RP5NnIz4rl04/OI8RP5NnIz4rl04/OI8RP5NnIz4rl04/97PJPmyFOj5/oWY/97PJPmyF\nOj5/oWY/97PJPmyFOj5/oWY/97PJPmyFOj5/oWY/0wrKPof2Xz3Zzmo/0wrKPof2Xz3Zzmo/\n0wrKPof2Xz3Zzmo/0wrKPof2Xz3Zzmo/ojwDv3Wxtj7160c/ojwDv3Wxtj7160c/ojwDv3Wx\ntj7160c/ojwDv3Wxtj7160c/lzgOvxgMlT44Y0c/lzgOvxgMlT44Y0c/lzgOvxgMlT44Y0c/\nlzgOvxgMlT44Y0c/qmSbvu92uT43nGE/qmSbvu92uT43nGE/qmSbvu92uT43nGE/qmSbvu92\nuT43nGE/C+tyvpQuBz9JvlA/C+tyvpQuBz9JvlA/C+tyvpQuBz9JvlA/C+tyvpQuBz9JvlA/\nJFwSvy7JgT1daFE/JFwSvy7JgT1daFE/JFwSvy7JgT1daFE/JFwSvy7JgT1daFE/DBHKvuq+\nXz24zWo/DBHKvuq+Xz24zWo/DBHKvuq+Xz24zWo/DBHKvuq+Xz24zWo/yu27vhCsGD6ODWs/\nyu27vhCsGD6ODWs/yu27vhCsGD6ODWs/yu27vhCsGD6ODWs/eIMTv90BFz7gyk0/eIMTv90B\nFz7gyk0/eIMTv90BFz7gyk0/eIMTv90BFz7gyk0/HGqOvWITmj0tp34/HGqOvWITmj0tp34/\nHGqOvWITmj0tp34/HGqOvWITmj0tp34/C5pivWm7UT4dLHo/C5pivWm7UT4dLHo/C5pivWm7\nUT4dLHo/C5pivWm7UT4dLHo/oWZKvh0sQT5CQnY/oWZKvh0sQT5CQnY/oWZKvh0sQT5CQnY/\noWZKvh0sQT5CQnY/Yp9avo96gj2rkHk/Yp9avo96gj2rkHk/Yp9avo96gj2rkHk/Yp9avo96\ngj2rkHk/A+SZvfEiFD/f5U8/A+SZvfEiFD/f5U8/A+SZvfEiFD/f5U8/A+SZvfEiFD/f5U8/\nk2cjvjiPET8rl04/k2cjvjiPET8rl04/k2cjvjiPET8rl04/k2cjvjiPET8rl04/bIU6vvez\nyT5/oWY/bIU6vvezyT5/oWY/bIU6vvezyT5/oWY/bIU6vvezyT5/oWY/h/ZfvdMKyj7Zzmo/\nh/ZfvdMKyj7Zzmo/h/ZfvdMKyj7Zzmo/h/ZfvdMKyj7Zzmo/AACAPwAAAAAAAAAA//7+PiXm\nBL8l5gS/D/8gv7pNCr+qlb++z1Iuv1a1xL5VtcS+AhJDv6qVv766TQq/z1IuvyAaEr8EL6S9\nhZ03vwKMzr55Uay9MwhQv5A7yr7GP3a+ckZMv7bQDr86qm2+kLM0v1/wqL1f8Ki96ixjv5j6\nrb00Znm+5Ehdv4Zber6GW3q+nhJYvzRmeb6Y+q295EhdvwQvpL0gGhK/hZ03vzuqbb620A6/\nj7M0v8Y/dr6QO8q+ckZMv3lRrL0CjM6+MwhQvyXmBL8l5gQ/D/8gv6qVv766TQo/z1Iuv1W1\nxL5WtcQ+AhJDv7pNCr+qlb8+z1IuvwQvpL0gGhI/hZ03v3lRrL0CjM4+MwhQv8Y/dr6QO8o+\nckZMvzqqbb620A4/kLM0v1/wqL1f8Kg96ixjvzRmeb6Y+q095Ehdv4Zber6GW3o+nhJYv5j6\nrb00Znk+5EhdvyAaEr8EL6Q9hZ03v7bQDr87qm0+j7M0v5A7yr7GP3Y+ckZMvwKMzr55Uaw9\nMwhQvyXmBD8l5gQ/D/8gv7pNCj+qlb8+z1Iuv1a1xD5VtcQ+AhJDv6qVvz66TQo/z1IuvyAa\nEj8EL6Q9hZ03vwKMzj55Uaw9MwhQv5A7yj7GP3Y+ckZMv7bQDj86qm0+kLM0v1/wqD1f8Kg9\n6ixjv5j6rT00Znk+5Ehdv4Zbej6GW3o+nhJYvzRmeT6Y+q095EhdvwQvpD0gGhI/hZ03vzuq\nbT620A4/j7M0v8Y/dj6QO8o+ckZMv3lRrD0CjM4+MwhQvyXmBD8l5gS/D/8gv6qVvz66TQq/\nz1Iuv1W1xD5WtcS+AhJDv7pNCj+qlb++z1IuvwQvpD0gGhK/hZ03v3lRrD0CjM6+MwhQv8Y/\ndj6QO8q+ckZMvzqqbT620A6/kLM0v1/wqD1f8Ki96ixjvzRmeT6Y+q295Ehdv4Zbej6GW3q+\nnhJYv5j6rT00Znm+5EhdvyAaEj8EL6S9hZ03v7bQDj87qm2+j7M0v5A7yj7GP3a+ckZMvwKM\nzj55Uay9MwhQvyXmBL8P/yA/JeYEv7pNCr/PUi4/qpW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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n\nvoid main(void) {\n  \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG)\n  vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n  \n#ifndef FIXED_QUADS\n  gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n  \n#ifdef IS_POINTS\n  gl_PointSize = POINTSIZE;\n#endif\n  \n  vCol = aCol;\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n  \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n  /* normz should be calculated *after* projection */\n  normz = (invPrMatrix*vNormal).z;\n#else\n  vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n  pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n  vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n  pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n  normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n  \n#ifdef NEEDS_VNORMAL\n  vNormal = vec4(normalize(vNormal.xyz/vNormal.w), 1);\n#endif\n  \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n  vTexcoord = aTexcoord;\n#endif\n  \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n  vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w;\n  gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n  \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n  vec4 pos = mvMatrix * vec4(aPos, 1.);\n  pos = pos/pos.w + vec4(aOfs,  0.);\n  gl_Position = prMatrix*pos;\n#endif\n  \n#ifdef FAT_LINES\n  /* This code was inspired by Matt Deslauriers' code in \n   https://mattdesl.svbtle.com/drawing-lines-is-hard */\n  vec2 aspectVec = vec2(uAspect, 1.0);\n  mat4 projViewModel = prMatrix * mvMatrix;\n  vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n  currentProjected = currentProjected/currentProjected.w;\n  vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n  vec2 currentScreen = currentProjected.xy * aspectVec;\n  vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n  float len = uLwd;\n  vec2 dir = vec2(1.0, 0.0);\n  vPoint = aPoint;\n  vLength = length(nextScreen - currentScreen)/2.0;\n  vLength = vLength/(vLength + len);\n  if (vLength > 0.0) {\n    dir = normalize(nextScreen - currentScreen);\n  }\n  vec2 normal = vec2(-dir.y, dir.x);\n  dir.x /= uAspect;\n  normal.x /= uAspect;\n  vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n  gl_Position = currentProjected + offset;\n#endif\n  \n#ifdef IS_BRUSH\n  gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\nvoid main(void) {\n  vec4 fragColor;\n#ifdef FAT_LINES\n  vec2 point = vPoint;\n  bool neg = point.y < 0.0;\n  point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n                 -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n  if (neg && length(point) <= 1.0) discard;\n#endif\n  point.y = min(point.y, 0.0);\n  if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n  \n#ifdef ROUND_POINTS\n  vec2 coord = gl_PointCoord - vec2(0.5);\n  if (length(coord) > 0.5) discard;\n#endif\n  \n#if NCLIPPLANES > 0\n  for (int i = 0; i < NCLIPPLANES; i++)\n    if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n    \n#ifdef FIXED_QUADS\n    vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n    vec3 n = normalize(vNormal.xyz);\n#endif\n    \n#ifdef IS_TWOSIDED\n    if ((normz <= 0.) != front) discard;\n#endif\n    \n#ifdef IS_LIT\n    vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n    vec3 lightdir;\n    vec4 colDiff;\n    vec3 halfVec;\n    vec4 lighteffect = vec4(emission, 0.);\n    vec3 col;\n    float nDotL;\n#ifdef FIXED_QUADS\n    n = -faceforward(n, n, eye);\n#endif\n    \n#if NLIGHTS > 0\n    for (int i=0;i<NLIGHTS;i++) {\n      colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n      lightdir = lightDir[i];\n      if (!viewpoint[i])\n        lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n      if (!finite[i]) {\n        halfVec = normalize(lightdir + eye);\n      } else {\n        lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n        halfVec = normalize(lightdir + eye);\n      }\n      col = ambient[i];\n      nDotL = dot(n, lightdir);\n      col = col + max(nDotL, 0.) * colDiff.rgb;\n      col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n      lighteffect = lighteffect + vec4(col, colDiff.a);\n    }\n#endif\n    \n#else // not IS_LIT\n    vec4 colDiff = vCol;\n    vec4 lighteffect = colDiff;\n#endif\n    \n#ifdef IS_TEXT\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef HAS_TEXTURE\n#ifdef TEXTURE_rgb\n    vec4 textureColor = lighteffect*vec4(texture2D(uSampler, vTexcoord).rgb, 1.);\n#endif\n    \n#ifdef TEXTURE_rgba\n    vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n    \n#ifdef TEXTURE_alpha\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n    float luminance = dot(vec3(1.,1.,1.), textureColor.rgb)/3.;\n    textureColor =  vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n    \n#ifdef TEXTURE_luminance\n    vec4 textureColor = vec4(lighteffect.rgb*dot(texture2D(uSampler, vTexcoord).rgb, vec3(1.,1.,1.))/3., lighteffect.a);\n#endif\n    \n#ifdef TEXTURE_luminance_alpha\n    vec4 textureColor = texture2D(uSampler, vTexcoord);\n    float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n    textureColor = vec4(lighteffect.rgb*luminance, lighteffect.a*textureColor.a);\n#endif\n    \n    fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n    if (textureColor.a < 0.1)\n      discard;\n    else\n      fragColor = textureColor;\n#else\n    fragColor = lighteffect;\n#endif // HAS_TEXTURE\n    \n#ifdef HAS_FOG\n    // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n    // In Exp and Exp2: use density = density/far\n    // fogF will be the proportion of fog\n    // Initialize it to the linear value\n    float fogF;\n    if (uFogMode > 0) {\n      fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n      if (uFogMode > 1)\n        fogF = mix(uFogParms.w, 1.0, fogF);\n      fogF = fogF*uFogParms.z;\n      if (uFogMode == 2)\n        fogF = 1.0 - exp(-fogF);\n      // Docs are wrong: use (density*c)^2, not density*c^2\n      // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n      else if (uFogMode == 3)\n        fogF = 1.0 - exp(-fogF*fogF);\n      fogF = clamp(fogF, 0.0, 1.0);\n      gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n    } else gl_FragColor = fragColor;\n#else\n    gl_FragColor = fragColor;\n#endif // HAS_FOG\n    \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true}},"evals":[],"jsHooks":[]}