# VectorPaint three-tube telescopes: check overlap and exposed length
Language: en
Canonical: [VectorPaint three-tube telescopes: check overlap and exposed length]()
中文：[中文 HTML]()
English: [English HTML]()
Published: 2026-11-09T00:00:00+08:00
Modified: 2026-11-09T09:37:10+08:00
Author: Bison
Build retracted and extended tube diagrams, checking diameters, seams and exposed lengths without treating outlines as mechanical constraints.
English translation of the [Chinese original](), translated on 2026-11-09. Original publication dates, attribution, code and version notes are retained.
A telescoping instrument is not three tubes glued end to end. Adjacent tubes overlap; extension changes exposed length rather than stretching the tubes themselves. Check three nested components in an original side view, manually arranging shapes and occlusion in VectorPaint without modelling optics or verifying real lenses, seals or travel.
## Preserve the complete dimensions of three tubes
Use one pixel per exercise unit. Give A,B,C complete axial lengths of 300 and diameters of 120,100,80 respectively. Put their common axis at y=450, with upper/lower edges symmetric about it. Begin with full rectangles in a checking view rather than drawing only exposed parts, so later shortening cannot go unnoticed. These are illustration settings, not manufacturable dimensions. Group each tube separately and retain text names instead of identifying the outer tube only by shade. Label axial lengths and diameters explicitly in the dimension list without exchanging those directions.
## Represent retracted nesting with intervals
For the first state use x intervals A100–400, B200–500, C300–600. A/B and B/C each overlap by 200. All three project over x300–400 without occupying one plane. Overall extent is 100–600, length 500 rather than three times 300. Record intervals externally and inspect overlap using temporary transparency. Transparency checks complete components; the final view should not expose every internal edge without explanation.
## Occlude inner tubes with their outer neighbours
Restore opaque fills: A covers the inserted part of B and B covers the inserted part of C. Visible extents become A100–400, B400–500, C500–600, with fine seam marks identifying diameter steps. A seam need not become a black wall cutting an inner tube, nor extend beyond outer-tube edges. Keep whole tubes in the check view; occlusion or visible segments in the final must represent the same intervals. Without decoration the outline should narrow from left to right, not grow wider through nesting.
## Move components instead of stretching them
Duplicate the set for extension: A remains100–400, B becomes300–600 and C500–800. Each length remains300, adjacent overlaps become100 and overall length700. Relative to the first state, B moves right100 and C right200, not both100. After rebuilding occlusion, visible lengths are300,200,200. Do not scale the whole view to width700, changing diameters, seams and complete lengths together. This checks static relationships rather than simulating physical operation.
## Place objective and eyepiece at distinct ends
Add a broader objective-rim indication at A’s left end and a small eyepiece at C’s right, labelling this orientation convention. An elliptical rim is a side-view device, not a calculation of physical aperture or focal length. The eyepiece moves with C while A’s rim remains fixed. Inspect end decorations separately rather than silently adding their width to the stated500/700 tube-set extents. Any overall-outline dimension must say whether end rings are included.
## Test the boundary with a non-overlapping copy
In a labelled wrong copy move C to650–950 while B stays300–600, creating a50-unit gap rather than continuous nesting. Preserve the correct state and identify lost overlap, not colour, as the fault. Restore C500–800 and recheck100 overlap and the shared axis. This counterexample sets no minimum physical insertion length; it only checks the model’s overlap requirement. A connected illustration does not establish real mechanical stability.
## Preserve state and dimension identities in output
Align states by A’s left endpoint, not independent bounding-box centres that make the fixed end drift. Save the source and open an exported PNG, reading complete lengths, overlaps and visible extents separately. Label checking versus presentation views. Hide temporary transparent references and interval markers actively when unwanted in output. For merged seams at reduced size, lighten strokes or enlarge the view instead of deleting an inner tube for tidiness. The final should still show three components rather than two.
## Troubleshoot dimensions, movement and occlusion
For changed diameters inspect accidental scaling; for only100 extra extension inspect C’s missing100 movement. For disconnection check interval overlap before stacking or blaming export. Change the relevant component alone, then recalculate total extent. Preserve both interval sets, every300-unit length, both overlap values and the counterexample so numbers and graphics remain mutually traceable. The result explains nesting, not completed mechanism design, lens calculation or physical-constraint verification.
## Related tutorials and sources
[VectorPaint layers and groups: make complex work easier to select and edit](), [VectorPaint wireframe boxes: distinguish visible edges, hidden edges and shared vertices]().
Checked on November 9, 2026: VectorPaint public version 1.0.8, requiring iOS / iPadOS 17.0 or later. Capability scope follows the [official App Store listing]() and [Apple public version lookup](). This is an original exercise to perform independently; use controls in your installed version. Manual construction and external records do not imply new automatic analysis features. No step-by-step physical-device, private-file or all-output-environment testing is claimed.