Vector and Matrix functions with Vector Product node in Maya

This document will explain how to use the vector product node in Maya to calculate vector cross and dot products as well as to find out object's translation in a custom space, as in to find out object's world space coordinates without moving it from the hierarchy or vice versa. This method bypasses the rotation problem that you get if trying to find out object’s world space by doing maths on the basic translation values of objects that have also rotations in the mix.

Vector Product node can be found under utilities in Hypershade. It has operation option which defines which calculation you want to perform, they include dot product, cross product, vector matrix product and point matrix product. You can attach 2 vectors into input1 and input2 of the vector product. You can also attach a matrix into the node; this does not show up on the attribute menu which is why you need to use the connection editor to do this. This will become necessary when trying to find out custom space translations. It also has a normalize option which you can switch on and off, based on your needs (more uses explained below)

Dot product

Output: float

Output represents the angle between the 2 input vectors. If the output is normalized output is the actual cosine value and will vary between -1 and 1.If the normalized output is one it signifies that the input vectors run parallel to each other. If the output is 0 the vectors are perpendicular. And if the output is -1 the vectors run in opposite directions

Cross Product

Output: vector

The output vector will be in right angle (perpendicular) to the input vectors. In other words the output vector is almost like the normal of the plane that is defined by the 2 input vectors.

Vector matrix Product and Point Matrix product

Output: vector/point

Point Matrix product allows you to find out object’s translations in a custom space i.e. under some other hierarchy in the scene that it currently is in.

Example scene:

hierarchy:

purpleCone (world/local t:0,4,0 r:0,0,0 s:1,1,1)

orangeSphere (local t:2,-2,2 r:45,45,45 s:1,1,1)

blueCube (local t:-3,-3,-3 r:0,0,0 s:1,1,1)

greenTorus (world/local t:-3,-3,-3 r:0,0,0 s:1,1,1)

To find out object's translation in it’s parents local space as in move the translation values up one level in the hierarchy without breaking the current hierarchy, you need to connect the parent object's xFormMatrix into the vector product node’s matrix input. You also need to connect the queried object's translation vector into the vector products input1 slot. The input2 vector will be left blank. Change the operation of the vector product node into `point matrix product` under the attribute editor. The resulting vector is the queried object's translation in the parent objects local space, if the parent object is under the world then you get the world space coordinates of the queried object.

In the example scene we could find out the blueCube's (bottom of the hierarchy) translation values under the purpleCone (top of the hierarchy) without braking the hierarchy. So we would connect the spheres xFormMatrix into the input matrix of a vectorProduct node and then connect the translate output of the cube into the first input vector of the vectorProduct node. Switch the vectorProduct node's operation into Point Matrix Product. The output is the translation of the cube as if it were under the cone. (t:-1.6. -5.6. 1.1)

Notice how the the rotations of the sphere are taken into account translation because we use matrices, without having to worry about rotation orders.

If you have an object buried under a hierarchy of multiple objects and you need to move up multiple levels, you can feed the output translate from the vector product into another vector product and attach the xFormMatrix of the next-object-up-in-the-hierarchy into the matrix input in the new vectorProduct node. This way you can walk up the hierarchy as you wish. On the other hand if you want to know the objects translation in world space you can do this easily by using the parent objects worldMatrix instead of the xFormMatrix and this will give you the world translation straight away.

You can also reverse the process and find out translation of an object upwards in the hierarchy, so for example finding out object’s, which is in the root of the scene (world space), translation under another object which is under multiple objects. In order to do this you need to connect the queried object’s translation into the input1 of the vector product node and connect the object’s worldInverseMatrix, under which you want to virtually move the queried objects translation space to, into the matrix input of the vector product node. The output will be the queried object’s translations as if it would be under the specified object which matrix you plugged into the vector product.

In our example scene we could query the greenToruse's translation, which are currently in worldspace as it is not part of the hierarchy in which the other belong to, under the orangeSphere, which already under the purpleCone. Connect the the orange Sphere's worldInverseMatrix into the vectroProduct node's matrix input slot in the connection editor. Then connect the greenToruses translation into the vectorProduct's input1 slot. Make sure the vector product operation is Point Matrix Product. The output is the translation of the torus as if it were under the sphere (t:-1.6. -1.1. -5.1).

I hope this will be usefull for some of you =)

Note about maya matrix maths:

Maya has a few matrix math nodes that are hidden. The can be created with createNode command in the script editor and found then in the outliner if you show all the scene nodes (un-check show only dag nodes).

These nodes include:

pointMatrixMult

multMatrix

fourByfourMatrix

passMatrix

addMatrix

holdMatrix