34:null 35:["$","title",null,{"children":"Straight lines, Arrows, and Braces along a Circle | XiongBiao | Observable"}] 3b:Ta64,{ const small_r = height / 3; const big_r = 1.2 * small_r; const svg = d3.select(DOM.svg(width, height)); const defs = svg.append("defs"); const arrowMarker = defs.append('marker') .attr('id', 'arrow') .attr('viewBox', [0, 0, 4, 4]) .attr('refX', 2) .attr('refY', 2) .attr('markerWidth', 4) .attr('markerHeight', 4) .attr('orient', 'auto-start-reverse') .append('path') .attr('d', `M 0 0 L 0 4 L 4 2 Z`) .attr('fill', 'black'); const smallCircle = svg.append("g") .attr("transform", `translate(${width / 2}, ${height / 2})`); const smallArc = d3.arc() .innerRadius(0) .outerRadius(small_r) .startAngle(-Math.PI / 2) .endAngle(Math.PI / 2 * 3); smallCircle.append("g") .append("path") .attr("d", smallArc()) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", 1); const bigCircle = svg.append("g") .attr("transform", `translate(${width / 2}, ${height / 2})`); const bigArc = d3.arc() .innerRadius(0) .outerRadius(big_r) .startAngle(-Math.PI / 2) .endAngle(Math.PI / 2 * 3); bigCircle.append("g") .append("path") .attr("d", bigArc()) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", 1); const lines = svg.append("g") .attr("transform", `translate(${width / 2}, ${height / 2})`); positionLine(lines, lineOptions.angle/180*Math.PI, lineOptions.r1, lineOptions.r2, lineOptions.haveArrow, lineOptions.arrowPosition); const arrows = svg.append("g") .attr("transform", `translate(${width / 2}, ${height / 2})`); positionArrow(arrows, arrowOptions.start_angle/180*Math.PI, arrowOptions.r, arrowOptions.angle/180*Math.PI, arrowOptions.haveArrow, arrowOptions.arrowPosition); const braces = svg.append("g") .attr("transform", `translate(${width / 2}, ${height / 2})`); positionBrace(braces, braceOptions.centerAngle/180*Math.PI, braceOptions.leftAngle/180*Math.PI, braceOptions.rightAngle/180*Math.PI, braceOptions.r1, braceOptions.r2, braceOptions.r3, braceOptions.dr, braceOptions.da/180*Math.PI); return svg.node(); }3c:Tc95,function positionBrace(svg, centerAngle, leftAngle, rightAngle, r1, r2, r3, dr, da) { let x1 = -r1*Math.cos(centerAngle-leftAngle-2*da); let y1 = -r1*Math.sin(centerAngle-leftAngle-2*da); let x2 = -r2*Math.cos(centerAngle-leftAngle-2*da); let y2 = -r2*Math.sin(centerAngle-leftAngle-2*da); svg.append("path") .attr("d", `M ${x1} ${y1} L ${x2} ${y2}`) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", "1") let cx = -(r2+dr)*Math.cos(centerAngle-leftAngle-2*da); let cy = -(r2+dr)*Math.sin(centerAngle-leftAngle-2*da); let x3 = -(r2+dr)*Math.cos(centerAngle-leftAngle-da); let y3 = -(r2+dr)*Math.sin(centerAngle-leftAngle-da); let x4 = -(r2+dr)*Math.cos(centerAngle-da); let y4 = -(r2+dr)*Math.sin(centerAngle-da); svg.append("path") .attr("d", `M ${x2} ${y2} Q ${cx} ${cy} ${x3} ${y3}`) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", "1") let d_left = `M ${x3} ${y3} A ${(r2+dr)} ${(r2+dr)} 0 0 1 ${x4} ${y4}`; if (leftAngle > Math.PI) { d_left = `M ${x3} ${y3} A ${(r2+dr)} ${(r2+dr)} 0 1 1 ${x4} ${y4}`; } svg.append("path") .attr("d", d_left) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", "1") let x5 = -(r2+2*dr)*Math.cos(centerAngle); let y5 = -(r2+2*dr)*Math.sin(centerAngle); let cx2 = -(r2+dr)*Math.cos(centerAngle); let cy2 = -(r2+dr)*Math.sin(centerAngle); svg.append("path") .attr("d", `M ${x4} ${y4} Q ${cx2} ${cy2} ${x5} ${y5}`) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", "1") let x6 = -(r3)*Math.cos(centerAngle); let y6 = -(r3)*Math.sin(centerAngle); svg.append("path") .attr("d", `M ${x5} ${y5} L ${x6} ${y6}`) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", "1") let x7 = -(r2+dr)*Math.cos(centerAngle+da); let y7 = -(r2+dr)*Math.sin(centerAngle+da); svg.append("path") .attr("d", `M ${x5} ${y5} Q ${cx2} ${cy2} ${x7} ${y7}`) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", "1") let x8 = -(r2+dr)*Math.cos(centerAngle+rightAngle+da); let y8 = -(r2+dr)*Math.sin(centerAngle+rightAngle+da); let d_right = `M ${x7} ${y7} A ${(r2+dr)} ${(r2+dr)} 0 0 1 ${x8} ${y8}`; if (rightAngle > Math.PI) { d_right = `M ${x7} ${y7} A ${(r2+dr)} ${(r2+dr)} 0 1 1 ${x8} ${y8}`; } svg.append("path") .attr("d", d_right) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", "1") let x9 = -r2*Math.cos(centerAngle+rightAngle+2*da); let y9 = -r2*Math.sin(centerAngle+rightAngle+2*da); let cx3 = -(r2+dr)*Math.cos(centerAngle+rightAngle+2*da); let cy3 = -(r2+dr)*Math.sin(centerAngle+rightAngle+2*da); svg.append("path") .attr("d", `M ${x8} ${y8} Q ${cx3} ${cy3} ${x9} ${y9}`) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", "1") let x10 = -r1*Math.cos(centerAngle+rightAngle+2*da); let y10 = -r1*Math.sin(centerAngle+rightAngle+2*da); svg.append("path") .attr("d", `M ${x9} ${y9} L ${x10} ${y10}`) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", "1") }3d:T42c,function positionArrow(svg, start_angle, r, angle, haveArrow, position) { let d = `M ${-Math.cos(start_angle)*r} ${-r*Math.sin(start_angle)} A ${r} ${r} 0 0 1 ${-Math.cos(start_angle+angle)*r} ${-r*Math.sin(start_angle+angle)}`; if (angle>Math.PI) { d = `M ${-Math.cos(start_angle)*r} ${-r*Math.sin(start_angle)} A ${r} ${r} 0 1 1 ${-Math.cos(start_angle+angle)*r} ${-r*Math.sin(start_angle+angle)}`; } if (haveArrow) { if (position === "start") { svg.append("path") .attr("d", d) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", "1") .attr("marker-start", "url(#arrow)") } if (position === "end") { svg.append("path") .attr("d", d) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", "1") .attr("marker-end", "url(#arrow)") } } else { svg.append("path") .attr("d", d) .attr("fill", "none") .attr("stroke", "black") .attr("stroke-width", "1") } }3e:[] 39:{"id":"337e9e88a703ac29","slug":"straight-lines-arrows-and-braces-along-a-circle","title":"Straight lines, Arrows, and Braces along a Circle","thumbnail":"7a52338c6c0f07e2357cec288494dafd823212cb95f252dffd2811c24a1c9de7","access_level":"public","create_time":"$D2026-03-19T02:53:59.635Z","update_time":"$D2026-03-19T05:28:33.862Z","view_time":null,"first_public_time":"$D2026-03-19T05:32:49.803Z","has_unpublished_edits":null,"fork":false,"stars":12,"starred":false,"owner":{"type":"team","id":"189a68e88fe366bd","login":"xiongbiao","name":"XiongBiao","avatar_url":"https://avatars-next.observableusercontent.com/a95188709ffcb422fcc635f47420feb25f69fd7305881a42b4a9907e87d2aaf0","tier":"free_2026","bio":"","following":false},"version":152,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"fc82b550d8112553","login":"xiongbiao","name":"XiongBiao","avatar_url":"https://avatars-next.observableusercontent.com/caf2b8f3d51ea1f56efa20730077b94beb57622ab029080cdb84a9ad89ac467d","tier":null,"bio":"","following":false}],"members":[{"type":"individual","id":"fc82b550d8112553","login":"xiongbiao","name":"XiongBiao","avatar_url":"https://avatars-next.observableusercontent.com/caf2b8f3d51ea1f56efa20730077b94beb57622ab029080cdb84a9ad89ac467d","tier":null,"role":"editor"},{"type":"team","id":"189a68e88fe366bd","login":"xiongbiao","name":"XiongBiao","avatar_url":"https://avatars-next.observableusercontent.com/a95188709ffcb422fcc635f47420feb25f69fd7305881a42b4a9907e87d2aaf0","tier":"free_2026","role":"viewer"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":2,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Straight lines, Arrows, and Braces along a Circle","cells":[{"id":0,"value":"# Straight lines, Arrows, and Braces along a Circle","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":126,"value":"

Line Options

\n ${viewof lineOptions}\n

Arrow Options

\n ${viewof arrowOptions}\n

Brace Options

\n ${viewof braceOptions}\n

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