GPv3: Compute the "curve plane normal" using a principal component analysis #117275

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Falk David · 2024-01-18T12:34:47+01:00

Falk David commented

2024-01-18 12:34:47 +01:00

It's often usefull to know if a grease pencil stroke lies on a plane and what the normal vector of that plane is.

Currently there is drawing.curve_plane_normals(). This tries computing such a normal using the newell method.
There are issues with this:

The newell method will output a vector with a length that is proportional to the signed area of the curve. E.g. if the curve forms a perfect figure-8, the vector would be 0 and the method fails.
The direction of the vector depends on the winding number. E.g. if the stroke is drawn in a clockwise order the vector will be different to when it is drawn anti-clockwise.
When the stroke is not in a plane, this vector becomes somewhat arbitrary.

A better method would use a PCA (https://en.wikipedia.org/wiki/Principal_component_analysis)

Get the centroid of points
Build a covariance matrix (sum of dot products of deltas from the centroid)
Use BLI_svd_m3 to do a singular value decomposition
The result is a rotation matrix and the variance along the 3 principal axes. plane normal would be the 3rd axis (smallest variance)

This not only will result in a better normal vector, it will also compute "how much the stroke is not on the plane".
Having this value can be useful to e.g. do a different computation for strokes that are "3D" vs "2D".

It's often usefull to know if a grease pencil stroke lies on a plane and what the normal vector of that plane is. Currently there is `drawing.curve_plane_normals()`. This tries computing such a normal using the newell method. There are issues with this: * The newell method will output a vector with a length that is proportional to the signed area of the curve. E.g. if the curve forms a perfect figure-8, the vector would be 0 and the method fails. * The direction of the vector depends on the winding number. E.g. if the stroke is drawn in a clockwise order the vector will be different to when it is drawn anti-clockwise. * When the stroke is not in a plane, this vector becomes somewhat arbitrary. A better method would use a PCA (https://en.wikipedia.org/wiki/Principal_component_analysis) * Get the centroid of points * Build a covariance matrix (sum of dot products of deltas from the centroid) * Use `BLI_svd_m3` to do a singular value decomposition * The result is a rotation matrix and the variance along the 3 principal axes. plane normal would be the 3rd axis (smallest variance) This not only will result in a better normal vector, it will also compute "how much the stroke is not on the plane". Having this value can be useful to e.g. do a different computation for strokes that are "3D" vs "2D".

Falk David added the

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label 2024-01-18 12:34:47 +01:00

Falk David added this to the Grease Pencil project 2024-01-18 12:34:49 +01:00

Falk David changed title from ~~GPv3: Compute the "curve plane normal"~~ to GPv3: Compute the "curve plane normal" using a principal component analysis

2024-01-18 12:35:17 +01:00

Lukas Tönne commented

2024-01-19 11:08:44 +01:00

Implementation of the method in geometry nodes, as proof-of-concept: #117322

Attached file uses the node to find principal components of randomized point cloud positions for testing purposes.

Implementation of the method in geometry nodes, as proof-of-concept: #117322 ![Screenshot_20240119_110017](/attachments/0bf0084e-b6a6-4393-941d-94e95e329aad) Attached file uses the node to find principal components of randomized point cloud positions for testing purposes. ![image](/attachments/1c340783-79f1-45e8-a4bb-78b04875546d)

svd_test_01.blend

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GPv3: Compute the "curve plane normal" using a principal component analysis #117275