Pattern from Features

From Features could generate quad mesh generation with given singularities.

Medial-axis-based generation of a smooth quad mesh without boundary singularities

Boundary Point Feature

If a four-sided patch has a corner labeled as ’feature point’, then the diagonal corresponding to this corner is added, to split the four-sided patch into two three-sided patches

Meshing with boundary point features

Inner Point Featrue

Inner point features modify the Delaunay triangulation, and the resulting set of patches, mainly by adding three-sided patches.

Meshing with inner point features

Curve features

The curve features are discretised and the resulting points added to the set of points used for the Delaunay triangulation, as for the boundaries.

Meshing with curve features.

Transformation rule for four-sided patches with curve feature points.

Ex 1: British Museum

Here are four different ways to build the British Museum using different features.

1. Pattern

1a. Create pattern

1b. Modify pattern

Once the initial quad mesh has been generated, the pattern can be relaxed. Relaxation of the Pattern is not a requirement for successfully finding horizontal and vertical equilibrium. However, relaxing the Pattern during early stages of the RV2 workflow will ensure that the pattern is smooth, which will also make the eventual ThrustDiagram has smooth force

2 + 3 + 4. Define boundary conditions, create form and force diagrams

We will use all of the boundary vertices as supports, but not the singularities (the point features on the surface that were fixed in the previous step).

5. Horizontal equilibrium

6. Vertical equilibrium

bm_vertical_equilibrium.zipbm_vertical_equilibrium.zip - 612KB

Exercise 2: Armadillo Vault from Features

Method 2: Relax the Pattern

After relaxation, unfix all the vertices of the pattern by following the instructions in the previous step Unfixing of the vertices can be done (or not even necessary, if they are intended to be used as anchors) during any point before the creation of the FormDiagram. However, for clarity of the procedures of the main workflow steps, all vertices are explicitly unfixed in this step.

Comparing pattern refinements

Left - Pattern from feature with target length 1, without smoothing or relaxation

Middle - Pattern from feature with target length 1, and 30 iterations of constrained Laplacian smoothing (notice the more evenly distributed vertices along the boundaries)

Right - Pattern From Feature with target length 1, 30 iterations of constrained Laplacian smoothing and relaxation with all boundary vertices fixed (notice the much smoother continuous edges).