Parametric Surface Functions

pl-parmodel-surface is a ChRIS ds plugin which projects surface meshes from a spherical function, with perfect vertex correspondence to given input meshes.

Abstract

pl-parmodel-surface produces surface meshes from a parametric spherical function. These are useful for modeling, because T-link thickness (Euclidean distance) between mathematical curves can be determined theoretically.

Resulting meshes have perfect vertex-to-vertex correspondence and are perfectly smooth (so long as the given function is differentiable).

Installation

pl-parmodel-surface is a ChRIS plugin, meaning it can run from either within ChRIS or the command-line.

Local Usage

To get started with local command-line usage, use Apptainer (a.k.a. Singularity) to run pl-parmodel-surface as a container:

apptainer exec docker://fnndsc/pl-parmodel-surface parm --equation ... input/ output/

Examples

A starting point can be obtained using create_tetra. The unit sphere should be placed in an incoming/ directory.

An interesting shape can be created by the formula r=20+5*sin(6*theta)*sin(phi), see the figure below.

The object can be created like this:

apptainer exec docker://fnndsc/pl-parmodel-surface:latest parm  \
    --equation '20+5*sin(10*theta)*sin(phi)' \
    incoming/ outgoing/

pl-parmodel-surface will also run surface_mask2 to produce a volume mask for the surface.