Fix derive for degree == 1 and update unit test

[justinthomas]

The logic in derive was incorrectly avoiding scaling control points for degree == 1. This removes the unnecessary logic and updates the derive_single_line_with_custom_knots unit test to demonstrate successful computation of the correct derivatives.

This is not yet ready to merge as the derive_discontinuous_lines_ignoring_epsilon unit test is currently failing.

[msteinbeck]

Hi @justinthomas,

thank you again for your efforts.

This is not yet ready to merge as the derive_discontinuous_lines_ignoring_epsilon unit test is currently failing.

Will you fix it?

[msteinbeck]

Did you know that TinySpline offers a function to sample splines: ts_bspline_sample. It might be easier to use.

[justinthomas]

Great point - I completely forgot about that functionality even though I use it frequently

[justinthomas]

Though, I'm leveraging the independent variable to confirm the slope, so I think I'll stick with ts_bspline_eval for now.

[msteinbeck]

That's a good point.

[justinthomas]

Happy to help, but I'm not sure what the expected behavior is for the failing unit test. The failure message is

There was 1 failure:
1) derive_discontinuous_lines_ignoring_epsilon: /home/.../tinyspline/test/c/derive.c:475: expected <1.000000> but was <1.428571>

Here's a quick link to the test:

tinyspline/test/c/derive.c

Line 434 in ba11df8

void derive_discontinuous_lines_ignoring_epsilon(CuTest *tc)

[justinthomas]

Ah, I think I understand - the multiplicity is what was throwing me off. I think the commit above is an appropriate fix.

[msteinbeck]

In this case, discontinuity must be ignored by ts_bspline_derive (epsilon is negative) by "removing" the control point at index 4 (x) and 5 (y). The points used to calculate the derivative are: [2, 2], [3, 3], [1, 1]. This yields a sequence of two points: [1, 1], [-2, -2] because the slope of [2, 2] and [3, 3] is [1, 1] and the slope of [3, 3] and [1, 1] is [-2, -2].

[msteinbeck]

Ah, I think I understand - the multiplicity is what was throwing me off. I think the commit above is an appropriate fix.

This looks very good. It shows that the expected slopes still correspond to the intuitive results. I wonder why scaling (0.7 and 0.3) is necessary.

Edit: Ok, now I understand.

[msteinbeck]

I really like that there are no longer any special cases for degree > 0.

[msteinbeck]

It might be easier to understand if you assert 2.f/2.f and 8.f/2.f (similar to derive_discontinuous_lines_ignoring_epsilon). Dividing by 2.f is necessary because span is 2.