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

evenodd fill + triangle mesh

Part 25 마무리 — 014 fill-rule="evenodd"(픽셀·winding)와 100 triangle mesh(GPU)는 같은 도형을 다른 방식으로 채웁니다. 둘 다 알아야 export·렌더 파이프를 고를 수 있습니다.

evenodd — ray parity

import { evenoddParityFromRayCast, classifyPointInPath } from "svg-matrix-core";

const polygon = [
  { x: 200, y: 120 },
  { x: 440, y: 120 },
  { x: 440, y: 300 },
  { x: 200, y: 300 }
];

const point = { x: 320, y: 210 };
const insideEo = evenoddParityFromRayCast(point, polygon);
const c = classifyPointInPath(point, parsePathD(`M ${polygon.map(p=>`${p.x} ${p.y}`).join(" L ")} Z`), "evenodd");
// insideEo ≈ c.insideEvenOdd

알고리즘

수평 ray → edge와 교차할 때마다 crossing +1 → 홀수면 inside.

030 scanline fill은 y 고정 후 x를 훑으며 같은 parity flip을 합니다 (084).

bow-tie · self-intersect (027)

nonzero: winding 누적
evenodd: crossing 홀수/짝수 — 중앙 “리본”이 비는 경우 많음

데모는 단순 사각형 + 중앙 테스트 점 — 초록(inside) / 빨강(outside). 별·8자 path는 027 데모와 함께 보세요.

triangle mesh — GPU path

import { triangulatePolygonWithHoles, earClipTriangulate } from "svg-matrix-core";

// donut
const { triangles } = triangulatePolygonWithHoles(outer, [hole]);

// WebGL: positions buffer → drawArrays(TRIANGLES)

083 입문 → 100 hole — 명시적 구멍.

두 파이프 비교

SVG 브라우저 렌더:
  path d + fill-rule → rasterizer (evenodd / nonzero)

편집기 / WebGL:
  path d → polygons → triangulate → GPU triangles
상황권장
정적 SVG exportfill-rule attribute만
WebGL 게임·지도mesh + hole bridge
CPU preview 픽셀scanline / evenoddParityFromRayCast
복잡 self-intersectevenodd raster 또는 boolean 후 mesh

evenodd만으로 hole?

compound path + evenodd(026)로 donut을 한 path로 그릴 수 있습니다. GPU는 여전히 hole을 명시하는 mesh(100)가 안전합니다 — parity와 triangle winding이 섞이지 않습니다.

Canvas 2D vs mesh

APIhole / evenodd
ctx.fill(path, "evenodd")브라우저가 처리
ctx.fill(triangles)직접 mesh — 085 gaussian 등과 합성

000 — SVG vs Canvas 역할 분담.

데모에서 볼 것

  • 파란 사각형 fill
  • 중앙 점 — evenoddParityFromRayCast → inside면 초록, outside면 빨강
  • readout: parity / scanline flip 설명

Part 25 학습 순서

100 triangulation holes → 101 WAAPI (브라우저 애니) → 102 evenodd vs mesh (정리)

Part 23–24 애니(088–099)와 연결: 공간은 svg-matrix, 시간 easing은 css-matrix.

Core API

  • evenoddParityFromRayCast, classifyPointInPath
  • triangulatePolygonWithHoles, earClipTriangulate
  • SVG_ANIMATION_TOPIC_MAP — 101

오늘의 핵심

evenodd = 픽셀 규칙, mesh = 기하 분해. bow-tie는 evenodd가 직관적이고, GPU는 hole을 bridge해서 삼각형으로 넘기세요.

최근 수정: 26. 5. 17. PM 4:35
Contributors: jinho.park.s3, Cursor
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WAAPI + SVG attributes