Linear Reduce geometry node

Compute the components of a reduced loss function.

There are various ways to measure how dissimilar two point attributes or two volumes are. One common way to do this is the root mean square of the differences. This is often used to define the loss function for machine learning (ML). The square root can be ommitted in this case, because in ML we only care about minimizing the loss not the actual value of the loss.

Let’s say we have a point attribute 's' and a point attribute 't'. Then we could compute, for each point, the difference between 's' and 't' at that point and square that difference. We could sum up all these squared differences and take the square root. This would give us a loss that tells us how dissimilar 's' is from 't'. Similarly, we could have volumes 's' and 't'. We could compute at each voxel, the difference between 's' and 't', square that difference, and sum up all the squared differences and take the square root of this.

Consider the case of a point attribute 's'. Often, we have an application where the point attribute 's' is known to be a linear combination of a fixed set of vectors. This happens in different ways in animation. For example, when using blend shapes. Another animation-related example is linear blend skinning. Here, the fixed set of vectors is defined by the capture weights and the coefficients that determine 's' in terms of this fixed set of vectors would be the components of the global transform matrices at the joints.

If 's' is a linear combination of a fixed set of vectors, then 's' is completely determined by the coefficients of that linear combination. If 't' is fixed as well, we may completely rewrite our loss function in terms of these coefficients. This is what Linear Reduce allows you to do.

Parameters ¶

Data Type

The source data to use for analysis.

Point Attributes

The P position attribute is used. This is batched into consecutive groups; so all the input samples should have the same number of points and be concatenated together.

Volumes

Each volume becomes a sample. All the volumes must match in resolution and tuple-size.

Point Attribute

The name of a point attribute.

Points per Sample

How many points will form each reduction vector for the analysis. This must divide evenly into the total number of points.

Mode

Choose between reducing and expanding.

Reduce

Use the given set of vectors to compute the components of the reduced loss function.

Expand

Combine the given set of vectors with given weights.