TorchCurves: Differentiable Parametric Curves

A PyTorch library called TorchCurves treats vector-valued parametric curves as learnable primitives, mapping batches of scalar inputs to points on curves represented in B-spline or Legendre polynomial bases with differentiation through both inputs and coefficients. The library's central operation makes curve coefficients trainable alongside network weights, positioning curves as first-class components in differentiable pipelines.

We present TorchCurves, a PyTorch library that treats vector-valued parametric curves as learnable primitives. Its central operation maps batches of scalar inputs to points on curves represented in B-spline or Legendre polynomial bases, with differentiation through both inputs and coefficients. Curv