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yiyuezhuo/projection_matrix_julia.ipynb

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projection_matrix_julia.ipynb
{
"cells": [
{
"cell_type": "markdown",
"id": "5cc38fcd",
"metadata": {},
"source": [
"http://www.codinglabs.net/article_world_view_projection_matrix.aspx\n",
"https://en.wikipedia.org/wiki/Rotation_matrix"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "8f08b86c",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n",
"(process:9752): GLib-GIO-WARNING **: 22:23:02.085: Unexpectedly, UWP app `KDEe.V.KDEConnect_21.1203.903.0_x64__7vt06qxq7ptv8' (AUMId `KDEe.V.KDEConnect_7vt06qxq7ptv8!KDEe.V.KDEConnect') supports 1 extensions but has no verbs\n"
]
}
],
"source": [
"using Plots\n",
"using LinearAlgebra"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "f225f7b5",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3×100 Matrix{Float64}:\n",
" 1.0 0.989899 0.979798 0.969697 … 0.030303 0.020202 0.010101 0.0\n",
" 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0\n",
" 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"interp(x, y) = hcat((range.(x, y, length=100) |> collect)...)'\n",
"interp([1,1,1], [0,1,1]) |> collect"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "c493b65b",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"┌ Warning: Skipped marker arg o.\n",
"└ @ Plots C:\\Users\\yiyue\\.julia\\packages\\Plots\\dNEbX\\src\\args.jl:1230\n"
]
},
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" 2293.45,162.866 2286.14,165.189 2278.83,167.513 2271.52,169.836 2264.21,172.16 2256.9,174.484 2249.59,176.807 2242.28,179.131 2234.97,181.455 2227.67,183.778 \n",
" 2220.36,186.102 2213.05,188.426 2205.74,190.749 2198.43,193.073 2191.12,195.396 2183.81,197.72 2176.5,200.044 2169.19,202.367 2161.88,204.691 2154.57,207.015 \n",
" 2147.26,209.338 2139.96,211.662 2132.65,213.985 2125.34,216.309 2118.03,218.633 2110.72,220.956 2103.41,223.28 2096.1,225.604 2088.79,227.927 2081.48,230.251 \n",
" 2074.17,232.575 2066.86,234.898 2059.55,237.222 2052.24,239.545 2044.94,241.869 2037.63,244.193 2030.32,246.516 2023.01,248.84 2015.7,251.164 2008.39,253.487 \n",
" 2001.08,255.811 1993.77,258.134 1986.46,260.458 1979.15,262.782 1971.84,265.105 1964.53,267.429 1957.23,269.753 1949.92,272.076 1942.61,274.4 1935.3,276.724 \n",
" 1927.99,279.047 1920.68,281.371 1913.37,283.694 1906.06,286.018 1898.75,288.342 1891.44,290.665 1884.13,292.989 1876.82,295.313 1869.52,297.636 1862.21,299.96 \n",
" 1854.9,302.284 1847.59,304.607 1840.28,306.931 1832.97,309.254 1825.66,311.578 1818.35,313.902 1811.04,316.225 1803.73,318.549 1796.42,320.873 1789.11,323.196 \n",
" 1781.81,325.52 1774.5,327.843 1767.19,330.167 1759.88,332.491 1752.57,334.814 1745.26,337.138 1737.95,339.462 1730.64,341.785 1723.33,344.109 1716.02,346.433 \n",
" 1708.71,348.756 1701.4,351.08 1694.1,353.403 1686.79,355.727 1679.48,358.051 1672.17,360.374 1664.86,362.698 1657.55,365.022 1650.24,367.345 1642.93,369.669 \n",
" 1635.62,371.992 1628.31,374.316 1621,376.64 1613.69,378.963 1606.39,381.287 1599.08,383.611 1591.77,385.934 1584.46,388.258 1577.15,390.582 1569.84,392.905 \n",
" 1557.18,392.131 1544.52,391.356 1531.86,390.582 1519.2,389.807 1506.54,389.032 1493.88,388.258 1481.22,387.483 1468.56,386.709 1455.9,385.934 \n",
" 1443.24,385.16 1430.58,384.385 1417.92,383.611 1405.26,382.836 1392.6,382.062 1379.94,381.287 1367.28,380.512 1354.62,379.738 1341.96,378.963 1329.3,378.189 \n",
" 1316.64,377.414 1303.98,376.64 1291.32,375.865 1278.66,375.091 1266,374.316 1253.34,373.542 1240.68,372.767 1228.02,371.992 1215.36,371.218 1202.7,370.443 \n",
" 1190.04,369.669 1177.38,368.894 1164.72,368.12 1152.06,367.345 1139.4,366.571 1126.74,365.796 1114.08,365.022 1101.42,364.247 1088.76,363.473 1076.1,362.698 \n",
" 1063.44,361.923 1050.78,361.149 1038.12,360.374 1025.46,359.6 1012.8,358.825 1000.15,358.051 987.485,357.276 974.825,356.502 962.165,355.727 949.506,354.953 \n",
" 936.846,354.178 924.186,353.403 911.526,352.629 898.866,351.854 886.206,351.08 873.546,350.305 860.886,349.531 848.227,348.756 835.567,347.982 822.907,347.207 \n",
" 810.247,346.433 797.587,345.658 784.927,344.883 772.267,344.109 759.608,343.334 746.948,342.56 734.288,341.785 721.628,341.011 708.968,340.236 696.308,339.462 \n",
" 683.648,338.687 670.988,337.913 658.329,337.138 645.669,336.363 633.009,335.589 620.349,334.814 607.689,334.04 595.029,333.265 582.369,332.491 569.709,331.716 \n",
" 557.05,330.942 544.39,330.167 531.73,329.393 519.07,328.618 506.41,327.843 493.75,327.069 481.09,326.294 468.431,325.52 455.771,324.745 443.111,323.971 \n",
" 430.451,323.196 417.791,322.422 405.131,321.647 392.471,320.873 379.811,320.098 367.152,319.323 354.492,318.549 341.832,317.774 329.172,317 316.512,316.225 \n",
" 323.821,313.902 331.13,311.578 338.44,309.254 345.749,306.931 353.058,304.607 360.367,302.284 367.676,299.96 374.986,297.636 382.295,295.313 \n",
" 389.604,292.989 396.913,290.665 404.222,288.342 411.531,286.018 418.841,283.694 426.15,281.371 433.459,279.047 440.768,276.724 448.077,274.4 455.386,272.076 \n",
" 462.696,269.753 470.005,267.429 477.314,265.105 484.623,262.782 491.932,260.458 499.242,258.134 506.551,255.811 513.86,253.487 521.169,251.164 528.478,248.84 \n",
" 535.787,246.516 543.097,244.193 550.406,241.869 557.715,239.545 565.024,237.222 572.333,234.898 579.643,232.575 586.952,230.251 594.261,227.927 601.57,225.604 \n",
" 608.879,223.28 616.188,220.956 623.498,218.633 630.807,216.309 638.116,213.985 645.425,211.662 652.734,209.338 660.044,207.015 667.353,204.691 674.662,202.367 \n",
" 681.971,200.044 689.28,197.72 696.589,195.396 703.899,193.073 711.208,190.749 718.517,188.426 725.826,186.102 733.135,183.778 740.444,181.455 747.754,179.131 \n",
" 755.063,176.807 762.372,174.484 769.681,172.16 776.99,169.836 784.3,167.513 791.609,165.189 798.918,162.866 806.227,160.542 813.536,158.218 820.845,155.895 \n",
" 828.155,153.571 835.464,151.247 842.773,148.924 850.082,146.6 857.391,144.276 864.701,141.953 872.01,139.629 879.319,137.306 886.628,134.982 893.937,132.658 \n",
" 901.246,130.335 908.556,128.011 915.865,125.687 923.174,123.364 930.483,121.04 937.792,118.717 945.101,116.393 952.411,114.069 959.72,111.746 967.029,109.422 \n",
" 974.338,107.098 981.647,104.775 988.957,102.451 996.266,100.127 1003.57,97.8038 1010.88,95.4802 1018.19,93.1566 1025.5,90.8329 1032.81,88.5093 1040.12,86.1857 \n",
" 1052.78,86.9602 1065.44,87.7348 1078.1,88.5093 1090.76,89.2838 1103.42,90.0584 1116.08,90.8329 1128.74,91.6075 1141.4,92.382 1154.06,93.1566 \n",
" 1166.72,93.9311 1179.38,94.7057 1192.04,95.4802 1204.7,96.2547 1217.36,97.0293 1230.02,97.8038 1242.68,98.5784 1255.34,99.3529 1268,100.127 1280.66,100.902 \n",
" 1293.32,101.677 1305.98,102.451 1318.64,103.226 1331.3,104 1343.96,104.775 1356.62,105.549 1369.28,106.324 1381.94,107.098 1394.6,107.873 1407.26,108.647 \n",
" 1419.92,109.422 1432.58,110.197 1445.24,110.971 1457.9,111.746 1470.56,112.52 1483.22,113.295 1495.88,114.069 1508.54,114.844 1521.2,115.618 1533.86,116.393 \n",
" 1546.52,117.167 1559.18,117.942 1571.84,118.717 1584.5,119.491 1597.16,120.266 1609.81,121.04 1622.47,121.815 1635.13,122.589 1647.79,123.364 1660.45,124.138 \n",
" 1673.11,124.913 1685.77,125.687 1698.43,126.462 1711.09,127.237 1723.75,128.011 1736.41,128.786 1749.07,129.56 1761.73,130.335 1774.39,131.109 1787.05,131.884 \n",
" 1799.71,132.658 1812.37,133.433 1825.03,134.207 1837.69,134.982 1850.35,135.757 1863.01,136.531 1875.67,137.306 1888.33,138.08 1900.99,138.855 1913.65,139.629 \n",
" 1926.31,140.404 1938.97,141.178 1951.63,141.953 1964.29,142.727 1976.95,143.502 1989.61,144.276 2002.27,145.051 2014.93,145.826 2027.59,146.6 2040.25,147.375 \n",
" 2052.91,148.149 2065.57,148.924 2078.23,149.698 2090.89,150.473 2103.55,151.247 2116.21,152.022 2128.87,152.796 2141.53,153.571 2154.19,154.346 2166.85,155.12 \n",
" 2179.51,155.895 2192.17,156.669 2204.83,157.444 2217.49,158.218 2230.15,158.993 2242.81,159.767 2255.47,160.542 2268.13,161.316 2280.79,162.091 2293.45,162.866 \n",
" 2293.45,1154.2 2286.14,1156.52 2278.83,1158.85 2271.52,1161.17 2264.21,1163.49 2256.9,1165.82 2249.59,1168.14 2242.28,1170.46 2234.97,1172.79 2227.67,1175.11 \n",
" 2220.36,1177.43 2213.05,1179.76 2205.74,1182.08 2198.43,1184.41 2191.12,1186.73 2183.81,1189.05 2176.5,1191.38 2169.19,1193.7 2161.88,1196.02 2154.57,1198.35 \n",
" 2147.26,1200.67 2139.96,1202.99 2132.65,1205.32 2125.34,1207.64 2118.03,1209.97 2110.72,1212.29 2103.41,1214.61 2096.1,1216.94 2088.79,1219.26 2081.48,1221.58 \n",
" 2074.17,1223.91 2066.86,1226.23 2059.55,1228.55 2052.24,1230.88 2044.94,1233.2 2037.63,1235.53 2030.32,1237.85 2023.01,1240.17 2015.7,1242.5 2008.39,1244.82 \n",
" 2001.08,1247.14 1993.77,1249.47 1986.46,1251.79 1979.15,1254.11 1971.84,1256.44 1964.53,1258.76 1957.23,1261.09 1949.92,1263.41 1942.61,1265.73 1935.3,1268.06 \n",
" 1927.99,1270.38 1920.68,1272.7 1913.37,1275.03 1906.06,1277.35 1898.75,1279.67 1891.44,1282 1884.13,1284.32 1876.82,1286.65 1869.52,1288.97 1862.21,1291.29 \n",
" 1854.9,1293.62 1847.59,1295.94 1840.28,1298.26 1832.97,1300.59 1825.66,1302.91 1818.35,1305.23 1811.04,1307.56 1803.73,1309.88 1796.42,1312.21 1789.11,1314.53 \n",
" 1781.81,1316.85 1774.5,1319.18 1767.19,1321.5 1759.88,1323.82 1752.57,1326.15 1745.26,1328.47 1737.95,1330.79 1730.64,1333.12 1723.33,1335.44 1716.02,1337.77 \n",
" 1708.71,1340.09 1701.4,1342.41 1694.1,1344.74 1686.79,1347.06 1679.48,1349.38 1672.17,1351.71 1664.86,1354.03 1657.55,1356.35 1650.24,1358.68 1642.93,1361 \n",
" 1635.62,1363.33 1628.31,1365.65 1621,1367.97 1613.69,1370.3 1606.39,1372.62 1599.08,1374.94 1591.77,1377.27 1584.46,1379.59 1577.15,1381.91 1569.84,1384.24 \n",
" 1557.18,1383.46 1544.52,1382.69 1531.86,1381.91 1519.2,1381.14 1506.54,1380.37 1493.88,1379.59 1481.22,1378.82 1468.56,1378.04 1455.9,1377.27 \n",
" 1443.24,1376.49 1430.58,1375.72 1417.92,1374.94 1405.26,1374.17 1392.6,1373.39 1379.94,1372.62 1367.28,1371.85 1354.62,1371.07 1341.96,1370.3 1329.3,1369.52 \n",
" 1316.64,1368.75 1303.98,1367.97 1291.32,1367.2 1278.66,1366.42 1266,1365.65 1253.34,1364.87 1240.68,1364.1 1228.02,1363.33 1215.36,1362.55 1202.7,1361.78 \n",
" 1190.04,1361 1177.38,1360.23 1164.72,1359.45 1152.06,1358.68 1139.4,1357.9 1126.74,1357.13 1114.08,1356.35 1101.42,1355.58 1088.76,1354.81 1076.1,1354.03 \n",
" 1063.44,1353.26 1050.78,1352.48 1038.12,1351.71 1025.46,1350.93 1012.8,1350.16 1000.15,1349.38 987.485,1348.61 974.825,1347.83 962.165,1347.06 949.506,1346.29 \n",
" 936.846,1345.51 924.186,1344.74 911.526,1343.96 898.866,1343.19 886.206,1342.41 873.546,1341.64 860.886,1340.86 848.227,1340.09 835.567,1339.31 822.907,1338.54 \n",
" 810.247,1337.77 797.587,1336.99 784.927,1336.22 772.267,1335.44 759.608,1334.67 746.948,1333.89 734.288,1333.12 721.628,1332.34 708.968,1331.57 696.308,1330.79 \n",
" 683.648,1330.02 670.988,1329.25 658.329,1328.47 645.669,1327.7 633.009,1326.92 620.349,1326.15 607.689,1325.37 595.029,1324.6 582.369,1323.82 569.709,1323.05 \n",
" 557.05,1322.27 544.39,1321.5 531.73,1320.73 519.07,1319.95 506.41,1319.18 493.75,1318.4 481.09,1317.63 468.431,1316.85 455.771,1316.08 443.111,1315.3 \n",
" 430.451,1314.53 417.791,1313.75 405.131,1312.98 392.471,1312.21 379.811,1311.43 367.152,1310.66 354.492,1309.88 341.832,1309.11 329.172,1308.33 316.512,1307.56 \n",
" 323.821,1305.23 331.13,1302.91 338.44,1300.59 345.749,1298.26 353.058,1295.94 360.367,1293.62 367.676,1291.29 374.986,1288.97 382.295,1286.65 \n",
" 389.604,1284.32 396.913,1282 404.222,1279.67 411.531,1277.35 418.841,1275.03 426.15,1272.7 433.459,1270.38 440.768,1268.06 448.077,1265.73 455.386,1263.41 \n",
" 462.696,1261.09 470.005,1258.76 477.314,1256.44 484.623,1254.11 491.932,1251.79 499.242,1249.47 506.551,1247.14 513.86,1244.82 521.169,1242.5 528.478,1240.17 \n",
" 535.787,1237.85 543.097,1235.53 550.406,1233.2 557.715,1230.88 565.024,1228.55 572.333,1226.23 579.643,1223.91 586.952,1221.58 594.261,1219.26 601.57,1216.94 \n",
" 608.879,1214.61 616.188,1212.29 623.498,1209.97 630.807,1207.64 638.116,1205.32 645.425,1202.99 652.734,1200.67 660.044,1198.35 667.353,1196.02 674.662,1193.7 \n",
" 681.971,1191.38 689.28,1189.05 696.589,1186.73 703.899,1184.41 711.208,1182.08 718.517,1179.76 725.826,1177.43 733.135,1175.11 740.444,1172.79 747.754,1170.46 \n",
" 755.063,1168.14 762.372,1165.82 769.681,1163.49 776.99,1161.17 784.3,1158.85 791.609,1156.52 798.918,1154.2 806.227,1151.87 813.536,1149.55 820.845,1147.23 \n",
" 828.155,1144.9 835.464,1142.58 842.773,1140.26 850.082,1137.93 857.391,1135.61 864.701,1133.29 872.01,1130.96 879.319,1128.64 886.628,1126.32 893.937,1123.99 \n",
" 901.246,1121.67 908.556,1119.34 915.865,1117.02 923.174,1114.7 930.483,1112.37 937.792,1110.05 945.101,1107.73 952.411,1105.4 959.72,1103.08 967.029,1100.76 \n",
" 974.338,1098.43 981.647,1096.11 988.957,1093.78 996.266,1091.46 1003.57,1089.14 1010.88,1086.81 1018.19,1084.49 1025.5,1082.17 1032.81,1079.84 1040.12,1077.52 \n",
" 1052.78,1078.29 1065.44,1079.07 1078.1,1079.84 1090.76,1080.62 1103.42,1081.39 1116.08,1082.17 1128.74,1082.94 1141.4,1083.72 1154.06,1084.49 \n",
" 1166.72,1085.26 1179.38,1086.04 1192.04,1086.81 1204.7,1087.59 1217.36,1088.36 1230.02,1089.14 1242.68,1089.91 1255.34,1090.69 1268,1091.46 1280.66,1092.24 \n",
" 1293.32,1093.01 1305.98,1093.78 1318.64,1094.56 1331.3,1095.33 1343.96,1096.11 1356.62,1096.88 1369.28,1097.66 1381.94,1098.43 1394.6,1099.21 1407.26,1099.98 \n",
" 1419.92,1100.76 1432.58,1101.53 1445.24,1102.3 1457.9,1103.08 1470.56,1103.85 1483.22,1104.63 1495.88,1105.4 1508.54,1106.18 1521.2,1106.95 1533.86,1107.73 \n",
" 1546.52,1108.5 1559.18,1109.28 1571.84,1110.05 1584.5,1110.82 1597.16,1111.6 1609.81,1112.37 1622.47,1113.15 1635.13,1113.92 1647.79,1114.7 1660.45,1115.47 \n",
" 1673.11,1116.25 1685.77,1117.02 1698.43,1117.8 1711.09,1118.57 1723.75,1119.34 1736.41,1120.12 1749.07,1120.89 1761.73,1121.67 1774.39,1122.44 1787.05,1123.22 \n",
" 1799.71,1123.99 1812.37,1124.77 1825.03,1125.54 1837.69,1126.32 1850.35,1127.09 1863.01,1127.86 1875.67,1128.64 1888.33,1129.41 1900.99,1130.19 1913.65,1130.96 \n",
" 1926.31,1131.74 1938.97,1132.51 1951.63,1133.29 1964.29,1134.06 1976.95,1134.84 1989.61,1135.61 2002.27,1136.38 2014.93,1137.16 2027.59,1137.93 2040.25,1138.71 \n",
" 2052.91,1139.48 2065.57,1140.26 2078.23,1141.03 2090.89,1141.81 2103.55,1142.58 2116.21,1143.36 2128.87,1144.13 2141.53,1144.9 2154.19,1145.68 2166.85,1146.45 \n",
" 2179.51,1147.23 2192.17,1148 2204.83,1148.78 2217.49,1149.55 2230.15,1150.33 2242.81,1151.1 2255.47,1151.87 2268.13,1152.65 2280.79,1153.42 2293.45,1154.2 \n",
" 2293.45,162.866 2293.45,172.879 2293.45,182.892 2293.45,192.906 2293.45,202.919 2293.45,212.933 2293.45,222.946 2293.45,232.96 2293.45,242.973 2293.45,252.987 \n",
" 2293.45,263 2293.45,273.014 2293.45,283.027 2293.45,293.041 2293.45,303.054 2293.45,313.068 2293.45,323.081 2293.45,333.094 2293.45,343.108 2293.45,353.121 \n",
" 2293.45,363.135 2293.45,373.148 2293.45,383.162 2293.45,393.175 2293.45,403.189 2293.45,413.202 2293.45,423.216 2293.45,433.229 2293.45,443.243 2293.45,453.256 \n",
" 2293.45,463.27 2293.45,473.283 2293.45,483.296 2293.45,493.31 2293.45,503.323 2293.45,513.337 2293.45,523.35 2293.45,533.364 2293.45,543.377 2293.45,553.391 \n",
" 2293.45,563.404 2293.45,573.418 2293.45,583.431 2293.45,593.445 2293.45,603.458 2293.45,613.471 2293.45,623.485 2293.45,633.498 2293.45,643.512 2293.45,653.525 \n",
" 2293.45,663.539 2293.45,673.552 2293.45,683.566 2293.45,693.579 2293.45,703.593 2293.45,713.606 2293.45,723.62 2293.45,733.633 2293.45,743.647 2293.45,753.66 \n",
" 2293.45,763.673 2293.45,773.687 2293.45,783.7 2293.45,793.714 2293.45,803.727 2293.45,813.741 2293.45,823.754 2293.45,833.768 2293.45,843.781 2293.45,853.795 \n",
" 2293.45,863.808 2293.45,873.822 2293.45,883.835 2293.45,893.849 2293.45,903.862 2293.45,913.875 2293.45,923.889 2293.45,933.902 2293.45,943.916 2293.45,953.929 \n",
" 2293.45,963.943 2293.45,973.956 2293.45,983.97 2293.45,993.983 2293.45,1004 2293.45,1014.01 2293.45,1024.02 2293.45,1034.04 2293.45,1044.05 2293.45,1054.06 \n",
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" 1569.84,392.905 1569.84,402.919 1569.84,412.932 1569.84,422.946 1569.84,432.959 1569.84,442.973 1569.84,452.986 1569.84,462.999 1569.84,473.013 1569.84,483.026 \n",
" 1569.84,493.04 1569.84,503.053 1569.84,513.067 1569.84,523.08 1569.84,533.094 1569.84,543.107 1569.84,553.121 1569.84,563.134 1569.84,573.148 1569.84,583.161 \n",
" 1569.84,593.174 1569.84,603.188 1569.84,613.201 1569.84,623.215 1569.84,633.228 1569.84,643.242 1569.84,653.255 1569.84,663.269 1569.84,673.282 1569.84,683.296 \n",
" 1569.84,693.309 1569.84,703.323 1569.84,713.336 1569.84,723.35 1569.84,733.363 1569.84,743.376 1569.84,753.39 1569.84,763.403 1569.84,773.417 1569.84,783.43 \n",
" 1569.84,793.444 1569.84,803.457 1569.84,813.471 1569.84,823.484 1569.84,833.498 1569.84,843.511 1569.84,853.525 1569.84,863.538 1569.84,873.552 1569.84,883.565 \n",
" 1569.84,893.578 1569.84,903.592 1569.84,913.605 1569.84,923.619 1569.84,933.632 1569.84,943.646 1569.84,953.659 1569.84,963.673 1569.84,973.686 1569.84,983.7 \n",
" 1569.84,993.713 1569.84,1003.73 1569.84,1013.74 1569.84,1023.75 1569.84,1033.77 1569.84,1043.78 1569.84,1053.79 1569.84,1063.81 1569.84,1073.82 1569.84,1083.83 \n",
" 1569.84,1093.85 1569.84,1103.86 1569.84,1113.87 1569.84,1123.89 1569.84,1133.9 1569.84,1143.92 1569.84,1153.93 1569.84,1163.94 1569.84,1173.96 1569.84,1183.97 \n",
" 1569.84,1193.98 1569.84,1204 1569.84,1214.01 1569.84,1224.02 1569.84,1234.04 1569.84,1244.05 1569.84,1254.06 1569.84,1264.08 1569.84,1274.09 1569.84,1284.1 \n",
" 1569.84,1294.12 1569.84,1304.13 1569.84,1314.14 1569.84,1324.16 1569.84,1334.17 1569.84,1344.18 1569.84,1354.2 1569.84,1364.21 1569.84,1374.22 1569.84,1384.24 \n",
" 316.512,316.225 316.512,326.239 316.512,336.252 316.512,346.266 316.512,356.279 316.512,366.293 316.512,376.306 316.512,386.32 316.512,396.333 316.512,406.347 \n",
" 316.512,416.36 316.512,426.373 316.512,436.387 316.512,446.4 316.512,456.414 316.512,466.427 316.512,476.441 316.512,486.454 316.512,496.468 316.512,506.481 \n",
" 316.512,516.495 316.512,526.508 316.512,536.522 316.512,546.535 316.512,556.548 316.512,566.562 316.512,576.575 316.512,586.589 316.512,596.602 316.512,606.616 \n",
" 316.512,616.629 316.512,626.643 316.512,636.656 316.512,646.67 316.512,656.683 316.512,666.697 316.512,676.71 316.512,686.724 316.512,696.737 316.512,706.75 \n",
" 316.512,716.764 316.512,726.777 316.512,736.791 316.512,746.804 316.512,756.818 316.512,766.831 316.512,776.845 316.512,786.858 316.512,796.872 316.512,806.885 \n",
" 316.512,816.899 316.512,826.912 316.512,836.926 316.512,846.939 316.512,856.952 316.512,866.966 316.512,876.979 316.512,886.993 316.512,897.006 316.512,907.02 \n",
" 316.512,917.033 316.512,927.047 316.512,937.06 316.512,947.074 316.512,957.087 316.512,967.101 316.512,977.114 316.512,987.127 316.512,997.141 316.512,1007.15 \n",
" 316.512,1017.17 316.512,1027.18 316.512,1037.19 316.512,1047.21 316.512,1057.22 316.512,1067.24 316.512,1077.25 316.512,1087.26 316.512,1097.28 316.512,1107.29 \n",
" 316.512,1117.3 316.512,1127.32 316.512,1137.33 316.512,1147.34 316.512,1157.36 316.512,1167.37 316.512,1177.38 316.512,1187.4 316.512,1197.41 316.512,1207.42 \n",
" 316.512,1217.44 316.512,1227.45 316.512,1237.46 316.512,1247.48 316.512,1257.49 316.512,1267.5 316.512,1277.52 316.512,1287.53 316.512,1297.54 316.512,1307.56 \n",
" 1040.12,86.1857 1040.12,96.1991 1040.12,106.213 1040.12,116.226 1040.12,126.24 1040.12,136.253 1040.12,146.266 1040.12,156.28 1040.12,166.293 1040.12,176.307 \n",
" 1040.12,186.32 1040.12,196.334 1040.12,206.347 1040.12,216.361 1040.12,226.374 1040.12,236.388 1040.12,246.401 1040.12,256.415 1040.12,266.428 1040.12,276.442 \n",
" 1040.12,286.455 1040.12,296.468 1040.12,306.482 1040.12,316.495 1040.12,326.509 1040.12,336.522 1040.12,346.536 1040.12,356.549 1040.12,366.563 1040.12,376.576 \n",
" 1040.12,386.59 1040.12,396.603 1040.12,406.617 1040.12,416.63 1040.12,426.643 1040.12,436.657 1040.12,446.67 1040.12,456.684 1040.12,466.697 1040.12,476.711 \n",
" 1040.12,486.724 1040.12,496.738 1040.12,506.751 1040.12,516.765 1040.12,526.778 1040.12,536.792 1040.12,546.805 1040.12,556.819 1040.12,566.832 1040.12,576.845 \n",
" 1040.12,586.859 1040.12,596.872 1040.12,606.886 1040.12,616.899 1040.12,626.913 1040.12,636.926 1040.12,646.94 1040.12,656.953 1040.12,666.967 1040.12,676.98 \n",
" 1040.12,686.994 1040.12,697.007 1040.12,707.021 1040.12,717.034 1040.12,727.047 1040.12,737.061 1040.12,747.074 1040.12,757.088 1040.12,767.101 1040.12,777.115 \n",
" 1040.12,787.128 1040.12,797.142 1040.12,807.155 1040.12,817.169 1040.12,827.182 1040.12,837.196 1040.12,847.209 1040.12,857.223 1040.12,867.236 1040.12,877.249 \n",
" 1040.12,887.263 1040.12,897.276 1040.12,907.29 1040.12,917.303 1040.12,927.317 1040.12,937.33 1040.12,947.344 1040.12,957.357 1040.12,967.371 1040.12,977.384 \n",
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},
"execution_count": 3,
"metadata": {},
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}
],
"source": [
"XY = [[1,1],[1,-1],[-1,-1],[-1,1]]\n",
"XYP = map(xy -> [xy;1], XY)\n",
"XYN = map(xy->[xy;-1], XY)\n",
"Mats = Matrix{Float64}[]\n",
"for XYZ in [XYP, XYN]\n",
" for i in range(1, 4)\n",
" push!(Mats, interp(XYZ[i], XYZ[i % 4 + 1]) |> collect)\n",
" end\n",
"end\n",
"for i in range(1, 4)\n",
" push!(Mats, interp(XYP[i], XYN[i]))\n",
"end\n",
"data = hcat(Mats...)\n",
"data = [data; fill(1, size(data, 2))']\n",
"\n",
"plot(data[1, :], data[2, :], data[3, :], marker=\"o\", xlabel=\"x\", ylabel=\"y\", zlabel=\"z\")"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "d179e4a8",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"orthographic_projection_gen (generic function with 1 method)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function orthographic_projection_gen(; width, height, Znear, Zfar)\n",
" orthographic_projection_mat = [\n",
" 1/width 0 0 0\n",
" 0 1/height 0 0\n",
" 0 0 -2/(Zfar - Znear) -(Zfar+Znear)/(Zfar-Znear)\n",
" 0 0 0 1\n",
" ]\n",
" return orthographic_projection_mat\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "95026a01",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4×4 Matrix{Int64}:\n",
" 1 0 0 0\n",
" 0 1 0 1\n",
" 0 0 1 1\n",
" 0 0 0 1"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"world_mat = [\n",
" 1 0 0 0\n",
" 0 1 0 0\n",
" 0 0 1 -3\n",
" 0 0 0 1\n",
"]\n",
"\n",
"camera_mat = [\n",
" 1 0 0 0\n",
" 0 1 0 1\n",
" 0 0 1 1\n",
" 0 0 0 1\n",
"]"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "c2d4af19",
"metadata": {},
"outputs": [
{
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" 1489.23,883.145 1489.23,886.053 1489.23,888.96 1489.23,891.868 1489.23,894.775 1489.23,897.683 1489.23,900.59 1489.23,903.498 1489.23,906.405 1489.23,909.313 \n",
" 1489.23,912.22 1489.23,915.128 1489.23,918.035 1489.23,920.943 1489.23,923.85 1489.23,926.758 1489.23,929.665 1489.23,932.572 1489.23,935.48 1489.23,938.387 \n",
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" 1057.46,1025.61 1057.46,1022.7 1057.46,1019.8 1057.46,1016.89 1057.46,1013.98 1057.46,1011.07 1057.46,1008.17 1057.46,1005.26 1057.46,1002.35 1057.46,999.445 \n",
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" 1144.69,766.846 1149.05,766.846 1153.41,766.846 1157.77,766.846 1162.13,766.846 1166.5,766.846 1170.86,766.846 1175.22,766.846 1179.58,766.846 1183.94,766.846 \n",
" 1188.3,766.846 1192.66,766.846 1197.02,766.846 1201.39,766.846 1205.75,766.846 1210.11,766.846 1214.47,766.846 1218.83,766.846 1223.19,766.846 1227.55,766.846 \n",
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" 1319.14,766.846 1323.5,766.846 1327.86,766.846 1332.22,766.846 1336.58,766.846 1340.95,766.846 1345.31,766.846 1349.67,766.846 1354.03,766.846 1358.39,766.846 \n",
" 1362.75,766.846 1367.11,766.846 1371.47,766.846 1375.84,766.846 1380.2,766.846 1384.56,766.846 1388.92,766.846 1393.28,766.846 1397.64,766.846 1402,766.846 \n",
" 1406.36,766.846 1410.73,766.846 1415.09,766.846 1419.45,766.846 1423.81,766.846 1428.17,766.846 1432.53,766.846 1436.89,766.846 1441.25,766.846 1445.62,766.846 \n",
" 1449.98,766.846 1454.34,766.846 1458.7,766.846 1463.06,766.846 1467.42,766.846 1471.78,766.846 1476.14,766.846 1480.51,766.846 1484.87,766.846 1489.23,766.846 \n",
" 1489.23,769.753 1489.23,772.661 1489.23,775.568 1489.23,778.476 1489.23,781.383 1489.23,784.291 1489.23,787.198 1489.23,790.106 1489.23,793.013 \n",
" 1489.23,795.921 1489.23,798.828 1489.23,801.736 1489.23,804.643 1489.23,807.551 1489.23,810.458 1489.23,813.366 1489.23,816.273 1489.23,819.181 1489.23,822.088 \n",
" 1489.23,824.996 1489.23,827.903 1489.23,830.811 1489.23,833.718 1489.23,836.626 1489.23,839.533 1489.23,842.441 1489.23,845.348 1489.23,848.255 1489.23,851.163 \n",
" 1489.23,854.07 1489.23,856.978 1489.23,859.885 1489.23,862.793 1489.23,865.7 1489.23,868.608 1489.23,871.515 1489.23,874.423 1489.23,877.33 1489.23,880.238 \n",
" 1489.23,883.145 1489.23,886.053 1489.23,888.96 1489.23,891.868 1489.23,894.775 1489.23,897.683 1489.23,900.59 1489.23,903.498 1489.23,906.405 1489.23,909.313 \n",
" 1489.23,912.22 1489.23,915.128 1489.23,918.035 1489.23,920.943 1489.23,923.85 1489.23,926.758 1489.23,929.665 1489.23,932.572 1489.23,935.48 1489.23,938.387 \n",
" 1489.23,941.295 1489.23,944.202 1489.23,947.11 1489.23,950.017 1489.23,952.925 1489.23,955.832 1489.23,958.74 1489.23,961.647 1489.23,964.555 1489.23,967.462 \n",
" 1489.23,970.37 1489.23,973.277 1489.23,976.185 1489.23,979.092 1489.23,982 1489.23,984.907 1489.23,987.815 1489.23,990.722 1489.23,993.63 1489.23,996.537 \n",
" 1489.23,999.445 1489.23,1002.35 1489.23,1005.26 1489.23,1008.17 1489.23,1011.07 1489.23,1013.98 1489.23,1016.89 1489.23,1019.8 1489.23,1022.7 1489.23,1025.61 \n",
" 1489.23,1028.52 1489.23,1031.43 1489.23,1034.33 1489.23,1037.24 1489.23,1040.15 1489.23,1043.06 1489.23,1045.96 1489.23,1048.87 1489.23,1051.78 1489.23,1054.69 \n",
" 1484.87,1054.69 1480.51,1054.69 1476.14,1054.69 1471.78,1054.69 1467.42,1054.69 1463.06,1054.69 1458.7,1054.69 1454.34,1054.69 1449.98,1054.69 \n",
" 1445.62,1054.69 1441.25,1054.69 1436.89,1054.69 1432.53,1054.69 1428.17,1054.69 1423.81,1054.69 1419.45,1054.69 1415.09,1054.69 1410.73,1054.69 1406.36,1054.69 \n",
" 1402,1054.69 1397.64,1054.69 1393.28,1054.69 1388.92,1054.69 1384.56,1054.69 1380.2,1054.69 1375.84,1054.69 1371.47,1054.69 1367.11,1054.69 1362.75,1054.69 \n",
" 1358.39,1054.69 1354.03,1054.69 1349.67,1054.69 1345.31,1054.69 1340.95,1054.69 1336.58,1054.69 1332.22,1054.69 1327.86,1054.69 1323.5,1054.69 1319.14,1054.69 \n",
" 1314.78,1054.69 1310.42,1054.69 1306.06,1054.69 1301.69,1054.69 1297.33,1054.69 1292.97,1054.69 1288.61,1054.69 1284.25,1054.69 1279.89,1054.69 1275.53,1054.69 \n",
" 1271.17,1054.69 1266.8,1054.69 1262.44,1054.69 1258.08,1054.69 1253.72,1054.69 1249.36,1054.69 1245,1054.69 1240.64,1054.69 1236.28,1054.69 1231.91,1054.69 \n",
" 1227.55,1054.69 1223.19,1054.69 1218.83,1054.69 1214.47,1054.69 1210.11,1054.69 1205.75,1054.69 1201.39,1054.69 1197.02,1054.69 1192.66,1054.69 1188.3,1054.69 \n",
" 1183.94,1054.69 1179.58,1054.69 1175.22,1054.69 1170.86,1054.69 1166.5,1054.69 1162.13,1054.69 1157.77,1054.69 1153.41,1054.69 1149.05,1054.69 1144.69,1054.69 \n",
" 1140.33,1054.69 1135.97,1054.69 1131.61,1054.69 1127.24,1054.69 1122.88,1054.69 1118.52,1054.69 1114.16,1054.69 1109.8,1054.69 1105.44,1054.69 1101.08,1054.69 \n",
" 1096.72,1054.69 1092.35,1054.69 1087.99,1054.69 1083.63,1054.69 1079.27,1054.69 1074.91,1054.69 1070.55,1054.69 1066.19,1054.69 1061.83,1054.69 1057.46,1054.69 \n",
" 1057.46,1051.78 1057.46,1048.87 1057.46,1045.96 1057.46,1043.06 1057.46,1040.15 1057.46,1037.24 1057.46,1034.33 1057.46,1031.43 1057.46,1028.52 \n",
" 1057.46,1025.61 1057.46,1022.7 1057.46,1019.8 1057.46,1016.89 1057.46,1013.98 1057.46,1011.07 1057.46,1008.17 1057.46,1005.26 1057.46,1002.35 1057.46,999.445 \n",
" 1057.46,996.537 1057.46,993.63 1057.46,990.722 1057.46,987.815 1057.46,984.907 1057.46,982 1057.46,979.092 1057.46,976.185 1057.46,973.277 1057.46,970.37 \n",
" 1057.46,967.462 1057.46,964.555 1057.46,961.647 1057.46,958.74 1057.46,955.832 1057.46,952.925 1057.46,950.017 1057.46,947.11 1057.46,944.202 1057.46,941.295 \n",
" 1057.46,938.387 1057.46,935.48 1057.46,932.572 1057.46,929.665 1057.46,926.758 1057.46,923.85 1057.46,920.943 1057.46,918.035 1057.46,915.128 1057.46,912.22 \n",
" 1057.46,909.313 1057.46,906.405 1057.46,903.498 1057.46,900.59 1057.46,897.683 1057.46,894.775 1057.46,891.868 1057.46,888.96 1057.46,886.053 1057.46,883.145 \n",
" 1057.46,880.238 1057.46,877.33 1057.46,874.423 1057.46,871.515 1057.46,868.608 1057.46,865.7 1057.46,862.793 1057.46,859.885 1057.46,856.978 1057.46,854.07 \n",
" 1057.46,851.163 1057.46,848.255 1057.46,845.348 1057.46,842.441 1057.46,839.533 1057.46,836.626 1057.46,833.718 1057.46,830.811 1057.46,827.903 1057.46,824.996 \n",
" 1057.46,822.088 1057.46,819.181 1057.46,816.273 1057.46,813.366 1057.46,810.458 1057.46,807.551 1057.46,804.643 1057.46,801.736 1057.46,798.828 1057.46,795.921 \n",
" 1057.46,793.013 1057.46,790.106 1057.46,787.198 1057.46,784.291 1057.46,781.383 1057.46,778.476 1057.46,775.568 1057.46,772.661 1057.46,769.753 1057.46,766.846 \n",
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" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
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" \n",
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" 1635.79,1363.33 1628.48,1365.65 1621.17,1367.97 1613.87,1370.3 1606.56,1372.62 1599.25,1374.94 1591.94,1377.27 1584.64,1379.59 1577.33,1381.91 1570.02,1384.24 \n",
" 1557.36,1383.46 1544.71,1382.69 1532.05,1381.91 1519.39,1381.14 1506.74,1380.37 1494.08,1379.59 1481.42,1378.82 1468.77,1378.04 1456.11,1377.27 \n",
" 1443.45,1376.49 1430.79,1375.72 1418.14,1374.94 1405.48,1374.17 1392.82,1373.39 1380.17,1372.62 1367.51,1371.85 1354.85,1371.07 1342.2,1370.3 1329.54,1369.52 \n",
" 1316.88,1368.75 1304.23,1367.97 1291.57,1367.2 1278.91,1366.42 1266.25,1365.65 1253.6,1364.87 1240.94,1364.1 1228.28,1363.33 1215.63,1362.55 1202.97,1361.78 \n",
" 1190.31,1361 1177.66,1360.23 1165,1359.45 1152.34,1358.68 1139.69,1357.9 1127.03,1357.13 1114.37,1356.35 1101.71,1355.58 1089.06,1354.81 1076.4,1354.03 \n",
" 1063.74,1353.26 1051.09,1352.48 1038.43,1351.71 1025.77,1350.93 1013.12,1350.16 1000.46,1349.38 987.802,1348.61 975.145,1347.83 962.488,1347.06 949.831,1346.29 \n",
" 937.174,1345.51 924.517,1344.74 911.86,1343.96 899.203,1343.19 886.546,1342.41 873.889,1341.64 861.233,1340.86 848.576,1340.09 835.919,1339.31 823.262,1338.54 \n",
" 810.605,1337.77 797.948,1336.99 785.291,1336.22 772.634,1335.44 759.977,1334.67 747.32,1333.89 734.663,1333.12 722.006,1332.34 709.349,1331.57 696.692,1330.79 \n",
" 684.035,1330.02 671.379,1329.25 658.722,1328.47 646.065,1327.7 633.408,1326.92 620.751,1326.15 608.094,1325.37 595.437,1324.6 582.78,1323.82 570.123,1323.05 \n",
" 557.466,1322.27 544.809,1321.5 532.152,1320.73 519.495,1319.95 506.838,1319.18 494.182,1318.4 481.525,1317.63 468.868,1316.85 456.211,1316.08 443.554,1315.3 \n",
" 430.897,1314.53 418.24,1313.75 405.583,1312.98 392.926,1312.21 380.269,1311.43 367.612,1310.66 354.955,1309.88 342.298,1309.11 329.641,1308.33 316.984,1307.56 \n",
" 324.292,1305.23 331.599,1302.91 338.907,1300.59 346.214,1298.26 353.522,1295.94 360.829,1293.62 368.137,1291.29 375.444,1288.97 382.752,1286.65 \n",
" 390.059,1284.32 397.367,1282 404.674,1279.67 411.982,1277.35 419.289,1275.03 426.597,1272.7 433.904,1270.38 441.212,1268.06 448.519,1265.73 455.827,1263.41 \n",
" 463.134,1261.09 470.442,1258.76 477.749,1256.44 485.057,1254.11 492.364,1251.79 499.672,1249.47 506.979,1247.14 514.286,1244.82 521.594,1242.5 528.901,1240.17 \n",
" 536.209,1237.85 543.516,1235.53 550.824,1233.2 558.131,1230.88 565.439,1228.55 572.746,1226.23 580.054,1223.91 587.361,1221.58 594.669,1219.26 601.976,1216.94 \n",
" 609.284,1214.61 616.591,1212.29 623.899,1209.97 631.206,1207.64 638.514,1205.32 645.821,1202.99 653.129,1200.67 660.436,1198.35 667.744,1196.02 675.051,1193.7 \n",
" 682.359,1191.38 689.666,1189.05 696.974,1186.73 704.281,1184.41 711.589,1182.08 718.896,1179.76 726.204,1177.43 733.511,1175.11 740.818,1172.79 748.126,1170.46 \n",
" 755.433,1168.14 762.741,1165.82 770.048,1163.49 777.356,1161.17 784.663,1158.85 791.971,1156.52 799.278,1154.2 806.586,1151.87 813.893,1149.55 821.201,1147.23 \n",
" 828.508,1144.9 835.816,1142.58 843.123,1140.26 850.431,1137.93 857.738,1135.61 865.046,1133.29 872.353,1130.96 879.661,1128.64 886.968,1126.32 894.276,1123.99 \n",
" 901.583,1121.67 908.891,1119.34 916.198,1117.02 923.506,1114.7 930.813,1112.37 938.121,1110.05 945.428,1107.73 952.735,1105.4 960.043,1103.08 967.35,1100.76 \n",
" 974.658,1098.43 981.965,1096.11 989.273,1093.78 996.58,1091.46 1003.89,1089.14 1011.2,1086.81 1018.5,1084.49 1025.81,1082.17 1033.12,1079.84 1040.43,1077.52 \n",
" 1053.08,1078.29 1065.74,1079.07 1078.4,1079.84 1091.05,1080.62 1103.71,1081.39 1116.37,1082.17 1129.02,1082.94 1141.68,1083.72 1154.34,1084.49 \n",
" 1166.99,1085.26 1179.65,1086.04 1192.31,1086.81 1204.97,1087.59 1217.62,1088.36 1230.28,1089.14 1242.94,1089.91 1255.59,1090.69 1268.25,1091.46 1280.91,1092.24 \n",
" 1293.56,1093.01 1306.22,1093.78 1318.88,1094.56 1331.53,1095.33 1344.19,1096.11 1356.85,1096.88 1369.51,1097.66 1382.16,1098.43 1394.82,1099.21 1407.48,1099.98 \n",
" 1420.13,1100.76 1432.79,1101.53 1445.45,1102.3 1458.1,1103.08 1470.76,1103.85 1483.42,1104.63 1496.07,1105.4 1508.73,1106.18 1521.39,1106.95 1534.05,1107.73 \n",
" 1546.7,1108.5 1559.36,1109.28 1572.02,1110.05 1584.67,1110.82 1597.33,1111.6 1609.99,1112.37 1622.64,1113.15 1635.3,1113.92 1647.96,1114.7 1660.61,1115.47 \n",
" 1673.27,1116.25 1685.93,1117.02 1698.59,1117.8 1711.24,1118.57 1723.9,1119.34 1736.56,1120.12 1749.21,1120.89 1761.87,1121.67 1774.53,1122.44 1787.18,1123.22 \n",
" 1799.84,1123.99 1812.5,1124.77 1825.16,1125.54 1837.81,1126.32 1850.47,1127.09 1863.13,1127.86 1875.78,1128.64 1888.44,1129.41 1901.1,1130.19 1913.75,1130.96 \n",
" 1926.41,1131.74 1939.07,1132.51 1951.72,1133.29 1964.38,1134.06 1977.04,1134.84 1989.7,1135.61 2002.35,1136.38 2015.01,1137.16 2027.67,1137.93 2040.32,1138.71 \n",
" 2052.98,1139.48 2065.64,1140.26 2078.29,1141.03 2090.95,1141.81 2103.61,1142.58 2116.26,1143.36 2128.92,1144.13 2141.58,1144.9 2154.24,1145.68 2166.89,1146.45 \n",
" 2179.55,1147.23 2192.21,1148 2204.86,1148.78 2217.52,1149.55 2230.18,1150.33 2242.83,1151.1 2255.49,1151.87 2268.15,1152.65 2280.8,1153.42 2293.46,1154.2 \n",
" 2293.46,162.866 2286.15,165.189 2278.85,167.513 2271.54,169.836 2264.23,172.16 2256.92,174.484 2249.62,176.807 2242.31,179.131 2235,181.455 2227.69,183.778 \n",
" 2220.39,186.102 2213.08,188.426 2205.77,190.749 2198.46,193.073 2191.16,195.396 2183.85,197.72 2176.54,200.044 2169.23,202.367 2161.93,204.691 2154.62,207.015 \n",
" 2147.31,209.338 2140,211.662 2132.7,213.985 2125.39,216.309 2118.08,218.633 2110.77,220.956 2103.47,223.28 2096.16,225.604 2088.85,227.927 2081.54,230.251 \n",
" 2074.24,232.575 2066.93,234.898 2059.62,237.222 2052.31,239.545 2045.01,241.869 2037.7,244.193 2030.39,246.516 2023.08,248.84 2015.78,251.164 2008.47,253.487 \n",
" 2001.16,255.811 1993.85,258.134 1986.55,260.458 1979.24,262.782 1971.93,265.105 1964.62,267.429 1957.32,269.753 1950.01,272.076 1942.7,274.4 1935.39,276.724 \n",
" 1928.09,279.047 1920.78,281.371 1913.47,283.694 1906.16,286.018 1898.86,288.342 1891.55,290.665 1884.24,292.989 1876.94,295.313 1869.63,297.636 1862.32,299.96 \n",
" 1855.01,302.284 1847.71,304.607 1840.4,306.931 1833.09,309.254 1825.78,311.578 1818.48,313.902 1811.17,316.225 1803.86,318.549 1796.55,320.873 1789.25,323.196 \n",
" 1781.94,325.52 1774.63,327.843 1767.32,330.167 1760.02,332.491 1752.71,334.814 1745.4,337.138 1738.09,339.462 1730.79,341.785 1723.48,344.109 1716.17,346.433 \n",
" 1708.86,348.756 1701.56,351.08 1694.25,353.403 1686.94,355.727 1679.63,358.051 1672.33,360.374 1665.02,362.698 1657.71,365.022 1650.4,367.345 1643.1,369.669 \n",
" 1635.79,371.992 1628.48,374.316 1621.17,376.64 1613.87,378.963 1606.56,381.287 1599.25,383.611 1591.94,385.934 1584.64,388.258 1577.33,390.582 1570.02,392.905 \n",
" 1557.36,392.131 1544.71,391.356 1532.05,390.582 1519.39,389.807 1506.74,389.032 1494.08,388.258 1481.42,387.483 1468.77,386.709 1456.11,385.934 \n",
" 1443.45,385.16 1430.79,384.385 1418.14,383.611 1405.48,382.836 1392.82,382.062 1380.17,381.287 1367.51,380.512 1354.85,379.738 1342.2,378.963 1329.54,378.189 \n",
" 1316.88,377.414 1304.23,376.64 1291.57,375.865 1278.91,375.091 1266.25,374.316 1253.6,373.542 1240.94,372.767 1228.28,371.992 1215.63,371.218 1202.97,370.443 \n",
" 1190.31,369.669 1177.66,368.894 1165,368.12 1152.34,367.345 1139.69,366.571 1127.03,365.796 1114.37,365.022 1101.71,364.247 1089.06,363.473 1076.4,362.698 \n",
" 1063.74,361.923 1051.09,361.149 1038.43,360.374 1025.77,359.6 1013.12,358.825 1000.46,358.051 987.802,357.276 975.145,356.502 962.488,355.727 949.831,354.953 \n",
" 937.174,354.178 924.517,353.403 911.86,352.629 899.203,351.854 886.546,351.08 873.889,350.305 861.233,349.531 848.576,348.756 835.919,347.982 823.262,347.207 \n",
" 810.605,346.433 797.948,345.658 785.291,344.883 772.634,344.109 759.977,343.334 747.32,342.56 734.663,341.785 722.006,341.011 709.349,340.236 696.692,339.462 \n",
" 684.035,338.687 671.379,337.913 658.722,337.138 646.065,336.363 633.408,335.589 620.751,334.814 608.094,334.04 595.437,333.265 582.78,332.491 570.123,331.716 \n",
" 557.466,330.942 544.809,330.167 532.152,329.393 519.495,328.618 506.838,327.843 494.182,327.069 481.525,326.294 468.868,325.52 456.211,324.745 443.554,323.971 \n",
" 430.897,323.196 418.24,322.422 405.583,321.647 392.926,320.873 380.269,320.098 367.612,319.323 354.955,318.549 342.298,317.774 329.641,317 316.984,316.225 \n",
" 324.292,313.902 331.599,311.578 338.907,309.254 346.214,306.931 353.522,304.607 360.829,302.284 368.137,299.96 375.444,297.636 382.752,295.313 \n",
" 390.059,292.989 397.367,290.665 404.674,288.342 411.982,286.018 419.289,283.694 426.597,281.371 433.904,279.047 441.212,276.724 448.519,274.4 455.827,272.076 \n",
" 463.134,269.753 470.442,267.429 477.749,265.105 485.057,262.782 492.364,260.458 499.672,258.134 506.979,255.811 514.286,253.487 521.594,251.164 528.901,248.84 \n",
" 536.209,246.516 543.516,244.193 550.824,241.869 558.131,239.545 565.439,237.222 572.746,234.898 580.054,232.575 587.361,230.251 594.669,227.927 601.976,225.604 \n",
" 609.284,223.28 616.591,220.956 623.899,218.633 631.206,216.309 638.514,213.985 645.821,211.662 653.129,209.338 660.436,207.015 667.744,204.691 675.051,202.367 \n",
" 682.359,200.044 689.666,197.72 696.974,195.396 704.281,193.073 711.589,190.749 718.896,188.426 726.204,186.102 733.511,183.778 740.818,181.455 748.126,179.131 \n",
" 755.433,176.807 762.741,174.484 770.048,172.16 777.356,169.836 784.663,167.513 791.971,165.189 799.278,162.866 806.586,160.542 813.893,158.218 821.201,155.895 \n",
" 828.508,153.571 835.816,151.247 843.123,148.924 850.431,146.6 857.738,144.276 865.046,141.953 872.353,139.629 879.661,137.306 886.968,134.982 894.276,132.658 \n",
" 901.583,130.335 908.891,128.011 916.198,125.687 923.506,123.364 930.813,121.04 938.121,118.717 945.428,116.393 952.735,114.069 960.043,111.746 967.35,109.422 \n",
" 974.658,107.098 981.965,104.775 989.273,102.451 996.58,100.127 1003.89,97.8038 1011.2,95.4802 1018.5,93.1566 1025.81,90.8329 1033.12,88.5093 1040.43,86.1857 \n",
" 1053.08,86.9602 1065.74,87.7348 1078.4,88.5093 1091.05,89.2838 1103.71,90.0584 1116.37,90.8329 1129.02,91.6075 1141.68,92.382 1154.34,93.1566 \n",
" 1166.99,93.9311 1179.65,94.7057 1192.31,95.4802 1204.97,96.2547 1217.62,97.0293 1230.28,97.8038 1242.94,98.5784 1255.59,99.3529 1268.25,100.127 1280.91,100.902 \n",
" 1293.56,101.677 1306.22,102.451 1318.88,103.226 1331.53,104 1344.19,104.775 1356.85,105.549 1369.51,106.324 1382.16,107.098 1394.82,107.873 1407.48,108.647 \n",
" 1420.13,109.422 1432.79,110.197 1445.45,110.971 1458.1,111.746 1470.76,112.52 1483.42,113.295 1496.07,114.069 1508.73,114.844 1521.39,115.618 1534.05,116.393 \n",
" 1546.7,117.167 1559.36,117.942 1572.02,118.717 1584.67,119.491 1597.33,120.266 1609.99,121.04 1622.64,121.815 1635.3,122.589 1647.96,123.364 1660.61,124.138 \n",
" 1673.27,124.913 1685.93,125.687 1698.59,126.462 1711.24,127.237 1723.9,128.011 1736.56,128.786 1749.21,129.56 1761.87,130.335 1774.53,131.109 1787.18,131.884 \n",
" 1799.84,132.658 1812.5,133.433 1825.16,134.207 1837.81,134.982 1850.47,135.757 1863.13,136.531 1875.78,137.306 1888.44,138.08 1901.1,138.855 1913.75,139.629 \n",
" 1926.41,140.404 1939.07,141.178 1951.72,141.953 1964.38,142.727 1977.04,143.502 1989.7,144.276 2002.35,145.051 2015.01,145.826 2027.67,146.6 2040.32,147.375 \n",
" 2052.98,148.149 2065.64,148.924 2078.29,149.698 2090.95,150.473 2103.61,151.247 2116.26,152.022 2128.92,152.796 2141.58,153.571 2154.24,154.346 2166.89,155.12 \n",
" 2179.55,155.895 2192.21,156.669 2204.86,157.444 2217.52,158.218 2230.18,158.993 2242.83,159.767 2255.49,160.542 2268.15,161.316 2280.8,162.091 2293.46,162.866 \n",
" 2293.46,1154.2 2293.46,1144.19 2293.46,1134.17 2293.46,1124.16 2293.46,1114.14 2293.46,1104.13 2293.46,1094.12 2293.46,1084.1 2293.46,1074.09 2293.46,1064.08 \n",
" 2293.46,1054.06 2293.46,1044.05 2293.46,1034.04 2293.46,1024.02 2293.46,1014.01 2293.46,1004 2293.46,993.983 2293.46,983.97 2293.46,973.956 2293.46,963.943 \n",
" 2293.46,953.929 2293.46,943.916 2293.46,933.902 2293.46,923.889 2293.46,913.875 2293.46,903.862 2293.46,893.849 2293.46,883.835 2293.46,873.822 2293.46,863.808 \n",
" 2293.46,853.795 2293.46,843.781 2293.46,833.768 2293.46,823.754 2293.46,813.741 2293.46,803.727 2293.46,793.714 2293.46,783.7 2293.46,773.687 2293.46,763.673 \n",
" 2293.46,753.66 2293.46,743.647 2293.46,733.633 2293.46,723.62 2293.46,713.606 2293.46,703.593 2293.46,693.579 2293.46,683.566 2293.46,673.552 2293.46,663.539 \n",
" 2293.46,653.525 2293.46,643.512 2293.46,633.498 2293.46,623.485 2293.46,613.471 2293.46,603.458 2293.46,593.445 2293.46,583.431 2293.46,573.418 2293.46,563.404 \n",
" 2293.46,553.391 2293.46,543.377 2293.46,533.364 2293.46,523.35 2293.46,513.337 2293.46,503.323 2293.46,493.31 2293.46,483.296 2293.46,473.283 2293.46,463.27 \n",
" 2293.46,453.256 2293.46,443.243 2293.46,433.229 2293.46,423.216 2293.46,413.202 2293.46,403.189 2293.46,393.175 2293.46,383.162 2293.46,373.148 2293.46,363.135 \n",
" 2293.46,353.121 2293.46,343.108 2293.46,333.094 2293.46,323.081 2293.46,313.068 2293.46,303.054 2293.46,293.041 2293.46,283.027 2293.46,273.014 2293.46,263 \n",
" 2293.46,252.987 2293.46,242.973 2293.46,232.96 2293.46,222.946 2293.46,212.933 2293.46,202.919 2293.46,192.906 2293.46,182.892 2293.46,172.879 2293.46,162.866 \n",
" 1570.02,1384.24 1570.02,1374.22 1570.02,1364.21 1570.02,1354.2 1570.02,1344.18 1570.02,1334.17 1570.02,1324.16 1570.02,1314.14 1570.02,1304.13 1570.02,1294.12 \n",
" 1570.02,1284.1 1570.02,1274.09 1570.02,1264.08 1570.02,1254.06 1570.02,1244.05 1570.02,1234.04 1570.02,1224.02 1570.02,1214.01 1570.02,1204 1570.02,1193.98 \n",
" 1570.02,1183.97 1570.02,1173.96 1570.02,1163.94 1570.02,1153.93 1570.02,1143.92 1570.02,1133.9 1570.02,1123.89 1570.02,1113.87 1570.02,1103.86 1570.02,1093.85 \n",
" 1570.02,1083.83 1570.02,1073.82 1570.02,1063.81 1570.02,1053.79 1570.02,1043.78 1570.02,1033.77 1570.02,1023.75 1570.02,1013.74 1570.02,1003.73 1570.02,993.713 \n",
" 1570.02,983.7 1570.02,973.686 1570.02,963.673 1570.02,953.659 1570.02,943.646 1570.02,933.632 1570.02,923.619 1570.02,913.605 1570.02,903.592 1570.02,893.578 \n",
" 1570.02,883.565 1570.02,873.552 1570.02,863.538 1570.02,853.525 1570.02,843.511 1570.02,833.498 1570.02,823.484 1570.02,813.471 1570.02,803.457 1570.02,793.444 \n",
" 1570.02,783.43 1570.02,773.417 1570.02,763.403 1570.02,753.39 1570.02,743.376 1570.02,733.363 1570.02,723.35 1570.02,713.336 1570.02,703.323 1570.02,693.309 \n",
" 1570.02,683.296 1570.02,673.282 1570.02,663.269 1570.02,653.255 1570.02,643.242 1570.02,633.228 1570.02,623.215 1570.02,613.201 1570.02,603.188 1570.02,593.174 \n",
" 1570.02,583.161 1570.02,573.148 1570.02,563.134 1570.02,553.121 1570.02,543.107 1570.02,533.094 1570.02,523.08 1570.02,513.067 1570.02,503.053 1570.02,493.04 \n",
" 1570.02,483.026 1570.02,473.013 1570.02,462.999 1570.02,452.986 1570.02,442.973 1570.02,432.959 1570.02,422.946 1570.02,412.932 1570.02,402.919 1570.02,392.905 \n",
" 316.984,1307.56 316.984,1297.54 316.984,1287.53 316.984,1277.52 316.984,1267.5 316.984,1257.49 316.984,1247.48 316.984,1237.46 316.984,1227.45 316.984,1217.44 \n",
" 316.984,1207.42 316.984,1197.41 316.984,1187.4 316.984,1177.38 316.984,1167.37 316.984,1157.36 316.984,1147.34 316.984,1137.33 316.984,1127.32 316.984,1117.3 \n",
" 316.984,1107.29 316.984,1097.28 316.984,1087.26 316.984,1077.25 316.984,1067.24 316.984,1057.22 316.984,1047.21 316.984,1037.19 316.984,1027.18 316.984,1017.17 \n",
" 316.984,1007.15 316.984,997.141 316.984,987.127 316.984,977.114 316.984,967.101 316.984,957.087 316.984,947.074 316.984,937.06 316.984,927.047 316.984,917.033 \n",
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},
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],
"source": [
"pm = orthographic_projection_gen(width=5, height=5, Znear=0.1, Zfar=10)\n",
"\n",
"let d = pm * inv(camera_mat) * world_mat * data\n",
" plot(d[1,:],d[2,:], marker=\"o\", xlim=(-1,1), ylim=(-1,1)) |> display\n",
" plot(d[1, :], d[2,:], d[3,:], marker=\"o\", xlabel=\"x\", ylabel=\"y\", zlabel=\"z\")\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "7e428d25",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"perspective_projection_gen (generic function with 1 method)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function perspective_projection_gen(;FOVx, FOVy, Zfar, Znear)\n",
" perspective_projection_matrix = [\n",
" atan(FOVx/2) 0 0 0\n",
" 0 atan(FOVy/2) 0 0\n",
" 0 0 -(Zfar+Znear)/(Zfar-Znear) -2*(Znear*Zfar)/(Zfar-Znear)\n",
" 0 0 -1 0\n",
" ]\n",
" return perspective_projection_matrix\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "6f034aaf",
"metadata": {},
"outputs": [
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