知道何时以及如何旋转对象 [英] Knowing when and how to rotate object

问题描述

下面的CSV给出了在给定时间t内具有id = 1的汽车的x,z坐标，以秒为单位.

The CSV below gives me the x,z coordinates of a car with id = 1 at a given time t in seconds.

我能够每秒精确地更新汽车游戏对象的变换位置.问题是，当汽车的方向发生变化时，我需要能够旋转(或实际转向)汽车以使其指向行驶方向.我现在尝试通过一个简单的Lerp旋转来做到这一点(然后使用标准资产CarController脚本使转弯之后更加逼真).

I am able to update the car gameobject's transform position at each second just fine. The issue is that when the car's direction changes, I need to be able to rotate (or realistically turn) the car to make it point in the direction it's going. I'm trying to do this with a simple Lerp rotation for now (and then use the standard asset CarController script to make a turn more realistic afterwards).

我当前遇到的问题是知道何时转弯，以及如何推断汽车的前进方向以及旋转方向.我该怎么办?

The current issue I'm having is knowing when the car is turning and how to conclude which direction it's going in, and therefore which way to rotate it. How could I go about this?

t,id,x,z
908,1,0.00,755.17
909,1,-1.50,732.50
910,1,-1.50,715.84
911,1,-1.50,699.17
912,1,-1.50,682.50
913,1,-1.50,679.19
914,1,-1.50,679.19
915,1,-1.50,679.19
916,1,-1.50,653.52
917,1,-1.50,636.85
918,1,-1.50,620.19
919,1,-1.50,603.52
920,1,-1.50,586.85
921,1,-1.50,570.19
922,1,-1.50,553.52
923,1,-1.50,536.85
924,1,-1.50,521.94
925,1,-1.50,521.94
926,1,-1.50,521.94
927,1,-1.50,521.94
928,1,-1.50,521.94
929,1,-1.50,521.94
930,1,-1.50,521.94
931,1,-1.50,496.28
932,1,-1.50,479.61
933,1,-1.50,462.94
934,1,-1.50,446.28
935,1,-1.50,429.61
936,1,-1.50,412.94
937,1,-1.50,396.28
938,1,-1.50,379.61
939,1,-1.50,378.74
940,1,-1.50,378.74
941,1,-1.50,378.74
942,1,-1.50,378.74
943,1,-1.50,378.74
944,1,-1.50,378.74
945,1,-1.50,378.74
946,1,-1.50,350.07
947,1,-1.50,333.40
948,1,-1.50,316.74
949,1,-1.50,300.07
950,1,-1.50,283.40
951,1,-1.50,266.74
952,1,-1.50,250.07
953,1,-1.50,233.40
954,1,-1.50,232.39
955,1,-1.50,232.39
956,1,-1.50,232.39
957,1,-1.50,232.39
958,1,-1.50,232.39
959,1,-4.50,209.72
960,1,-4.50,193.05
961,1,-4.50,176.39
962,1,-4.50,159.72
963,1,-4.50,143.05
964,1,-4.50,126.39
965,1,-4.50,109.72
966,1,-4.50,93.05
967,1,-4.50,76.39
968,1,-4.50,59.72
969,1,-4.50,43.05
970,1,-4.50,26.39
971,1,-4.50,9.72
972,1,-4.50,6.00
973,1,-4.50,6.00
974,1,-4.50,6.00
975,1,-4.50,6.00
976,1,-4.50,6.00
977,1,-4.50,6.00
978,1,-4.50,6.00
979,1,-4.50,6.00
980,1,-4.50,6.00
981,1,-4.50,6.00
982,1,-4.50,6.00
983,1,-4.50,6.00
984,1,28.22,-4.50
985,1,49.25,-4.50
986,1,69.00,-4.50
987,1,87.67,-4.50
988,1,105.12,-4.50
989,1,121.45,-4.50
990,1,136.32,-4.50
991,1,149.74,-4.50
992,1,161.36,-4.50
993,1,171.13,-4.50
994,1,179.02,-4.50
995,1,185.12,-4.50
996,1,189.57,-4.50
997,1,192.60,-4.50
998,1,194.49,-4.50
999,1,195.56,-4.50
1000,1,196.11,-4.50
1001,1,196.37,-4.50
1002,1,196.48,-4.50
1003,1,196.54,-4.50
1004,1,196.54,-4.50
1005,1,196.60,-4.50
1006,1,196.60,-4.50
1007,1,197.25,-4.50
1008,1,198.58,-4.50
1009,1,200.53,-4.50
1010,1,200.53,-4.50
1011,1,201.35,-4.50
1012,1,201.45,-4.50
1013,1,202.27,-4.50
1014,1,202.27,-4.50
1015,1,202.60,-4.50
1016,1,202.60,-4.50
1017,1,202.60,-4.50
1018,1,202.60,-4.50
1019,1,202.60,-4.50
1020,1,202.60,-4.50
1021,1,202.60,-4.50
1022,1,202.60,-4.50
1023,1,202.60,-4.50
1024,1,202.60,-4.50
1025,1,202.60,-4.50
1026,1,202.60,-4.50
1027,1,202.60,-4.50
1028,1,202.60,-4.50
1029,1,202.60,-4.50
1030,1,202.60,-4.50
1031,1,202.60,-4.50
1032,1,202.60,-4.50
1033,1,202.60,-4.50
1034,1,202.60,-4.50
1035,1,203.32,-4.50
1036,1,204.85,-4.50
1037,1,206.85,-4.50
1038,1,206.98,-4.50
1039,1,207.90,-4.50
1040,1,207.90,-4.50
1041,1,208.48,-4.50
1042,1,208.48,-4.50
1043,1,208.48,-4.50
1044,1,208.48,-4.50
1045,1,208.48,-4.50
1046,1,208.48,-4.50
1047,1,208.48,-4.50
1048,1,208.48,-4.50
1049,1,208.48,-4.50
1050,1,208.48,-4.50
1051,1,208.48,-4.50
1052,1,208.48,-4.50
1053,1,208.48,-4.50
1054,1,208.48,-4.50
1055,1,209.48,-4.50
1056,1,211.48,-4.50
1057,1,214.45,-4.50
1058,1,214.45,-4.50
1059,1,214.45,-4.50
1060,1,214.45,-4.50
1061,1,214.45,-4.50
1062,1,214.45,-4.50
1063,1,214.45,-4.50
1064,1,214.45,-4.50
1065,1,214.45,-4.50
1066,1,242.67,-1.50
1067,1,264.63,-1.50
1068,1,286.36,-1.50
1069,1,307.90,-1.50
1070,1,329.29,-1.50
1071,1,350.45,-1.50
1072,1,371.40,-1.50
1073,1,392.12,-1.50
1074,1,412.58,-1.50
1075,1,432.75,-1.50
1076,1,452.60,-1.50
1077,1,472.06,-1.50
1078,1,491.06,-1.50
1079,1,509.51,-1.50
1080,1,527.29,-1.50
1081,1,544.25,-1.50
1082,1,560.23,-1.50
1083,1,575.01,-1.50
1084,1,588.37,-1.50
1085,1,600.11,-1.50
1086,1,610.06,-1.50
1087,1,618.16,-1.50
1088,1,624.44,-1.50
1089,1,629.05,-1.50
1090,1,632.22,-1.50
1091,1,634.21,-1.50
1092,1,635.36,-1.50
1093,1,635.95,-1.50
1094,1,636.23,-1.50
1095,1,636.35,-1.50
1096,1,636.42,-1.50
1097,1,636.42,-1.50
1098,1,636.48,-1.50
1099,1,636.48,-1.50
1100,1,636.48,-1.50
1101,1,637.48,-1.50
1102,1,639.48,-1.50
1103,1,642.45,-1.50

推荐答案

请注意，这里还有一个后续问题:

Note that there is a follow-up question here: Unity: turning a car realistically given target point and direction

据我了解，问题是

• 我们在特定时间获得了一系列物体位置
• 期望的输出是一组矢量，这些矢量描述了对象所面对的方向，这要考虑到对象在其当前运动方向上所面对的约束.

这很容易计算，但首先要小心.车辆将指向当前行驶的方向并不总是现实的，尤其是在转弯时.急转弯时，汽车会打滑和漂移.飞机和火箭通过将自己指向不移动并产生推力的方向来精确地操纵.除非在顺风下航行，否则帆船不能指向其前进的方向.等等.您可能会发现您需要一种更细微的方法，但是在跑步之前要走路.

That's straightforward to compute, but a caution first. It does not always look realistic for a vehicle to be pointing in the direction that it is currently moving, particularly if it is turning. Cars skid and drift when turning sharply. Airplanes and rockets maneuver precisely by pointing themselves in the direction that they are not moving and producing thrust. Sailboats are incapable of pointing in the direction they are moving unless they are moving dead downwind. And so on. You might find that you need a more nuanced approach, but walk before you run.

但是确定速度矢量很简单. 速度是位置的第一时间导数，您拥有位置和时间.

But determining the velocity vector is straightforward. Velocity is the first time derivative of position, and you have position and time.

最简单的方法是将当前"位置和下一个"位置相减，然后除以时间差:

The simplest thing to do is to take the "current" position and the "next" position, subtract them, and divide by the time difference:

  t, id,     x,      z
908,  1,  0.00, 755.17
909,  1, -1.50, 732.50

从第二个减去第一个以获得增量:

Subtract the first from the second to get the deltas:

  t, id, Δt,    Δx,     Δz
908,  1,  1, -1.50, -22.67

速度是距离除以时间，因此速度向量v _平均值为(Δx/Δt，Δz/Δt)，因此这就是指向汽车的方向.

Velocity is distance divided by time, so the velocity vector v_average is (Δx/Δt, Δz/Δt), so that's the direction you should point your car.

• 锻炼:您可以在每个点上计算加速度向量吗?加速度是位置相对于时间的 second 导数.第三个是混蛋"，因为我们认为加速度的突然变化是生涩的"运动.你能计算出来吗?

• Exercise: Can you compute the acceleration vectors at each point? Acceleration is the second derivative of position with respect to time. The third is "jerk", because we perceive a sudden change in acceleration as a "jerky" movement; can you compute it?

锻炼:假设您获得了一个初始位置和一个速度的时间序列；您可以采用另一种方法，并从速度中产生位置吗?

Exercise: Suppose you are given an initial position and a time series of velocities; can you go the other way, and produce the positions from the velocities?

锻炼:假设您的物体具有特定的质量，并且为您提供了初始位置，初始速度和力矢量的时间序列.您可以计算速度和位置吗? (提示:关于力，质量和加速度之间的关系，牛顿告诉我们什么?)

Exercise: Suppose your object has a particular mass, and you are given an initial position, an initial velocity, and a time series of force vectors. Can you compute the velocities and positions? (Hint: what does Newton tell us about the relationship between force, mass and acceleration?)

锻炼:太空中的火箭指向其加速的方向，而不是指向运动的方向.但是太空中的火箭是无摩擦的，汽车之所以能工作，是因为道路上有摩擦，所以汽车往往会指向其行驶的方向. 失去牵引力的汽车不必指向行驶方向.您能提出一个模型来确定汽车何时失去牵引力吗?

Exercise: Rockets in space point in the direction they are accelerating, not the direction they are moving. But rockets in space are frictionless, and cars only work because there is friction against the road, so cars tend to point in the direction they are moving. A car that loses traction need not be pointing in the direction it is moving. Can you come up with a model for determining when a car loses traction?

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