feat: compute rect-line distance exactly

[samestep]

Description

This PR provides a rectLineDist function which differentiably computes the exact signed distance from the origin to the Minkowski difference of a rectangle and a line, and modifies the implementation of the shapeDistance function added by #1328 to use this when one shape is a Line and the other is an Equation or Text (as opposed to the previous implementation, which used a bounding circle as an approximation instead of a bounding box). I also added a new example to the registry to demonstrate visually that this works.

Implementation strategy and design decisions

The reason to export a new rectLineDist function, instead of just using shapeDistance, is that sometimes we want to phrase an objective or constraint as if something is a straight line segment, even if the actual shape being drawn is something else, like a quadratic Bézier curve in the case of #1317. Using shapeDistance requires you to actually have a genuine Line shape in the diagram.

Also, we didn't have an xor autodiff function before, so I added one here. While I was doing that, I noticed that some comments in the autodiff types file were out of date, so I updated them.

I changed the variation for parallel-lines-euclidean because for some reason this patch was causing it to take a long time to optimize (almost ten seconds) with the old variation.

Checklist

• I have commented my code, particularly in hard-to-understand areas
• I have reviewed any generated registry diagram changes

[codecov]

Codecov Report

Merging #1332 (227465f) into main (76a91e5) will increase coverage by 0.33%.
The diff coverage is 95.08%.

@@            Coverage Diff             @@
##             main    #1332      +/-   ##
==========================================
+ Coverage   61.55%   61.89%   +0.33%     
==========================================
  Files          65       65              
  Lines        8055     8103      +48     
  Branches     1884     1887       +3     
==========================================
+ Hits         4958     5015      +57     
+ Misses       2989     2980       -9     
  Partials      108      108              

Impacted Files	Coverage Δ
packages/core/src/contrib/Functions.ts	39.46% <0.00%> (-0.07%)	⬇️
packages/core/src/types/ad.ts	100.00% <ø> (ø)
packages/core/src/utils/Wasm.ts	98.33% <ø> (ø)
packages/core/src/contrib/Queries.ts	91.03% <96.49%> (+14.03%)	⬆️
packages/core/src/engine/Autodiff.ts	79.41% <100.00%> (+0.02%)	⬆️
packages/core/src/engine/AutodiffFunctions.ts	100.00% <100.00%> (ø)

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Latest commit:	227465f
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Branch Preview URL:	https://rect-line-dist.penrose-72l.pages.dev

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[github-actions]

± Registry diff

M	circle-example-euclidean.svg
M	collinear-euclidean.svg
M	congruent-triangles-euclidean.svg
M	cubic-bezier-cubic-bezier.svg
M	incenter-triangle-euclidean.svg
A	lines-around-rect-rect-line-dist.svg
M	parallel-lines-euclidean.svg
M	siggraph-teaser-euclidean-teaser.svg
M	small-graph-disjoint-rect-line-horiz.svg

📊 Performance

Key

Note that each bar component rounds up to the nearest 100ms, so each full bar is an overestimate by up to 400ms.

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      compilation labelling optimization rendering

Data

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3d-projection-fake-3d-linear-algebra                ▝▞▖
allShapes-allShapes                                 ▝▚▚▄▄
arrowheads-arrowheads                               ▝▞▖
caffeine-structural-formula                         ▝▀▀▀▞▚▖
center-shrink-circle-animation                      ▝▞▖
circle-example-euclidean                            ▝▀▚▀▀▀▖
closest-point-test-closest-point                    ▝▀▀▀▀▀▀▀▞▖
collinear-euclidean                                 ▝▀▞▖
congruent-triangles-euclidean                       ▝▀▀▚▚
continuousmap-continuousmap                         ▝▚▚
cubic-bezier-cubic-bezier                           ▝▀▞▀▚
glutamine-molecules-basic                           ▝▀▚▚
half-adder-distinctive-shape                        ▝▀▞▖
hypergraph-hypergraph                               ▝▀▀▀▚▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▖
incenter-triangle-euclidean                         ▝▀▚▚
lagrange-bases-lagrange-bases                       ▝▚▚
lines-around-rect-rect-line-dist                    ▝▚▚
matrix-matrix-addition-matrix-ops                   ▝▚▚
matrix-matrix-division-elementwise-matrix-ops       ▝▚▚
matrix-matrix-multiplication-elementwise-matrix-ops ▝▚▚
matrix-matrix-multiplication-matrix-ops             ▝▀▞▖
matrix-matrix-subtraction-matrix-ops                ▝▚▚
matrix-transpose-matrix-ops                         ▝▚▚
matrix-vector-left-multiplication-matrix-ops        ▝▚▚
matrix-vector-right-multiplication-matrix-ops       ▝▚▚
midsegment-triangles-euclidean                      ▝▀▚▚
mobius-mobius                                       ▝▞▖
non-convex-non-convex                               ▝▀▞▖
one-water-molecule-atoms-and-bonds                  ▝▞▖
parallel-lines-euclidean                            ▝▀▚▚
persistent-homology-persistent-homology             ▝▀▀▚▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▚▖
points-around-line-shape-distance                   ▝▀▚▚
points-around-polyline-shape-distance               ▝▀▀▚▚
points-around-star-shape-distance                   ▝▀▀▀▚▚
quaternion-group-group-theory-cayley-graph          ▝▀▀▞▖
quaternion-group-group-theory-multiplication-table  ▝▀▀▀▄▞▄
scalar-vector-division-matrix-ops                   ▝▚▚
scalar-vector-left-multiplication-matrix-ops        ▝▚▚
scalar-vector-right-multiplication-matrix-ops       ▝▚▚
siggraph-teaser-euclidean-teaser                    ▝▀▀▞▖
small-graph-disjoint-rect-line-horiz                ▝▀▀▞▖
small-graph-disjoint-rects                          ▝▚▚
small-graph-disjoint-rects-large-canvas             ▝▞▖
small-graph-disjoint-rects-small-canvas             ▝▚▚
tree-tree                                           ▝▀▞▖
tree-venn                                           ▝▀▚▚
tree-venn-3d                                        ▝▀▞▄▄
two-triangles-triangle-mesh-3d                      ▝▚▚
two-vectors-perp-vectors-dashed                     ▝▚▚
vector-vector-addition-matrix-ops                   ▝▚▚
vector-vector-division-elementwise-matrix-ops       ▝▚▚
vector-vector-multiplication-elementwise-matrix-ops ▝▚▚
vector-vector-outerproduct-matrix-ops               ▝▚▚
vector-vector-subtraction-matrix-ops                ▝▚▚
vector-wedge-exterior-algebra                       ▝▚▚
wet-floor-atoms-and-bonds                           ▝▀▞▀▚
word-cloud-example-word-cloud                       ▝▀▞▖
wos-laplace-estimator-walk-on-spheres               ▝▀▚▚
wos-nested-estimator-walk-on-spheres                ▝▀▀▚▀▀▚
wos-offcenter-estimator-walk-on-spheres             ▝▀▚▀▀▖
wos-poisson-estimator-walk-on-spheres               ▝▀▚▀▚

[joshsunshine]

modifies the implementation of the shapeDistance function added by #1328 to use this when one shape is a Line and the other is an Equation or Text

After reading the code, it looks like the shapeDistance function calls rectLineDist for all RectLike shapes which also includes Rectangle and Image. @samestep, is that correct?

[samestep]

@joshsunshine No, that is not correct:

penrose/packages/core/src/contrib/Queries.ts

Line 275 in af2f8b5

else if ((t1 === "Text" || t1 === "Equation") && t2 === "Line")

[joshsunshine]

I am glad I asked. Why didn't you add Rectangle and Image to that else if? Is there a reason this doesn't work for those shapes?

[samestep]

Nope, no reason not to do that! Do you want me to do it in this PR, or in a followup?

[joshsunshine]

Nope, no reason not to do that! Do you want me to do it in this PR, or in a followup?

This PR.

[samestep]

@joshsunshine Done.