MATLAB: How to get rotation matrix from 3d points

rotationvector

I have 3 3d points and I need to find rotation matrix from these points.

P1(-401.428, 485.929, 772.921)

P2(-21.4433, 475.611, 772.511)

P3(-400.982, 483.56, 403.703)

How could I compute 3×3 rotation matrix? They are orthogonal. And I set P1 as a reference point.

Best Answer

All the rotation matrix are orthogonal. To find rotation matrix for each axis please refer rotx. For more information about Matrix rotation refer this link.

Related Solutions

MATLAB: InterX issues. Showing intersection when there is none.

The intersections are actually there.

The issue is just in plotting. Straight lines between two points aren't straight on a semilog plot. When you just plot the endpoints, the graph connects them with a straight line, but that's gives the wrong impression of what is going on. Try this, and plot the intermediate points on the line to verify what is going on:

x = [474340.3995,524156.1613,541142.4149,552506.6795,561267.9028,568490.4265,574683.7004,580134.2233,585020.362,589461.2825,593540.8503,597320.4975,600846.6755,604155.4287,607275.3319,610229.4529,613036.7033,615712.797,618270.9443,620722.3654,623076.6783,625342.1952,627526.1525,629634.8924,631674.007,633648.4539,635562.6512,637420.5538,639225.7175,640981.3521,642690.3653,644355.4008,645978.8694,647562.9764,649109.7448,650621.0348,652098.5618,653543.911,654958.5502,656343.8419,657701.0529,659031.3635,660335.8748,661615.6166,662871.5525,664104.5863,665315.5667,666505.2915,667674.5119,668823.936,669954.2319,671066.0311,672159.9305,673236.4956,674296.2621,675339.7382,676367.4066,677379.7258,678377.1319,679360.0403,680328.8464,681283.9274,682225.643,683154.3369,684070.3372,684973.9578,685865.499,686745.2483,687613.4809,688470.461,689316.4416,690151.6657,690976.3667,691790.7688,692595.0873,693389.5296,694174.2951,694949.5757,695715.5566,696472.4159,697220.3254,697959.4511,698689.9527,699411.9849,700125.6968,700831.2326,701528.7315,702218.3284,702900.1535,703574.3331,704240.9891,704900.24,705552.2001,706196.9805,706834.6888,707465.4293,708089.303,708706.4082,709316.8401,709920.6909,710518.0505,711109.0059,711693.6417,712272.04,712844.2807,713410.4412,713970.5969,714524.8211,715073.1849,715615.7576,716152.6063,716683.7965,717209.3918,717729.4541,718244.0434,718753.2183,719257.0357,719755.5508,720248.8174,720736.8878,721219.8129,721697.6421,722170.4236,722638.204,723101.0288,723558.9421,724011.9869,724460.2049,724903.6365,725342.3212,725776.2971,726205.6013,726630.2699,727050.3377,727465.8386,727876.8055,728283.2703,728685.2638,729082.8158,729475.9554,729864.7104,730249.1079,730629.1742,731004.9343,731376.4128,731743.633,732106.6177,732465.3886,732819.9666,733170.3719,733516.6239,733858.7409,734196.7407,734530.6403,734860.4557,735186.2023,735507.8946,735825.5466,736139.1712,736448.7808,736754.3868,737056.0002,737353.631,737647.2885,737936.9813,738222.7172,738504.5035,738782.3463,739056.2515,739326.224,739592.2679,739854.3866,740112.5829,740366.8588,740617.2154,740863.6533,741106.1722,741344.7711,741579.4481,741810.2007,742037.0257,742259.9187,742478.8751,742693.889,742904.954,743112.0627,743315.2069,743514.3776,743709.565,743900.7584,744087.946,744271.1155,744450.2533,744625.345,744796.3754,744963.3282,745126.1859,745284.9303,745439.5421,745590.0007,745736.2847,745878.3714,746016.237,746149.8564,746279.2035,746404.2507,746524.9693,746641.3292,746753.2989,746860.8454,746963.9343,747062.5299,747156.5946,747246.0892,747330.973,747411.2035,747486.7363,747557.5251,747623.5217,747684.6758,747740.9351,747792.2449,747838.5483,747879.7861,747915.8962,747946.8143,747972.4729,747992.8021,748007.7287,748017.1761,748021.0648,748019.3116,748011.8294,747998.5277,747979.3114,747954.0813,747922.7338,747885.1601,747841.2468,747790.8745,747733.9186,747670.2482,747599.7259,747522.2075,747437.5414,747345.5684,747246.1208,747139.022,747024.0859,746901.1162,746769.9057,746630.2352,746481.873,746324.5736,746158.0769,745982.1064,745796.3687,745600.5512,745394.3211,745177.3229,744949.177,744709.4768,744457.7864,744193.6376,743916.5266,743625.9098,743321.2003,743001.762,742666.9045,742315.8767,741947.8585,741561.9525,741157.1737,740732.4368,740286.5425,739818.1597,739325.8052,738807.8189,738262.3335,737687.2372,737080.1277,736438.2549,735758.4471,735037.0179,734269.6441,733451.2046,732575.5635,731635.2738,730621.1594,729521.7143,728322.2084,727003.3085,725538.8523,723892.0547,722008.568,719802.5609,717124.9548,713675.3544,708656.2519,695288.3237,692543.5757,679839.234,674874.4744,671243.1081,668254.3748,665653.5344,663315.5013,661168.7281,659168.1163,657283.2432,655492.5279,653780.0557,652133.7215,650544.0828,649003.6176,647506.2267,646046.889,644621.4159,643226.2732,641858.4481,640515.3494,639194.7301,637894.6278,636613.3171,635349.272,634101.1354,632867.6946,631647.8605,630440.6513,629245.1781,628060.6331,626886.2802,625721.4457,624565.5119,623417.9103,622278.1167,621145.6462,620020.0494,618900.9087,617787.8355,616680.467,615578.4643,614481.51,613389.3063,612301.5732,611218.0474,610138.4806,609062.6384,607990.2989,606921.2523,605855.2996,604792.2519,603731.9294,602674.1612,601618.7845,600565.6437,599514.5904,598465.4826,597418.1845,596372.5658,595328.5015,594285.8719,593244.5615,592204.4594,591165.4587,590127.4567,589090.3537,588054.0539,587018.4646,585983.496,584949.0612,583915.076,582881.4587,581848.13,580815.013,579782.0326,578749.116,577716.1922,576683.192,575650.0479,574616.6939,573583.0658,572549.1004,571514.7363,570479.9132,569444.5719,568408.6544,567372.1039,566334.8646,565296.8816,564258.1008,563218.4691,562177.9343,561136.4447,560093.9496,559050.3987,558005.7426,556959.9322,555912.9192,554864.6556,553815.0942,552764.1878,551711.8899,550658.1545,549602.9356,548546.1877,547487.8656,546427.9245,545366.3194,544303.0061,543237.94,542171.077,541102.3732,540031.7845,538959.2671,537884.7773,536808.2713,535729.7053,534649.0357,533566.2186,532481.2104,531393.967,530304.4446,529212.5991,528118.3863,527021.7618,525922.6811,524821.0996,523716.9723,522610.2541,521500.8995,520388.863,519274.0985,518156.5599,517036.2005,515912.9734,514786.8313,513657.7265,512525.611,511390.4361,510252.153,509110.7121,507966.0635,506818.1568,505666.941,504512.3644,503354.375,502192.92,501027.9461,499859.3991,498687.2245,497511.3667,496331.7696,495148.3764,493961.1294,492769.97,491574.839,490375.6761,489172.4202,487965.0095,486753.3807,485537.4701,484317.2126,483092.5422,481863.3918,480629.693,479391.3765,478148.3716,476900.6064,475648.0079,474390.5015,473128.0114,471860.4603,470587.7695,469309.8588,468026.6464,466738.0489,465443.9813,464144.3568,462839.0868,461528.0809,460211.247,458888.4908,457559.7159,456224.8241,454883.7149,453536.2855,452182.4307,450822.0432,449455.013,448081.2274,446700.5714,445312.927,443918.1732,442516.1865,441106.8398,439690.0032,438265.5433,436833.3233,435393.2028,433945.0379,432488.6807,431023.9793,429550.7776,428068.9155,426578.228,425078.5457,423569.6942,422051.4943,420523.7612,418986.3048,417438.9293,415881.4328,414313.6073,412735.2382,411146.1041,409545.9767,407934.6199,406311.7903,404677.2359,403030.6965,401371.9029,399700.5765,398016.4289,396319.1614,394608.4646,392884.0175,391145.4872,389392.5284,387624.7824,385841.8763,384043.4229,382229.0192,380398.2456,378550.6653,376685.8232,374803.2446,372902.4341,370982.8743,369044.0249,367085.3206,365106.1697,363105.9527,361084.02,359039.6902,356972.2478,354880.9407,352764.9779,350623.5261,348455.7073,346260.5948,344037.2098,341784.5171,339501.4205,337186.7581,334839.2964,332457.7244,330040.6467,327586.5756,325093.9229,322560.9904,319985.9587,317366.8758,314701.6429,311987.9989,309223.5034,306405.5159,303531.1729,300597.3617,297600.6892,294537.4469,291403.5686,288194.5823,284905.5525,281531.0118,278064.8797,274500.3648,270829.8458,267044.7272,263135.2607,259090.3232,254897.1386,250540.9229,246004.4276,241267.3439,236305.5107,231089.8444,225584.8631,219746.601,213519.5811,206832.2774,199590.0474,191663.6022,182869.0817,172930.9967,161406.2398,147505.414,129574.8612,102902.9417,24346.9394;]
y = [1,13.692,26.3839,39.0759,51.7679,64.4599,77.1518,89.8438,102.5358,115.2278,127.9197,140.6117,153.3037,165.9957,178.6876,191.3796,204.0716,216.7635,229.4555,242.1475,254.8395,267.5314,280.2234,292.9154,305.6074,318.2993,330.9913,343.6833,356.3753,369.0672,381.7592,394.4512,407.1431,419.8351,432.5271,445.2191,457.911,470.603,483.295,495.987,508.6789,521.3709,534.0629,546.7548,559.4468,572.1388,584.8308,597.5227,610.2147,622.9067,635.5987,648.2906,660.9826,673.6746,686.3666,699.0585,711.7505,724.4425,737.1344,749.8264,762.5184,775.2104,787.9023,800.5943,813.2863,825.9783,838.6702,851.3622,864.0542,876.7462,889.4381,902.1301,914.8221,927.514,940.206,952.898,965.59,978.2819,990.9739,1003.6659,1016.3579,1029.0498,1041.7418,1054.4338,1067.1258,1079.8177,1092.5097,1105.2017,1117.8936,1130.5856,1143.2776,1155.9696,1168.6615,1181.3535,1194.0455,1206.7375,1219.4294,1232.1214,1244.8134,1257.5054,1270.1973,1282.8893,1295.5813,1308.2732,1320.9652,1333.6572,1346.3492,1359.0411,1371.7331,1384.4251,1397.1171,1409.809,1422.501,1435.193,1447.8849,1460.5769,1473.2689,1485.9609,1498.6528,1511.3448,1524.0368,1536.7288,1549.4207,1562.1127,1574.8047,1587.4967,1600.1886,1612.8806,1625.5726,1638.2645,1650.9565,1663.6485,1676.3405,1689.0324,1701.7244,1714.4164,1727.1084,1739.8003,1752.4923,1765.1843,1777.8763,1790.5682,1803.2602,1815.9522,1828.6441,1841.3361,1854.0281,1866.7201,1879.412,1892.104,1904.796,1917.488,1930.1799,1942.8719,1955.5639,1968.2559,1980.9478,1993.6398,2006.3318,2019.0237,2031.7157,2044.4077,2057.0997,2069.7916,2082.4836,2095.1756,2107.8676,2120.5595,2133.2515,2145.9435,2158.6355,2171.3274,2184.0194,2196.7114,2209.4033,2222.0953,2234.7873,2247.4793,2260.1712,2272.8632,2285.5552,2298.2472,2310.9391,2323.6311,2336.3231,2349.0151,2361.707,2374.399,2387.091,2399.7829,2412.4749,2425.1669,2437.8589,2450.5508,2463.2428,2475.9348,2488.6268,2501.3187,2514.0107,2526.7027,2539.3946,2552.0866,2564.7786,2577.4706,2590.1625,2602.8545,2615.5465,2628.2385,2640.9304,2653.6224,2666.3144,2679.0064,2691.6983,2704.3903,2717.0823,2729.7742,2742.4662,2755.1582,2767.8502,2780.5421,2793.2341,2805.9261,2818.6181,2831.31,2844.002,2856.694,2869.386,2882.0779,2894.7699,2907.4619,2920.1538,2932.8458,2945.5378,2958.2298,2970.9217,2983.6137,2996.3057,3008.9977,3021.6896,3034.3816,3047.0736,3059.7656,3072.4575,3085.1495,3097.8415,3110.5334,3123.2254,3135.9174,3148.6094,3161.3013,3173.9933,3186.6853,3199.3773,3212.0692,3224.7612,3237.4532,3250.1452,3262.8371,3275.5291,3288.2211,3300.913,3313.605,3326.297,3338.989,3351.6809,3364.3729,3377.0649,3389.7569,3402.4488,3415.1408,3427.8328,3440.5247,3453.2167,3465.9087,3478.6007,3491.2926,3503.9846,3516.6766,3529.3686,3542.0605,3554.7525,3567.4445,3580.1365,3592.8284,3605.5204,3618.2124,3630.9043,3643.5963,3656.2883,3668.9803,3681.6722,3694.3642,3707.0562,3719.7482,3732.4401,3745.1321,3757.8241,3770.5161,3783.208,3795.9,3795.9,3783.208,3770.5161,3757.8241,3745.1321,3732.4401,3719.7482,3707.0562,3694.3642,3681.6722,3668.9803,3656.2883,3643.5963,3630.9043,3618.2124,3605.5204,3592.8284,3580.1365,3567.4445,3554.7525,3542.0605,3529.3686,3516.6766,3503.9846,3491.2926,3478.6007,3465.9087,3453.2167,3440.5247,3427.8328,3415.1408,3402.4488,3389.7569,3377.0649,3364.3729,3351.6809,3338.989,3326.297,3313.605,3300.913,3288.2211,3275.5291,3262.8371,3250.1452,3237.4532,3224.7612,3212.0692,3199.3773,3186.6853,3173.9933,3161.3013,3148.6094,3135.9174,3123.2254,3110.5334,3097.8415,3085.1495,3072.4575,3059.7656,3047.0736,3034.3816,3021.6896,3008.9977,2996.3057,2983.6137,2970.9217,2958.2298,2945.5378,2932.8458,2920.1538,2907.4619,2894.7699,2882.0779,2869.386,2856.694,2844.002,2831.31,2818.6181,2805.9261,2793.2341,2780.5421,2767.8502,2755.1582,2742.4662,2729.7742,2717.0823,2704.3903,2691.6983,2679.0064,2666.3144,2653.6224,2640.9304,2628.2385,2615.5465,2602.8545,2590.1625,2577.4706,2564.7786,2552.0866,2539.3946,2526.7027,2514.0107,2501.3187,2488.6268,2475.9348,2463.2428,2450.5508,2437.8589,2425.1669,2412.4749,2399.7829,2387.091,2374.399,2361.707,2349.0151,2336.3231,2323.6311,2310.9391,2298.2472,2285.5552,2272.8632,2260.1712,2247.4793,2234.7873,2222.0953,2209.4033,2196.7114,2184.0194,2171.3274,2158.6355,2145.9435,2133.2515,2120.5595,2107.8676,2095.1756,2082.4836,2069.7916,2057.0997,2044.4077,2031.7157,2019.0237,2006.3318,1993.6398,1980.9478,1968.2559,1955.5639,1942.8719,1930.1799,1917.488,1904.796,1892.104,1879.412,1866.7201,1854.0281,1841.3361,1828.6441,1815.9522,1803.2602,1790.5682,1777.8763,1765.1843,1752.4923,1739.8003,1727.1084,1714.4164,1701.7244,1689.0324,1676.3405,1663.6485,1650.9565,1638.2645,1625.5726,1612.8806,1600.1886,1587.4967,1574.8047,1562.1127,1549.4207,1536.7288,1524.0368,1511.3448,1498.6528,1485.9609,1473.2689,1460.5769,1447.8849,1435.193,1422.501,1409.809,1397.1171,1384.4251,1371.7331,1359.0411,1346.3492,1333.6572,1320.9652,1308.2732,1295.5813,1282.8893,1270.1973,1257.5054,1244.8134,1232.1214,1219.4294,1206.7375,1194.0455,1181.3535,1168.6615,1155.9696,1143.2776,1130.5856,1117.8936,1105.2017,1092.5097,1079.8177,1067.1258,1054.4338,1041.7418,1029.0498,1016.3579,1003.6659,990.9739,978.2819,965.59,952.898,940.206,927.514,914.8221,902.1301,889.4381,876.7462,864.0542,851.3622,838.6702,825.9783,813.2863,800.5943,787.9023,775.2104,762.5184,749.8264,737.1344,724.4425,711.7505,699.0585,686.3666,673.6746,660.9826,648.2906,635.5987,622.9067,610.2147,597.5227,584.8308,572.1388,559.4468,546.7548,534.0629,521.3709,508.6789,495.987,483.295,470.603,457.911,445.2191,432.5271,419.8351,407.1431,394.4512,381.7592,369.0672,356.3753,343.6833,330.9913,318.2993,305.6074,292.9154,280.2234,267.5314,254.8395,242.1475,229.4555,216.7635,204.0716,191.3796,178.6876,165.9957,153.3037,140.6117,127.9197,115.2278,102.5358,89.8438,77.1518,64.4599,51.7679,39.0759,26.3839,13.692,1;]
h1 = 7.1807*10^5;
h2 = 8.5108*10^5;
p1 = 749.0750;
p2 = 10100;
semilogy(x(20:580),y(20:580))
hold all
plot([h1 h2],[p1 p2],'rx')
plot(linspace(h1,h2,100),linspace(p1,p2,100),'r') % Plot the intermediate points

MATLAB: How to find rotation matrix from 4 rectangle points

Wouldn't the rotation matrix be

rotMatrix = pDistorted \ pStraight

Best Answer

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MATLAB: InterX issues. Showing intersection when there is none.

MATLAB: How to find rotation matrix from 4 rectangle points

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