fix line inversion

[ffreyer]

Description

Fixes #3544 and #3584.

Still need to understand what exactly is wrong here...

What's wrong?

The problem here was with what perspective projection does with points behind the camera. We can investigate with a simplified perspective projection matrix:

near = 1.0
far = 9.0
proj = Makie.Mat2f(
    -(far + near) / (far - near),       -1.0,
    -2.0 * near * far / (far - near),    0.0
)

This mirrors Makies implementation with -1.0 >= p[1] >= -9.0 being the visible area in front of the camera (p[1] matching z). Some results:

• proj * Point2f(-10, 1) = (10.25, 10.0) -> (1.025, 1) clipped beyond far (> 1)
• proj * Point2f(-4, 1) = (2.75, 4.0) -> (0.6875, 1) visible (-1 <= z <= 1)
• proj * Point2f(-0.5, 1) = (-1.625, 0.5) -> (-3.25, 1) clipped before near (< -1)
• proj * Point2f(0, 1) = (-2.25, 0.0) -> (-Inf, NaN) singularity, clipped before near (< -1)
• proj * Point2f(1, 1) = (-3.5, -1.0) -> (3.5, 1) clipped beyond far (> 1)

As the last example suggests anything behind the camera/viewer ends up beyond the far plane in clip space with a perspective projection matrix. This is why lines and linesegments start going the other direction in the issues linked above. This is usually avoided by clipping before applying the w-normalization using -w <= xyz <= w to identify valid point.

What's the fix?

Since our linewidths are in pixel space we need to go pixel space before opengl (etc) does clipping. So we need to do a w normalization to get the correct coordinates. The solution I ended up going with is doing the clipping manually, in some sense.

The problematic case here is just "vertex behind camera". If that case arises (clip.w = -1.0 * view.z > 0.0) the shaders are now moving vertices along line direction towards the near plane. In clip space the near plane is at z / w = -1 so we can get the appropriate scaling from
$$\frac{p_z + t v_z}{p_w + t v_w} = -1$$

TODO:

• fix missing line segments in WGLMakie (poly refimg)

Type of change

• Bug fix (non-breaking change which fixes an issue)

Checklist

• Added an entry in CHANGELOG.md (for new features and breaking changes)
• Added or changed relevant sections in the documentation
• Added unit tests for new algorithms, conversion methods, etc.
• Added reference image tests for new plotting functions, recipes, visual options, etc.

[ffreyer]

master

inverts directions

neutral	zoomed

clamp clip_pos.w to 0

results in some kind of NaN discard for me, I think. Will be GPU dependent

neutral	zoomed

clamp to epsilon

... bends

neutral	zoomed

---

I think this is happening because the perspective camera inverts space behind eyeposition (with a singularity at eyeposition). Haven't had time to look into it that deeply. If that's the case the correct solution might be to truncate lines to be in front of the camera. Restricting clip.w might be an ok temporary fix...

[ffreyer]

Constructing vertices with the original pos.w

results in correct placement but messes with anti-aliasing and shape...

neutral	zoomed

[ffreyer]

Scaling line segments to start in front / at edge of visible area

seems to fix everything but I need to test some more and think the math through

neutral	zoomed

[MakieBot]

Compile Times benchmark

Note, that these numbers may fluctuate on the CI servers, so take them with a grain of salt. All benchmark results are based on the mean time and negative percent mean faster than the base branch. Note, that GLMakie + WGLMakie run on an emulated GPU, so the runtime benchmark is much slower. Results are from running:

using_time = @ctime using Backend
# Compile time
create_time = @ctime fig = scatter(1:4; color=1:4, colormap=:turbo, markersize=20, visible=true)
display_time = @ctime Makie.colorbuffer(display(fig))
# Runtime
create_time = @benchmark fig = scatter(1:4; color=1:4, colormap=:turbo, markersize=20, visible=true)
display_time = @benchmark Makie.colorbuffer(fig)

	using	create	display	create	display
GLMakie	3.50s (3.38, 3.60) 0.08+-	427.97ms (408.84, 443.40) 12.34+-	549.20ms (533.51, 599.60) 23.09+-	7.63ms (7.44, 8.12) 0.22+-	26.11ms (25.88, 26.33) 0.17+-
breaking-0.21	3.51s (3.44, 3.57) 0.05+-	427.74ms (409.25, 446.57) 14.41+-	551.77ms (533.97, 580.62) 17.46+-	7.68ms (7.44, 7.96) 0.18+-	26.15ms (25.94, 26.39) 0.15+-
evaluation	1.00x invariant, -0.01s (-0.09d, 0.86p, 0.06std)	1.00x invariant, 0.23ms (0.02d, 0.98p, 13.38std)	1.00x invariant, -2.57ms (-0.13d, 0.82p, 20.27std)	1.01x invariant, -0.05ms (-0.23d, 0.68p, 0.20std)	1.00x invariant, -0.04ms (-0.27d, 0.62p, 0.16std)
CairoMakie	3.01s (2.97, 3.03) 0.03+-	320.47ms (318.23, 322.90) 1.47+-	146.37ms (145.58, 147.68) 0.83+-	7.27ms (7.19, 7.32) 0.05+-	617.13μs (614.97, 620.00) 1.60+-
breaking-0.21	3.00s (2.96, 3.04) 0.03+-	318.97ms (317.52, 321.86) 1.38+-	140.15ms (138.86, 141.29) 0.82+-	7.30ms (7.27, 7.33) 0.02+-	603.86μs (598.77, 607.77) 3.35+-
evaluation	1.00x invariant, 0.01s (0.31d, 0.57p, 0.03std)	1.00x invariant, 1.51ms (1.06d, 0.07p, 1.43std)	0.96x slower X, 6.22ms (7.57d, 0.00p, 0.82std)	1.00x invariant, -0.03ms (-0.77d, 0.18p, 0.04std)	0.98x slower X, 13.28μs (5.06d, 0.00p, 2.47std)
WGLMakie	3.61s (3.52, 3.71) 0.07+-	422.53ms (410.21, 439.96) 9.66+-	9.34s (9.23, 9.49) 0.11+-	9.60ms (9.30, 10.18) 0.29+-	70.61ms (69.32, 72.11) 1.00+-
breaking-0.21	3.58s (3.50, 3.67) 0.06+-	417.05ms (408.73, 427.04) 7.41+-	9.32s (9.10, 9.55) 0.18+-	9.44ms (9.19, 9.87) 0.24+-	70.20ms (69.48, 70.79) 0.43+-
evaluation	0.99x invariant, 0.03s (0.40d, 0.47p, 0.07std)	0.99x invariant, 5.47ms (0.64d, 0.26p, 8.54std)	1.00x invariant, 0.02s (0.16d, 0.78p, 0.14std)	0.98x invariant, 0.17ms (0.63d, 0.27p, 0.26std)	0.99x invariant, 0.41ms (0.54d, 0.34p, 0.72std)

[ffreyer]

Added refimg test:

master	pr