## Split & Bevel

The Split & Bevel tool looks like this and is located on the Modify Tab of the Toolbar. This tool creates an offset from a face or bevels the entire hull. Click the Split & Bevel button. The value field and 'Uniform' checkbox appear on the modify tab. Geodesica prompts you to pick a primal face (Make sure primal facets are visible). #### Modifier Keys

Two modifier keys can be used with this tool. If the Shift key is down the operation is applied to all faces in the lattice. If the Control key is down, the original edges are deleted and ‘prisms’ are formed at the original vertices. If both the Control and Shift keys are down, the prisms are removed resulting in a bevelled hull. The dual is regenerated automatically. No modifier keys: single Shift key modifier: all Control key modifier: all + prisms Control and Shift keys: bevel

When performing a Split & Bevel, a face will be ignored if:

1. The face is on the truncation plane.
2. The face contains vertices flagged false for centroid calculation.
3. The face contains vertices flagged as truncation mid splits.

### Uniform Option

Fig 2: Tool applied 4 times. Left facets: 'Uniform' on (turquoise).
Right facets: 'Uniform' off (mustard).

Fig 1: Detail of rectangle in Fig. 2 (above). Uniform On. d = Bevel value.

#### Uniform On

For each vertex of the original face pF, the angle between its edges is bisected to give angle a. The split value d becomes the opposite side 'O' of a right triangle, and the new vertex V2 is placed at the end of its hypotenuse which is coincident with the bisection vector. IE the displacement of V2 along the bisection vector is the length of the hypotenuse:

H = O / sin(a)

This ensures that split face edges remain parallel with original face edges. In this instance the offset is uniform: d1 = d2 = d3 = d4.

#### Uniform Off

This simply moves vertices toward the facet centroid. For each vertex [pV] of the original face pF, a new vertex is inserted at distance d along a line that joins pV to the centroid of pF. (The split value d is the length of the diagonal between each successive vertex). In this instance the offset is not uniform unless the original face is a regular polygon.

#### Parallel Edges, Obtuse and Reflex Angles

When Uniform is on, parallel edges and reflex angles are handled thus: Fig. 3. Coplanar cell Fig. 4. Non-coplanar cell

There is a caveat splitting faces with parallel edges. As the tool is used repeatedly, vertices start to converge. In fig. 5. vertex A is converging on vertex B which is subtended by two parallel edges. Eventually, B overlaps A (fig. 6). Now the edges leaving B are superimposed and cannot be bisected. If this happens Geodesica will show a warning dialog and use a default bisection angle of 15°. To remedy the situation use the 'Collapse Edge' tool from B to A, or the 'Kill Vertex' tool to clean up the geometry. It is then safe to use the Split & Bevel tool again. Fig. 5 Fig. 6