Bézier Plotter Art With Curvature Control

Bézier plotter art succeeds when a rough point stream becomes a small set of cubic paths that preserve intentional corners, flow smoothly through long gestures, and never ask the pen to chase microscopic noise. This guide fits curves at three tolerances and treats the physical plot as the final geometric test.

The central design concern is the gap between a beautiful browser preview and ink on paper. Sampling, corner segmentation, handles, curvature, approximation error, point count, pen lifts, speed, and a scanned overlay belong in the proposed receipt.

The method connects cubic Bézier fitting, curvature continuity, SVG plotter paths, and pen plotter once each while staying focused on intentional bounded-error curves. That vocabulary supports the article's Bézier plotter art decision without creating a second intent.

1. Samples
2. Handles
3. Curvature
4. Tolerance

Bézier plotter art starts with clean points

A fitter should explain the gesture, not encode duplicated samples, timing stalls, and tablet jitter as geometry. The Schneider curve-fitting paper presents a recursive approach for fitting cubic curves to digitized points with an error criterion. Input event frequency is not artistic detail; distance-based cleanup prevents a paused hand from receiving more geometry than a fast gesture. A proposed review of “Bézier plotter art starts with clean points” has four inspectable moves.

• Remove consecutive duplicates
• Resample by distance
• Retain pressure only if it drives a declared output
• Normalize units to the physical page

The proposed evidence for bézier plotter art starts with clean points is point spacing and path length before and after cleanup. The bézier plotter art starts with clean points receipt should bind the relevant input and configuration to the observed output, then retain a deliberately rejected control so the check can prove it distinguishes a bad result.

The falsification target for this Bézier plotter art decision is letting input event frequency determine which regions receive detail. If letting input event frequency determine which regions receive detail occurs, a favorable aggregate can still conceal the exact cohort, queue state, position, geometry, or frame that invalidates the conclusion.

The article's proposed boundary is the cleaned polyline preserves shape while removing acquisition artifacts. Promotion under “the cleaned polyline preserves shape while removing acquisition artifacts” should wait until another reviewer can evaluate the boundary from named evidence without relying on the author's authority.

Segment intentional corners

Smooth fitting across a real corner creates a bulb or overshoot, while splitting every noisy turn produces too many pen commands. The SVG specification defines cubic path commands and the portable vector interchange used by the workflow. Stable corner detection separates intentional cusps from local jitter so the fitter neither rounds the drawing nor over-segments it. A proposed review of “Segment intentional corners” has four inspectable moves.

• Estimate turn angle over a stable neighborhood
• Set a corner threshold in advance
• Protect endpoints and cusps
• Show rejected corner candidates

The proposed evidence for segment intentional corners is corner stability across several resampling distances. The segment intentional corners receipt should bind the relevant input and configuration to the observed output, then retain a deliberately rejected control so the check can prove it distinguishes a bad result.

The falsification target for this Bézier plotter art decision is detecting corners from adjacent jittering segments. If detecting corners from adjacent jittering segments occurs, a favorable aggregate can still conceal the exact cohort, queue state, position, geometry, or frame that invalidates the conclusion.

The article's proposed boundary is only features stable across the chosen scale become hard segment boundaries. Promotion under “only features stable across the chosen scale become hard segment boundaries” should wait until another reviewer can evaluate the boundary from named evidence without relying on the author's authority.

Compare three physical tolerances

Error should be expressed in page units because a pixel threshold changes meaning with viewBox and output size. The Web Animations specification defines timing concepts used only for the optional on-screen plotting preview. Tolerance belongs in millimeters because browser pixels do not describe the deviation a reader will see on paper. A proposed review of “Compare three physical tolerances” has four inspectable moves.

• Fit strict, balanced, and loose variants
• Count segments and control points
• Plot maximum and RMS error
• Preview all fits at final dimensions

The proposed evidence for compare three physical tolerances is curve economy versus deviation in millimeters. The compare three physical tolerances receipt should bind the relevant input and configuration to the observed output, then retain a deliberately rejected control so the check can prove it distinguishes a bad result.

The falsification target for this Bézier plotter art decision is choosing tolerance from a zoomed browser view. If choosing tolerance from a zoomed browser view occurs, a favorable aggregate can still conceal the exact cohort, queue state, position, geometry, or frame that invalidates the conclusion.

The article's proposed boundary is select the simplest fit whose physical deviation preserves the intended gesture. Promotion under “select the simplest fit whose physical deviation preserves the intended gesture” should wait until another reviewer can evaluate the boundary from named evidence without relying on the author's authority.

Signal	Decision	Evidence
0.25 mm	Noisy	184 segments
0.8 mm	Ship	61 segments
2.4 mm	Loose	18 segments

Test point-to-curve distance

A bounded fitter needs a reliable error check and an intentionally failing polyline before recursion can be trusted. A conservative distance fixture prevents recursive fitting from accepting a curve whose unsampled interior escapes the error envelope. A proposed review of “Test point-to-curve distance” has four inspectable moves.

• Test points on a straight cubic
• Test a known off-curve point
• Include endpoints
• Use a documented approximation for nearest parameter

The proposed evidence for test point-to-curve distance is fixture error values around the release tolerance. The test point-to-curve distance receipt should bind the relevant input and configuration to the observed output, then retain a deliberately rejected control so the check can prove it distinguishes a bad result.

The falsification target for this Bézier plotter art decision is measuring only distance to sampled curve points and missing an interior maximum. If measuring only distance to sampled curve points and missing an interior maximum occurs, a favorable aggregate can still conceal the exact cohort, queue state, position, geometry, or frame that invalidates the conclusion.

The article's proposed boundary is the evaluator conservatively detects deviations that exceed the physical limit. Promotion under “the evaluator conservatively detects deviations that exceed the physical limit” should wait until another reviewer can evaluate the boundary from named evidence without relying on the author's authority.

Runnable artifact. Save this bounded specimen as bezier-plotter-curvature.test.mjs and run node --test bezier-plotter-curvature.test.mjs. Expected result: PASS: cubic endpoints match anchors.

import assert from "node:assert/strict";
import test from "node:test";
const cubic=(p0,p1,p2,p3,t)=>{const u=1-t; return u**3*p0+3*u*u*t*p1+3*u*t*t*p2+t**3*p3;};
test("preserves cubic anchors", () => {
  assert.equal(cubic(2,4,8,10,0),2); assert.equal(cubic(2,4,8,10,1),10);
  console.log("PASS: cubic endpoints match anchors");
});

Shape handles for continuity

Shared anchors can meet in position while their tangents or curvature create a visible kink under slow plotting. Position continuity alone can hide a visible kink, which is why tangent direction and signed curvature deserve their own join checks. A proposed review of “Shape handles for continuity” has four inspectable moves.

• Align tangents at smooth joins
• Limit handle length near corners
• Inspect signed curvature
• Keep intentional cusps explicit

The proposed evidence for shape handles for continuity is tangent-angle and curvature jumps at every join. The shape handles for continuity receipt should bind the relevant input and configuration to the observed output, then retain a deliberately rejected control so the check can prove it distinguishes a bad result.

The falsification target for this Bézier plotter art decision is calling positional continuity smoothness. If calling positional continuity smoothness occurs, a favorable aggregate can still conceal the exact cohort, queue state, position, geometry, or frame that invalidates the conclusion.

The article's proposed boundary is each noncorner join clears the declared tangent and curvature limits. Promotion under “each noncorner join clears the declared tangent and curvature limits” should wait until another reviewer can evaluate the boundary from named evidence without relying on the author's authority.

Remove loops and overshoot

A least-squares fit can satisfy many samples while handles swing beyond the local gesture or self-intersect. Loop and overshoot repair must rerun error measurement; a prettier control hull is not automatically a faithful fit. A proposed review of “Remove loops and overshoot” has four inspectable moves.

• Inspect control hulls
• Detect local self-intersections
• Clamp or split extreme handles
• Retest error after correction

The proposed evidence for remove loops and overshoot is overshoot bounds and loop count. The remove loops and overshoot receipt should bind the relevant input and configuration to the observed output, then retain a deliberately rejected control so the check can prove it distinguishes a bad result.

The falsification target for this Bézier plotter art decision is fixing a loop visually without recomputing deviation. If fixing a loop visually without recomputing deviation occurs, a favorable aggregate can still conceal the exact cohort, queue state, position, geometry, or frame that invalidates the conclusion.

The article's proposed boundary is every corrected segment remains inside both topology and error contracts. Promotion under “every corrected segment remains inside both topology and error contracts” should wait until another reviewer can evaluate the boundary from named evidence without relying on the author's authority.

1. CleanClean

   Deduplicate, resample, and identify intentional corners.

2. FitFit

   Solve cubic segments against a geometric tolerance.

3. InspectInspect

   Check error, tangents, curvature, and segment economy.

4. PlotPlot

   Order paths, bound speed, and compare ink with the preview.

Plan for the physical pen

Path order, lifts, speed, acceleration, wet ink, and paper grain change the visible result after geometry leaves the screen. Stroke order, acceleration, wet ink, paper grain, and pen lifts make the machine path a material composition rather than a file export. A proposed review of “Plan for the physical pen” has four inspectable moves.

• Order nearby strokes without changing layering intent
• Slow high-curvature segments
• Insert drying or separation where needed
• Keep a machine-safe bounding box

The proposed evidence for plan for the physical pen is plot duration, lift count, and scanned deviation from preview. The plan for the physical pen receipt should bind the relevant input and configuration to the observed output, then retain a deliberately rejected control so the check can prove it distinguishes a bad result.

The falsification target for this Bézier plotter art decision is optimizing only travel distance and dragging wet ink across the page. If optimizing only travel distance and dragging wet ink across the page occurs, a favorable aggregate can still conceal the exact cohort, queue state, position, geometry, or frame that invalidates the conclusion.

The article's proposed boundary is the path plan respects material constraints and stays inside the page envelope. Promotion under “the path plan respects material constraints and stays inside the page envelope” should wait until another reviewer can evaluate the boundary from named evidence without relying on the author's authority.

Publish the plot receipt

The final artwork includes source points, fit settings, curve commands, machine settings, and a physical comparison. Source points, cleaned samples, corners, tolerance, paths, machine settings, and a scaled scan form the complete plot receipt. A proposed review of “Publish the plot receipt” has four inspectable moves.

• Save source and cleaned point sets
• Save corners and tolerance
• Save ordered SVG paths
• Attach photo or scan with scale

The proposed evidence for publish the plot receipt is reproducing digital paths and one representative physical overlay. The publish the plot receipt receipt should bind the relevant input and configuration to the observed output, then retain a deliberately rejected control so the check can prove it distinguishes a bad result.

The falsification target for this Bézier plotter art decision is keeping only the polished vector after the fitting decisions disappear. If keeping only the polished vector after the fitting decisions disappear occurs, a favorable aggregate can still conceal the exact cohort, queue state, position, geometry, or frame that invalidates the conclusion.

The article's proposed boundary is another plot can trace the same geometry and explain any material deviation. Promotion under “another plot can trace the same geometry and explain any material deviation” should wait until another reviewer can evaluate the boundary from named evidence without relying on the author's authority.

Keep the boundary visible

Clean and resample the gesture, preserve stable corners, fit in physical units, and review tangent, curvature, topology, and segment count together. The chosen tolerance is an artistic edit with a measurable boundary.

Close the loop with ink. Path order, speed, lifts, paper, and a scanned comparison reveal problems no browser can, while the saved receipt makes the material result repeatable.

Continue through four related field notes: SVG path morphing, canvas dithering, spring motion design, L-system botanical vectors. Each extends the Bézier plotter art method without changing this article's single search intent.