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Correct interpolation of integer POD types for Catmull Rom
interpolation as implemented in eaf416693dcb.
**Problem description**
`attribute_math::DefaultMixer<T>::mix_in()` assumes/asserts positive
weights but the basis function for Catmull-Rom splines generates
negative weights (see image in revision). Passing negative weights will
yield correct result as sum(weights) = 1 (after multiplication by 0.5)
but the assert is still triggered in debug builds. This patch adjusts
the behavior by extending the mix functions with mix4(). The benefit
of using mix#() over a DefaultMixer is that the result no longer needs
to be divided by the weight sum, instead utilizing that the basis weight
sum is constant (see plot).
**Changes**
* Added mix4() and updated catmull_rom::interpolate() to use it.
* Removed TODOs from catmull_rom functions.
* Moved mix definitions to be ordered as 2, 3, 4 in the header.
**Implementation specifics**
`catmull_rom::interpolate()` uses a constexpr to differentiate between
POD types which multiplies the result with 0.5 after weighting the
values, this reduces the number of multiplications for 1D, 2D, 3D
vectors (https://godbolt.org/z/8M1z9Pxx6). While this could be
considered unnecessary, I didn't want to change the original behavior
as it could influence performance (did not measure performance here
as this should ensure the logic is ~identical for FP types).
Differential Revision: https://developer.blender.org/D15997
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The trim functionality is implemented in the geometry module, and
generalized a bit to be potentially useful for bisecting in the future.
The implementation is based on a helper type called `IndexRangeCyclic`
which allows iteration over all control points between two points on a
curve.
Catmull Rom curves are now supported-- trimmed without resampling first.
However, maintaining the exact shape is not possible. NURBS splines are
still converted to polylines using the evaluated curve concept.
Performance is equivalent or faster then a 3.1 build with regards to
node timings. Compared to 3.3 and 3.2, it's easy to observe test cases
where the node is at least 3 or 4 times faster.
Differential Revision: https://developer.blender.org/D14481
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This commit moves the subdivide curve node implementation to the
geometry module, changes it to work on the new curves data-block,
and adds support for Catmull Rom curves. Internally I also added
support for a curve domain selection. That isn't used, but it's
nice to have the option anyway.
Users should notice better performance as well, since we can avoid
many small allocations, and there is no conversion to and from the
old curve type.
The code uses a similar structure to the resample node (60a6fbf5b599)
and the set type node (9e393fc2f125). The resample curves node can be
restructured to be more similar to this soon though.
Differential Revision: https://developer.blender.org/D15334
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`curve_segment_num` -> `segments_num`.
The "curve" prefix is reduntant for a function in the curve namespace.
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Replace tot/amount & size with num, in keeping with T85728.
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87e9451d660e8288d missed updating the behavior for Catmull Rom curves.
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A follow-up to e253f9f66d6f. Follow the policy from T85728
completely (using "num" as a prefix) and rename another function.
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Rename "size" variables and functions to use "num" instead,
based on T85728 (though this doesn't apply to simple C++
containers, it applies here). Rename "range" to "points" in
some functions, so be more specific.
Differential Revision: https://developer.blender.org/D14431
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This is a follow up to rB2252bc6a5527cd7360d1ccfe7a2d1bc640a8dfa6.
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This patch adds evaluation for NURBS, Bezier, and Catmull Rom
curves for the new `Curves` data-block. The main difference from
the code in `BKE_spline.hh` is that the functionality is not
encapsulated in classes. Instead, each function has arguments
for all of the information it needs. This makes the code more
reusable and removes a bunch of unnecessary complications
for keeping track of state.
NURBS and Bezier evaluation works the same way as existing code.
The Catmull Rom implementation is new, with the basis function
based on Cycles code. All three types have some basic tests.
For NURBS and Catmull Rom curves, evaluating positions is the
same as any generic attribute, so it's implemented by the generic
interpolation to evaluated points. Bezier curves are a bit special,
because the "handle" control points are stored in a separate attribute.
This patch doesn't include generic interpolation to evaluated points
for Bezier curves.
Ref T95942
Differential Revision: https://developer.blender.org/D14284
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