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adding tutorial for spline#987

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This is a WIP PR and will try to complete it as soon as possible.

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One other thought: do we want to include a mention of beziers here for comparison? Maybe something about why you'd want to use one or the other even if we don't explain the whole bezier API?


### Advanced Spline Shapes and Customization

So far we've been drawing a single curve segment defined by four points. Now, let's explore more advanced possibilities: creating complex shapes from multiple spline segments, closing splines into continuous loops, and customizing the spline’s properties (like its tightness or endpoint handling) to achieve different effects.
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I almost wonder if we should start withbeginShape/endShape right after showing a singlespline() as the main thing in the tutorial, since I imagine drawing bigger curves and smooth closed curves is a more common use than getting points/tangents along a single segment.

How do you feel about moving this + the closed loop bit up, giving them their own headings (e.g. "Spline Shapes" and "Closed Spline Loops" or something like that?) and then includingsplinePoint/splineTangent under the advanced section?

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cool thumbnail for the article btw!

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*Splines vs. Bezier Curves*

`bezier()` uses a start point, an end point, and extra control points that pull the curve but are not on the curve.

`spline()` makes a curve that passes through all the points you give.

Use `splines` when the curve must go through specific coordinates.
Use `Beziers` when you want to shape the curve with off-curve handles.
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Btw, I already explain splines and bezier for comparison together. Do you mean adding more description to it?

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As before, I think a very simple image might be a helpful complement to the text

@perminder-17perminder-17 marked this pull request as ready for reviewDecember 6, 2025 10:28
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I really appreciate how in-depth this is! My only major request here is to complement the intro and initial descriptions with very, very beginner-friendly graphics, that require no knowledge of any trigonometry at all


## Introduction

Splines are smooth curves that interpolate through a series of points,forming gentle, flowing shapes. A spline is a smooth curve defined by a set of points, with a function that lets you compute additional points smoothly between them. This makes it easy to draw natural-looking curves without manually specifying tangents.
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Minor: "A spline is a smooth curve defined by a set of points" -> "These curves are defined by a set of points"

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"with a function that lets you compute additional points smoothly between them" -> "and a function that determines how additional points are computed between them."

It might be better to give visual example right here of 2 different functions than to describe more verbally

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"This makes it easy to draw natural-looking curves without manually specifying tangents." -> remove "without manually specifying tangents" as the general style of tutorials is more beginner- and learner-friendly, so cannot assume "tangents" is understood

Comment on lines +120 to +127
*Splines vs. Bezier Curves*

`bezier()` uses a start point, an end point, and extra control points that pull the curve but are not on the curve.

`spline()` makes a curve that passes through all the points you give.

Use `splines` when the curve must go through specific coordinates.
Use `Beziers` when you want to shape the curve with off-curve handles.
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As before, I think a very simple image might be a helpful complement to the text

import Callout from "../../../components/Callout/index.astro";

## Introduction

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One more comment: Though the title connects splines to curves and shapes, the introduction jumps right into splines. I think it would be very helpful to provide a very brief intro summary of when someone would need to learn about splines (when you want to make curvy shapes_

Thanks to@SableRaf for the input and for suggesting this wonderful video:https://www.youtube.com/watch?v=jvPPXbo87ds - maybethe introduction in this video specifically can be an inspiration, or at least a linked resource people could check out?

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