Mercurial > cortex

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     4 

     5 (ConeJoint

     6 	RigidBody A

     7 	RigidBody B

     8 	Vector3f PivotA

     9 	Vector3f PivotB

    10 	Matrix3f RotA

    11 	Matrix3f RotB

    12 )

    13 

    14 Parameters:

    15 

    16 The specification of a cone joint depends on local coordinates,

    17 that is coordinates relative to the given rigid bodies.

    18 

    19 ***

    20 DIGRESSION ABOUT LOCAL COORDINATES

    21 

    22 Each rigid body has its own coordinate system.

    23 If an object is placed, unrotated, at the origin of the world,

    24 then its coordinate system is the same as the world's coordinate

    25 system. In other words, the origin of the object coincides with the

    26 origin of the world, and the XYZ axes of the object coincide with the

    27 XYZ axes of the world.

    28 

    29 When you translate the object, its "origin" goes with it.

    30 The origin of the object is always the center of the object.

    31 

    32 When you rotate the object, its axes go with it.

    33 For example, if you rotate the object pi/2 radians righthandedly

    34 about the Z axis, its own X axis will move to coincide with the

    35 world's Y axis; its own Y axis will move to coincide with the

    36 world's -X axis; its Z axis will remain aligned with the world's

    37 Z-axis.

    38 

    39 

    40 In such a way, you can see the way in which the translations and rotations of an

    41 object alter its local coordinates.

    42 

    43 

    44 ## a haphazard elaboration of the above

    45 

    46 Converting from world coordinates to local coordinates amounts to

    47 finding the transformation that undoes all the rotations and

    48 translations that the Object has suffered, then applying that

    49 undoing-transformation to the world coordinates.

    50 

    51             +position of obj   +rot of obj

    52 world axes  ---------------> x -----------> obj axes

    53 

    54 

    55 1. Start with the world coordinates of the Object and a test-object.

    56 2. Subtract the world coordinates of the Object from each. Now the

    57 Object is at the origin (though still has its rotation, if any) and

    58 the test-object is somewhere else (irrelevant).

    59 3. Rotate the whole world about the origin so that the Object becomes

    60 unrotated. Now the object is unrotated at the origin, and the

    61 test-object is somewhere else.

    62 4. That somewhere-else is the coordinates of the test-object as seen

    63 from the Object's own coordinate system (the system in which the Object is always

    64 unrotated and centered at the origin)

    65 

    66 cf: get-subjective-rotation

    67 cf: get-subjective-position

    68 

    69 ***

    70 

    71 

    72 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

    73 

    74 Now, to understand the ConeJoint constructor: 

    75 Suppose you have the position of the cone joint picked out, as well as its

    76 orientation (orientation aka rotation matters because the limits of

    77 rotation are taken with respect to the xy and xz plane of the _joint's_

    78 coordinate system. This is what the documentation means by "by

    79 default, the x-axis").

    80 

    81 Then: 

    82 Pivot-a is the position of the joint, as expressed in the coordinate

    83 system of object-a.

    84 Pivot-a is the position of the joint again, this time as expressed in

    85 the coordinate system of object-b.

    86 

    87 (Use get-subjective-position to calculate this conveniently)

    88 

    89 

    90 Rot-a is the orientation of the joint, as expressed in the

    91 coordinate system of object-a. By default, it is aligned with a's

    92 coordinate system, making the cone's axis along a's x-axis, and its

    93 limits of rotation in a's xy and xz planes.

    94 

    95 Analogously for b.

    96 

    97 If inconsistent pivot locations are given, it's possible to recover by

    98 moving the objects. I think the engine prefers to keep object b still

    99 and move everything else, but it may not always be so.

   100 

   101 If inconsistent rotations are given ... I don't know what

   102 happens. Beez happens.

   103 

   104 

   105 Modulo a bunch of forced object migration because your pivots give

   106 inconsistent indicators of where the joint should be expected, etc., this is

   107 how the method works.

   108 

   109 

   110 

   111 # Another implementation option would have been to specify the positions and

   112 # rotations of THREE things --- object A, object B, and the joint --- all in terms of world

   113 # coordinates. This wouldn't be any more or less fragile (i.e. subject to explosions

   114 # of inconsistency) but it might be nice to avoid those

   115 # transformations into local coordinates, even if we had to introduce

   116 # more parameters into such a new method

   117 # (specifically, the position and orientation of the joint would be new).

   118 

   119 # I wouldn't mind because after all, don't we already  need to keep in mind the position and orientation of the

   120 # joint in the existing method? Lest it explode in inconsistency? I

   121 # suggest we create a clojure method that creates cone joints in the

   122 # transformation-free way.

   123 # cf. joint-create, my first attempt

   124 

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   127
author	Robert McIntyre <rlm@mit.edu>
date	Sat, 07 Jan 2012 00:58:47 -0700
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