feat: add library support for 3D ellipses #1711
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± Registry diff📊 PerformanceKeyNote that each bar component rounds up to the nearest 100ms, so each full bar is an overestimate by up to 400ms. If a row has only one bar instead of four, that means it's not a trio and the bar just shows the total time spent for that example, again rounded up to the nearest 100ms. Data |
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This (draft) PR provides functionality for drawing 3D ellipses using a single 2D
Ellipseshape. The 2D ellipse is an exact, rather than approximate, representation of the 3D ellipse under perspective projection.Changes already made:
projectEllipsetoFunctions.tsprojectEllipsein Style, via a function of the same namerotationfield to theEllipseshape, which is needed to draw projected ellipsesStill in progress:
rotationis set to a nonzero angle)projectEllipseby properly handling the case whereQBis close to zero.projectEllipseto use a model, projection, and view matrix, so that 3D ellipses can be drawn in the same context as other 3D shapes (lines, polygons, etc.).projectEllipseto return a final argument indicating whether the project ellipse is front- or back-facing relative to the oriented plane of projection.projectSpherethat draws the silhouette of a 3D sphere as an ellipse, under perspective projection.Future Work
In general, it is possible to obtain an exact or near-exact vectorization of two classes of 3D objects:
Quadric surfaces include ellipsoids, paraboloids, and hyperboloids (with spheres, cylinders, and cones as important special cases). Under perspective projection, all of these curves become (pieces of) ellipses, parabolas, or hyperbolas in the plane. SVG can exactly represent parabolas (via quadratic Bézier curves) and ellipses; hyperbolas are well-approximated by two Bézier curves and two lines.
A rough "pipeline" that handles this more general class resembles the one used in this PR:
Each of these steps is conceptually not a big deal, but takes some elbow grease to actually develop the specific formulas (especially for clipping). This is a much larger project than can be addressed in the current PR, and is left to future work.