Defining a Custom Shape

This guide demonstrates how to extend smds by defining your own custom manifold shape. We will implement a Circular shape as an example.

Purpose of Custom shapes

Custom shapes allow you to define manifold geometries that are not provided in the default smds package. This is useful when your data lies on a specific manifold structure that you want to model explicitly, so that our library does not limit your ideas!

For a list of all available built-in shapes, please refer to the Available Shapes.

Example: custom Circle

In this example, we define a shape representing a circle. Points are defined by a 1D scalar (angle or normalized position). The distance is the chord length through the circle.

Implementation

import numpy as np
from numpy.typing import NDArray
from smds.shapes import BaseShape

class MyCircle(BaseShape):
    y_ndim = 1

    @property
    def normalize_labels(self) -> bool:
        return self._normalize_labels

    def __init__(self, radious: float = 1.0, normalize_labels: bool = True):
        self.radious = radious
        self._normalize_labels = normalize_labels

    def _compute_distances(self, y: NDArray[np.float64]) -> NDArray[np.float64]:
        delta = np.abs(y[:, None] - y[None, :])
        delta = np.minimum(delta, 1 - delta)
        return 2 * np.sin(np.pi * delta)

Usage

# Define points on the circle (normalized 0-1)
points = np.array([0.0, 0.25, 0.5])

# Instantiate the shape
circle_shape = MyCircle()

# Compute the distance matrix
distances = circle_shape(points)

print(distances)