Laplacian Smoothing

Wed, 03 Feb 2021 00:00:00 +0000

I implemented laplacian smoothing in my core c++ pipeline using the discrete formulation of the cotangent laplace operator.

As a test case, I tried “over-smoothing” a typical mesh to see it reduce along the medial axes. Below you see my source mesh before smoothing:

And after several iterations:

And now several more:

Procedural Geometry with Parametric Modeling

Sat, 01 Aug 2020 00:00:00 +0000

I implemented several parametric modeling techniques with my homebrew geometry / math libraries in C++ and rendered in UE4.

Solid of Revolution

Essentially you take a curve (perhaps a b-spline, pick your favorite) and revolve about an axis of rotation, creating vertices and triangles as you step.

A more formal treatment is available at https://en.wikipedia.org/wiki/Solid_of_revolution

solid of revolution

Here’s another curve

solid of revolution

Extrusion

Here’s a curve knot that I extruded along the path “profile” of a knot.

extrusion

Geometry | Ben Ahlbrand CV

Laplacian Smoothing

Procedural Geometry with Parametric Modeling

Solid of Revolution

Extrusion