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I have a continuous curve in high dimensional space, and I'd like to visualize it in lower dimensional (2D or 3D) space to get an intuition of what it looks like. I'm familiar with PCA and t-SNE, but those operate on point sets, not curves. Is there something analogous for curves?

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An approximate solution can be taking some samples from those curves and then apply the known methods on the sample points. Finally, connect those samples in the new reduced space.

Definitely, The number of samples have some effect on the accuracy of the result. And it depends on the dimension of those curves and their structure.

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