Improved algorithm for mitre joints on thick lines

[rmitton]

The current implementation for rendering thick lines suffers from issues when the lines meet at extreme angles. A 90-degree bend will cause the thickness of the line to contract by around 30%. In the case of a rectangle, this causes the entire rectangle to be the wrong thickness:

I've modified the algorithm to counteract this effect by placing the mitre vertices at a distance that preserves the correct thickness. The new algorithm works for vertices up to 90-degrees; past that, it would be impossible to fix without actually inserting new vertices. Seeing as rectangles are by far the most common UI element, this seems an acceptable compromise.

[ocornut]

Thank you Richard, will look into it soon.
Linking to #2183 and the old unmerged #288 for non-AA path.

[ocornut]

Merged this now, thank you!

I've modified the algorithm to counteract this effect by placing the mitre vertices at a distance that preserves the correct thickness. The new algorithm works for vertices up to 90-degrees; past that, it would be impossible to fix without actually inserting new vertices.

It would be interesting to see what it would take to make this modification.
In particular, triangles are very much affected (see #2183) and perhaps it would make sense to have some sort of specialization for them if a general solution is too costly.

Logs from rough perf measurement system (not very precise!)

Before, Debug, x12
,perf,perf_draw_prim_rect_stroke,3.454,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_stroke_thick,3.707,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_filled,0.806,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_rounded_stroke,9.762,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_rounded_stroke_thick,10.144,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_rounded_filled,8.837,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_circle_stroke,9.732,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_circle_stroke_thick,10.113,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_circle_filled,9.309,,12,Debug,X86,Windows,MSVC,2019-04-29

After, Debug, x12
,perf,perf_draw_prim_rect_stroke,2.924,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_stroke_thick,3.143,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_filled,0.911,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_rounded_stroke,8.757,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_rounded_stroke_thick,9.455,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_rounded_filled,7.999,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_circle_stroke,9.873,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_circle_stroke_thick,10.422,,12,Debug,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_circle_filled,9.682,,12,Debug,X86,Windows,MSVC,2019-04-29

Before, Release x12
,perf,perf_draw_prim_rect_stroke,0.495,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_stroke_thick,0.642,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_filled,1.170,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_rounded_stroke,2.040,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_rounded_stroke_thick,2.561,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_rounded_filled,1.673,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_circle_stroke,2.684,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_circle_stroke_thick,3.028,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_circle_filled,2.431,,12,Release,X86,Windows,MSVC,2019-04-29

After, Release x12
,perf,perf_draw_prim_rect_stroke,0.474,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_stroke_thick,0.609,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_filled,1.176,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_rounded_stroke,1.919,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_rounded_stroke_thick,2.470,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_rect_rounded_filled,1.562,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_circle_stroke,2.715,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_circle_stroke_thick,3.104,,12,Release,X86,Windows,MSVC,2019-04-29
,perf,perf_draw_prim_circle_filled,2.432,,12,Release,X86,Windows,MSVC,2019-04-29

[ocornut]

An update on this can be found here:
#4053 (comment)

(TL;DR; this PR did partially fix an earlier regression from Jan 2019 but we somehow still carried part of that regression even after April 2019)