# discretize.TreeMesh.refine_vertical_trianglular_prism#

TreeMesh.refine_vertical_trianglular_prism(self, triangle, h, levels, finalize=True, diagonal_balance=None)#

Refine the `TreeMesh` along the trianglular prism to the desired level.

Refines the TreeMesh by determining if a cell intersects the given trianglular prism(s) to the prescribed level(s).

Parameters:
triangle(`N`, 3, `dim`) array_like

The nodes of the bottom triangle(s).

h(`N`) array_like

The height of the prism(s).

levels`int` `or` (`N`) array_like `of` `int`

The level to refine intersecting cells to.

finalizebool, `optional`

Whether to finalize after refining

diagonal_balancebool or `None`, `optional`

Whether to balance cells diagonally in the refinement, None implies using the same setting used to instantiate the TreeMesh`.

Examples

We create a simple mesh and refine the TreeMesh such that all cells that intersect the line segment path are at the given levels.

```>>> import discretize
>>> import matplotlib.pyplot as plt
>>> import matplotlib.patches as patches
>>> mesh = discretize.TreeMesh([32, 32, 32])
>>> mesh.max_level
5
```

Next we define the bottom points of the prism, its heights, and the level we want to refine to, then refine the mesh.

```>>> triangle = [[0.14, 0.31, 0.21], [0.32, 0.96, 0.34], [0.87, 0.23, 0.12]]
>>> height = 0.35
>>> levels = 5
>>> tree_mesh.refine_vertical_trianglular_prism(triangle, height, levels)
```

Now lets look at the mesh.

```>>> v = tree_mesh.cell_levels_by_index(np.arange(tree_mesh.n_cells))
>>> fig, axs = plt.subplots(1, 3, figsize=(12,4))
>>> tree_mesh.plot_slice(v, ax=axs, normal='x', grid=True, clim=[2, 5])
>>> tree_mesh.plot_slice(v, ax=axs, normal='y', grid=True, clim=[2, 5])
>>> tree_mesh.plot_slice(v, ax=axs, normal='z', grid=True, clim=[2, 5])
>>> plt.show()
```