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Technical Architecture: ESIGN Act, Quadratic Bézier Smoothing & In-Memory Coordinate Mapping

Under the United States Electronic Signatures in Global and National Commerce Act (ESIGN, 15 U.S.C. § 7001), the Uniform Electronic Transactions Act (UETA), and the European Union eIDAS Regulation (No 910/2014), an electronic signature possesses full legal enforceability when intent to sign, attribution to the signer, and document record integrity are maintained. While corporate signing platforms (DocuSign, Adobe Sign) harvest non-disclosure agreements, executive salaries, and biometric signatures onto remote cloud databases, LocalDoc performs 100% of signature capture, coordinate projection, and document stream fusion in volatile client memory:

• Quadratic Bézier Tangent Interpolation: Drawing on capacitive touchscreens or via mouse pointers often generates jagged, polygonal line artifacts due to discrete hardware sampling rates. LocalDoc intercepts pointermove events, computes midpoint tangents between consecutive coordinates Mi = (Pi + Pi+1) / 2, and applies continuous quadratic Bézier curves (ctx.quadraticCurveTo(Pi}.x, Pi}.y, Mi}.x, Mi}.y)). This produces an authentic, fluid pen-on-paper aesthetic with velocity-adjusted stroke pressure.
• Inverted Cartesian Coordinate Space Translation: In HTML5 DOM and CSS coordinates, the origin (0, 0) sits at the top-left corner with Y increasing downward. Conversely, the PDF ISO 32000-1 specification establishes the coordinate origin (0, 0) at the bottom-left corner of the page's /MediaBox with Y increasing upward. LocalDoc computes the exact scale factor and affine matrix transformation:
  xpdf = (xdom − rect.left) × (pageWidth / rect.width)
ypdf = pageHeight − [(ydom − rect.top) × (pageHeight / rect.height)] − sigHeightpdf This guarantees sub-millimeter placement accuracy across standard A4, US Letter, and non-standard architectural legal sizes.
• Direct ISO 32000-1 Stream Injection & Vector Clarity: When fusing the signature into the PDF, LocalDoc embeds the transparent PNG signature bitmap as an indirect /XObject image dictionary in the page's /Resources table. It appends isolated content stream operators (q [scaleX 0 0 scaleY posX posY] cm /SigImg Do Q). This leaves the original vector fonts, underlying contract text, and cryptographic structure completely untouched without blurry raster downsampling.
• Certified Timestamp Seals: Date and time seals are compiled into native vector text runs alongside your signature. The seal records the exact ISO 8601 calendar date, UTC timestamp, and document integrity mark into the document tree.
• Complete Memory Quarantine & Zero-Trace Privacy: Biometric handwritten signatures represent sensitive personal identifiers. LocalDoc quarantines all signature stroke data, rendered canvases, and intermediate binary streams within private JavaScript heap closures. The moment your signed PDF is exported, memory pointers are released for garbage collection. Zero biometric data, signatures, or contract terms ever touch a remote server.