SVG Graphics Geometry
Guide
css-matrix
Guide
css-matrix
  • Part 0. SVG 기초

    • SVG란 무엇인가
    • viewBox와 user space
    • transform attribute와 matrix
    • SVG 문서 구조와 기본 도형
  • Part 1. Path grammar

    • path d 명령어 — M, L, Z
    • H, V — 축 정렬 직선
    • C — cubic Bézier
    • Q — quadratic Bézier
    • S, T — smooth continuation
    • A — elliptical arc
    • path bounding box
  • Part 2. Stroke geometry

    • 점에서 stroke까지의 거리
    • join, cap, miter limit
    • stroke align과 outline 개념
    • miter length 공식
  • Part 3. Fill rules

    • nonzero vs evenodd
    • fill hit testing
  • Part 4. Path sampling

    • flatten tolerance
    • path length
    • point at length와 tangent
  • Part 5. Paint servers

    • linearGradient 좌표
    • clipPath와 mask 개념
  • Part 6. Path editor capstone

    • path handle 모델
    • handle hit testing
    • handle drag로 segment 갱신
    • mini path editor — SVG round-trip
  • Part 7. Fill & winding deep dive

    • winding vs ray casting
    • compound path — 여러 subpath
    • self-intersection
    • path boolean
    • fill vs stroke hit 우선순위
    • scanline parity
  • Part 8. Pattern & gradient

    • radialGradient
    • pattern tile
    • gradientUnits와 spreadMethod
  • Part 9. SVG filter & Figma effects

    • Figma DROP_SHADOW → SVG filter
    • filter chain 개요
    • blur · offset · merge
    • inner shadow
    • layer blur vs background blur
    • Figma effect 매핑표 전체
  • Part 10. Figma ↔ SVG bridge

    • vector network vs path d
    • fill · stroke export
    • boolean operations export
    • mask · clip export
  • Part 11. Icon design

    • pixel grid · optical alignment
    • fill vs stroke icons
    • symbol · sprite · currentColor
    • path simplification
  • Appendix A. SVG in CSS

    • currentColor · CSS theming
    • sprite data URI
    • SVG optimization pipeline
  • Appendix B. Engine extras

    • dash offset animation
    • adaptive flatten
    • arc → cubic 변환
    • multi-subpath editing
  • Part 12. Foundations primer

    • capability map
    • coordinate stack
  • Part 13. Figma ↔ SVG (deep)

    • Figma paint gap map
    • radial · angular gradient export
    • image · pattern fill
    • stroke align export
    • blend mode · layer opacity
  • Part 14. SVG spec breadth

    • markers — 화살표와 dash 끝
    • text · textPath
    • paint-order · opacity · filters
    • arc flatten 통합
  • Part 15. Curve calculus

    • de Casteljau subdivision
    • flatness와 chord error
    • 곡률 κ와 법선
    • arc center parameterization
    • G¹ smooth — S와 T
    • shoelace signed area
  • Part 16. Intersection & proximity

    • segment intersection
    • line ∩ cubic · curve ∩ curve
    • closest point on curve
  • Part 17. Offset curves

    • normal offset sampling
    • offset cusps
  • Part 18. Transform algebra

    • affine inverse & decompose
    • transform path vs group
  • Part 19. Rational curves

    • circle as cubic — κ constant
    • rational curves & exact arcs
  • Part 20. Tessellation & pixels

    • convex triangulation · ear clipping
    • evenodd parity → pixels
  • Part 21. Compositing math

    • Gaussian blur kernel
    • Porter–Duff & premultiplied α
  • Part 22. Math topic map

    • SVG 수학 주제 지도
  • Part 23. SVG animation

    • SMIL — animate 속성
    • SMIL — animateTransform
    • SMIL — animateMotion
    • stroke dash draw-on
    • CSS offset-path motion
    • path morph
    • JS motion along path
  • Part 24. Motion precision

    • uniform speed along path
    • cubic–cubic intersection
    • SVGPathElement length API
    • SMIL keyTimes & keySplines
    • degree elevation Q→C
  • Part 25. GPU mesh & WAAPI

    • triangulation with holes
    • WAAPI + SVG attributes
    • evenodd fill + triangle mesh

path bounding box

편집기 selection marquee, viewBox 자동 맞춤, gradient objectBoundingBox, export crop은 path 전체를 덮는 axis-aligned bbox가 필요합니다. 008·009에서 segment 하나의 tight bbox를 봤다면, 여기서는 여러 segment를 union합니다.

데모에서 볼 것

데모 path:

M 120 300 C 200 40, 440 360, 520 80
  • 파란 stroke + 연한 fill — cubic 한 segment
  • 회색 점 — from, cp1, cp2, to
  • 주황 점선 rect — 선택된 bbox 모드 결과

toolbar:

mode동작
exact (C/Q 해석)bboxOfPath — 008 bboxOfCubicBezier
control hull only네 control의 AABB — 느슨한 상한
flatten samplebboxOfPathSampled — sample steps 슬라이더

readout에 exact cubic vs sample(N) 크기가 함께 나옵니다. hull 모드는 주황 rect가 더 큰 경우가 많고, sample은 step을 줄이면 과소 bbox가 될 수 있습니다.

반환 형식

{ x, y, width, height }  // min corner + size (SVG <rect>와 동일)

빈 path → { x: 0, y: 0, width: 0, height: 0 }.

세 가지 방법 (복습)

방법API특징
Control hullbezierControlHullBBox([p0, cp…, p3])항상 덮음 · handle이 멀면 selection 과대
Anchor만bezierControlHullBBox([p0, p3])과소 — 곡선이 rect 밖으로 나감
해석 tightbboxOfCubicBezier / bboxOfQuadraticBezierB′(t)=0 + 끝점 (008)
Flatten samplebboxOfPathSampledstep·ε에 의존 · 검증·레거시

bboxOfPath — segment union

import { bboxOfPath, bboxOfPathSampled, parsePathD } from "svg-matrix-core";

const segments = parsePathD("M 120 300 C 200 40, 440 360, 520 80");

const exact = bboxOfPath(segments);
// C/Q: 해석 · A: sampleArc · L: 끝점

const sampled = bboxOfPath(segments, { mode: "sample", stepsPerCurve: 24 });
// bboxOfPathSampled와 동일 — 전 segment flatten 후 min/max
box = null
for (segment of segments)
  box = unionBBox(box, segmentBBox(segment))
typesegmentBBox
M점 하나 (width/height 0)
Lfrom·to min/max
CbboxOfCubicBezier
QbboxOfQuadraticBezier
AarcSegmentToCubics → sample (stepsPerArc, 기본 24)

011 arc는 타원 호 해석 bbox가 무겁기 때문에 cubic sample로 근사합니다. 065 flatten 품질과 같은 sampleArc 경로.

bboxOfPathSampled

const points = flattenPathSegments(segments, options);
// xs/ys min/max → bbox

016 flatten과 동일한 polyline에서 bbox를 구합니다. stepsPerCurve·stepsPerArc가 작으면 tight bbox보다 작아질 수 있습니다.

실무 연결

용도bbox + α
Selection UIbboxOfPath + strokeWidth/2 + handle pad
Fit view / cameracompound path 전체 union
gradientUnits="objectBoundingBox"019 objectBoundingBoxToUserSpace
Hit broad-phaserect 겹침 후 segment test (004)
Transform bake080 후 bboxOfPath — 좌표계 통일

subpath

Z로 닫힌 여러 subpath가 있어도 bboxOfPath는 flat segment 리스트 전체를 union합니다. subpath별 bbox가 필요하면 segmentsToSubpaths 후 각각 bboxOfPath.

padding

function padBBox(b, px) {
  return { x: b.x - px, y: b.y - px, width: b.width + 2 * px, height: b.height + 2 * px };
}

검증 루틴

const a = bboxOfPath(segments);
const b = bboxOfPathSampled(segments, { stepsPerCurve: 64, stepsPerArc: 48 });
// max(|a.x-b.x|, …) < 1px 이면 sampling 파이프라인 OK

C/Q만 있는 path에서는 exact와 고 step sample이 거의 일치해야 합니다.

Core API

함수역할
bboxOfPathC/Q 해석 + A sample union
bboxOfPathSampledflatten-only bbox
bboxOfCubicBezier, bboxOfQuadraticBeziersegment tight
bezierControlHullBBoxcontrol 점 AABB
unionBBox내부 (export 없음)

관련

  • 008 C bbox · 009 Q · 011 A sample · 016 flatten · 019 gradient units

오늘의 핵심

  • tight bbox = 극값 (008); control hull은 안전하지만 느슨합니다.
  • 끝점만 min/max하면 selection이 잘립니다.
  • bboxOfPath는 C/Q 해석 + arc sample union; flatten bbox는 step이 부족하면 과소입니다.
  • 편집기는 bboxOfPath + pad를 매 프레임 쓰고, arc-heavy path는 stepsPerArc를 키우거나 011 convertArcsInPathD 후 해석 cubic bbox를 고려하세요.
최근 수정: 26. 5. 17. PM 4:35
Contributors: jinho.park.s3, Cursor
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A — elliptical arc