解析几何解题 → 交互网页 这个技能产出什么 一个可直接用浏览器打开的单页 HTML（三栏）： - 左栏 ：题面 + 动态控制台 —— 一个可变参数滑块（如直线倾斜角 θ / 动点参数 t）驱动实时 重算的几何量（交点坐标、斜率、数量积、弦长、面积…），以及"理论范围条"或"定值指示"。 - 中栏 ：分步解析（公式用 KaTeX ），可一键收起把空间让给画板。 - 右栏 ：2D Canvas 动态几何画板（圆锥曲线 + 动直线/动点 + 向量 + 点标注 + 网格坐标轴）， 叠加画笔涂鸦工具栏。 形态与目标模板 一致。 依赖（重要） 计算核心 依赖 sympy 。运行脚本前先确认有能 import sympy 的 解释器： （本机用 ，sympy 1.14）。 缺库时 ：若 import 报错（sympy 或后续任何库）， 先询问用户是否安装 ，同意后再装 （ ）或换一个已装该库的解释器； 不要未经询问直接装 。 下文 均指这个能跑通依赖的解释器。 工作流程 第 1 步：得到 problem spec（三入口归一） 把题目整理成结构化 spec（曲线类型与参数、已知点/条件、所求类型与对象、语言）。 - 文字题 ：直接抽取。 - 图片 ：视觉读图抽取，并 把识别到的题目回显给用户确认 （题面/曲线/参数/所求/语言）再继续。 - 随机出题 ：选曲线 + 题型，随机参数 → ker…

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解析几何解题 → 交互网页 这个技能产出什么 一个可直接用浏览器打开的单页 HTML（三栏）： - 左栏 ：题面 + 动态控制台 —— 一个可变参数滑块（如直线倾斜角 θ / 动点参数 t）驱动实时 重算的几何量（交点坐标、斜率、数量积、弦长、面积…），以及"理论范围条"或"定值指示"。 - 中栏 ：分步解析（公式用 KaTeX ），可一键收起把空间让给画板。 - 右栏 ：2D Canvas 动态几何画板（圆锥曲线 + 动直线/动点 + 向量 + 点标注 + 网格坐标轴）， 叠加画笔涂鸦工具栏。 形态与目标模板 一致。 依赖（重要） 计算核心 依赖 sympy 。运行脚本前先确认有能 import sympy 的 解释器： （本机用 ，sympy 1.14）。 缺库时 ：若 import 报错（sympy 或后续任何库）， 先询问用户是否安装 ，同意后再装 （ ）或换一个已装该库的解释器； 不要未经询问直接装 。 下文 均指这个能跑通依赖的解释器。 工作流程 第 1 步：得到 problem spec（三入口归一） 把题目整理成结构化 spec（曲线类型与参数、已知点/条件、所求类型与对象、语言）。 - 文字题 ：直接抽取。 - 图片 ：视觉读图抽取，并 把识别到的题目回显给用户确认 （题面/曲线/参数/所求/语言）再继续。 - 随机出题 ：选曲线 + 题型，随机参数 → ker…

,display:false},{left:'\\\\(',right:'\\\\)',display:false},{left:'\\\\[',right:'\\\\]',display:true}],throwOnError:false}); }\n\n function buildConsole(){\n // 题目\n document.getElementById('prob-title').textContent = (DATA.lesson&&DATA.lesson.title)||'';\n document.getElementById('prob-body').innerHTML = (DATA.lesson&&DATA.lesson.problem)||'';\n document.getElementById('console-title').textContent = BOARD.consoleTitle || UI.consoleTitle;\n document.getElementById('sol-title-text').textContent = UI.solutionTitle;\n document.getElementById('sol-vlabel').textContent = UI.solutionTitle;\n\n // 参数滑块\n const p=BOARD.param;\n if(p){\n document.getElementById('param-block').classList.remove('hidden');\n document.getElementById('param-label').innerHTML = (p.label||p.name)+' :';\n const s=document.getElementById('param-slider');\n s.min=p.min; s.max=p.max; s.step=p.step||0.5; s.value=(p.value!==undefined?p.value:p.min);\n const ticks=document.getElementById('param-ticks');\n ticks.innerHTML = (p.ticks||[`${p.min}${p.unit||''}`, `${p.max}${p.unit||''}`]).map(t=>`\u003cspan>${t}\u003c/span>`).join('');\n s.addEventListener('input', update);\n }\n // 读数行容器（值在 update 里填）\n const ro=document.getElementById('readouts');\n ro.innerHTML = (BOARD.readouts||[]).map(r=>{\n if(r.highlight) return `\u003cdiv class=\"flex justify-between items-center pt-1\">\u003cspan class=\"text-slate-800 font-semibold\">${r.label}:\u003c/span>\u003cspan id=\"ro-${r.id}\" class=\"text-base font-bold bg-teal-50 text-teal-700 px-3 py-1 rounded-lg border border-teal-200\">—\u003c/span>\u003c/div>`;\n return `\u003cdiv class=\"flex justify-between border-b border-dashed border-slate-200 pb-2\">\u003cspan>${r.label}:\u003c/span>\u003cspan id=\"ro-${r.id}\" class=\"font-bold\" style=\"color:${r.color?col(r.color):'#0f172a'}\">—\u003c/span>\u003c/div>`;\n }).join('');\n\n // 范围条\n if(BOARD.rangeBar){ document.getElementById('rangebar-block').classList.remove('hidden');\n document.getElementById('rangebar-cur').textContent = UI.current;\n const rl=document.getElementById('rangebar-range'); rl.innerHTML = BOARD.rangeBar.label||''; }\n\n // 定值指示器\n if(BOARD.constant){ document.getElementById('constant-block').classList.remove('hidden');\n document.getElementById('constant-val').innerHTML = '≡ '+(BOARD.constant.label||''); }\n\n // 答案区间（参数轴）：高亮 [lo,hi] 子区间\n if(BOARD.answerBand){ const ab=BOARD.answerBand;\n document.getElementById('answerband-block').classList.remove('hidden');\n document.getElementById('answerband-cur').textContent = '当前 '+((BOARD.param&&BOARD.param.name)||'值')+':';\n document.getElementById('answerband-label').innerHTML = ab.label||'';\n const L=((ab.lo-ab.min)/(ab.max-ab.min))*100, R=((ab.max-ab.hi)/(ab.max-ab.min))*100;\n const fill=document.getElementById('answerband-fill');\n fill.style.left=Math.max(L,0)+'%'; fill.style.right=Math.max(R,0)+'%'; }\n\n // 图例\n const legend=document.getElementById('legend'); const items=[];\n (BOARD.conics||[]).forEach(c=>{ if(c.legend!==false) items.push(`\u003cdiv class=\"flex items-center gap-2\">\u003cspan class=\"w-3 h-1.5 inline-block rounded\" style=\"background:${col(c.color||'curve')}\">\u003c/span> ${c.label||c.name}\u003c/div>`); });\n (BOARD.legend||[]).forEach(it=> items.push(`\u003cdiv class=\"flex items-center gap-2\">\u003cspan class=\"w-3 h-1.5 inline-block rounded\" style=\"background:${col(it.color)}\">\u003c/span> ${it.text}\u003c/div>`));\n legend.innerHTML=items.join('');\n\n // 解析步骤\n const sb=document.getElementById('solution-body');\n sb.innerHTML=(DATA.steps||[]).map((st,i)=>{\n const no=String(i+1).padStart(2,'0');\n return `\u003cdiv class=\"${i>0?'border-t border-slate-100 pt-5':''}\">\n \u003cdiv class=\"flex items-start gap-4 mb-4\">\n \u003cspan class=\"w-8 h-8 rounded-full bg-indigo-100 text-indigo-600 flex items-center justify-center font-bold font-mono text-sm flex-shrink-0\">${no}\u003c/span>\n \u003ch3 class=\"text-lg font-bold text-slate-900 pt-0.5\">${st.title||''}\u003c/h3>\n \u003c/div>\n \u003cdiv class=\"prose max-w-none text-slate-700 leading-relaxed text-sm md:text-base space-y-3\">${st.content||''}\u003c/div>\n \u003c/div>`;\n }).join('');\n\n renderKatex(document.body);\n }\n\n // ===================== 主更新循环 =====================\n let curParam = BOARD.param ? (BOARD.param.value!==undefined?BOARD.param.value:BOARD.param.min) : 0;\n function update(){\n if(BOARD.param){ const s=document.getElementById('param-slider'); curParam=parseFloat(s.value);\n const p=BOARD.param; const dec=p.step?(p.step\u003c0.1?2:(p.step\u003c1?1:0)):0;\n document.getElementById('param-val').textContent = fmt(curParam, dec)+(p.unit||''); }\n const scene=buildScene(curParam);\n const ros=computeReadouts(scene);\n ros.forEach(r=>{ const el=document.getElementById('ro-'+r.id); if(el){ el.textContent=r.text; if(r.dyncolor) el.style.color=r.dyncolor; } });\n // 范围条指针\n if(BOARD.rangeBar){ const rb=BOARD.rangeBar; const tracked=ros.find(r=>r.id===rb.of);\n if(tracked && tracked.scalar!==null){ const pct=((tracked.scalar-rb.min)/(rb.max-rb.min))*88+6;\n document.getElementById('rangebar-ptr').style.left=Math.min(Math.max(pct,0),100)+'%'; } }\n // 答案区间指针（参数轴）\n if(BOARD.answerBand){ const ab=BOARD.answerBand; const pct=((curParam-ab.min)/(ab.max-ab.min))*100;\n document.getElementById('answerband-ptr').style.left=Math.min(Math.max(pct,0),100)+'%'; }\n draw(scene);\n }\n function resetPlot(){ const p=BOARD.param; if(!p) return; const s=document.getElementById('param-slider');\n s.value=(p.standard!==undefined?p.standard:(p.value!==undefined?p.value:p.min)); update(); }\n window.resetPlot=resetPlot;\n\n // ===================== 画笔涂鸦叠加层 =====================\n const drawCanvas=document.getElementById('draw-canvas'); const dctx=drawCanvas.getContext('2d');\n let penMode=null,isDrawing=false,penColor='#ffffff',penSize=3,strokes=[],curStroke=null;\n function resizeDrawCanvas(){ const rect=drawCanvas.parentElement.getBoundingClientRect(); const dpr=window.devicePixelRatio||1;\n drawCanvas.width=rect.width*dpr; drawCanvas.height=rect.height*dpr; drawCanvas.style.width=rect.width+'px'; drawCanvas.style.height=rect.height+'px';\n dctx.setTransform(1,0,0,1,0,0); dctx.scale(dpr,dpr); redrawStrokes(rect.width,rect.height); }\n function redrawStrokes(w,h){ 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rect=drawCanvas.getBoundingClientRect(); redrawStrokes(rect.width,rect.height);});\n undoBtn.addEventListener('click',()=>{if(!strokes.length)return; strokes.pop(); const rect=drawCanvas.getBoundingClientRect(); redrawStrokes(rect.width,rect.height);});\n penSizeInput.addEventListener('input',()=>{penSize=parseInt(penSizeInput.value,10);});\n swatches.forEach(sw=>sw.addEventListener('click',()=>{penColor=sw.dataset.color; swatches.forEach(s=>{s.classList.remove('ring-2','ring-white');s.classList.add('ring-1','ring-slate-600');}); sw.classList.remove('ring-1','ring-slate-600'); sw.classList.add('ring-2','ring-white'); if(penMode!=='pen')setMode('pen');}));\n updateToolbarUI();\n\n // ===================== 解析面板收起 / 展开 =====================\n const solutionPanel=document.getElementById('solution-panel'),solutionBody=document.getElementById('solution-body'),toggleSolutionBtn=document.getElementById('toggle-solution'),solTitle=document.getElementById('sol-title'),solVlabel=document.getElementById('sol-vlabel'),solHeader=document.getElementById('sol-header'),solChevron=document.getElementById('sol-chevron');\n let solutionCollapsed=false;\n function applySolutionState(){ solutionBody.classList.toggle('hidden',solutionCollapsed); solChevron.classList.toggle('rotate-180',solutionCollapsed);\n solutionPanel.classList.toggle('lg:w-[360px]',!solutionCollapsed); solutionPanel.classList.toggle('lg:w-14',solutionCollapsed); solutionPanel.classList.toggle('lg:px-2',solutionCollapsed);\n solHeader.classList.toggle('lg:flex-col',solutionCollapsed); solHeader.classList.toggle('lg:gap-3',solutionCollapsed); solTitle.classList.toggle('lg:hidden',solutionCollapsed); solVlabel.classList.toggle('lg:block',solutionCollapsed);\n toggleSolutionBtn.title=solutionCollapsed?UI.expand:UI.collapse; requestAnimationFrame(resizeCanvas); }\n solutionPanel.addEventListener('transitionend',e=>{if(e.propertyName==='width')resizeCanvas();});\n toggleSolutionBtn.addEventListener('click',()=>{solutionCollapsed=!solutionCollapsed; applySolutionState();});\n\n // ===================== 启动 =====================\n window.addEventListener('resize',resizeCanvas);\n window.onload=()=>{ buildConsole(); resizeCanvas(); };\n \u003c/script>\n\u003c/body>\n\u003c/html>\n","content_type":"text/html; charset=utf-8","language":"markup","size":49389,"content_sha256":"aaeead79a8b2ba560622a5f5137d96195bfac599fc2cd9f9c227d69bca4ccfbd"}],"content_json":{"type":"doc","content":[{"type":"heading","attrs":{"level":1},"content":[{"text":"解析几何解题 → 交互网页","type":"text"}]},{"type":"heading","attrs":{"level":2},"content":[{"text":"这个技能产出什么","type":"text"}]},{"type":"paragraph","content":[{"text":"一个可直接用浏览器打开的单页 HTML（三栏）：","type":"text"}]},{"type":"bullet_list","content":[{"type":"list_item","content":[{"type":"paragraph","content":[{"text":"左栏","type":"text","marks":[{"type":"strong"}]},{"text":"：题面 + 动态控制台 —— 一个可变参数滑块（如直线倾斜角 θ / 动点参数 t）驱动实时 重算的几何量（交点坐标、斜率、数量积、弦长、面积…），以及\"理论范围条\"或\"定值指示\"。","type":"text"}]}]},{"type":"list_item","content":[{"type":"paragraph","content":[{"text":"中栏","type":"text","marks":[{"type":"strong"}]},{"text":"：分步解析（公式用 ","type":"text"},{"text":"KaTeX","type":"text","marks":[{"type":"strong"}]},{"text":"），可一键收起把空间让给画板。","type":"text"}]}]},{"type":"list_item","content":[{"type":"paragraph","content":[{"text":"右栏","type":"text","marks":[{"type":"strong"}]},{"text":"：2D Canvas 动态几何画板（圆锥曲线 + 动直线/动点 + 向量 + 点标注 + 网格坐标轴）， 叠加画笔涂鸦工具栏。","type":"text"}]}]}]},{"type":"paragraph","content":[{"text":"形态与目标模板 ","type":"text"},{"text":"/Users/wuyi/code/code2026/6/template/code_artifact.html","type":"text","marks":[{"type":"code_inline"}]},{"text":" 一致。","type":"text"}]},{"type":"heading","attrs":{"level":2},"content":[{"text":"依赖（重要）","type":"text"}]},{"type":"paragraph","content":[{"text":"计算核心 ","type":"text"},{"text":"lib/analytic_kernel.py","type":"text","marks":[{"type":"code_inline"}]},{"text":" 依赖 ","type":"text"},{"text":"sympy","type":"text","marks":[{"type":"strong"}]},{"text":"。运行脚本前先确认有能 import sympy 的 解释器：","type":"text"},{"text":"python3 -c \"import sympy\"","type":"text","marks":[{"type":"code_inline"}]},{"text":"（本机用 ","type":"text"},{"text":"/opt/homebrew/bin/python3.11","type":"text","marks":[{"type":"code_inline"}]},{"text":"，sympy 1.14）。","type":"text"}]},{"type":"paragraph","content":[{"text":"缺库时","type":"text","marks":[{"type":"strong"}]},{"text":"：若 import 报错（sympy 或后续任何库），","type":"text"},{"text":"先询问用户是否安装","type":"text","marks":[{"type":"strong"}]},{"text":"，同意后再装 （","type":"text"},{"text":"python3 -m pip install \u003c库名>","type":"text","marks":[{"type":"code_inline"}]},{"text":"）或换一个已装该库的解释器；","type":"text"},{"text":"不要未经询问直接装","type":"text","marks":[{"type":"strong"}]},{"text":"。 下文 ","type":"text"},{"text":"python3","type":"text","marks":[{"type":"code_inline"}]},{"text":" 均指这个能跑通依赖的解释器。","type":"text"}]},{"type":"heading","attrs":{"level":2},"content":[{"text":"工作流程","type":"text"}]},{"type":"heading","attrs":{"level":3},"content":[{"text":"第 1 步：得到 problem spec（三入口归一）","type":"text"}]},{"type":"paragraph","content":[{"text":"把题目整理成结构化 spec（曲线类型与参数、已知点/条件、所求类型与对象、语言）。","type":"text"}]},{"type":"bullet_list","content":[{"type":"list_item","content":[{"type":"paragraph","content":[{"text":"文字题","type":"text","marks":[{"type":"strong"}]},{"text":"：直接抽取。","type":"text"}]}]},{"type":"list_item","content":[{"type":"paragraph","content":[{"text":"图片","type":"text","marks":[{"type":"strong"}]},{"text":"：视觉读图抽取，并","type":"text"},{"text":"把识别到的题目回显给用户确认","type":"text","marks":[{"type":"strong"}]},{"text":"（题面/曲线/参数/所求/语言）再继续。","type":"text"}]}]},{"type":"list_item","content":[{"type":"paragraph","content":[{"text":"随机出题","type":"text","marks":[{"type":"strong"}]},{"text":"：选曲线 + 题型，随机参数 → kernel 求解，用 ","type":"text"},{"text":"analytic_kernel.is_clean(...)","type":"text","marks":[{"type":"code_inline"}]},{"text":" 判答案 是否规整，不规整就重抽。","type":"text"}]}]}]},{"type":"blockquote","content":[{"type":"paragraph","content":[{"text":"输出语言跟随提示词语言","type":"text","marks":[{"type":"strong"}]},{"text":"：英文提示 → 英文网页，中文 → 中文。spec 记下 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+ 动态控制台（一个 可变参数滑块驱动实时重算的几何量 + 理论范围/定值指示），中栏 KaTeX 分步解析，右栏 2D Canvas 动态几何画板（椭圆/双曲线/抛物线/圆 + 动直线/动点 + 向量 + 标注 + 画笔涂鸦）。 支持三入口——给定文字题、随机出题、上传题目图片识别后解题。覆盖求标准方程、弦长、向量 数量积范围/定值、三角形面积最值、定点、定值（斜率之积）、轨迹、离心率等题型，统一\"设含参 直线 x=my+c + 联立 + 韦达 + 换元/常数分离\"，并由 sympy 精确计算驱动（答案、坐标、步骤 数值、交互引擎的理论范围同源一致）。其它 agent 也可调用本技能生成此类网页。形态与 edu-solid-geometry 平行，但用 Canvas-2D + KaTeX（非 Three.js）。 触发词：解析几何, 圆锥曲线, 椭圆, 双曲线, 抛物线, 直线与圆锥曲线, 焦点弦, 弦长, 数量积取值范围, 向量数量积, 定点问题, 定值问题, 斜率之积, 三角形面积最值, 轨迹方程, 离心率, 解这道解析几何题, 随机出一道圆锥曲线题, 这张图里的解析几何题; analytic geometry, conic sections, ellipse, hyperbola, parabola, chord length, dot product range, fixed point, fixed value, locus, eccentricity, interactive analytic geometry solution page."}},"renderedAt":1793666381998}

解析几何解题 → 交互网页 这个技能产出什么 一个可直接用浏览器打开的单页 HTML（三栏）： - 左栏 ：题面 + 动态控制台 —— 一个可变参数滑块（如直线倾斜角 θ / 动点参数 t）驱动实时 重算的几何量（交点坐标、斜率、数量积、弦长、面积…），以及"理论范围条"或"定值指示"。 - 中栏 ：分步解析（公式用 KaTeX ），可一键收起把空间让给画板。 - 右栏 ：2D Canvas 动态几何画板（圆锥曲线 + 动直线/动点 + 向量 + 点标注 + 网格坐标轴）， 叠加画笔涂鸦工具栏。 形态与目标模板 一致。 依赖（重要） 计算核心 依赖 sympy 。运行脚本前先确认有能 import sympy 的 解释器： （本机用 ，sympy 1.14）。 缺库时 ：若 import 报错（sympy 或后续任何库）， 先询问用户是否安装 ，同意后再装 （ ）或换一个已装该库的解释器； 不要未经询问直接装 。 下文 均指这个能跑通依赖的解释器。 工作流程 第 1 步：得到 problem spec（三入口归一） 把题目整理成结构化 spec（曲线类型与参数、已知点/条件、所求类型与对象、语言）。 - 文字题 ：直接抽取。 - 图片 ：视觉读图抽取，并 把识别到的题目回显给用户确认 （题面/曲线/参数/所求/语言）再继续。 - 随机出题 ：选曲线 + 题型，随机参数 → ker…