Creating static points on deforming and splitting geo

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Ok, please help. I cannot find a way to select scattered points on a changing geo without getting completely new ones in the group after the geo deforms/splits.
To give you reference, I have a sphere (cell) which will split into two halves (2 separate geos), close the seams (adding new prims/points) and themselves becoming 2 different spheres. After that, again splitting into 4 spheres and so on.
I've added random points on mother sphere and I want them to remain the same after splitting. I've tried many - as I thought - good ideas, such as:
- enumerate SOP to have id attribute for each point and group expression node to select 20% of them - but as soon as splitting occurs, IDs of the right half of mother sphere change and I get another set of points
- point generate + VEX to center points to primitives and using them - but the same thing occurs as above
- time-shifting rest mother sphere, copying points to wires from ends SOP and using att interpolate together with sourceprimuv - no luck, the scattered points immediately jump to closed seam side of the left sphere.
- uv texture each sphere (I have separate ids for each geo generated) and scattering using texture space - it basically works, but several crucial points jitter and mirror disappear/appear during sphere moving and splitting.

It is probably a noob problem, since I am not a Houdini/VEX expert, but there is surely an easy way to achieve this and I'm too tired
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Nobody?
Edited by AdamuKv - Nov. 27, 2019 11:24:45
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