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# ===============================================================================
# Transformations
# ===============================================================================
def get_world_mirror_matrix(plane):
"""
Create a mirror matrix for a given plane.
Parameters
----------
plane: `str`
The plane to mirror across. Must be one of 'xy', 'yz', or 'xz'.
Returns
-------
mirror_matrix: `jax.Array`
The mirror matrix for the given plane.
"""
if plane.lower() == 'xy':
# Mirroring across the XY plane (change Z coordinate)
mirror_matrix = jnp.array([[1, 0, 0], [0, 1, 0], [0, 0, -1]])
elif plane.lower() == 'yz':
# Mirroring across the YZ plane (change X coordinate)
mirror_matrix = jnp.array([[-1, 0, 0], [0, 1, 0], [0, 0, 1]])
elif plane.lower() == 'xz':
# Mirroring across the XZ plane (change Y coordinate)
mirror_matrix = jnp.array([[1, 0, 0], [0, -1, 0], [0, 0, 1]])
else:
raise ValueError("Invalid plane. Choose 'xy', 'yz', or 'xz'.")
return mirror_matrix
def mirror_points(points, mirror_matrix):
"""
Mirror points across a given plane.
Parameters
----------
points: `jax.Array`
The points to mirror.
mirror_matrix: `jax.Array`
The mirror matrix.
Returns
-------
mirrored_points: `jax.Array`
The mirrored points.
"""
return points @ mirror_matrix
# ===============================================================================
# Grid functions
# ===============================================================================
def get_grid_tile_quarter(grid_size, grid_num_pts):
"""
Get the 3D coordinates of a quarter tile of a control point grid.
Parameters
----------
grid_size: `int`
The size of the grid.
grid_num_pts: `int`
The number of points along one side of the grid.
Returns
-------
tile: `jax.Array`
The 3D coordinates.
"""
half_grid_size = grid_size / 2.0
grid_step = half_grid_size / (grid_num_pts - 1.0)
pt0 = [grid_step, grid_step, 0.0]
pt1 = [half_grid_size, grid_step, 0.0]
pt2 = [grid_step, half_grid_size, 0.0]
pt3 = [half_grid_size, half_grid_size, 0.0]
return jnp.array([pt0, pt1, pt2, pt3])
def calculate_grid_from_tile_quarter(tile):
"""
Generate an ordered grid of control points from a quarter tile.
Parameters
----------
tile: `jax.Array`
The 3D coordinates of a quarter tile.
Returns
-------
grid_points: `jax.Array`
The 3D coordinates of the grid.
"""
grid_points = tile
# mirror tile once
mirrored_points = mirror_points(grid_points, get_world_mirror_matrix("yz"))
grid_points = jnp.concatenate((grid_points, mirrored_points))
# mirror tile again
mirrored_points = mirror_points(grid_points, get_world_mirror_matrix("xz"))
grid_points = jnp.concatenate((grid_points, mirrored_points))
return grid_points
def get_grid_tile_half(grid_size, grid_num_pts):
"""
Get the 3D coordinates of a half tile of a control point grid.
Parameters
----------
grid_size: `int`
The size of the grid.
grid_num_pts: `int`
The number of points along one side of the grid.
Returns
-------
tile: `jax.Array`
The 3D coordinates.
"""
tile_quarter = get_grid_tile_quarter(grid_size, grid_num_pts)
# mirror tile once
mirrored_points = mirror_points(tile_quarter, get_world_mirror_matrix("yz"))
return jnp.concatenate((tile_quarter, mirrored_points))
def calculate_grid_from_tile_half(tile):
"""
Generate an ordered grid of control points from a half tile.
Parameters
----------
tile: `jax.Array`
The 3D coordinates of a half tile.
Returns
-------
grid_points: `jax.Array`
The 3D coordinates of the grid.
"""
grid_points = tile
# mirror tile once
mirrored_points = mirror_points(grid_points, get_world_mirror_matrix("xz"))
grid_points = jnp.concatenate((grid_points, mirrored_points))
return grid_points
def get_grid_tile_full(grid_size, grid_num_pts):
"""
Get the 3D coordinates of a full tile of a control point grid.
Parameters
----------
grid_size: `int`
The size of the grid.
grid_num_pts: `int`
The number of points along one side of the grid.
Returns
-------
tile: `jax.Array`
The 3D coordinates.
"""
tile = get_grid_tile_quarter(grid_size, grid_num_pts)
return calculate_grid_from_tile_quarter(tile)
def calculate_grid_from_tile_full(tile):
"""
Generate an ordered grid of control points from a full tile.
Parameters
----------
tile: `jax.Array`
The 3D coordinates of a full tile.
Returns
-------
grid_points: `jax.Array`
The 3D coordinates of the grid.
"""
grid_points = tile
return grid_points
# ===============================================================================
# Grids
# ===============================================================================
class PointGrid:
"""
A grid of control points.
Parameters
----------
tile: `jax.Array`
The 3D coordinates of a tile.
num_pts: `int`
The number of points along one side of the grid.
Notes
-----
The order of the points in a 4x4 grid must be:
3 7 11 15
2 6 10 14
1 5 9 13
0 4 8 12
"""
def __init__(self, tile, num_pts) -> None:
self.tile = tile
self.num_pts = num_pts
# Reindexing map: the 16 mirrored control points must be arranged in
# the specific order expected by the Bezier surface evaluator (column-major,
# matching the convention used in the original paper's Rhino/Grasshopper
# pipeline). This ordering is fixed for all grid sizes and symmetry modes.
self.indices = [15, 13, 5, 7, 14, 12, 4, 6, 10, 8, 0, 2, 11, 9, 1, 3]
def points(self, transform=None):
"""
Get the reindexed and transformed control points of the grid.
Parameters
----------
transform: `jax.Array` or `None`, optional
The translation vector.
If `None`, the control points are returned without any transformation.
Returns
-------
points: `jax.Array`
The control points.
"""
tile = self.tile
if transform is not None:
tile = self.tile + transform
points = self.points_grid(tile)
grid_points = self.reindex_grid(points)
return jnp.reshape(grid_points, (self.num_pts, self.num_pts, 3))
def reindex_grid(self, points):
"""
Reconfigure the grid using hard-coded indices.
Parameters
----------
points: `jax.Array`
The control points.
Returns
-------
reindexed_points: `jax.Array`
The reindexed control points.
"""
return points[self.indices, :]
def points_grid(self, tile):
"""
Generate the control points of the grid from a tile.
Parameters
----------
tile: `jax.Array`
The 3D coordinates of a tile.
Returns
-------
points: `jax.Array`
The control points.
"""
raise NotImplementedError
class PointGridSymmetricDouble(PointGrid):
"""
A doubly-symmetric grid of control points.
Parameters
----------
size: `int`
The size of the grid.
num_pts: `int`
The number of points along one side of the grid.
"""
def __init__(self, size, num_pts):
tile = get_grid_tile_quarter(size, num_pts)
super().__init__(tile, num_pts)
def points_grid(self, tile):
return calculate_grid_from_tile_quarter(tile)
class PointGridSymmetric(PointGrid):
"""
A symmetric grid of control points.
Parameters
----------
size: `int`
The size of the grid.
num_pts: `int`
The number of points along one side of the grid.
"""
def __init__(self, size, num_pts):
tile = get_grid_tile_half(size, num_pts)
super().__init__(tile, num_pts)
def points_grid(self, tile):
"""
Generate the control points of the grid from a tile.
Parameters
----------
tile: `jax.Array`
The 3D coordinates of a tile.
Returns
-------
points: `jax.Array`
The control points.
"""
return calculate_grid_from_tile_half(tile)
class PointGridAsymmetric(PointGrid):
"""
An asymmetric grid of control points.
Parameters
----------
size: `int`
The size of the grid.
num_pts: `int`
The number of points along one side of the grid.
"""
def __init__(self, size, num_pts):
tile = get_grid_tile_full(size, num_pts)
super().__init__(tile, num_pts)
def points_grid(self, tile):
"""
Generate the control points of the grid from a tile.
Parameters
----------
tile: `jax.Array`
The 3D coordinates of a tile.
Returns
-------
points: `jax.Array`
The control points.
"""
return calculate_grid_from_tile_full(tile)
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